University of Southern California Dissertations and Theses

An Econometric Overhead Model Of An Aerospace Firm

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An Econometric Overhead Model Of An Aerospace Firm

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Content 70- 25,021 EBERHARDT, Duane Q m in , 1934— AN EC O N O M ETR IC O V E R H E A D M O D E L O F AN AEROSPACE FIRM. U n iv e r sity o f Southern C a lifo r n ia , Ph.D., 1970 E conom ics, fin a n ce University Microfilms, A X ERO X Company, Ann Arbor, Michigan AN ECONOMETRIC OVERHEAD MODEL OF AM AEROSPACE FIRM by Duane O rpin E b e rh a rd t A D i s s e r t a t i o n P r e s e n te d t o th e FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA I n P a r t i a l F u l f i l l m e n t o f th e R equirem ents f o r th e D egree DOCTOR OF PHILOSOPHY (Econom ics) Ju ne 1970 UNIVERSITY O F SOUTHERN CALIFORNIA THE GRADUATE SCHOO L UNIVERSITY PARK LOS ANGELES, CA LIFO RN IA 9 0 0 0 7 This dissertation, written by ................. DJ[AJS!E...O.RRXN..EBERHARD.T.............. under the direction of h% JJ.... Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Gradu ate School, in partial fulfillment of require ments of the degree of D O C T O R OF P H I L O S O P H Y T Dean D^,...AP?a„7,„1970. DISSERTATION COMMITTEE^ hair man To Melva Lee, f o r fo u r y e a rs o f r e a s s u r a n c e ii ACKNOWLEDGEMENTS The a u th o r i s in d e b te d t o P r o f e s s o r s G erhard T i n t n e r , John H. N ie d e rc o rn , and C. M ichael White f o r t h e i r c o u n se l d u rin g th e p r e p a r a t i o n o f t h i s s tu d y . iii TABLE OP CONTENTS CHAPTER PAGE I . INTRODUCTION............................................................................ 1 D e s c r i p t i o n o f F o r e c a s t i n g Environm ent . . . 2 Model C h a r a c t e r i s t i c s ............................................ 6 U s e f u ln e s s o f P r e d i c t i o n s .................................. 9 O u tlin e o f Subsequent C h a p te rs . . . . . . . 12 I I . THE FIRM....................................................................................... . . 13 G en eral D e s c r ip t i o n o f th e F irm ................... 13 D e t a i le d D e s c r ip t i o n o f t h e F i r m .............. 15 I I I . THE DATA...................................................................................... 3^ S e l e c t i o n o f S e r ie s D u ra tio n .................................... 36 A djustm ent o f Overhead D a ta ............................. ^3 A c t i v i t y V a r ia b le s ............................................................. 55 Summary o f D ata P r e p a r a t i o n P ro c e d u re s . . . 68 D e f l a t i o n o f D o lla r V a r i a b l e s ........................ 71 IV. DERIVATION OF MODEL........................................................ 8l P ro c ed u re Used i n D eveloping Model ..................... 8l E q u a tio n s f o r L a b o r-O rie n te d A cco u n ts. . . . 9^ E q u a tio n s f o r o t h e r M ajor-P o ol A ccoun ts. . . 122 E q u a tio n s f o r Spares P o o l.....................................186 A ccounts Not E stim a te d ................................................... 198 V. VALIDATION OF MODEL.......................................................... 205 T ech niq ues f o r V a l id a ti n g a M odel.................205 iv CHAPTER PAGE V a l i d a t i n g th e Overhead Model. .....................................210 VI. NEED FOR UPDATING MODEL................................................................221 V I I. SUGGESTIONS FOR FURTHER RESEARCH............................................226 F u r t h e r V a l id a ti o n o f t h e M odel.....................................226 Using th e Model..............................................................................227 I n c o r p o r a ti n g U nw ieldly A ccoun ts .......................... 228 C lo sin g th e M odel.........................................................................230 Using P r o b a b i l i s t i c E q u a t i o n s ..........................................232 BIBLIOGRAPHY............................................................................................................235 APPENDICES.................................................................................................................244 v LIST OP TABLES TABLE PAGE 1. C o n trib u tio n o f L abor and Overhead C osts to T o ta l C o s t s ....................................................................................... 19 2. C o r r e c tin g 1959 - I960 D ata t o 1963 A ccounting Method ....................................................................... 46 3. C o rre c tin g 1959 - 1963 D ata t o 1968 A ccounting Method ....................................................................... 48 4. A rith m e tic Sum o f R e d i s t r i b u t i o n A ccounts B efore and A f t e r C o r r e c t i n g D a ta ..........................................51 5. C o r re c tin g 1959 - 1964 D ata t o 1969 A ccounting Method ....................................................................... 54 6. C o r re c tio n F a c to r f o r Labor D a ta ................................................57 7- D ire c t Labor D ata: D o l l a r s , H ours, and Wage R a t e s ..................................................................................................59 8. Comparison o f T o ta l E n g in e e r in g Labor D o lla rs B efo re and A f t e r A d j u s t i n g .................................... 60 9. C o rr e c tio n s t o P e rs o n n e l D a t a .....................................................64 10. Year-end and A verage P e rs o n n e l D a t a ......................................66 11. F in a n c i a l O p e r a tin g V a r i a b l e s ............................................... 67 12. P ric e T r e n d s ...................................................................................................79 13. F o re c a st f o r G.N.P. I m p l i c i t P r ic e I n d e x ............................93 14. A ctu al v s . F o r e c a s t V a lu es f o r A c t i v i t y V a r i a b l e s ...............................................................................................211 vi TABLE PAGE 15. E n g in e e r in g F o r e c a s t E r r o r s ........................................................213 16. F a c to ry F o r e c a s t E r r o r s . ....................................................... 214 17. A d m i n is tr a t iv e F o r e c a s t E r ro r s ........................................ 215 18. S p a re s F o r e c a s t E r r o r s ............................................................ 217 19. Average Account E r r o r s w ith V a rio u s F o r e c a s t i n g M ethods........................................................................218 20. F o r e c a s t S e n s i t i v i t y t o New D a t a ............................................224 vii LIST OP FIGURES FIGURE PAGE 1. S e t t i n g P r ic e s on Com mercial P r o d u c t s .............................. 31 2. E n g in e e rin g I n d i r e c t L abor .................................................... 97 3. F a c to ry I n d i r e c t Labor .............................................................. 98 4. A d m in is tr a tiv e I n d i r e c t L a b o r .....................................................101 5. E n g in e e rin g H o lid a y s . ............................... ' ............................102 6 . F a c to ry H olid ay s .............................................................................. 103 7. A d m in is tr a tiv e H o l i d a y s ....................................................................10*J 8 . E n g in e e rin g V a c a t i o n s ......................................................................... 106 9. F a c to ry V a c a t i o n s ................................................................................... 107 10. A d m in is tr a tiv e V a c a tio n s ......................................................... 108 11. E n g in e e rin g Group I n s u r a n c e ..........................................................I l l 12. F a c to ry Group I n s u r a n c e .................................................................... 112 13- A d m in is tr a tiv e Group I n s u r a n c e .......................................... 113 14. E n g in e e rin g R e t i r e m e n t ....................................................................115 15. A d m in is tr a tiv e R e t i r e m e n t ...............................................................116 16. E n g in e e rin g S o c i a l S e c u r i t y 118 j 17. F a c to ry S o c ia l S e c u r i t y ....................................................................119 18. A d m in is tr a tiv e S o c i a l S e c u r i t y .......................................... 121 1 9 . E n g in e e rin g S u p p lie s ................................................................... 125 20. F a c to ry S u p p lie s ............................................................................. 127 21. A d m in is tr a tiv e S u p p l i e s ....................................................................128 22. E n g in e e rin g S e r v i c e s Charged .............................................. 130 23. F a c to ry S e r v ic e s Charged ......................................................... 131 v i i i FIGURE PAGE 24. A d m i n i s t r a t i v e S e r v ic e s C harged.................................................132 25. E n g in e e r in g T r a i n in g .................................................................... 134 26. A d m i n i s t r a t i v e T r a i n in g . . . .................................................136 27. E n g in e e r in g S e r v ic e s P urchased ........................................... 138 28. F a c to r y S e r v ic e s P urchased ..................................................... 139 29. A d m i n is tr a t iv e S e r v ic e s P u rc h a s e d ............................................141 30. E n g in e e r in g E n te r ta i n m e n t................................................................142 31. A d m i n i s t r a t i v e E n t e r t a i n m e n t ......................................................144 32. E n g in e e r in g Company A i r c r a f t ................................................ 145 33. A d m i n is tr a t iv e Company A i r c r a f t ................................................. 146 34. E n g in e e r in g R e p a ir and M a i n t e n a n c e .......................................148 35. A d m i n i s t r a t i v e R e p a ir and M a in te n a n c e ..................................149 36. E n g in e e r in g T r a v e l ......................................................................... 151 37* F a c to r y T r a v e l .........................................................................................152 3 8 . A d m i n i s t r a t i v e T r a v e l ..........................................................................153 39* F a c to r y C r a t i n g .........................................................................................155 40. P r o d u c tio n A n a l y s i s ...............................................................................156 41. F r e i g h t ............................................................................................................. 158 42. H e a t, L ig h t , W ater, and Pow er......................................................160 4 3 . R e a l P ro p e r ty T a x e s ........................................................ 161 44. B u i l d i n g and P r o p e r ty R e n t a l s .......................'............................163 45. T e le p h o n e and T e l e g r a p h .....................................................................164 46. M is c e lla n e o u s Employment Expense ...................................... 166 47. Employee M o rale.........................................................................................168 ix FIGURE PAGE 48. C o rp o rate A l l o c a t i o n ........................................................ 170 4 9 . P ro p o s a l E xpenses ............................................................................. 172 50. A d v e r ti s in g E x p e n s e s............................................................................173 51. F r a n c h is e Tax . .................................................................................175 52. Dues and D o n a tio n s.................................................................................177 53. O th e r E n g in e e rin g E x p e n s e s ............................................................ 179 54. O th er A d m in is tr a tiv e E xpenses ............................................... 180 55- E n g in e e r in g R e d i s t r i b u t i o n ............................................................ 182 5 6 . F a c to ry R e d i s t r i b u t i o n . - ..................................................................183 57. A d m in is tr a tiv e R e d i s t r i b u t i o n .............................................. 184 5 8 . S p a re s I n d i r e c t Labor ................................................................... 188 5 9 . S p a res F rin g e B e n e f i t s .......................................................................190 60. S p a res S o c ia l S e c u r i t y .......................................................................191 61. S p a res R e t i r e m e n t .................................................................................193 62. S p ares Group I n s u r a n c e .......................................................................19^ 6 3 . S p ares S u p p l i e s ......................................................................................196 64. S p ares Packing and C r a t i n g .............................................................197 6 5 . O th er Spares E x p e n s e s ........................... 199 66. S p a res R e d i s t r i b u t i o n ................................................................... 200 x CHAPTER I INTRODUCTION The o v erh ead model developed In t h i s s tu d y r e p r e - i s e n t s an a tte m p t t o "m echanize" a g r e a t d e a l o f work now b e in g done m an u ally w ith in an a e ro sp a ce f ir m . The u l t i m a t e aim o f t h e stu d y was t o dev elo p a model t h a t would p ro v id e r e a s o n a b le and m e a n in g fu l lo n g -ra n g e f o r e c a s t s f o r a number of o v e rh e a d a c c o u n ts . By " lo n g -ra n g e " i s meant o ut t o te n y e a r s i n th e f u t u r e . "R easonable" means t h a t t h e f o r e c a s t v a lu e s a r e i n th e v i c i n i t y o f numbers t h a t m ight be g e n e r a te d by a know ledgeable human f o r e c a s t o r . And " m e a n in g fu l" im p lie s t h a t m a n a g e ria l a c t i o n can r e s u l t when t h e f o r e c a s t v a lu e s become o u t o f l i n e f o r one re a so n o r a n o th e r . Obvi o u s ly , u l t i m a t e p r e c i s i o n i s n o t i n d i c a t e d by any o f t h e s e t h r e e m odel q u a l i t i e s . 1 One a d d i t i o n a l d e s i r e d q u a l i t y was s i m p l i c i t y . I t is easy t o c o n c e iv e o f a model t h a t p r o v id e s t h e r e q u i r e d a c c u ra c y and c r e d i b i l i t y , b u t which i s p r e d i c a t e d on a com p le x m odel and an e x h a u s tiv e p r e - f o r e c a s t e f f o r t each tim e th e model i s u s e d . Such a model may l i e a few g e n e r a t i o n s beyond t h e p r e s e n t m odel. However, t h e i n i t i a l i n t e n t was •'■Charles C. H o lt, e t . a l . , P la n n in g , P r o d u c t i o n , I n v e n t i o n s , and Work Force TEnglewood C l i f f s , N. J . : P r e n t i c e - H a l l , I n c . , I9 6 0 ), p . 64. 1 t o d e v elo p a model t h a t was sim ple t o u t i l i z e and sim p le to r e v i s e and u p d a t e . 2 In o th e r, w o rd s, what was d e s i r e d was a model t h a t e li m in a te d some d e t a i l s o f th e firm b u t s t i l l was s u f f i c i e n t l y c lo s e t o r e a l i t y t o be h e l p f u l . 3 The model d e s c r i b e d i n th e f o llo w in g c h a p t e r s , i t i s hop ed, s a t i s f i e s b o th o f t h e s e c r i t e r i a . T h is i n t r o d u c t o r y c h a p te r w i l l f i r s t d i s c u s s t h e f o r e c a s t i n g environm ent o f the f ir m . F o llo w in g t h a t w i l l be a b r i e f d i s c u s s i o n o f th e overhead model t h a t w i l l be d e v e l oped i n t h e rem a in d e r o f t h i s s tu d y . I . DESCRIPTION OF FORECASTING ENVIRONMENT The p a r t i c u l a r a e ro sp a c e firm u n d e r a n a l y s i s p e r form s a v a r i e t y o f p la n n in g p r o c e s s e s . I n f a c t , w i t h in th e f ir m a re s e v e r a l com plete d e p artm e n ts whose p rim a ry f u n c tio n i s t o p ro v id e management w ith numerous f o r e c a s t s o f v a rio u s t y p e s . Of p a r t i c u l a r im portance a re t h e t e n - y e a r f o r e c a s t s g e n e r a te d each y e a r . There i s a s u b s t a n t i a l amount o f e f f o r t c o n ta in e d i n each f o r e c a s t , and a num ber o f d e p a rtm e n ts c o n t r i b u t e p o r t i o n s o f th e f o r e c a s t . 2T. C. Koopmans, Three E ssays o n th e S t a t e o f Eco- nomic S c ien c e (New York: McGraw-Hill Book C o ., I n c . , 1 957 ), p ." m :------- 3g . A. S t e i n e r , Top Management P la n n in g (London: The M acm illan Company, 1969), p. 439. 3 BUDGET FORECAST The p r e s e n t method o f f o r e c a s t i n g b e g in s w ith a s a l e s p r o j e c t i o n by p ro d u c t l i n e f o r each o f th e t e n y e a rs i n th e f o r e c a s t . The f i r s t y e a r o f th e t e n i s th e bud get y e a r , so named because th e f o r e c a s t f o r t h a t y e a r i s th e b u d g e t to be m a in ta in e d d u r in g th e y e a r . Thus, th e budget p e rfo rm s th e two c l a s s i c a l f u n c t i o n s , i . e . , as a p la n and a s a control.** The overhead bud g et r e p r e s e n t s one a s p e c t o f th e o v e r a l l firm b u d g e t. I t i s p r e p a r e d by a group o f s p e c i a l i s t s who m a in ta in more o r l e s s c o n t i n u a l c o n ta c t w ith th e v a r i o u s overhead a c c o u n ts th ro u g h o u t th e y e a r . In a d d i t i o n t o p r e p a r in g s p e c i f i c f o r e c a s t s t h e m s e lv e s , th e s e s p e c i a l i s t s c o - o r d i n a te th e o v erh ead f o r e c a s t i n g e f f o r t co ndu cted by o t h e r i n d i v i d u a l s and groups w i t h i n th e f irm . Each y e a r , an o v e rh e ad b u d g e t i s p r e p a re d which c o n ta in s f o r e c a s t s f o r each o f th e 280 a c c o u n ts which com p r i s e o v e rh e ad . Because th e p e rfo rm an c e o f th e firm d u rin g th e budget y e a r i s compared c o n t i n u a l l y w ith t h i s o verhead b u d g e t ( i . e . , th e c o n t r o l f u n c t i o n o f th e b u d g e t) , i t i s d o u b tf u l t h a t th e p r e p a r a t i o n o f t h e o v erh ead budget w i l l e v e r be d e le g a te d to an e c o n o m e tric m odel. Such a model i s e n t i r e l y too i n s e n s i t i v e to u n iq u e s i t u a t i o n s t h a t make th e **A. C. S te d r y , Budget C o n tr o l and C ost B ehavio r (Englewood C l i f f s , N. J . l P r e n t i c e - H a l l , I n c . , i 960) , p. 3 . budget y e a r d i f f e r e n t from any p r i o r y e a r upon which an e c o n o m e tric model i s p r e d i c a t e d . I n a word, th e o v e rh e a d budget i s and w i l l l i k e l y rem ain a r a t h e r d e t a i l e d document t h a t i s p r e p a r e d i n a d e c e n t r a l i z e d , hand-made f a s h i o n . TEN-YEAR FORECAST The t e n - y e a r f o r e c a s t was developed from th e bud g et i n an e v o l u t i o n a r y manner. Because th e v a r io u s d e p a rtm e n ts p r o v id e d f o r e c a s t s f o r t h a t f i r s t b u d g e t y e a r , they a ls o were a sk ed t o p ro v id e f o r e c a s t s f o r th e l a s t nine y e a r s . U n f o r t u n a t e l y , t h i s f o r c e d th e m anagers t o p ro v id e alm o st as much in f o r m a tio n f o r each o f th e l a s t nine y e a r s as th e y had f o r th e f i r s t y e a r. The o n ly s i g n i f i c a n t s i m p l i f i c a t i o n was to accum ulate some o f th e a c c o u n ts , r e d u c in g t o 90 th e number o f acco unt f o r e c a s t s r e q u i r e d . But one i s now fa c e d w ith an anomaly: th e d e p a r t ments p ro v id e h i g h e r management w ith e x q u i s i t e d e t a i l on f u t u r e p r o j e c t s t h a t a r e only n eb ulo us a t b e s t . The s a l e s p r o j e c t i o n s g e n e r a te d by u p p er management, which form th e b a s i s f o r th e f o r e c a s t , a re r e a l l y q u i te u n r e l i a b l e . T h is u n r e l i a b i l i t y i s g e n e r a te d p r i m a r i l y b ecau se o f t h r e e un knowns: (1) unknown custom er p r e f e r e n c e s ; (2) unknown custo m er " a f f l u e n c e " ; and (3) unknown a b i l i t y t o win th e c o n t r a c t i n t h e fa c e o f c o m p e titio n . Because o f t h e s e unknowns, i t was f e l t t h a t a b e t t e r m ethod m ight be developed to g e n e r a te t h e l a s t n in e y e a r s o f th e t e n - y e a r f o r e c a s t , p a r t i c u l a r l y t h e o v e rh e ad f o r e c a s t . T h is new method would be p re m ise d on a th o ro u g h a n a l y s i s o f h i s t o r i c a l r e l a t i o n s h i p s betw een o v e rh e a d c o s ts and v a r i o u s e x p la n a to r y v a r i a b l e s such as p r o f i t s , wage- r a t e s , p e r s o n n e l , f a c i l i t i e s , c a p i t a l , e t c . I t t h e r e f o r e c o u ld p r o v id e b e t t e r f o r e c a s t s th an th e p r e s e n t m e th o d .5 B e sid es im p ro v in g th e q u a l i t y o f th e f o r e c a s t , h o w ev er, such a method would f a c i l i t a t e th e a n a l y s i s o f th e e f f e c t s o f a l t e r n a t i v e s a l e s p rem ise s on th e r e s u l t s . A t h i r d advan ta g e would be th e speed o f f o r e c a s t p r e p a r a t i o n once th e model i s o p e r a t i o n a l . F i n a l l y , a l a s t a d v a n ta g e i s an im provem ent o f m anagem ent’s u n d e rs ta n d in g o f th e p ro b lem — a f e a t u r e common t o most m o d e l- b u ild in g .^ In p a s s i n g , a comment sh o u ld be made r e g a r d i n g the v a l i d i t y o f a t e n - y e a r f o r e c a s t as opposed to one t h a t i s e i t h e r s h o r t e r o r lo n g e r . O r i g i n a l l y , th e f o r e c a s t p e r io d was only f i v e y e a r s . However, th e g e s t a t i o n p e r i o d a s s o c i a t e d w ith a e ro s p a c e p ro d u c ts c o n s i s t s of (1) t h e tim e r e q u ir e d t o re c o g n iz e a p a r t i c u l a r need p lu s (2) t h e tim e to d e v elo p a p ro d u c t r e s p o n s iv e t o t h a t need p lu s (3) th e time 5M artin S h u b ik , "Economics, Management S c i e n c e , and O p e r a tio n s R e s e a rc h ," Review o f Economics and S t a t i s t i c s , XL (A ug ust, 1 9 5 8 ), p. 219. ^R. A. Hammon, B u sin ess H o riz o n s , V ( S p r i n g , 1963)* P. 74. needed t o p ro d u ce th e product.*^ The t o t a l d u r a t i o n o f t h i s g e s t a t i o n p e r i o d has le n g th e n e d so much d u r in g t h e p a s t few y e a r s t h a t a t e n - y e a r p e rio d i s n o t a t a l l e x c e s s i v e f o r p l a n n in g p u r p o s e s . I I . MODEL CHARACTERISTICS W hether I t i s done by hand o r by u s i n g a m odel, t h e f o r e c a s t i s an a tte m p t t o e s t im a t e what w i l l o c c u r , n o t what management hopes w i l l occur.® T hus, t h i s model sh o u ld f o r e c a s t , i . e . , i t sh o u ld n o t o p tim iz e c o s t s , b u t m erely t r a n s l a t e m anagem ent’s p rem ises i n t o u s e f u l p r e d i c t i o n s o f t h e f u t u r e . The jo b o f o p tim iz in g must be done e x t e r n a l l y t o t h i s model i n th e p r e m i s e - p r e p a r a t io n s t a g e . T h is means t h a t i n th e p r e m is e - p r e p a r a t io n s t a g e , management would be a b le t o maximize th e p a y o ff o f a g iv e n in v e s tm e n t , o r to d e te rm in e th e e f f e c t s o f c o n c e n tr a ti n g funds i n p a r t i c u l a r l i n e s o f b u s i n e s s i n o r d e r t o o u t-p e rf o rm t h e c o m p e titio n . The f o r e c a s t model would t h e n ' t r a n s l a t e t h e s e o p tim iz e d (o r su b o p tim iz e d ) s a l e s p rem ises i n t o p r e d i c t e d o v e rh e ad c o s t s . To acco m p lish t h i s g o a l, th e model sh o u ld be ?E. K. W arren, Long Range P la n n in g : The E x e c u tiv e V iew point (Englewood C l i f f s , N. J . : P r e n t i c e - H a l l , I n c . , 1 9 6 6 ), p. 23. ®Colin R obinson, "Some P r i n c i p l e s o f F o r e c a s t i n g i n B u s in e s s ," J o u r n a l o f I n d u s t r i a l E con om ics, XIV (Novem b e r , 1965)9 P* 10. a b s t r a c t , s t a b l e , and s te a d y s t a t e , t o use F o r r e s t e r ' s d e f i n i t i o n . 9 I t would ap p ear t h a t a l i n e a r model would be p r e f e r a b l e to a n o n - l i n e a r model b e cau se o f s i m p l i c i t y o f c a l c u l a t i o n s . Such a c h o ic e i s made r e c o g n iz in g t h a t the l i n e a r e q u a tio n i s somewhat l i m i t e d i n l o g i c a l m ea n in g .10 In d e fe n s e o f t h i s d e c i s i o n , i t can be p o in te d o u t t h a t T in b e rg en defends l i n e a r i t y by s t a t i n g t h a t " in a m a jo r ity o f c a s e s , i t i s v e ry hard t o f i n d s y s te m a t i c d e v ia tio n s from l i n e a r i t y . " 11 F u rth e rm o re , th e l i n e a r form p ro v id e s a good, s a f e a p p ro x im atio n t o n o n - l i n e a r o p e r a t i o n s . 12 Such a model has t h e same q u a l i t i e s as a number o f macroecenomic eco n o m etric m odels t h a t have been developed r e c e n t l y . That i s , th e t y p i c a l m acroecenom ic econo m etric model i s p r e d i c t i v e (no o p t i m i z a t i o n f u n c t i o n ) , l a r g e l y l i n e a r , s t a b l e and s t e a d y - s t a t e . W hether i t i s dynamic o r s t a t i c depends on th e p re s e n c e o f d i f f e r e n c e e q u a tio n s among th e v a rio u s e q u a tio n s c o m p risin g th e model. Thus, a s u b s t a n t i a l amount o f r e l i a n c e w i l l be p la c e d on e x ta n t e c o n o m etric m odels in d e v e lo p in g th e ° J . W. F o r r e s t e r , I n d u s t r i a l Dynamics (New York: John Wiley and Sons, I n c . , 19 6 1), p . 49. 10Mordekai E z e k ie l and K a rl A. Fox, Methods of C o r r e l a t i o n and R e g re ss io n A n a ly s is (New York: John Wiley and Sons, I n c . , 19 6 7 ), p. 67. 11J . T in b e rg e n , E c o n o m etrics (New York: The B la k i s t o n Company, 1951)> P* 205. 12F o r r e s t e r , o£. c i t . , p. 50. f i r m 's o v e rh e ad m odel. Of p a r t i c u l a r im p o rtan ce i s th e K le in -G o ld b e rg e r m odel w hich was f i r s t p u b lis h e d in 1 9 6 4 .^ T h is model i s e s p e c i a l l y r e l e v a n t b e ca u se o f th e g r e a t q u a n tity o f s u p p le m e n ta ry in f o r m a tio n t h a t has been pub l i s h e d i n s u b s e q u e n t a r t i c l e s and boo k s. T his su b seq u en t in f o r m a tio n h as d e l i n e a t e d fla w s i n th e K le in -G o ld b e rg e r model and th e m ethods f o r v a l i d a t i n g th e model. S p e c if i c r e f e r e n c e s w i l l be made when t h e s u b j e c t s a re d is c u s s e d in th e t e x t . S p e c i f i c r e f e r e n c e sh o u ld be made a t t h i s tim e to a s i m i l a r e c o n o m e tric model d e v elo p ed f o r th e Sun O il Com p a n y .1* * The a u th o r o f t h i s s tu d y c o n s id e re d a number o f a l t e r n a t i v e s , i n c l u d i n g s t o c h a s t i c models r a t h e r than d e t e r m i n i s t i c m o d els, and ended up s e l e c t i n g an e con om etric model of th e ty p e d e s c r i b e d above. The r a t i o n a l e was t h a t such a model most c l o s e l y f i t th e needs o f th e firm f o r a p r e d i c t i v e t o o l , and was s i g n i f i c a n t l y s im p le r t o develop. Note t h a t a d e t e r m i n i s t i c model d o e s n 't imply t h a t the f o r e c a s t v a lu e s a re known p r e c i s e l y , b u t r e p r e s e n t s a mean 1 3l . R. K le in and A. S. G o ld b e rg e r, An Econom etric Model of th e U n ite d S t a t e s : 1929-1952 (Amsterdam: N orth- H olland P u b l i s h i n g Company, 1 9 6 4 ). 1 4 G. W. G e r s h e f s k i , The Development and A p p lic a t i o n of a C o rp o rate F i n a n c i a l M odel, Sun O il Company (Oxford, Ohio: The P la n n in g E x e c u tiv e s I n s t i t u t e , 1968), pp. 34-36. 9 o r ex p ec te d v a lu e o f f o r e c a s t . ^ i t sh o u ld be borne in mind t h a t a d i s p e r s i o n e x i s t s around t h i s c e n t r a l t r e n d and t h a t o f f - t r e n d v a lu e s a r e l i k e l y w ith a p p r o p r i a te p r o b - a b i s t i c e x p e c t a t i o n s I I I . USEFULNESS OF PREDICTIONS The u l t i m a t e g o a l o f e c o n o m e tric s i s to a c h ie v e r e l i a b l e p r e d i c t i o n s .^ 7 The developm ent o f an eco n o m etric model cap a b le o f p r o v i d i n g such p r e d i c t i o n s in v o lv e s h i s to r y in two p h a s e s : when d e r i v i n g th e " r e p r o d u c ib le p a t t e r n s " o r e q u a tio n s u se d in t h e model and when v a l i d a t i n g th e model. T here i s some c o n cern i n th e l i t e r a t u r e t h a t such h i s t o r y may n o t be an i n d i c a t i o n o f th e f u t u r e . T h e i l and H assel s t a t e t h a t f o r e c a s t s b a sed on h i s t o r i c a l d a ta i n v a r i a b l y u n d e r e s t i m a t e change. 18*3.9 Vagner c i t e s the 15g. H. O r c u t t , "Views on S im u la tio n and Models o f S o c ia l S y s te m s," Symposium on S im u la tio n Models: M ethodol ogy and A p p l i c a t i o n s t o th e B e h a v io ra l S c i e n c e s , e d . A. C. Hoggatt and F. E. B a ld e r s t o n ( C i n c i n n a t i : S outh-W estern P u b lis h in g C o ., 1963)» p . 231. ^ K l e i n and G o ld b e rg e r, 0£ . c i t . , p . 74. 17g. T i n t n e r , M ethodology o f M athem atical Eco nomics and E c o n o m e tric s (C hicago: U n i v e r s i ty of Chicago P r e s s , 1968), p . 84. 18h. T h e i l , Economic F o r e c a s ts and P o lic y (Amsterdam: N o r th - H o lla n d P u b l is h in g C o ., 1961), p . 49- 19w. H a s s e l , " Q u a n t i t a t i v e P la n n in g o f Economic P o lic y i n th e N e t h e r l a n d s ," Q u a n t i t a t i v e P la n n in g o f E co nomic P o l i c y , ed . B. G. Hickman (W ashington: The B rookings I n s t i t u t i o n , 196 5) , pp. 163-178. 10 o f t - u t t e r e d c la im t h a t " c o n d itio n s t h i s y e a r a r e un iq u e" to u n d e rs c o r e t h e id e a t h a t a model may do j u s t f i n e a t r e p ro d u c in g h i s t o r i c a l d a ta and y e t be p oor a t f o r e c a s t i n g f u t u r e d a t a . ^ E z e k ie l and Pox s t a t e " In any a r e a s u b j e c t d i r e c t l y o r i n d i r e c t l y t o human i n f l u e n c e , no m ethod o f s e l e c t i n g o b s e r v a tio n s w i l l g u a ra n te e t h a t th e r e l a t i o n s e s tim a te d i n one tim e p e r io d w i l l a p p ly t o th e c o rr e s p o n d in g u n i v e r s e s a t some l a t e r d a t e . " ^ F o r r e s t e r c la im s t h a t i t i s d o u b t f u l t h a t a complex b u s in e s s w ith i t s i n h e r e n t fe e d b a c k mechanism can e v e r be m e a n in g fu lly s i m u la t e d by u s in g a model b ased on a sequence o f o b s e r v a t i o n s o f th e f i r m ’s n o rm al p erfo rm an ce. He even goes so f a r as t o s t a t e t h a t t h e u s e f u ln e s s o f models need n o t r e s t on t h e i r a b i l i t y to p r e d i c t a s p e c i f i c p a th i n th e f u t u r e , and ex c lu d e s t e s t s o f i t s p r e d i c t i o n s a b i l i t y from h i s v a l i d a t i o n p r o c e d u r e . ^2 In s p i t e o f t h e s e a d m o n itio n s , th e a n a l y s t must be gu id ed by t h e p ro v e rb , "The p a s t i s p r o l o g u e ." W ithout s tu d y in g h i s t o r y , we can n o t hope t o be a b le t o p r e d i c t m e a n in g f u lly . W hat's m ore, ex ce p t f o r academ ic e x e r c i s e s , 20h . M. Wagner, " P r a c t i c a l S l a n ts on O p e ra tio n s R e s e a r c h ," H arvard B u sin e ss Review , XXXXI (M ay-June, 1963), p. 66. 2 l E z e k i e l and Pox, o£. c i t . , p. 330. 2 2 p o r r e s t e r , o jd. c i t . , p . 5^* 11 u n le s s a model has some p r e d i c t i v e c a p a b i l i t y , i t w i l l n o t be u s e f u l t o t h e b u sin e ssm a n t h a t w ants t o reduce th e un c e r t a i n t y o f t h e f u t u r e . 2 3 Overhead f o r e c a s t s w i l l t h e r e f o r e be b a sed on an o verhead model which i s p re m ise d on h i s t o r i c a l d a t a . T h is i s e q u iv a le n t t o s t a t i n g t h a t t h e model assumes an absence oh o f s t r u c t u r a l change i n th e f u t u r e . T his same a ssu m p tio n makes i t a c c e p ta b le t o e x t r a p o l a t e beyond t h e ra n g e o f t h e d a t a . E z e k ie l and Fox (among many o t h e r s ) warn t h a t such e x t r a p o l a t i o n s a re h a z a rd o u s. 25 However, th e y go on t o add t h a t "a p r i o r i know ledge o f th e r e l a t i o n s , b a se d on t e c h n i c a l f a c t s and th e o r i e s , o r on o t h e r e v id e n c e , may j u s t i f y e x t r a p o l a t i o n s .. ." 2^ The absence o f s t r u c t u r a l change sh o u ld allow e x t r a p o l a t i o n o f th e r e g r e s s i o n e q u a tio n s (b u t i t sh o u ld be b orne i n mind t h a t an elem ent o f r i s k h as been in c o r p o r a te d w ith th e a d o p tio n o f t h i s a s s u m p t io n ) . 23 c a r l F. C h r i s t , "A gg reg ate E conom etric M odels," American Economic R eview , XXXXVI (J u n e , 1956), p. 402. 2i*L. H urw icz, " P r e d i c t i o n and L e a s t S q u a re s ," S t a t i s t i c a l I n f e r e n c e i n Dynamic Economic M odels, ed. T j a i l i n g C. Koopmans (New York: John Wiley and Sons, I n c . , 1950), p. 263. 25 E z e k ie l and Fox, 0£ . c i t . , p. 322. ^ E z e k i e l and Fox, 0£ . c i t . , p. 323. IV. OUTLINE OP SUBSEQUENT CHAPTERS 12 The su b se q u e n t c h a p te r s w i l l d e l i n e a t e th e e f f o r t expended i n d e v e lo p in g t h i s o v erh ead m odel. C h a p te r two d e s c r i b e s th e f ir m u n d e r a n a l y s i s . C h a p te r t h r e e d e s c r i b e s t h e d a t a upon which th e overhead e c o n o m e tric e q u a tio n s a re b a s e d . C h a p te r f o u r d is c u s s e s th e r e s u l t s o f th e r e g r e s s i o n a n a l y s e s . The v a l i d i t y o f th e r e s u l t a n t model i s v e r i f i e d i n C h a p te r f i v e . The s e n s i t i v i t y o f th e f o r e c a s t s t o t h e i n t r o d u c t i o n o f new d a t a i s exam ined i n Chap t e r s i x . F i n a l l y , C hap ter seven g iv e s a c r i t i q u e o f th e model and d e s c r i b e s a d d i t i o n a l work t h a t c o u ld be done t o im prove on t h e m odel. CHAPTER I I THE FIRM B efore em barking on a d i s c u s s i o n ab o u t th e o v e r head e c o n o m etric m odel, th e r e a d e r must have a r e a s o n a b ly com plete u n d e r s ta n d in g o f th e f ir m u n d e r s tu d y . T his d i s c u s s io n w i l l b e g in w ith a b r i e f d e s c r i p t i o n o f th e firm i n g e n e r a l te rm s . F o llo w in g t h i s w i l l be a more d e t a i l e d d e s c r i p t i o n o f th e a s p e c t s o f th e firm which i n t e r a c t w ith o v e rh e ad . Most o f th e r e s e a r c h r e p r e s e n t e d by t h i s c h a p t e r was acc o m p lish e d w ith o r a l i n te r v ie w s w ith p e r s o n n e l i n th e f ir m u n d e r a n a l y s i s s i n c e no u s e f u l w r i t t e n d e s c r i p t i o n i s a v a i l a b l e - e i t h e r i n t e r n a l o r e x t e r n a l t o th e fir m . How e v e r , th o s e f e a t u r e s o f th e f i r m t h a t a r e a p p l i c a b l e to th e i n d u s t r y as a whole a re r e f e r e n c e d a p p r o p r i a t e l y . To s i m p li f y m a t t e r s i n th e f u t u r e d i s c u s s i o n , th e term " firm " w i l l be u se d w henever s p e a k in g o f firm s i n gen e r a l , b u t "Firm" ( i . e . , c a p i t a l i z e d ) w i l l be used w henever r e f e r r i n g t o th e s p e c i f i c f i r m u n d e r a n a l y s i s . I . GENERAL DESCRIPTION OF THE FIRM The Firm u n d e r a n a l y s i s i s an a e ro sp a c e f ir m . As i s t y p i c a l o f t h i s i n d u s t r y , t h i s Firm i s a s u b s i d i a r y o f a l a r g e r " c o n g lo m e ra te ." The F ir m ’s main l i n e o f b u s in e s s c o n s i s t s o f m a n u fa c tu rin g a ir f r a m e com ponents. P r i n c i p a l i4 cu sto m ers a re th e U. S. governm ent, f o r e i g n g o v ern m en ts, and d o m estic and i n t e r n a t i o n a l firm s o f v a r i o u s t y p e s , p a r t i c u l a r l y a i r l i n e s . As i s t y p i c a l o f t h i s i n d u s t r y , th e Firm re a p s a r e l a t i v e l y l a r g e a f t e r - t a x r e t u r n p e r d o l l a r o f i n v e s t e d c a p i t a l ( i n e x c e ss o f $4 r e t u r n p e r d o l l a r i n v e s t e d ) , b u t a low r e t u r n p e r d o l l a r o f s a l e s (aro u n d 2 1/2% ) . These c h a r a c t e r i s t i c s im ply t h a t th e Firm i s a b le t o pro duce a l a r g e o u tp u t v a lu e from a r e l a t i v e l y s m a ll amount o f f i x e d a s s e t s . In o t h e r w o rd s, i t p r o v id e s h i g h - p r i c e d p r o d u c ts made w ith a l a r g e amount o f l a b o r and p u rc h a s e d m a t e r i a l s , w ith a m inim al in v e s tm e n t i n la n d and c a p i t a l . W hile i t may be obvious t o some r e a d e r s , i t i s w orth p o i n t i n g o u t th e one f e a t u r e t h a t makes th e a e ro sp a c e i n d u s t r y d i f f e r e n t from o t h e r i n d u s t r i e s . In th e a e ro sp a c e i n d u s t r y , " th e governm ent agency cu sto m e r h as as h i s f i r s t g o a l th e achievem ent o f d i f f i c u l t t a s k s r e q u i r i n g e x o ti c new te c h n iq u e s and s u p e r - r e l i a b i l i t i e s . He w ants a d e fin e d t e c h n i c a l p e r f o r m a n c e / r e l i a b i l i t y a c h ie v e m e n t, and se co n d a r i l y would l i k e i t a t a minimum c o s t . "3 T his d i f f e r s l"T he F o rtu n e D ir e c to r y o f th e 500 L a r g e s t U. S. I n d u s t r i a l C o r p o r a t i o n s ," F o rtu n e M agazine, June 15, 1968, p. 20 7 . 2A erospace I n d u s t r i e s A s s o c ia t io n o f A m erica, The In d u stry -G o v e rn m e n t A erospace R e l a t i o n s h i p , V ol. I I (Menlo Park: S ta n f o r d R ese arch I n s t i t u t e , 1963) , p. 104. 3w. R. P u r c e l l , J r . , Commercial P r o f i t s from De- fe n s e -S p a c e Technology (B oston: The Shur C o ., 1 9 6 4 ), p. 2. 15 from th e norm al cu sto m e r who te n d s t o g iv e c o s t a h ig h p r i o r i t y , te n d in g to t r a d e - o f f q u a l i t y a g a i n s t re d u c e d p r i c e . And n o te t h a t th e nongovernm ent cu sto m er i s i n t e r e s t e d i n th e same d eg ree o f p erfo rm an c e and r e l i a b i l i t y as th e gov ernm ent cu stom er, so th e d i s t i n c t i o n betw een cu stom ers which i s made below i s made f o r r e a s o n s o t h e r th a n p ro d u c t d i f f e r e n t i a t i o n . A nother s i g n i f i c a n t d i f f e r e n c e betw een th e a e r o space in d u s t r y and o t h e r m a n u fa c tu rin g i n d u s t r i e s i s th e method o f s e l l i n g . The n o n - a e ro s p a c e f ir m t y p i c a l l y b u i l d s som ething and th e n t r i e s to s e l l i t a f t e r w a r d . The a e r o space f ir m , on th e o t h e r h a n d , u s u a l l y n e g o t i a t e s a con t r a c t b e fo r e u n d e rta k in g a s u b s t a n t i a l amount o f th e work i n a p r o j e c t . T h is d i s t i n c t i o n i s im p o r ta n t b e ca u se th e a e ro sp a c e firm can be p a r t i a l l y o r f u l l y funded d u rin g th e m a n u fa c tu rin g phase s i n c e th e work i s u n d e r c o n t r a c t , w hereas th e n o n -a e ro sp a c e f ir m u s u a l l y must w a it u n t i l th e p ro d u c t i s s o ld b e f o r e r e c o u p in g any c o s t s . T h is te n d s t o red u c e s i g n i f i c a n t l y t h e amount o f w orking c a p i t a l which th e a e ro sp a c e firm must keep t i e d up i n work i n p r o c e s s . I I . DETAILED DESCRIPTION OP THE FIRM The u n d e r ly in g p u rp o se o f th e Firm i s t o develop p r o f i t s by m a n u fa c tu rin g and s e l l i n g a e ro s p a c e p r o d u c ts . As su c h , th e Firm i s dom inated by a l a r g e f a c t o r y o p e ra t i o n . D i r e c t l y s u p p o r tin g t h i s o p e r a t i o n i s a s m a l l e r b u t 16 s t i l l s u b s t a n t i a l e n g in e e r i n g b ra n c h . S u p p o rtin g b o th f a c t o r y and e n g in e e r i n g b ra n c h e s a re an a d m i n i s t r a t i v e b ran c h and a s p a r e - p a r t s b r a n c h . These l a t t e r two b ra n c h e s p r o v id e f i n a n c i a l , m a r k e tin g , a d m i n i s t r a t i v e , and o t h e r a s s i s t a n c e t o th e f a c t o r y and e n g in e e r in g b r a n c h e s . The s i m p l e s t way o f d e s c r i b i n g th e Firm i s a lo n g th e l i n e s o f c o s t e x p e n d i t u r e s , b e a r i n g in mind th e above s t r u c t u r e o f th e Firm . These c o s t s can be b ro ken down i n t o t h r e e main c a t e g o r i e s : l a b o r , m a t e r i a l s , and o v e rh e ad . When p r o f i t i s added t o t h e l i s t , we have th e f o u r main f i n a n c i a l ele m e n ts o f th e Firm . Each o f th e s e w i l l be d i s cu ssed below , s t a r t i n g w ith l a b o r . LABOR At th e o u t s e t , a d i s t i n c t i o n must be made betw een two c a t e g o r i e s o f l a b o r : d i r e c t l a b o r and i n d i r e c t l a b o r . D ir e c t l a b o r e x p e n d i tu r e s a re c h arg ed d i r e c t l y t o a s p e c i f i c p r o j e c t and w i l l be d i s c u s s e d h e r e . I n d i r e c t l a b o r i s a p a r t o f o v e rh e a d and w i l l be d is c u s s e d in a su b se q u e n t s e c t i o n . E n g in e e r in g and f a c t o r y manhours com prise th e l a r g e s t s h a r e s o f manhours charg ed d i r e c t l y t o a p r o j e c t . However, a s m a ll amount o f a d m i n i s t r a t i v e e f f o r t i s a l s o charged " d i r e c t " ; t h e s e l a t t e r h ours a re c h arg ed by p e r so n n e l who a re a s s i s t i n g th e cu sto m er a t th e s i t e where th e p r o d u c ts a r e b e in g u t i l i z e d . They a r e a c c o u n te d f o r 17 in th e a d m i n i s t r a t i v e b ra n c h as a m a t t e r o f c o n v en ien c e. As m ight be e x p e c te d , t h e r e i s a re a s o n a b ly d i s t i n c t p a t t e r n t h a t emerges when we compare th e tim in g o f e n g in e e r in g and f a c t o r y e f f o r t s , w ith th e e n g in e e r in g e f f o r t p r e c e d in g th e f a c t o r y e f f o r t . A good c o r r e l a t i o n (0 .6 8 ) can be found betw een one y e a r ’s f a c t o r y h o u rs and e n g in e e r i n g h ou rs f o r th e p re v io u s y e a r s . However, th e e n g in e e r in g e f f o r t does n o t cea se when th e p r o d u c tio n b e g in s b e c a u se c o n ti n u a l r e v i s i o n s f i n d t h e i r way to th e en g i n e e r s and th e n down t o th e f a c t o r y . T h is e n g in e e r in g e f f o r t i s l a b e l e d " s u s t a i n i n g e n g i n e e r i n g . " N e ith e r f a c t o r y n o r e n g in e e r i n g h ou rs a re as homo geneous as has been h i n t e d . W ith in t h e s e b ro ad c a t e g o r i e s a re found some s i g n i f i c a n t s u b - g r o u p s : p la n n i n g , t o o l i n g , p r o d u c t i o n , and q u a l i t y a s s u r a n c e f o r th e f a c t o r y , and nu merous t e c h n i c a l d i s c i p l i n e s i n e n g i n e e r i n g . A q u e s tio n a r i s e s as t o what l e v e l o f d i s a g g r e g a t i o n an a n a l y s i s sh o u ld p ro c e e d , s in c e each f u r t h e r d i s a g g r e g a t i o n i n j e c t s a d d i t i o n a l co m plexity i n t o th e s tu d y . S in c e th e p r e s e n t model was e n v is io n e d as a p la n n in g m odel, i t was d e c id e d to t r e a t b o th f a c t o r y and e n g in e e r in g as homogeneous b ran c h es w ith o u t f u r t h e r d i s a g g r e g a t i o n . T h is f a c i l i t a t e s some o f th e co m p u tatio n s w ith o u t harm ing t h e o v e r a l l v a l i d i t y o f th e m odel. T h is must be r e g a r d e d as a weakness o f th e s tu d y , b u t t h e r e i s no good a l t e r n a t i v e s in c e a g g re g a te o v erh ead d a ta a re only com piled on a b ra n c h -w id e b a s i s . 18 MATERIALS AND SUBCONTRACTS I t i s i n t e r e s t i n g t o n o te t h a t j u s t a few y e a r s a g o , buying s u b s t a n t i a l amounts o f s e m i - f i n i s h e d ite m s was done only when t h e prim e c o n t r a c t o r ' s f a c i l i t i e s were o v e r lo a d e d . T h is stemmed from th e w id e sp re a d b e l i e f t h a t su b c o n t r a c t i n g was more e x p e n siv e th a n making th e item.** I t i s now r e c o g n iz e d t h a t s u b c o n t r a c t o r s o f t e n can m a n u fa ctu re s p e c i f i c components a t a lo w er c o s t th a n can th e prim e con t r a c t o r . T h is l e a d s t o s u b s t a n t i a l s u b c o n t r a c ti n g even when th e f irm has e x c e s s c a p a c i t y . However, t h e r e u n d o u b t e d ly i s a s t r o n g d r i v e t o b u i l d t h e s e item s in - h o u s e , p r o v i d in g an eco n o m ical method can be d e v e lo p e d . Prom t h e a b o v e , i t would p ro b a b ly be conclud ed t h a t more and more o f th e c o s t o f o u tp u t i s b e in g p u rc h a s e d e ls e w h e re . A g la n c e a t T ab le 1 w i l l r e v e a l t h a t t h e oppo s i t e i s t r u e : i n - h o u s e d i r e c t l a b o r and o v erh ead e x p e n se s have r i s e n d r a m a t i c a l l y d u r in g th e p a s t t e n y e a r s . A s i g n i f i c a n t re a s o n b e h in d t h i s i s i n th e method i n which th e U. S. Government buys f i n i s h e d goods. In r e c e n t y e a r s , th e U. S. Government has o f t e n "given" th e c o n t r a c t o r v a r i o u s p i e c e s o f equipm ent so th e y can be i n s t a l l e d in th e F ir m ’s p r o d u c t. Such item s a r e l a b e l e d Government F u r n is h e d E quipm ent, o r GFE. GFE i s im p o rta n t ^John S. Day, S u b c o n t r a c ti n g P o lic y i n t h e A lr - frame I n d u s t r y (Norwood, M ass.: T h e - P lim pto n P r e s s , 1 9 5 6 ), pp. 121-124. TABLE 1 CONTRIBUTION OP LABOR AND OVERHEAD COSTS TO TOTAL COSTS 1959 - 1968 PERCENT OP TOTAL COSTS YEAR DIRECT LABOR OVERHEAD TOTAL 1959 15* 23* 38* i 960 18 27 45 1961' 19 29 48 1962 21 29 50 1963 16 26 42 1964 24 34 58 1965 26 39 65 1966 28 39 67 1967 25 40 65 1968 27 44 71 20 i n t h i s a n a l y s i s b e ca u se t h e Firm h a n d le s th e GFE w ith o u t e i t h e r b u y in g o r s e l l i n g i t . The c o s t s in v o lv e d w ith GFE a re t h e r e f o r e l i m i t e d t o t h e l a b o r in v o lv e d i n i n s t a l l i n g th e equipm ent i n th e F ir m 's p r o d u c t , p lu s a sm a ll amount o f a d m i n i s t r a t i v e e f f o r t i n a c c o u n tin g f o r th e GFE. P ro f i t s n o rm a lly a re a s s o c i a t e d w ith c o s t s , and t h e s e c o s t s , o f c o u r s e , in c lu d e th e c o s t s o f m a t e r i a l s and equipm ent p u rc h a s e d from o t h e r s . S in c e GFE i s e x c lu d e d from c o s t s , p r o f i t s a re red u c ed p r o p o r t i o n a t e l y . OVERHEAD Overhead co m p rise s t h e l a s t m ajo r elem en t o f c o sts. T h is e lem en t i s composed o f f o u r o v e rh e ad p o o l s : e n g i n e e r i n g , f a c t o r y , a d m i n i s t r a t i o n , and s p a r e s . Each p o o l c o n s i s t s o f a number o f o v e rh e a d a c c o u n ts (as many as n i n e t y ) t o w hich a p p r o p r i a t e c o s t s a r e c h a rg e d . F o r exam ple, i n each p o o l i s an a c c o u n t l a b e l e d " S o c ia l S e c u r i t y T a x e s ." Whenever some payment i s made f o r s o c i a l s e c u r i t y t a x e s , i t i s c h arg ed t o t h a t a c c o u n t i n th e a p p r o p r i a t e p o o l. The p o o l, o f c o u r s e , i s d e te rm in e d by th e ty p e o f l a b o r p e r formed by th e c h a r g in g d e p a rtm e n t. The a c c o u n ts w i t h i n each p o o l can be s e g r e g a te d i n t o two m ajor c a t e g o r i e s : i n d i r e c t l a b o r and n o n - la b o r . I n d i r e c t L abor E x p e n d itu re s E x p e n d itu re s f o r i n d i r e c t l a b o r c o n s i s t o f wages p a id t o w orkers t h a t a i d i n th e o v e r a l l o p e r a t io n o f th e 21 f i r m , b u t w hich can n o t ch arg e d i r e c t l y t o a p r o j e c t . In e n g i n e e r i n g , some o f th e r e s e a r c h and t e s t i n g f u n c t i o n s f a l l w i t h i n t h i s c l a s s i f i c a t i o n . In th e f a c t o r y , i n d u s t r i a l e n g in e e r i n g i s a r e p r e s e n t a t i v e exam ple o f an i n d i r e c t o r g a n i z a t i o n . The a d m i n i s t r a t i v e o v erh ead p o o l c o n t a i n s th e l a r g e s t amount o f i n d i r e c t l a b o r s i n c e i t i s h e re t h a t c h a rg e s a re made f o r such f u n c t i o n s as m a r k e tin g , l e g a l c o u n s e l, f i n a n c e , and c o m p u te r- o rie n te d l a b o r . The s p a r e s i n d i r e c t l a b o r p o o l i s r e l a t i v e l y s m a ll, c o n ta in i n g c h a rg e s f o r th o s e a d m i n i s t r a t i v e a c t i v i t i e s a s s o c i a t e d w ith s p a r e p a r t s . In a d d i t i o n to such wage i t e m s , t h e r e a r e a number o f o t h e r w a g e - r e la t e d c h arg es w i t h in th e d e f i n i t i o n o f i n d i r e c t l a b o r . These in c lu d e most o f th e f r i n g e b e n e f i t s f o r b o th th e d i r e c t and i n d i r e c t w orkers i n each c a t e g o r y . T h u s, th e e n g in e e r i n g overhead p ool c o n ta in s c h a rg e s f o r v a c a t i o n s , h o l i d a y s , management i n c e n t i v e c o m p e n sa tio n , em p lo y e e s a v in g s p l a n s , e t c . , f o r e n g in e e r s c h a rg in g d i r e c t as w e ll as f o r p e rs o n s c h a rg in g i n d i r e c t t o th e e n g in e e r in g p o o l. A lso i n c lu d e d h e re a re e x p e n d itu r e s f o r such item s as o v e rtim e premium ( i . e . , th e " h a l f " i n " t i m e - a n d - a - h a l f " ) , employee t r a i n i n g , and l a y o f f b e n e f i t s . Non-Labor O verhead The n o n - l a b o r c a te g o ry o f o v e rh e ad c h a rg e s i s a 22 c a t c h - a l l , and ch arg es made a g a i n s t th e many a c c o u n ts w i t h i n t h i s c a te g o ry a r e v a r i e d . Some o f t h e s e te n d t o vary w ith th e w o rk lo ad , such as s u p p l i e s , p e r i s h a b l e t o o l s and eq u ip m en t, and u t i l i t i e s . O th e r c h a rg e s a r e more a k in t o th e f i x e d expenses o f t h e c l a s s i c a l f i r m , such as a d v e r t i s i n g e x p e n s e s , i n s u r a n c e , and some t a x e s . 5 i n th e a e r o sp ace and o t h e r i n d u s t r i e s , t h e s e l a t t e r e x p en ses a re o f t e n l a b e l e d " n o n c o n t r o l la b l e " o r " s e m i c o n t r o l l a b l e " t o i d e n t i f y t h e i r f i x e d n a t u r e . ^ The way th e Firm e v e n t u a l l y i s re im b u rse d f o r o v e rh e ad expenses i s as f o l l o w s , u s i n g e n g in e e r in g as an exam ple: 1. The t o t a l amount c h a rg e d t o th e a d m i n i s t r a t i v e ov erh ead p o o l i s d i v id e d by t h e a d m i n i s t r a t i v e b a s e . T his b a se i s a p p ro x im a te ly e q u a l t o th e combined number o f e n g i n e e r i n g and f a c t o r y m anhours. The r e s u l t a n t f i g u r e i s l a b e le d " a d m i n i s t r a t i v e b u r d e n ." 2. The t o t a l amount c h a rg e d t o th e e n g in e e r in g o v erhead p o o l i s d iv id e d by t h e t o t a l number o f d i r e c t en g i n e e r i n g m anhours. The r e s u l t a n t f i g u r e i s l a b e l e d "en g i n e e r i n g b u rd e n ." 3. The t o t a l amount expended f o r s a l a r i e s f o r 5 j . M. C la rk , The Economics o f O verhead C osts (C hicago: The U n i v e r s i ty o f C hicago P r e s s , 1 9 2 3 ), p. 46. ^Harry T ip p e r , J r . , C o n t r o l l i n g O verhead (New York: American Management A s s o c i a t i o n , 1 9 ^ 6 ), p . 25. 23 e n g in e e r in g em ployees i n th e tim e p e r i o d i s d i v i d e d by th e number o f d i r e c t m anhours. T h is f i g u r e i s th e a v e ra g e wage p e r h o u r f o r e n g i n e e r s . 4. The cu sto m e r i s charged an amount e q u a l t o th e sum o f th e t h r e e f i g u r e s c i t e d abov e, i . e . , th e a d m i n i s t r a t i v e bu rd en p lu s th e e n g in e e r in g b u rd en p lu s th e a v e ra g e wage. T here i s one q u a l i f i c a t i o n t o be made t o t h i s p ro ce d u re : i f t h e work i s expended i n p r o d u c in g s p a r e p a r t s , an a d d i t i o n a l b u rd en i s added t o th e s e l l i n g p r i c e j u s t l i k e a s a l e s t a x . T his l a t t e r bu rd en i s l a b e l e d " s p a r e s h a n d lin g and a d m i n i s t r a t i o n e x p e n s e ." T h is e x p en se i s ap p ro x im a te ly e q u a l t o th e t o t a l s p a r e s o v e rh e a d exp en se d i v id e d by th e t o t a l v a lu e o f th e s p a r e p a r t s p ro d u ced i n th e p e r io d . Note t h a t no m ention has been made o f m a t e r i a l s expended d u r in g th e h o u r o u r e n g in e e r has worked. Some m a t e r i a l ex p en ses a re c o n ta in e d w i t h i n o v e rh e a d . The r e m aining c o s t s (and by f a r th e m ost) a r e added t o th e l a b o r " b i l l " d e s c r i b e d ab ove, w ith no a d d i t i o n a l o v e rh e a d c o s t s b e in g added. T h is means t h a t a l l o v e rh e a d ex p en se s a re assumed t o be l in k e d w ith th e e x p e n d itu r e o f l a b o r r a t h e r th a n w ith use o f m a t e r i a l s . PROFIT From t h e p o i n t o f view o f o v e rh e a d , p r o f i t i s 2H I n t e r e s t i n g b e c a u se o f i t s e f f e c t s on some o v erh ead e x p e n s e s . When tim e s a re good and s a l e s a re e x p an d in g , o v e r head w i l l a l s o expand. When tim e s a re bad and s a l e s a re s ta g n a n t o r d e c l i n i n g , t h e r e I s u s u a l l y p r e s s u r e t o red u c e o v erh ead e x p e n se s. T h is p r e s s u r e may o r may n o t be su c c e s s f u l . 7 In t h e a e r o s p a c e f i r m , t h e r e a r e s i g n i f i c a n t me chanism s which c o n t r o l what p r o f i t s w i l l b e . These mech anism s a re r e l a t e d t o th e ty p e o f c o n t r a c t u n d er which th e p ro d u c t i s b e in g fu n d e d . P r o f i t on Government C o n tr a c ts The a n n u a l p r o f i t a s s o c i a t e d w ith U. S. Government work depends on t h e ty p e o f c o n t r a c t in v o lv e d . The two b a s i c c a t e g o r i e s o f c o n t r a c t s a r e F ix ed P r ic e c o n t r a c t s and Cost Reimbursement c o n t r a c t s . W ithin each c a te g o ry a re nu merous v a r i a t i o n s .® A f irm f i x e d p r i c e c o n t r a c t p ro v id e s f o r a p r i c e t h a t i s n o t a d j u s t a b l e , and I s b a se d on a prom ise by th e c o n t r a c t o r to d e l i v e r th e goods a t t h a t p r i c e . T his type o f c o n t r a c t i s th e one p r e f e r r e d In governm ent p ro cu re m en t, b ecau se i t p la c e s th e l a r g e s t r i s k on th e c o n t r a c t o r s in c e 7 T ip p e r, o j d. c i t ., p. 23. ^ G ilb e rt A. Cunee, Government C o n tr a c ts Handbook (W ashington: M achinery and A l l i e d P ro d u c ts I n s t i t u t e and C o u n c il f o r T e c h n o lo g ic a l Advancem ent, 1 9 6 2 ), p. 37- 25 a l l a d v e rs e c o s t movements a re met by h im .9 To com pensate f o r t h i s r i s k , t h i s c o n t r a c t y i e l d s th e l a r g e s t p r o f i t r a t e p e r d o l l a r o f s a l e s ( c u r r e n t l y around 10$). O th e r f i x e d p r i c e c o n t r a c t s a re th e R e d e te rm in a - b l e , t h e I n c e n t i v e , and th e E s c a l a t i o n . A ll o f t h e s e p r o v id e some mechanism whereby th e governm ent cu sto m e r s h a r e s a t l e a s t some o f th e r i s k . S in c e t h i s i s th e c a s e , th e p r o f i t r a t e on t h e s e c o n t r a c t s has been red u ced a p p r o p r i a t e l y . 10 C ost reim b u rse m e n t c o n t r a c t s have a number o f form s: no f e e , c o s t - s h a r i n g , f i x e d f e e , i n c e n t i v e f e e , and t i m e - a n d - m a t e r i a l s . O b v io u sly , th e m agnitude o f th e p r o f i t o r fe e i s d e p en d e n t on which c o n t r a c t i s n e g o t i a t e d . How- e v e r , c e t e r i s p a r i b u s , th e r i s k t o th e Firm h e re i s l e s s th a n w ith f i x e d - p r i c e c o n t r a c t s , so th e p r o f i t r a t e i s low e r . Such c o n t r a c t s a r e s u i t a b l e when th e n a tu r e and com p l e x i t y o f th e p ro d u c t a re such t h a t c o s t s c a n n o t be p r e d i c t e d w ith s u f f i c i e n t a cc u ra c y to p e rm it t h e use o f a f i x e d - p r i c e c o n t r a c t . By a llo w in g th e firm to be re im b u rs e d f o r a l l o f i t s c o s t s , th e government i s a b le t o r e duce i t s t o t a l e x p e n d i tu r e s s in c e th e allo w ance f o r r i s k i s ^Armed S e r v i c e s Procurem ent R e g u la tio n (W ashing to n : U. Si Government P r i n t i n g O f f i c e , 19 6 8 ), p . 324. 10Herman 0. S t e k l e r , The S t r u c t u r e and P erform ance o f th e A ero space I n d u s t r y (B e rk e le y : Univ. o f C a l i f o r n i a P r e s s , 1 9 6 5 ), p . 5CK 26 re d u c e d . In r e c e n t y e a r s , th e use o f th e c o s t - r e i m b u r s e - ment c o n t r a c t has been l i m i t e d t o s m a ll e r p r o d u c tio n con t r a c t s and e s p e c i a l l y to r e s e a r c h and developm ent con t r a c t s . • L1 I t sh o u ld be a p p a r e n t t h a t th e F ir m 's p r o f i t i n a g iv e n y e a r can be i n f lu e n c e d by th e ty p e o f c o n t r a c t nego t i a t e d . F o r exam ple, i f a f ir m u n d e r e s tim a te s i t s c o s t s (as u s u a l l y seems t o be th e c a s e ^ A S ) ^ an(j ^ g f i rm i S o p e r a t i n g und er a F ix e d P r ic e c o n t r a c t , th e e x c e ss ex penses come out o f p r o f i t s . These p r o f i t s can be th o s e which th e f irm hoped t o e a rn on t h a t p r o j e c t . Once th o s e p r o f i t s have been "used u p ," p r o f i t s made on o t h e r p r o j e c t s must be s p e n t t o c o v er c o s t s . From t h i s i t i s c l e a r t h a t r a t h e r w ild f l u c t u a t i o n s i n p r o f i t s can be e x p e r ie n c e d i f th e f ir m i s a poor e s t i m a t o r o f c o s t s . T here i s a n o th e r more im p o rta n t r e a s o n why th e c o n t r a c t ty p e w i l l i n f lu e n c e p r o f i t s . T h is stem s from th e way i n which moneys a r e g iv en t o th e f ir m as work p ro g r e s s e s . With c o s t reim b u rsem en t c o n t r a c t s , th e f ir m r e c e iv e s weekly payments from th e c u sto m e r, w ith th e s i z e o f 11Cunee, o£. c i t . , pp. 38-39* John F. L aw rence, "C-5A: Boondoggle— o r Good D eal?" Los A ngeles T im es, June 8, 19693 p. H-10. l^ A ero sp a c e I n d u s t r i e s A s s o c ia t io n o f A m erica, o p . c i t . , pp. 165-167. 27 th e payment d ep en d e n t on a c t u a l c o s t s i n c u r r e d p lu s a c e r t a i n p e rc e n ta g e f o r profit.-*-** On th e o t h e r h a n d , a f i x e d p r i c e c o n t r a c t i s ad m in i s t e r e d q u i t e d i f f e r e n t l y . H e re, th e f ir m and custo m er n e g o t i a t e th e s i z e o f p r o g r e s s paym ents t o be p a id d u r in g th e c o n t r a c t . These p r o g r e s s paym ents a r e funds g iv e n t o th e f ir m to p a r t i a l l y re im b u rse i t f o r c o s t s expended. P r o g r e s s paym ents a r e only g iv e n on c o n t r a c t s t h a t l a s t lo n g e r th a n s i x m onths, and a r e c u s to m a r ily a g iv e n p e r c e n t o f t o t a l c o s t s as i n c u r r e d . C u r r e n t l y , p r o g r e s s paym ents r e p r e s e n t 80# o f c o s t s , a lth o u g h th e f i g u r e was only 70# p r i o r t o March 1, 196 9*^ P r o g r e s s paym ents a r e p a id t o th e f ir m w i th in a week a f t e r th e c o s t s a re docum ented and b i l l e d t o th e c u s tom er (which i s u s u a l l y done as q u ic k ly as p o s s i b l e by th e F irm ). From t h i s i t i s c l e a r t h a t th e Firm c o l l e c t s 80tf ; f o r e v ery $1.00 s p e n t i n f u l f i l l i n g a f i x e d - p r i c e c q n t r a c t , w ith c o l l e c t i o n o c c u r r i n g e s s e n t i a l l y s im u lta n e o u s ly w ith th e c o s t e x p e n d i tu r e . The cu sto m e r re p a y s th e firm f o r th e u n reim b u rsed c o s t s a t t h e tim e th e p ro d u c t i s d e l i v e r e d ( i . e . , " s o ld " ) to th e cu sto m e r. A lso p a id a t tim e o f s a l e a re a l l p r o f i t s 3-* * Armed S e r v ic e s P rocu rem ent R e g u l a t i o n , o p . c i t . , p. Ei»9- • ^ Armed S e r v ic e s P rocurem ent R e g u l a t i o n , o p . c i t . , pp. E50-E51. 28 a t t r i b u t a b l e t o th e c o n t r a c t . With a long c o n t r a c t , th e u n reim b u rse d e x p en se s o b v io u s ly can b u i l d up t o a s u b s t a n t i a l l e v e l . In o r d e r t o keep th e f ir m g o in g , c u r r e n t p r o f i t s must be u t i l i z e d t o c o v e r c o s t s . While t h i s may n o t be to o much o f a problem w ith a s i n g l e c o n t r a c t , th e p r o f i t p i c t u r e may be a f f e c t e d s i g n i f i c a n t l y i f th e f ir m un d e r ta k e s a number o f such f i x e d p r i c e c o n t r a c t s s im u lta n e o u s ly . P r o f i t on Commercial C o n tra c ts T here i s no d i r e c t r e l a t i o n s h i p betw een i n c u r r e d c o s t s and r e c e i p t s w ith com m ercial b u s i n e s s . For t h i s r e a s o n , f l u c t u a t i o n s i n p r o f i t can be even more pronounced th a n w ith m i l i t a r y c o n t r a c t s . The main re a s o n f o r t h e s e f l u c t u a t i o n s i s t h a t th e f ir m may be r e q u i r e d t o p ro v id e very l a r g e sums o f money to c o v e r c o s t s d u rin g th e d e v e l opment phase o f th e p r o d u c t. O f f s e t t i n g th e s e funds may be p a r t i a l paym ents p ro v id e d by th e c u sto m e rs— u s u a l l y some p e r c e n t o f th e d e l i v e r e d p r i c e . These p a r t i a l p ay m ents, how ever, com prise o nly a p o r t i o n o f t o t a l c o s t s , and i t i s g e n e r a l l y a c c e p te d t h a t l a r g e sums o f money must be d i v e r t e d from what would be p r o f i t ( o r borrow ed) to cov er developm ent c o s t s o f m ajor com m ercial p r o d u c ts . A lso s i g n i f i c a n t i s th e p r i c i n g scheme o f commer c i a l a e ro s p a c e p r o d u c t . T y p i c a l l y , firm s i n t h i s i n d u s t r y a re fa c e d w ith d e c l i n i n g c o s t s as th e c u m u lativ e p r o d u c t i o n 29 q u a n t i t y i n c r e a s e s . T his e f f e c t has been dubbed " l e a r n i n g , " and i s p r e s e n t i n v i r t u a l l y a l l m a n u fa c tu rin g in d u s t r i e s . 1^ The main d i f f e r e n c e betw een th e a e ro s p a c e i n d u s t r y and o t h e r m a n u fa c tu rin g i n d u s t r i e s i s t h a t th e p r o d u c ti o n q u a n t i t y i n th e a e ro s p a c e i n d u s t r y i s r e l a t i v e l y s h o r t . T h is means t h a t l e a r n i n g can o c c u r th ro u g h o u t th e p r o d u c t i o n r u n . In o t h e r i n d u s t r i e s i n which th e p ro d u c t i o n ru n i s much l o n g e r , th e e f f e c t s o f l e a r n i n g a re l a r g e ly d i s s i p a t e d on th e f i r s t a r t i c l e s , w ith a s t e a d y - s t a t e b e in g a c h ie v e d w h e rein th e l a b o r and m a t e r i a l i n p u ts a r e v i r t u a l l y c o n s t a n t . 1? F u rth e rm o re , s in c e l a b o r com p rises so much more o f th e c o s t s i n th e a e ro s p a c e i n d u s t r y , th e l e a r n i n g e f f e c t i s l i k e l y t o be more pronounced th a n i n o t h e r m a n u fa c tu rin g i n d u s t r i e s . 1^ As th e a e ro s p a c e f irm c o n te m p la te s em barking on a com m ercial v e n t u r e , i t r e c o g n iz e s th e p re s e n c e o f b o th l e a r n i n g and c o m p e titio n . I t cannot hope t o s e l l any p r o d u c ts i f i t t r i e s t o c o v er a l l c o s ts r i g h t from th e b e g in n in g b e c a u se c o s t s a re h ig h and a sh a rp c o m p e tito r w i l l ■^Harold A sh er, C o s t- Q u a n tity R e l a t i o n s h i p s i n th e A irfram e I n d u s t r y , The Rand C o r p o r a tio n , J u ly 1, 1956, p . l 8 . ^ N i c h o l a s B a l o f f , "The L e a rn in g Curve— Some C o n t r o v e r s i a l I s s u e s , " J o u r n a l o f I n d u s t r i a l E co nom ics, XIV ( J u l y , 1 9 6 6 ), p . 27^ ^ W . B. H irschm ann, " P r o f i t from th e L e a rn in g C u rv e ," H arvard B u sin e ss Review , XXXXII (J a n u a r y - F e b r u a r y , 1 9 6 4 ), p . 1 2 6 . 30 u n d e r p r ic e and c a p tu r e th e m a rk e t. T hus, a f irm must look ahead and e s t i m a t e th e e x p e c te d s h a r e o f th e m arket i t can c a p tu r e a t v a r io u s p ro d u c t p r i c e s . To d e te rm in e th e b e s t p r i c e t o c h a r g e , th e firm w i l l use a l i t t l e m icroeconom ics and draw up a sim ple su p p ly and demand graph ( t h i s may be o nly a m e n ta l p r o c e s s , b u t t h a t i s what i s e f f e c t i v e l y d o n e ). The demand sc h e d u le w i l l be b a se d on th e f i r m ’s e x p e c te d s a l e s a t each p o s s i b l e p r i c e . The demand cu rv e (D) w i l l be downward s l o p i n g a f t e r th e b e s t p o s s i b l e c l a s s i c a l t r a d i t i o n , as shown i n F ig u re 1. The su p p ly c u rv e , b a s e d on c o s t s , can a l s o be drawn (p ro b a b ly more a c c u r a t e l y th a n th e demand s c h e d u l e ) . Because o f l e a r n i n g , t h i s su p p ly s c h e d u le w i l l be downward- s l o p i n g i n s t e a d o f th e u s u a l u p w a r d -s lo p in g . F ig u re 1 shows such a su p p ly s c h e d u le — one t h a t i s th e c u m u lativ e a v erag e c o s t curve (S).19 Note t h a t th e e l a s t i c i t y o f th e su p p ly curve i s l e s s th a n th e e l a s t i c i t y o f th e demand c u r v e . I f th e firm were t o s e l e c t th e p r i c e PQ, i . e . , th e p r i c e where th e su pply and demand c u rv e s i n t e r s e c t , th e f ir m would j u s t b re a k even. But th e f ir m w ants t o do b e t t e r th a n j u s t b re a k e v en , so i t w i l l compute a new 19J . w. Noah and R. W. S m ith , C o s t-Q u a n tity C a l c u l a t o r , The Rand C o r p o r a tio n , J a n u a r y , 1962, pp. 3-5* 31 PRICE FIGURE 1 . — SETTING PRICES ON COMMERCIAL PRODUCTS 32 i n t e r s e c t i o n — one t h a t i s a t th e p o i n t where th e demand curve i n t e r s e c t s a su p p ly c u rv e which in c l u d e s some p r o f i t ( S ’ ) . T h is i n t e r s e c t i o n o c c u rs a t a l a r g e r q u a n t i t y and a low er p r i c e th a n th e o r i g i n a l i n t e r s e c t i o n . In p a s s i n g , i t i s i n t e r e s t i n g t o n o te t h e e f f e c t o f u n d e r e s t i m a t in g t h e F ir m ’ s s h a re o f m a rk e t. I f th e t r u e demand i s D1 r a t h e r t h a n D, th e q u a n t i t y s o ld w i l l i n c r e a s e from Q' t o Q" even th o ugh p r i c e s t a y s a t P T. T his means th e Firm w i l l re a p s u b s t a n t i a l p r o f i t s — e q u a l t o AB p e r u n i t — becau se th e e l a s t i c i t y o f th e su p p ly c u rv e i s l e s s th a n th e e l a s t i c i t y o f th e demand c u rv e . The r e a s o n b e h in d t h i s long d i s c u s s i o n a b o u t p r i c in g i s b e ca u se o f th e im pact on p r o f i t s . In th e f i r s t y e a r s o f th e p r o d u c t i o n r u n , l a r g e l o s s e s a re n o t only p o s s i b l e b u t l i k e l y . P a r t i a l payment s c h e d u le s may o f f s e t t h i s problem p a r t i a l l y , b u t t y p i c a l l y p r e s e n t p r o f i t s must be i n v e s te d i n hopes o f f u t u r e r e t u r n s . A nother i n t e r e s t in g o b s e r v a t i o n i s t h a t p r o f i t s on com m ercial v e n tu r e s can be c o m p le te ly d iv o r c e d from th e i n c u r r i n g o f c o s t s , p a r t i c u l a r l y i n th e e a r l y developm ent y e a rs o f a new p r o d u c t. C o n clu sio n s About P r o f i t s From th e above d i s c u s s i o n , i t i s c l e a r t h a t p r o f i t s a s s o c i a t e d w ith b o th m i l i t a r y and com m ercial v e n tu r e s can f l u c t u a t e s u b s t a n t i a l l y . For t h i s r e a s o n , p r o f i t (o r p erhaps e x p e c te d p r o f i t ) o f t e n i s a p o o r e x p la n a to r y v a r i a b l e f o r many o v erh ead c o s t s s i n s p i t e o f a p r i o r i f e e l i n g s t o th e c o n t r a r y . T h is w i l l be b o rn e o u t i n C h a p te r 5, inasm uch as o v erh ead a c c o u n t e q u a t io n s which c o n ta in e d p r o f i t as an e x p la n a to r y v a r i a b l e o f t e n r e s u l t e d i n u n a c c e p ta b le f o r e c a s t s . CHAPTER III THE DATA A s i g n i f i c a n t c o n s i d e r a t i o n i n eco n o m etric a n a ly s e s o f tim e s e r i e s d a ta i s th e c o n s i s t e n c y o f t h a t d a ta th ro u g h o u t i t s d u r a t i o n . T y p i c a l l y , i t i s found t h a t th e q u a l i t y o f th e d a t a d e t e r i o r a t e s as th e tim e span i s le n g th e n e d b a c k w a r d . T h i s d e t e r i o r a t i o n stem s from two c a u s e s : (1) changes i n th e a c c o u n tin g m ethods, and (2) l e s s com prehensive methods o f c o l l e c t i n g d a ta . When w orking w ith company d a t a r a t h e r th a n na t i o n a l o r r e g i o n a l d a t a , t h i s problem o f d a ta d e t e r i o r a t i o n te n d s to be even more pro n o u n ced . T his i s m ostly due t o o r g a n i z a t i o n a l changes t h a t a re c o n t i n u a l l y ta k i n g p l a c e . ^ i t would p ro b a b ly s u r p r i s e th e r e a d e r i f he were t o f i n d o u t how l i t t l e c o n s i s t e n t and a g g re g a te d c o s t d a t a e x i s t i n th e Firm u n d e r s tu d y . A few c u r r e n t a g g re g a te d r e p o r t s a re always a v a i l a b l e , b u t even th e s e te n d to be in c o m p le te , and can not be found f o r p a s t p e r io d s I j a p a n , Economic P la n n in g Agency, E conom etric Models f o r Medium-Term Economic P la n : 19o*t - 1968, A ugu st, 1965, p. lb - 2L. R. K le in , I n t r o d u c t i o n t o E conom etrics (Englewood C l i f f s , N. J7 ! P r e n t i c e - H a l l , I n c . , 1962), p. 267- 3 j . J o h n s to n , S t a t i s t i c a l Cost A n a ly sis (New York: McGraw-Hill Book C o ., I n c , , i 96 0 ) , p . 28. 34 t h a t a re more th a n a few y e a r s ago. B asic c o s t d a ta u su a l l y a r e a v a i l a b l e f o r h i s t o r i c a l p e r i o d s , b u t only i n th e most d i s a g g r e g a t e d form im a g in a b le . I t i s p o s s i b l e f o r an a n a l y s t t o c o n s t r u c t v a r io u s c o s t acco u n t tim e s e r i e s by a g g re g a tin g t h e s e b a s i c d a t a in a c o n s i s t e n t m anner. How e v e r , t h i s would be com parable t o u s in g p o p u la tio n cen sus q u e s t i o n n a i r e s t o b u i l d up a g g re g a te d p o p u la tio n c h a r a c t e r i s t i c s f o r l a r g e c i t i e s . I t would n o t only be tim e - consum ing, b u t would a l s o r e q u i r e an i n ti m a t e knowledge o f th e d a t a — a knowledge t h a t i s found only i n e x p e r t s on th e subj e c t s . In t h e c a se o f th e F irm ’s o v erh ead a c c o u n ts , f o r t u n a t e l y , th e a n a l y s t i s n ' t n e a r l y so bad o f f . An a n n u al overhead summary i s p u b lis h e d by th e Firm ( f o r i n t e r n a l use o n l y ) . These summaries b re a k down o v erh ead c o s t s i n t o as many as 90 numbered a c c o u n ts f o r each p o o l. Each o f th e s e summaries c o n s i s t s o f f o u r y e a rs o f h i s t o r i c a l d a ta p lu s th e f o r e c a s t f o r th e coming y e a r . T hus, th e r e p o r t p u b lis h e d in March o f 1969 c o n ta in s a c t u a l d a ta f o r th e y e a rs 1965 - 1968 and th e f o r e c a s t f o r th e y e a r 1969• By u s in g a s e r i e s o f such r e p o r t s , i t i s p o s s i b l e t o con s t r u c t a tim e s e r i e s o f a n n u al accoun t d a t a which can be used f o r e c o n o m e tric a n a l y s e s . A lthough i t was im p o s s ib le to o b t a i n e v ery a n n u a l summary r e p o r t f o r use i n t h i s man n e r , i t was p o s s i b l e t o f i n d s u f f i c i e n t r e p o r t s t o p r o v id e th e o v e rla p and co v erag e r e q u i r e d f o r c e r t i f y i n g d a t a c o n s is te n c y as d is c u s s e d below . I n th e c a se o f some o f th e a c t i v i t y v a r i a b l e s , e . g . , p r o f i t s and f i x e d a s s e t s , a c o n s i s t e n t s e r i e s o f d a t a were a lr e a d y a v a i l a b l e b e c a u se i n t e r n a l changes do n o t a f f e c t them . The b a s i c c o n s i d e r a t i o n t h e r e f o r e r e v o lv ed around th e a v a i l a b i l i t y o f th e o v e rh e ad d a t a , which w i l l be d e s c r i b e d f i r s t . The d i s c u s s i o n w i l l th e n t u r n t o t h e a v a i l a b i l i t y and c o n s i s t e n c y o f th e a c t i v i t y v a r i a b l e s . The l a s t s u b j e c t d is c u s s e d i n t h i s c h a p t e r i s th e d e s i r a b i l i t y and te c h n iq u e s u sed i n d e f l a t i n g th e d a ta . I . SELECTION OP SERIES DURATION Having a v a i l a b l e a " l i b r a r y ' ’ o f an n u al overhead r e p o r t s , i t was f i r s t n e c e s s a r y t o d e te rm in e how lo n g a tim e s e r i e s sh o u ld be d e v e lo p e d . F o r n a t i o n a l economic d a t a , s e r i e s as lo n g as 60 y e a r s a r e a v a i l a b l e . 1 * However, th e w ell-know n K le in G o ld b e rg e r model was o r i g i n a l l y based on o nly a 2 2 -y e a r s e r i e s (n o t i n c l u d i n g th e t h r e e war y e a r s which were e x c l u d e d ) . 5 The r u l e i n e c o n o m etric a n a l y se s seems to be t o develop as lo n g a s e r i e s as i s p o s s i b l e and p r a c t i c a b l e . I n th e Firm , v i r t u a l l y c o n t i n u a l r e o r g a n i z a t i o n s **Japan, Economic P la n n in g Agency, o£. c i t . , p. 18. 5l . R. K le in and A. S. G o ld b e rg e r, An E conom etric Model o f th e U n ite d S t a t e s : 1929 - 1952 (Amsterdam: N o rth -H o lla n d P u b l is h in g Company, 1 9 ^ ) , p. 131. 37 a re t a k i n g p l a c e . Each o f t h e s e r e o r g a n i z a t i o n s te n d s t o i n j e c t v a r i a t i o n s i n t o th e d a t a which make i t d i f f i c u l t t o develop lo n g , c o n s i s t e n t tim e s e r i e s . Many o f t h e s e r e o r g a n i z a t i o n s do n o t a l t e r th e o v erh ead a c c o u n ts , s in c e th e change may m erely be th e t r a n s f e r r i n g o f a group o f employees from one p o i n t t o a n o th e r w ith in th e same o v e r head p o o l. O th e r c h a n g e s, how ever, a re s i g n i f i c a n t from th e p o in t o f view o f t h e o v e rh e ad a n a l y s t . One such change c o n s i s t s o f t r a n s f e r r i n g em ployees (and t h e i r c o s t s ) from po o l to p o o l. An example o f t h i s was th e movement o f th e c o s ts a s s o c i a t e d w ith th e F ir m ’s s c i e n t i f i c com puter f a c i l i t y from th e e n g in e e r i n g p o o l t o th e a d m i n i s t r a t i v e p o o l. A nother common change i s th e movement o f p e r s o n n e l from i n d i r e c t c h a rg e s t o d i r e c t c h a r g e s . O r i g i n a l l y , t h e F irm ’ s r e l i a b i l i t y group c h arg ed a l l o f i t s l a b o r t o th e i n d i r e c t l a b o r o v e rh e a d a c c o u n t; c o s t s now a re ch arg ed d i r e c t l y to th e a p p r o p r i a t e p r o j e c t . In a n a ly z in g th e o v erh ead d a t a , i t was d e c id e d t h a t a l l d a ta sh o u ld be p r e s e n t e d a lo n g t h e l i n e s o f th e p r e s e n t (1969) a c c o u n tin g m ethod. T h is sim ple c o n c lu s io n was made by r e c o g n i z i n g th e p u rp o se o f th e model i t s e l f , nam ely, t o f o r e c a s t i n t o th e f u t u r e . I t would be u n r e a l i s t i c t o p r o v id e such a f o r e c a s t u n l e s s i t was b a se d on th e most r e c e n t method o f a c c o u n tin g , s in c e m anagem ent’ s frame o f r e f e r e n c e presum ably i s a l s o b ased on t h a t a c c o u n tin g m ethod. No m a t t e r which y e a r ’s a c c o u n tin g method i s s e l e c t e d , t h e r e would be f o u r y e a rs o f c o n s i s t e n t d a t a con t a i n e d i n t h e a p p r o p r i a t e overhead summary r e p o r t ( i . e . , th e f o u r y e a r s o f h i s t o r i c a l d a t a ) . Because t h e 1969 me th o d o f a c c o u n tin g was s e l e c t e d , th e h i s t o r i c a l d a t a cov e re d th e y e a r s 1965 - 1968. Of c o u r s e , f o u r - y e a r s ' d a t a a re n o t enough t o a cc o m p lish t h e g o a l o f an e c o n o m e tric model s i n c e t h e r e a re to o few d e g re e s o f freedom to p e rfo rm m u l t i p l e r e g r e s s i o n s . ^ A com parison betw een th e 1964 d a ta as r e p o r t e d i n th e 1968 and 1969 o v erh ead r e p o r t s , how ever, r e v e a l e d t h a t a few a c c o u n tin g changes had ta k e n p la c e betw een p u b l i c a t i o n s , w ith 13 a c c o u n ts out o f a t o t a l o f 280 b e in g a f f e c t e d . T hu s, th e only way t h a t th e tim e s e r i e s c o u ld be e x te n d e d back beyond 1965 was t o a d j u s t p r i o r d a ta so th e y were c o n s i s t e n t w ith th e 1965 - 1968 d a ta . S i m i l a r l y , a com parison betw een 1964 d a t a i n th e 1965 and 1968 o v e rh e ad r e p o r t s a l s o i n d i c a t e d some a c c o u n t in g changes had been made (26 a c c o u n ts were a f f e c t e d ) . These n e c e s s i t a t e d a d j u s t i n g th e 1961 - 1963 d a t a so th e y were c o n s i s t e n t w ith th e 1965 - 1968 d a t a and th e now- c o n s i s t e n t 1964 d a t a . A few more a d ju s tm e n ts (3 a c c o u n ts ) ^ C h a rle s T. C la rk and Lawrence L. S chkade, S t a t i s t i c a l Methods f o r B u sin e ss D e c isio n s ( C i n c i n n a t i : S o u th -W este rn P u b l i s h i n g C o ., 1969) , p . 646. 39 were needed to make th e 1959 - I960 d a t a c o n s i s t e n t w ith l a t e r d a t a . The q u e s tio n th e n a r i s e s : how many a d ju s tm e n ts can be t o l e r a t e d ? " T o le r a t i o n " h e re r e f e r s t o d a t a q u a l i t y , s i n c e each a d ju s tm e n t can i n j e c t u n c e r t a i n t y i n t o th e a d j u s t e d a c c o u n ts . T here i s a s tr o n g m o tiv a tio n t o i n c o r p o r a t e lo n g e r s e r i e s o f d a ta f o r th e f o llo w in g t h r e e re a s o n s : 1. With a s h o r t e r s e r i e s , th e s t a n d a r d e r r o r s o f th e r e g r e s s i o n c o e f f i c i e n t s te n d t o be l a r g e r , s in c e th e number o f o b s e r v a t i o n s a p p e a rs i n th e d e n o m in ato r o f th e s t a n d a r d e r r o r f o r m u la .7 T h is means t h a t r e g r e s s i o n c o e f f i c i e n t s w i l l te n d t o be l e s s s i g n i f i c a n t th a n w ith a lo n g e r s e r i e s . 2. With a s h o r t e r s e r i e s , t h e r e may be i n s u f f i c i e n t tim e f o r th e v a r io u s e f f e c t s to be no t i c e a b l e i n th e d a t a . T his means t h a t i t w i l l be more d i f f i c u l t t o o b t a i n r e g r e s s i o n e q u a tio n s t h a t a c c u r a t e l y r e f l e c t th e u n d e r l y i n g v a r i a b l e s i n f l u e n c i n g th e d a t a . 3. The use o f la g g e d endogenous v a r i a b l e s "u ses up" a f u l l y e a r o f d a ta f o r each y e a r la g g e d . 7M ordecai E z e k ie l and K arl A. Pox, Methods o f C o r r e l a t i o n and R e g re ss io n A n a ly s is (New York: John Wiley and Sons, I n c . , 19 57), p. 283. 40 S in c e a dynamic model was a n t i c i p a t e d (which im p lie s u s in g la g g e d v a r i a b l e s ) , a d d i t i o n a l d a t a were d e s i r a b l e . A f t e r c o m p le tin g much o f th e work u s in g e i g h t - y e a r s ' d a t a , i t was found t h a t o nly a m odest e f f o r t was needed to add two more y e a r s ' d a t a (o n ly 3 a c c o u n ts needed t o be a d j u s t e d ) . However, t o d e v elo p d a t a f o r y e a rs p r i o r t o t h i s ( i . e . , p r i o r t o 1959) a p p a r e n t l y i s n o t j u s t i f i e d . T his c o n c lu s io n stems from an a c c o u n t- b y - a c c o u n t com parison betw een 1959 d a t a i n th e 1962 and 1963 o v e rh e ad r e p o r t s . T his com parison showed t h a t 68 a c c o u n ts d i f f e r e d . Out o f t h i s 68, 42 a c c o u n ts d i f f e r e d by a s much as $1000 and 13 d i f f e r e d by as much as $ 1 0 ,0 0 0 . Comparing th e s e numbers w ith th e 26 a c c o u n ts t h a t need ed t o be a d j u s t e d f o r 1964 shows t h a t th e amount o f e f f o r t i s n ' t p r o h i b i t i v e . T h is i s e s p e c i a l l y t r u e s in c e many o f t h e p e r c e n ta g e c o r r e c t i o n s were a ls o s m a ll. However, a c l o s e r lo o k a t th e d a ta com parison showed t h a t th e r e q u i r e d c o r r e c t i o n f a c t o r s would be much more e r r a t i c th a n f o r th e l a t e r y e a r s . On th e o t h e r hand, th e c o r r e c t i o n f a c t o r s f o r th e l a t e r y e a r s were q u i t e con s i s t e n t , and t h i s c o n s is te n c y te n d s t o i n d i c a t e a m easure o f v a l i d i t y f o r th e c o r r e c t i o n p r o c e d u r e . As an example o f what th e 1959 - 1961 d a ta com p a r i s o n r e v e a l e d , a look can be ta k e n a t th e e n g in e e r in g i n d i r e c t l a b o r a cc o u n t (which i s n ’ t th e w o rst a c c o u n t) . ill The d i f f e r e n c e s betw een th e 1962 and 1963 a c c o u n tin g me th o d s showed up as d i s p a r i t i e s i n th e 1959 - 1961 e n t r i e s f o r t h i s a c c o u n t. The p e r c e n ta g e d i s p a r i t i e s were 18$, 3355., and 41J5, f o r an a v e ra g e o f 31% - But such an averag e would g r o s s ly o v e r e s tim a te th e t r u e c o r r e c t i o n f o r 1959 and g r o s s ly u n d e re s tim a te t h e t r u e c o r r e c t i o n f o r 1961. I t does n o t seem a d v is a b l e t o a d j u s t th e 1955 - 1958 d a ta w ith c o r r e c t i o n f a c t o r s t h a t can be so v a r i a b l e . On th e b a s i s o f t h e above r a t i o n a l e , i t was de c id e d t o a tte m p t t o use 1 0 - y e a r s ' d a t a i n th e s tu d y . I t i s f e l t t h a t t e n - y e a r s ' d a t a a re s u f f i c i e n t f o r th e problem u n der a n a l y s i s f o r t h r e e r e a s o n s . F i r s t , th e t e n y e a rs t h a t a re a v a i l a b l e a re t h e l a t e s t t e n y e a r s r a t h e r th a n some e a r l i e r p e r i o d . As s t a t e d ab ove, tim e s e r i e s n e a r l y always d e t e r i o r a t e as tim e i s e x te n d e d b ackw ard, so even i f th e o ld e r d a ta were a v a i l a b l e , i t would n o t be c e r t a i n t h a t th e y would be c o n s i s t e n t w ith p r e s e n t d a t a , e s p e c i a l l y th e a d ju s te d d a ta . Second, i t can be hoped t h a t th e s m a ll s e r i e s w i l l y i e l d a p p ro x im a te ly th e same r e s u l t s as a lo n g e r s e r i e s . K le in r e p o r t s t h a t Monte C a rlo s t u d i e s have d e m o n stra te d t h a t th e " r e l a t i v e p e rfo rm an c e o f d i f f e r e n t e s t i m a t i o n me th o d s in such sm a ll sam ples has been as would be p r e d i c t e d from l a r g e sample th e o ry ." ® Of c o u r s e , K le in d o e s n 't ^ K le in , oj). c i t . , p.. 2 6 7 . H2 i n d i c a t e how w e ll a s e r i e s o f t e n y e a r s would f a r e i n such an a n a l y s i s — he may be t h i n k i n g t h a t a 2 5 -y e a r s e r i e s i s s h o r t . The t h i r d r e a s o n f o r u s in g th e t e n - y e a r s e r i e s i s t h a t th e model u n d e r developm ent was meant t o be a s t a r t in g p o i n t i n term s o f b o th tim e and c o m p le x ity . I f r e a so n ab ly c r e d i b l e r e s u l t s can be o b ta in e d w ith a t e n - y e a r s e r i e s o f d a t a , t h i s may be j u s t i f i c a t i o n f o r l a t e r im provem ents t h a t e x te n d th e d a t a s e r i e s f u r t h e r back i n t o th e F irm ’s h i s t o r y . In p a s s i n g , n o te t h a t no r e f e r e n c e h as been made to th e p o s s i b i l i t y o f u s in g m onthly r a t h e r th a n a n n u al d a ta . A lthough d i f f i c u l t , i t would be p o s s i b l e t o con s t r u c t a s e r i e s o f a cc o u n t d a ta on a m onthly ( o r even w eekly) b a s i s . The re a s o n f o r u s in g an n u al d a ta i s n o t one o f economy o f e f f o r t , how ever, b u t b e ca u se m onthly d a ta would c o n ta in s i g n i f i c a n t in te rd e p e n d e n c e betw een s u c c e s s iv e o b s e r v a t i o n s .9 T h is would be p a r t i c u l a r l y t r u e o f such a c c o u n ts as s o c i a l s e c u r i t y , v a c a t i o n , and h o lid a y expenses which have pronounced s e a s o n a l p a t t e r n s . The f o llo w in g d i s c u s s i o n d e l i n e a t e s th e a d j u s t ment p ro c e d u re u n d e rta k e n to o b t a i n a r e a s o n a b ly c o n s i s t e n t t e n - y e a r s e r i e s o f d a t a . Bear i n mind th ro u g h o u t 9 j . T in b e rg e n , E co n o m etrics (New York: The B la k is to n C o ., 1 9 5 1 ), p . 208. 43 t h i s d i s c u s s i o n t h a t r e l a t i v e l y few a c c o u n ts a r e a c t u a l l y b e in g a d j u s t e d . In o t h e r w o rd s, t h e m a j o r i t y o f a c c o u n ts a re c o n s i s t e n t th ro u g h o u t th e t e n - y e a r p e r i o d as th e y ap p e a re d i n th e f i v e - y e a r o v erh ead r e p o r t s . I I . ADJUSTMENT OP OVERHEAD DATA T here a re two s o u rc e s o f i n c o n s i s t e n c i e s i n th e d a ta : th e s e a re l a b e l e d ’' e x p l i c i t " changes and " i m p l i c i t " ch an g es. The e x p l i c i t changes r e f e r t o o bvio u s a l t e r a t i o n s i n th e a c c o u n tin g methods w hich show up as d i s t i n c t v a r i a t i o n s betw een a cco u n t e n t r i e s i n d i f f e r e n t overhead sum m aries. These w i l l be d i s c u s s e d i n d e t a i l below . The i m p l i c i t changes r e f e r t o s u b t i l e changes i n th e a c c o u n tin g method which cannot be i d e n t i f i e d i n th e d a t a . An example would be two changes t h a t j u s t b a la n c e o u t , o r a l t e r a t i o n s t h a t a re to o sm a ll t o show up b e c a u se o f ro u n d in g o f d a ta i n th e o v erh ead r e p o r t s . I t i s e x p e c te d t h a t such sm a ll changes w i l l c o n tin u e t o o c c u r i n th e f u t u r e as th e y have In th e p a s t , b u t t h a t th e y a re so m inor t h a t no s i g n i f i c a n t changes i n f u t u r e d a ta need be a n t i c i p a t e d . E x p l i c i t changes i n th e d a t a were h a n d le d i n t h r e e s t e p s : 1. F i r s t , th e 1959 - I960 d a ta were a d ju s te d so th e y were c o n s i s t e n t w ith th e 1961 - 1962 d a ta shown In th e 1963 o v e rh e ad r e p o r t . 44 2. Second, t h e 1959 - 1963 d a t a were a d j u s t e d so th e y w ere c o n s i s t e n t w ith th e 1964 d a t a as r e p o r t e d i n th e 1968 o v e rh e ad r e p o r t . 3* T h i r d , th e 1959 - 1964 d a ta were a d j u s t e d to t h e 1965 - 1968 d a t a shown i n th e 1969 o v e r head r e p o r t . B r i e f l y , th e method t h a t was used was as f o llo w s : F i r s t , o v e rla p p in g o v e rh e ad r e p o r t s were used to i d e n t i f y a c c o u n ts t h a t showed e v id e n c e o f changed a c c o u n tin g me th o d s . T his e v id e n c e c o n s i s t e d o f d i f f e r e n t amounts ap p e a r in g in th e a c c o u n t e n t r y i n two d i f f e r e n t o v erhead r e p o r t s as p r e v i o u s l y d i s c u s s e d . N ext, a c o r r e c t i o n f a c t o r was computed and a p p l i e d to d a ta f o r which t h e r e was no o v e r l a p . T his c o r r e c t i o n f a c t o r was e q u a l to th e p e r c e n ta g e d i s p a r i t y t h a t was e v id e n t i n th e o v e rla p p in g d a t a . The r a t i o n a l e h e re i s t h a t i f th e o v e rla p p e d d a t a a re d i f f e r e n t by (sa y ) 5% when th e a c c o u n tin g method was changed, th e n o n -o v e rla p p e d d a t a w i l l a l s o be d i f f e r e n t by ab out 5/6. While t h i s p r o b a b ly i s n o t p r e c i s e l y t r u e , i t i s hoped t h a t th e r e s u l t a n t c o r r e c t i o n s a r e f a i r l y sm a ll i n a b s o l u te amount so t h a t any e r r o r s i n j e c t e d i n t o th e d a ta a r e lik e w is e s m a ll. ADJUSTING THE 1959 - I960 DATA TO THE 1963 ACCOUNTING METHOF~ The f i r s t s t e p i n th e a n a l y s i s was t o c o r r e c t any 45 d i s c r e p a n c i e s i n th e 1959 - I960 d a t a . What was d e s i r e d was to make c e r t a i n t h a t a l l 1959 - I960 d a t a w ere d e r iv e d from th e same a c c o u n tin g method as th e 1961 - 1963 d a t a . An a c c o u n t- b y - a c c o u n t com parison betw een 1961 - 1962 d a ta as p u b l is h e d i n th e 1963 and 1965 o v e rh e ad r e p o r t s showed t h a t t h e r e were only t h r e e a c c o u n ts t h a t d i f f e r e d . These were th e e n g in e e r in g i n d i r e c t s a l a r y and wage a c c o u n t, th e e n g in e e r i n g company a i r c r a f t a c c o u n t, and th e f a c t o r y p e r i s h a b l e equipm ent a c c o u n t. F or each o f th e s e t h r e e a c c o u n ts , th e p e r c e n t d i s p a r i t y was found betw een d a t a f o r 1961 and 1962 as r e p o r t e d i n th e 1963 and 1965 o v erh ead r e p o r t s . The a v erag e p e r c e n t d i s p a r i t y was computed and a p p li e d t o th e 1959 and I960 d a t a f o r th e t h r e e a c c o u n ts . The r e s u l t s o f t h i s c o r r e c t i o n p ro c e s s a re shown i n T a b le 2. I t can be seen t h a t th e p e r c e n ta g e c o r r e c t i o n s a re l a r g e , b u t th e a b s o l u te c o r r e c t i o n s a re l a r g e only i n th e c a se o f e n g in e e r in g i n d i r e c t s a l a r i e s and w ages. An e s t i m a t e o f th e m agnitude o f any e r r o r t h a t c o u ld be i n j e c t e d i n t o th e d a ta f o r t h i s acco u n t i s g iv en i n th e s e c t i o n d e v o te d t o d i r e c t l a b o r d o l l a r s . ADJUSTING THE 1959 - 1963 OVERHEAD DATA TO THE 1968 ACCOUNTING METHOD A m ajo r r e o r g a n i z a t i o n o c c u r r e d i n 1964, e s p e c i a l l y i n th e e n g in e e r i n g b r a n c h . T h is r e o r g a n i z a t i o n was f i r s t r e f l e c t e d i n th e 1965 o v erh ead r e p o r t . T h is r e p o r t TABLE 2 CORRECTING 1959 - I960 DATA TO 1963 ACCOUNTING METHOD Based on Comparison Between 1961 and 1962 Data in 1963 and 1965 Overhead Reports PERCENTAGE DISPARITY BETWEEN ACCOUNTING METHODS ADJUSTED ($1000 VALUES ’ s) ACCOUNT 1961 1962 Average 1959 I960 Engineering: Salaries and Wages -5 0 .7 -5 0 .7 - 5 0 .7 $154 $151 Company Owned Aircraft - 4 2 .7 - 67.0 - 5 4 .8 4 4 Factory: Perishable Equipment - 3 6 .8 - 3 2 .2 - 3 4 .5 11 14 c o n ta in e d d a t a f o r 1961 - 1964 t h a t were c o n s i s t e n t w ith I t h a t 1965 method o f a c c o u n tin g . ! A nother r e o r g a n i z a t i o n o c c u rre d i n 1967 > and t h i s | i was f i r s t r e p o r t e d i n th e 1968 overhead r e p o r t . T h is r e - t p o r t a ls o c o n ta in e d f o u r - y e a r s ' d a t a (1964 - 1967) . | T hus, 1964 d a t a were a v a i l a b l e i n two fo rm s: t h e ; f i r s t conform ing t o th e 1965 a c c o u n tin g method and th e s e c - i j ond conform ing t o th e 1968 m ethod. By com paring t h e s e d a ta ! on an a c c o u n t-b y - a c c o u n t b a s i s , a t o t a l o f 26 a c c o u n ts werej found t o d i f f e r . These a c c o u n ts and th e m agnitude o f th e ! d i f f e r e n c e s a r e c o n ta in e d i n T ab le 3.. While 26 a c c o u n ts would a p p ea r t o be a l a r g e num- ; b e r — p e rh a p s to o l a r g e — a c l o s e r i n s p e c t i o n r e v e a l s s e v e r a l ; I p e r t i n e n t f a c t s : ; ! 1. G e n e r a ll y , e i t h e r th e a b s o l u te o r p e r c e n ta g e j d i s p a r i t y i s s m a ll. For exam ple, 24 o f th e 26 a c c o u n ts have a b s o l u te d i s p a r i t i e s o f l e s s th a n $22,000 o r p e rc e n ta g e d i s p a r i t i e s o f l e s s th a n 22$, o r b o th . E ig h te e n o f th e a c c o u n ts have a b s o l u te d i s p a r i t i e s o f l e s s th a n $10,000 o r p e r c e n ta g e d i s p a r i t i e s o f l e s s th a n 10$, o r b o th . I t i s u n l i k e l y t h a t s i g n i f i c a n t e r r o r s co u ld be i n j e c t e d i n t o th e 1959 - 1963 d a t a when th e a b s o l u te and p e rc e n ta g e c o r r e c t i o n j f a c t o r s a re as s m a ll as t h i s . TABLE 3 CORRECTING 1959 - 1963 DATA TO 1968 ACCOUNTING METHOD D o lla r Amounts i n $ 1 0 0 0 's ACCOUNT DISPARITY IN 1964 DATA CORRECTED AMOUNT AMOUNT PERCENT 1959 I960 1961 1962 1963 Engineering: Indirect Salaries and V/ages $ 17 5-2% $ 162 $ 158 $ 264 $ 306 $ 331 Holiday Pay-Hourly 5 14.0 29 30 36 41 39 Holiday Pay-Salary 14 12.4 86 92 108 130 125 Vacation Pay-Hourly 1 1.7 37 38 44 56 54 Management Incentive Plan -3 - 4 .0 28 0 40 68 74 Services Credited-Other -26 - 2 1 .3 -3 -5 -4 -6 -37 Redistribution -193 -37*4 259 249 284 384 331 Factory: Indirect Salaries and Wages -5 - 0 .2 2265 2114 2401 2901 2880 Shop Supplies -18 - 1 3 .1 98 76 81 98 103 Holiday Pay-Hourly 30 12.5 217 201 222 265 268 Holiday Pay-Salary 8 12.8 54 53 58 70 65 Redistribution -50 - 1 3 .6 240 242 216 170 251 TABLE 3— Continued ACCOUNT DISPARITY IN 1964 DATA CORRECTED AMOUNT AMOUNT PERCENT 1959 I960 1961 1962 1963 A d m i n i s t r a t i v e : I n d i r e c t S a l a r i e s and Wages $ 43 2.6% $1301 $1289 $1407 $1579 $1725 H oliday Pay-H ourly 2 12.9 18 17 19 22 22 H oliday P a y -S a la ry 6 14.2 37 37 41 47 46 V a c a tio n P a y -S a la ry 1 1.2 52 51 59 69 81 Management I n c e n t iv e P la n 3 7.4 28 1 30 45 46 B l u e p r in t and P h o to g ra p h ic 4 4.6 74 70 84 115 99 E n te rta in m e n t 1 4.0 24 18 18 23 20 T ra v e l 10 12.9 86 76 68 83 95 R e lo c a tio n Allowances 2 34.6 9 8 11 11 20 R e d i s t r i b u t i o n 211 18 .5 -697 -693 -795 -977 -1016 S p a r e s : Pack ing and C r a tin g -21 - 3 4 .2 54 58 73 81 64 H oliday Pay-H ourly 1 13.4 7 8 11 14 12 H oliday P a y -S a la ry 1 14.0 3 4 5 6 6 R e d i s t r i b u t i o n 13 5.8 154 154 250 396 423 50 | i 2. The o n ly two a c c o u n ts w hich had b o th l a r g e a b s o l u t e and l a r g e p e r c e n ta g e c o r r e c t i o n s were t h e " r e d i s t r i b u t i o n " a c c o u n ts f o r th e e n g i n e e r i n g and a d m i n i s t r a t i v e p o o ls . These r e - j d i s t r i b u t i o n a c c o u n ts r e p r e s e n t t h e mechanism ! whereby c o s t s a r e s h u t t l e d betw een p o o ls w i t h - j o u t u s in g th e numbered a c c o u n ts t o keep t r a c k j o f t h e amounts s h i f t e d . S in c e th e s e a r e m ere-j ly such j u g g l i n g a c c o u n ts , a check o f th e a r i t h m e t i c sum o f th e f o u r r e d i s t r i b u t i o n a c - ! i c o u n ts sh o u ld g iv e an i n d i c a t i o n o f w h e th er e r r o r s have c r e p t i n t o th e a d ju s tm e n t p r o c e s s . ; The r e s u l t s o f such a com parison betw een th e a r i t h m e t i c sum o b ta in e d f o r 1964 u s in g b o th i t h e 1965 and 1968 a c c o u n tin g m ethods a r e a s ! f o llo w s (a s shown i n T able 4 ): t h e sums a re -$39»000 v s . - $ 4 7 ,0 0 0 , f o r a d i f f e r e n c e o f : 1 o n ly $ 8 ,0 0 0 .10 T h is means t h a t $8,000 more | was c h arg ed t o th e c o r p o r a te o f f i c e u n d e r th e new method th a n u n d e r th e p r i o r m ethod. We sh o u ld look f o r s i m i l a r sm a ll d i s p a r i t i e s b e tween th e a d j u s t e d and u n a d ju s te d a r i t h m e t i c 10The sums a re n o t e q u a l t o z e ro h e re b e ca u se an i a d d i t i o n a l group i s b e in g ch arg ed f o r o v erh ead e x p e n s e s . j ;This group c o n ta in s em ployees w orking f o r th e c o n g lo m e ra te 1 o r g a n i z a t i o n b u t which a r e u s in g overhead s e r v i c e s o f t h e | 'Firm. TABLE 4 ARITHMETIC SUM OP REDISTRIBUTION ACCOUNTS BEFORE AND AFTER CORRECTING DATA D o l l a r Amounts i n $1000‘ , s ARITHMETIC REDISTRIBUTION SUM OF ACCOUNTS DIFFERENCE BETWEEN ARITHMETIC SUMS YEAR BEFORE CORRECTION AFTER CORRECTION AMOUNT PERCENT 1959 $-18 $-43 $26 3.0£ I960 -28 -49 21 2.5 1961 -35 -34 -1 0 .1 1962 -26 -28 2 0 .2 1963 -40 -11 29 2.4 1964 -39 -47 8 3-5 VJl means o f t h e r e d i s t r i b u t i o n a c c o u n ts f o r 1959 - 1963* Prom T able 4 i t can be seen t h a t i n 1961 and 1962 t h e r e i s v i r t u a l l y no d i f f e r e n c e betw een th e two r e d i s t r i b u t i o n sums. In 1963, t h e d i f f e r e n c e i s $ 2 9 ,0 0 0 , which i s somewhat l a r g e r th a n i n 1959 and j i 96 0. T h is 1963 d i f f e r e n c e r e p r e s e n t s o n ly j i 1 2 .4 # o f t h e s m a ll e s t r e d i s t r i b u t i o n a c c o u n t. | T hus, i t i s u n l i k e l y t h a t th e e r r o r cau sed by j i c o r r e c t i n g th e d a t a c o u ld exceed 2 .4 # , and i t j i s l i k e l y t h a t th e e r r o r i s much l e s s , s in c e j t h e l a r g e r r e d i s t r i b u t i o n a c c o u n ts a ls o u n - j d o u b te d ly s h a r e i n any e r r o r s . i The r e s u l t a n t a d j u s t e d v a lu e s f o r th e 26 a c c o u n ts | a re shown in t h e r i g h t - h a n d p o r t i o n o f T able 3. j ADJUSTING THE 1959 - 1964 OVERHEAD DATA TO THE 1969 ACCOUNTING METHOD The l a s t c o r r e c t i o n t h a t was needed c o n s i s t e d o f j a d j u s t i n g th e 1959 - 1967 d a t a t o th e 1969 a c c o u n tin g m ethod. Of c o u r s e , a p a r t o f t h i s had a lr e a d y been done by th e p e r s o n n e l who p u b l i s h th e o v erh ead summary r e p o r t s , nam ely, th e 1965 - 1967 d a t a . T hus, a l l t h a t was needed was t o a d j u s t t h e 1959 - 1964 d a ta t o th e 1969 a c c o u n tin g method. The c o r r e c t i o n f a c t o r s were computed a lo n g th e l i n e s d is c u s s e d w ith t h e p r i o r a d ju s tm e n ts . A s i g n i f i c a n t d i f f e r e n c e i s t h a t t h r e e y e a rs o f o v e r la p p in g d a t a were a v a i l a b l e r a t h e r th a n j u s t one o r tw o. A dvantage was ta k e n o f t h i s f a c t by a g a i n 'a v e r a g i n g th e p e r c e n t d i s p a r i t i e s f o r t h e t h r e e y e a r s o f o v e rla p i n e s t i m a t i n g th e r e q u i r e d c o r - I r e c t i o n f a c t o r s t o ap ply t o th e 1959 - 1964 d a t a . j C o r r e c t io n f a c t o r s were computed f o r a t o t a l o f ; 13 d i s p a r a t e a c c o u n ts : i n d i r e c t s a l a r i e s and wages f o r a llj i f o u r p o o l s , h o lid a y pay f o r s a l a r i e d and h o u rly p e rs o n n e l , i n a l l f o u r p o o ls (b ec au se an a d d i t i o n a l h o lid a y had been j g iv e n t o e m p lo y e e s), and an e n g in e e r in g a c c o u n t l a b e l l e d " o t h e r i n d i r e c t s a l a r i e s . " T able 5 shows t h e p e rc e n ta g e d i s p a r i t i e s and th e j i r e v i s e d 1959 - 1964 d a t a . S e v e ra l c o n c lu s io n s can be drawn i from t h i s t a b l e : i 1. The c o r r e c t i o n t o th e h o l id a y pay a c c o u n ts wasj i e x tre m e ly c o n s i s t e n t (aro u n d 1 1 $ ), so i t i s j i i u n l i k e l y t h a t a g r e a t d e a l o f e r r o r c o u ld e n - j i t e r h e r e . 2. The s i z e o f th e p e rc e n ta g e c o r r e c t i o n s f o r th e l a t t e r t h r e e i n d i r e c t s a l a r y and wage a c c o u n ts and th e e n g in e e r in g " o t h e r i n d i r e c t s a l a r i e s " a cc o u n t a re a l l sm a ll (0 .4 $ and 1 .2 $ , r e s p e c t i v e l y ) . In a b s o l u te t e r m s , t h e s e amount t o $11,000 o r l e s s — and t y p i c a l l y much l e s s . I t i i s n ’t l i k e l y t h a t a s i g n i f i c a n t e r r o r co u ld e n t e r th e a n a l y s i s i f c o r r e c t i o n f a c t o r s as TABLE 5 CORRECTING 1959 - 1964 DATA TO 1969 ACCOUNTING METHOD PERCENT DISPARITY BETWEEN ACCOUNTING METHODS REVISED DATA ($ 1 00 0fs) ACCOUNT 1965 1966 1967 average 1959 I960 1961 1962 1963 1964 Engineering: Indirect Salaries and Wages Other Indirect Salaries Holiday Pay-Hourly Holiday Pay-Salary -9.75S 1.2 11.1 11.1 -11.358 1.1 11.0 11.1 -12.355 0.9 11.2 11.1 -11.155 1.1 11.1 11.1 $144 75 32 96 $141 83 33 101 $215 103 40 120 $272 118 45 144 $294 108 43 139 $301 92 44 140 Factory: Indirect Salaries and Wages - 0 .4 - 0 .4 - 0 .4 - 0 .4 2255 2105 2391 2889 2868 2598 Holiday Pay-Hourly 11.1 11.1 11.1 11.1 241 224 247 294 298 297 Holiday Pay-Salary 11.0 11.2 11.1 11.1 60 59 64 78 73 80 Administration: Indirect Salaries and Wages - 0 .4 - 0 .4 - 0 .4 - 0 .4 1301 1299 1467 1579 1725 1681 Holiday Pay-Hourly 10.7 11.0 11.1 10.9 20 18 21 24 24 22 Holiday Pay-Salary 11.1 11.1 11.1 11.1 41 41 45 52 51 58 Spares: Indirect Salaries and Wages - 0 .4 - 0 .4 - 0 .4 - 0 .4 2 39 275 341 463 444 297 Holiday Pay-Hourly 10.5 9 .1 11.1 10.2 8 9 12 16 14 7 Holiday Pay-Salary 12.0 10.9 11.9 11.6 4 4 5 7 6 6 s m a ll as t h e s e a r e u t i l i z e d . 3. The e n g in e e r in g i n d i r e c t s a l a r i e s and wages a cco u n t has a f a i r l y l a r g e a v e ra g e c o r r e c t i o n ( 1 1 . ISO, and t h i s amounts t o ab o u t $38,000 i n 1964. T h is c o r r e c t i o n was a r e s u l t o f a s i g n i f i c a n t change i n t h e e n g in e e r in g b r a n c h , i . e . , one i n which d e p artm e n t m anagers began c h a rg in g t h e i r s a l a r i e s d i r e c t l y t o p r o j e c t s r a t h e r th a n t o th e i n d i r e c t wage a c c o u n t as had been c u sto m ary . A lso , th e c o r r e c t i o n s f o r 1985 - 1967 a r e n o t as c o n s i s t e n t as w ith o t h e r a c c o u n ts , v a r y in g betw een 9*7% and 1 2 .3 $ . While t h i s amount o f v a r i a t i o n i s n ' t to o l a r g e , i . e . , around $ 9 ,0 0 0 , i t would be w o rth w h ile t o keep t h i s a cc o u n t i n mind when e v a l u a t i n g th e r e g r e s s i o n e q u a tio n s i n th e n e x t c h a p t e r . Of a l l th e a c c o u n ts t h a t have been c o r r e c t e d , t h i s one would a p p e a r t o be th e one most l i k e l y t o have t h e l a r g e s t e r r o r s as a r e s u l t o f th e c o r r e c t i o n p r o c e s s . I I I . ACTIVITY VARIABLES B e sid e s th e overh ead acco u n t d a t a , i t was n e c e s s a ry t o p ro v id e c o n s i s t e n t s e r i e s o f Firm a c t i v i t y v a r i a b l e s . These a re v a r i a b l e s a s s o c i a t e d w ith th e o p e r a t i o n o f th e F irm , such as b ran c h p e r s o n n e l , b ra n c h d i r e c t l a b o r h o u rs and d o l l a r s , f ix e d a s s e t s , and p r o f i t s . Some o f t h e s e d a t a a re p u b lis h e d i n th e a n n u a l f i v e - y e a r o v erh ead r e p o r t s d e s c r ib e d above. O th e rs had t o be d e r iv e d from o t h e r s o u r c e s . DIRECT LABOR DOLLARS AND HOURS E n g in e e rin g and f a c t o r y d i r e c t l a b o r d o l l a r s and | l h o u rs f i g u r e s a re p u b lis h e d a n n u a lly i n t h e f i v e - y e a r o v e r-| j head r e p o r t s . Except f o r th e t o t a l s , t h e s e s e r i e s a r e n o t ; i c o n s i s t e n t becau se some p e r s o n n e l c l a s s i f i c a t i o n s have moved from i n d i r e c t t o d i r e c t . The mechanism used t o a d j u s t t h e s e s e r i e s was j | i d e n t i c a l t o t h a t u sed in a d j u s t i n g i n c o n s i s t e n t overhead a c c o u n ts . T h is was a t h r e e - s t e p c o r r e c t i o n p r o c e d u r e . The! S f i r s t s t e p was t o c o r r e c t th e 1959 - I960 d a t a t o th e 1965 ; j a c c o u n tin g m ethod. T h is o n ly was r e q u i r e d f o r e n g in e e r in g j I d i r e c t l a b o r d o l l a r s and h o u r s . The p e r c e n ta g e c o r r e c t i o n j i f a c t o r s were 8.2# and 6.7%, r e s p e c t i v e l y , as shown i n T able! j 6. S in ce th e m agnitude o f t h e u n a d ju s te d numbers i s q u i t e j l a r g e , th e s e c o r r e c t i o n f a c t o r s r e p r e s e n t f a i r l y l a r g e ab s o l u t e c o r r e c t i o n s . I t may be r e c a l l e d t h a t l a r g e c o r r e c t i o n s were a l s o computed f o r e n g in e e r i n g i n d i r e c t l a b o r d o l l a r s (which a re a p a r t o f o v e rh e a d ). What has happened , o f c o u r s e , i s a s h i f t i n g o f l a b o r c o s t s from i n d i r e c t t o d i r e c t . The second s te p was t o c o r r e c t t h e 1959 - 1963 TABLE 6 CORRECTION FACTORS FOR LABOR DATA - ENGINEERING FACTORY Direct Direct Labor Labor Dollars Hours Direct Direct Labor Labor Dollars Hours Disparity in Year’s Data (1963 vs. 1965 Methods) 1961 1962 Average 8.45S 6.75? 7 .8 6 .8 8.2 6 .7 0 0 0 0 0 0 Disparity in Year’s Data (1965 vs. 1968 Methods) 1964 -2.55S -0.456 - 2 .5 ? -0.45S Disparity in Year’s Data C1968 vs. 1969 Methods) 1965 1966 1967 Average 0.55S — 0.456 0 .4 - 0 .5 0 .4 - 0 .4 0 .4 - 0 . 4 0.156 -0.455 0 .2 - 0 .5 0 .1 - 0 .4 0 .1 - 0 .4 58 d a t a t o t h e 1968 a c c o u n tin g m ethod. T h is was done by com p u t in g th e d i s p a r i t y betw een th e 196*1 d a ta as r e p o r t e d w ith th e 1968 method o f a c c o u n tin g and th e 1965 a c c o u n tin g m ethod. The d i s p a r i t y f o r b o th d o l l a r s and h o u rs f i g u r e s was a b o u t 2 1/255 i n e n g in e e r in g and 1/255 In th e f a c t o r y . The t h i r d s t e p was t o c o r r e c t th e 1959 - 1964 d a t a t o th e 1969 a c c o u n tin g m ethod. The m ag n itu d es o f th e c o r r e c t i o n f a c t o r s (b ased on t h e o v e r la p p in g d a t a f o r 1965 - 19.67) were a l l l e s s th a n 1 /2 $ . The c a l c u l a t i o n s d e s c r ib e d h e re a r e c o n ta in e d In T ab le 6. The r e s u l t a n t d a ta s e r i e s a r e c o n ta in e d i n T ab le 7. The most s u s p e c t a c c o u n ts th ro u g h o u t th e e n t i r e a d ju s tm e n t p r o c e s s a r e th e e n g in e e r in g l a b o r a c c o u n ts — b o th d i r e c t and i n d i r e c t . S u s p ic io n i s a ro u se d b e ca u se t h e s e a r e l a r g e a c c o u n ts and have r e l a t i v e l y l a r g e c o r r e c t i o n f a c t o r s a p p li e d to them . I t i s p o s s i b l e t o p ro v id e a check f o r t h e v a l i d i t y ! o f th e a d j u s t e d d a t a f o r t h e s e a c c o u n ts by summing th e d i r e c t and i n d i r e c t l a b o r c h a rg e s f o r any one y e a r . T h is i s done i n T ab le 8. For 1959 and i 96 0, I t can be se en t h a t ! t h e t o t a l a f t e r a d j u s t i n g d i f f e r s from th e t o t a l b e fo r e a d j u s t i n g by 1.155 o r l e s s . S i m i l a r l y , th e d i s p a r i t y i s 2.4/5 f o r 1961 - 1964. I t t h e r e f o r e would a p p e a r t h a t s i g - 1 n i f l c a n t e r r o r s have n o t been in tr o d u c e d i n t o th e d a t a as 1 a r e s u l t o f th e a d ju s tm e n t p ro c e d u r e . TABLE 7 DIRECT LABOR DATA: DOLLARS, HOURS, AND WAGE RATES YEAR DIRECT LABOR DOLLARS($1000) ENGINEERING FACTORY TOTAL DIRECT LABOR ENGINEERING HOURS(1 0 0 0 ’s) FACTORY TOTAL DIRECT W AGE ENGINEERING RATE ( $/HOUR) FACTORY TOTAL 1959 $2575 $4744 $ 731S 623 1733 2356 $4.13 $2.74 $3.11 I 960 2805 4228 703: 652 1455 2107 4.30 2.9 1 3.34 1961 3294 4897 8193 848 1569 2417 3.88 3.12 3.39 1962 4045 6114 10159 912 2029 2941 4.44 3.01 3.45 1963 3504 6014 95l€ 718 1922 2640 4.88 3-13 3.61 1964 3342 5867 920S 644 1808 2452 5.19 3.24 3 .7 6 1965 3978 5724 9702 745 1712 2457 5.34 3.34 3.95 1966 5788 6326 1211* 1018 1787 2805 5.69 3.54 4.3 2 1967 5073 7477 12550 856 . 1997 2853 5 .9 3 3.74 4.40 1968 6996 6103 13099 1126 1497 2623 6.2 1 4.08 5.00 VJl VO TABLE 8 COMPARISON OP TOTAL ENGINEERING LABOR DOLLARS BEFORE AND AFTER ADJUSTING Dollar Amounts in Thousands YEAR DIRECT PLUS INDIRECT LABOR DOLLARS BEFORE ADJUSTING AFTER ADJUSTING DIFFERENCE PERCENT DIFFERENCE 1959 $2746 $2719 $-27 -1.05S I960 2957 2946 -11 - 0 .4 1961 3615 3529 -86 - 2 .4 1962 4421 4316 -105 - 2 .4 1963 3893 3798 -95 - 2 .4 1964 3734 3643 -91 - 2 .4 WAGE RATE In a large firm, there is a diversity of wage rates, even among personnel accomplishing the same task. An average wage rate must therefore be determined which is representative of the group as a whole. In the Firm, an average wage rate for the engi neering and factory branches is computed by dividing the total direct labor expenditure by the total number of direct hours. Thus, these are average direct wage rates and not wage rates for the entire branch since indirect labor is ignored. It Is not possible to compute a similar average for indirect personnel because indirect manhour data are . not compiled. While impossible to verify statistically, there is a strong a priori case for assuming that indirect wage rates closely parallel the trend in direct wage rates. For a firm to do otherwise would result in widespread dis content among one of the two classes of workers (whichever was being "left behind"). In the regressions which follow,j it will be assumed that indirect labor rates are related to direct labor rates through this type of informal mecha- j 1 nism. I t i s i n t e r e s t i n g t o n o te t h a t i n 1961, th e a v e r age e n g in e e r i n g wage d e c r e a s e d . T h is seem in g ly u n l i k e l y ! o c c u rr e n c e to o k p la c e d u rin g a p e rio d o f Firm e x p a n sio n which fo llo w e d a number o f c o n t r a c t i o n y e a r s . D u rin g | 62 ! c o n t r a c t i o n s , th e a v erag e s e n i o r i t y o f em ployees r i s e s , and w ith i t r i s e s t h e a v erag e wage r a t e . When e x p a n sio n o c c u r s , most new em ployees a re r e l a t i v e l y in e x p e r ie n c e d , and t h e s e have r e l a t i v e l y low wage r a t e s . On b a l a n c e , th e ad d i t i o n o f t h e s e j u n i o r em ployees was a b le t o p u l l down th e a v e ra g e wage r a t e , even though th e g e n e r a l t r e n d i s upward. The a v erag e d i r e c t wage r a t e i s computed f o r th e whole Firm by d i v i d i n g th e sum o f e n g in e e r in g and f a c t o r y d i r e c t l a b o r d o l l a r s by th e sum o f e n g in e e r in g and f a c t o r y d i r e c t h o u r s . The t h r e e wage r a t e s e r i e s which were d e riv e d by d i v i d i n g l a b o r d o l l a r s by h ours a r e g iv e n i n T able 7. PERSONNEL P e rs o n n e l r e p r e s e n t a s to c k v a r i a b l e , w h ile most o f th e o t h e r o p e r a t in g v a r i a b l e s a re flow v a r i a b l e s . I t was t h e r e f o r e n e c e s s a r y t o ta k e t h e p u b lis h e d y e a r - e n d p e r so n n e l f i g u r e s and a v erag e them . T h is a v e r a g in g p r o c e s s was done by ad d in g th e y e a r - e n d f i g u r e t o th e y e a r - b e g i n n in g f i g u r e ( i . e . , l a s t y e a r 's y e a r - e n d f i g u r e ) and d i v id in g by two. ! i B efore a v e r a g in g , how ever, i t was f i r s t n e c e s s a r y j I t o a d j u s t f o r a c c o u n tin g c h a n g e s. While t o t a l p e rs o n n e l I i were unchanged, t h e r e v i s e d a c c o u n tin g m ethods s h i f t e d : i p e r s o n n e l from p o o l t o po ol and betw een i n d i r e c t and d i - j 1 I r e c t . Because o f th e im pact on t h e o v erhead m odel, i t was n e c e s s a r y t o a d j u s t f o r t h e s e s h i f t s and keep s e p a r a t e ta b - : u l a t i o n s f o r d i r e c t and i n d i r e c t p e r s o n n e l . The a d ju s tm e n t te c h n iq u e b a s i c a l l y i s as b e f o r e , e x c e p t f o r th e c o r r e c t i o n s t o e n g in e e r i n g i n d i r e c t p e r s o n n e l f o r 1959 - I960* S in c e t h e r e were no o t h e r p e rs o n - i n e l changes i n t h e s e ^ y e a r s , i t was a p p a r e n t t h a t th e i n c re a s e d number o f p e r s o n n e l c l a s s i f i e d as d i r e c t must have j o r i g i n a l l y been c l a s s i f i e d as i n d i r e c t . T hus, a p e rc e n ta g e c o r r e c t i o n was computed f o r d i r e c t p e r s o n n e l , and th e n th e a b s o l u te amount o f change was a p p li e d t o t h e i n d i r e c t p e r s o n n e l d a ta . The p e rs o n n e l c o r r e c t i o n f a c t o r s a re shown in T ab le 9. I t can be se e n t h a t two o f t h e c o r r e c t i o n f a c t o r s a r e f a i r l y la r g e as b a se d on t h e 1965 ” 1967 d a ta ( - 3 0 .3 ? and + 18.1? f o r t h e i n d i r e c t e n g in e e r i n g and d i r e c t a d m in i- ! s t r a t i v e p e rs o n n e l v a l u e s ) . The a b s o l u t e m agnitu des o f | t h e s e changes a re r e l a t i v e l y s m a l l , how ever. A lso, th e t o t a l e n g in e e r in g p lu s a d m i n i s t r a t i v e p e r s o n n e l f i g u r e s be-1 I f o r e and a f t e r t h e c o r r e c t i o n d i f f e r by l e s s th a n 0 . 3 ? s so i th e e r r o r s cannot be s i g n i f i c a n t even thou gh th e p e rc e n ta g e i 1 c o r r e c t i o n s a re l a r g e . T h is l a t t e r check i s v a l i d s in c e i n t e r p o o l s h i f t s o c c u r r e d i n a d d i t i o n t o i n t r a p o o l s h i f t s . A f i n a l check was made on t h i s c o r r e c t i o n p r o c e s s . T h is was t o o b t a i n t o t a l y e a r - e n d p e rs o n n e l f i g u r e s and compare them w ith th e y e a r - e n d f i g u r e s p r i o r t o a d j u s t i n g . I t was found t h a t t h e r e was l e s s t h a n 0 .1 ? d i s p a r i t y i n TABLE 9 CORRECTIONS TO PERSONNEL DATA YEAR-END DATA ENGINEERING ADMINISTRATIVE DIRECT INDIRECT DIRECT INDIRECT PERSONNEL PERSONNEL PERSONNEL PERSONNEL Disparity in Year’s Data (1963 vs. 1965 Methods) 1961 3.1* * 0 0 1962 3 .1 * 0 0 Average 3.1 * 0 0 Disparity in Year’s Data (1968 vs. 1969 Methods) 1965 - 2 .4 # -2 8 .0 # 16.4# 2.4# 1966 - 1 .8 - 3 1 .1 17.6 2.6 1967 - 2 .4 - 31.8 2 0 .3 1.9 Average - 2 .2 - 3 0 .3 18 .1 2 .3 * E n g in e e rin g i n d i r e c t p e rs o n n e l f o r 1959 - I960 were c o r r e c t e d by s u b t r a c t i n g th e a b s o l u te amount o f th e c o r r e c t i o n t o d i r e c t p e r s o n n e l. 65 1962 - 1964, l e s s th a n 0.2% d i s p a r i t y i n 1961, l e s s th a n 0.4# d i s p a r i t y i n I9 6 0 , and about 0 . 7 % d i s p a r i t y i n 1959* Of c o u r s e , i f any o f th e a b s o l u t e e r r o r s were c o n c e n tr a te d ; w i t h in a s i n g l e p o o l , th e p e rc e n ta g e e r r o r s would be l a r g e r . The a v e ra g e a n n u a l f i g u r e s which were d e r iv e d from th e y e a r- e n d f i g u r e s a r e shown in T able 10. PROFITS P r o f i t d a t a were o b ta in e d from Firm income s t a t e m e n ts, and a r e l i s t e d i n T ab le 11. P r o f i t s a re n o t a f f e c t e d by th e ty p e s o f a c c o u n tin g changes d e s c r ib e d above, s in c e c o s t s a r e re im b u rse d w h e th er th e y a r e d i r e c t o r o v e r head e x p e n se s. C o n se q u e n tly , no a d ju s tm e n ts t o th e pub l i s h e d d a t a were r e q u i r e d . FIXED ASSETS The F i r m 's f ix e d a s s e t d a ta are, com piled a t t h e end o f th e y e a r i n a s p e c i a l r e p o r t . L ike p e r s o n n e l , fixed; a s s e t s r e p r e s e n t a s to c k v a r i a b l e r a t h e r th a n a flo w , so an a v erag e f i g u r e was r e q u i r e d . T h is av erag e was o b ta in e d by j ad d in g th e y e a r - e n d f i g u r e t o l a s t y e a r 's y e a r- e n d f i g u r e j and d i v i d i n g by tw o. The r e s u l t a n t a v erag e f i g u r e s a re l i s t e d i n T ab le 11. TOTAL SALES AND SPARES SALES T o t a l s a l e s and s p a r e s s a l e s d a ta were o b ta in e d | 1959 I960 1961 1962 1963 1964 1965 1966 1967 1968 CT p; 1959 I960 1961 1962 1963 1964 1965 1966 1967 1968 TABLE 10 YEAR-END AND AVERAGE PERSONNEL DATA ___________YEAR-END DATA___________ E n g l- Admini- n e e r ln g F a c to ry s t r a t l v e S p ares 361 875 45 7 380 918 46 10 478 958 82 ' 17 480 1134 76 22 412 988 70 18 400 1057 97 14 480 985 104 12 546 1116 92 14 519 998 93 15 704 879 116 34 12 308 161 45 12 318 160 49 8 334 174 64 10 384 185 80 13 324 175 51 17 330 162 28 18 339 178 26 18 386 187 30 14 343 189 28 14 340 212 26 AVERAGE DATA FOR YEAR E n g l- Admini- n e e r in g F a c to ry s t r a t l v e S p ares 361* 875* 45* 7* 370 896 45 9 430 938 64 14 479 1046 79 20 446 1011 73 20 406 1023 84 16 440 1020 101 13 513 1050 98 13 532 1057 92 15 612 938 104 24 12* 308* 161* 45* 13 313 160 47 10 326 167 58 9 362 180 74 11 371 180 66 15 342 168 40 18 334 170 27 18 362 182 28 16 365 188 29 14 342 200 27 s in c e no 1958 d a t a were a v a i l a b l e t o compute a v erag e d a ta . C P v CPv YEAR 1959 I960 1961 1962 1963 1964 1965 1966 1967 1968 TABLE 11 FINANCIAL OPERATING VARIABLES Thousands o f D o lla r s INTER FIXED ASSETS* COMPANY NET PROFIT YEAR-END AVERAGE TOTAL SALES SPARES SALES SALES $ -596 $3189 $3189 -2514 3143 3166 11-26 2956 3050 2160 3116 3036 2271 3658 3387 2065 4013 3836 2269 4077 4045 2966 4817 4447 1280 5377 5097 760 6366 5872 *Book v a lu e ( c o s t l e s s d e p r e c i a t i o n ) av erag e f i g u r e f o r 1959 i s assumed $51,180 $ 9,378 $ 994 37,554 9,844 198 44,883 13,781 3,900 57,980 20,649 7,564 68,003 17,700 3,681 50,389 8,584 2,278 49,852 4,872 1,816 57,293 5,210 1,422 61,576 6,152 14,415 52,321 5,726 8,571 No d a t a a v a i l a b l e f o r 1958, so e q u a l to th e y e a r - e n d f i g u r e . a\ -< 68 ] from th e Firm income s t a t e m e n t s , and no a d ju s tm e n ts were r e q u i r e d . The d a t a a re l i s t e d i n T ab le 11. TREND A t r e n d v a r i a b l e was in c lu d e d t o a c c o u n t f o r ite m s t h a t vary w ith th e p a ssa g e o f tim e . The v a lu e f o r t h i s t r e n d v a r i a b l e was 1 i n 1959 and 10 in 1968. OTHER VARIABLES S e v e ra l a d d i t i o n a l v a r i a b l e s were d e r iv e d from th e o p e r a t i n g v a r i a b l e s j u s t d e s c r i b e d . Two o f t h e s e a re t o t a l d i r e c t d o l l a r s and h o u r s , which were found by ad ding th e f i g u r e s f o r e n g in e e r in g and th e f a c t o r y . The lo g a r ith m o f p r o f i t which was used i n o b t a i n i n g e s t i m a t e s f o r manage ment i n c e n t i v e com pensation ( th e lo g a rith m o f p r o f i t was s e t t o z e ro w henever p r o f i t s were n e g a t i v e ) . The lo g arith m , o f th e t r e n d v a r i a b l e was used when th e t i m e - r e l a t e d e f f e c t ; te n d e d t o a c t " s a t u r a t e d , " i . e . , when th e grow th r a t e d e c l i n e d . IV. SUMMARY OF DATA PREPARATION PROCEDURE | I t i s w o rth w h ile to summarize th e c o r r e c t i o n s i ! made t o t h e d a ta as j u s t d i s c u s s e d . The f o llo w in g p o i n t s j a r e s i g n i f i c a n t : ! 1. R e l a t i v e l y few a c c o u n ts r e q u i r e d any a d j u s t - j in g . N u m e ric a lly , a d j u s t i n g was r e q u i r e d f o r j t h r e e a c c o u n ts i n 1959 and I9 6 0 , 26 i n 1959 - | 1963, and 13 i n 1959 - 1964. A number o f t h e s e l a t t e r a c c o u n ts were t h e same a c c o u n ts j j t h a t had been p r e v i o u s l y a d j u s t e d . j i Most o f th e a c c o u n ts n e e d in g a d j u s t i n g were j j e i t h e r sm a ll o r r e q u i r e d s m a ll a b s o l u te a d - j j u s t m e n t s . C o r r e c t io n s o f t h e s e ty p e s a r e n o t l i k e l y t o i n j e c t s i g n i f i c a n t e r r o r s i n t o ! th e a n a l y s i s . j A few l a r g e a c c o u n ts r e q u i r e d f a i r l y l a r g e p e rc e n ta g e a d ju s tm e n t s , which means t h a t th e a b s o l u te c o r r e c t i o n s w ere a l s o l a r g e . The a c c o u n ts t h a t f e l l i n t o t h i s c a t e g o r y •were th e r e d i s t r i b u t i o n a c c o u n ts f o r t h e e n g i n e e r - : ln g and a d m i n i s t r a t i v e p o o l s , p lu s th e e n g i n e e r in g i n d i r e c t s a l a r i e s and wages a c c o u n t. | An a d d i t i o n a l check on th e r e d i s t r i b u t i o n a c c o u n ts showed t h a t i t i s u n l i k e l y t h a t s i g - ’ n i f i c a n t e r r o r s c o u ld be e n t e r i n g th e a n a l y s i s t h e r e . A check on th e e n g in e e r in g i n d l - j j i r e c t s a l a r i e s and wages a c c o u n t f o r th e e a r l y y e a rs showed t h a t e r r o r s sh o u ld be sm a ll ( s i n c e th e t o t a l amount o f d i r e c t p lu s i n d i r e c t d o l l a r s d i f f e r e d by a s m a ll amount a f t e r j j c o r r e c t i o n s as compared t o b e f o r e th e c o r - j r e c t i o n s ) . Even f o r t h e i n t e r m e d i a t e y e a r s , th e e r r o r s a re n o t p r o h i b i t i v e as shown by .... 70 | th e same t e s t . However, t h i s a c c o u n t u n d e r went two a d ju s tm e n ts and i n g e n e r a l r e p r e - l s e n t s th e one a c c o u n t t h a t co u ld c o n ta in th e j l a r g e s t e r r o r s . On th e b a s i s o f th e abo v e, i t would a p p e a r t h a t j th e d a t a u sed i n th e a n a l y s i s a r e r e l a t i v e l y f r e e from e r r o r s which c o u ld cause b i a s i n t h e r e g r e s s i o n e q u a tio n s ] i i and th e c o n c lu s io n s t h a t can be drawn from them . One l a s t p o in t sh o u ld be made b e f o r e l e a v in g th e j i s u b j e c t o f d a ta c o n s i s t e n c y . T h is r e f e r s t o th e c o n s i s t - j ency o f th e d a ta as th e y a re p u b l is h e d i n t h e summary o v e r - ; head r e p o r t s . I t i s a p p a re n t t h a t some a d j u s t i n g has a l re a d y o c c u rre d i n th e d a t a . T h is i s b e c a u se some o f th e f o u r - y e a r s ' d a ta o r i g i n a l l y r e f l e c t d i f f e r e n t a c c o u n tin g m ethods. j For p u rp o se s h e r e , i t must be assumed t h a t th e | p u b lis h e d d a t a a re a c c e p ta b ly c o n s i s t e n t . T h is assu m p tio n j i s re a s o n a b le b e ca u se th e p e r s o n n e l a d j u s t i n g th e d a t a a re i s p e c i a l i s t s in overhead a c c o u n ts . S p e c i f i c i n d i v i d u a l s a re r e s p o n s i b l e f o r p r e p a r in g each p o o l f o r e c a s t each y e a r , and th e y draw on t h e i r own knowledge as w e ll as on th e know le d g e o f o t h e r s p e c i a l i s t s . S in ce t h e y work w ith more d i s a g g re g a te d d a ta as w e ll as an i n t i m a t e knowledge o f th e j acco u n t s t r u c t u r e s , i t would a p p e a r t h a t t h e p u b lis h e d r e - i ! v is e d d a t a a r e q u i t e good from an e c o n o m e tric p o i n t o f | view . I V. DEFLATION OF DOLLAR VARIABLES ! i 1 The f i r s t q u e s t io n t o be answ ered when d i s c u s s i n g j d e f l a t i o n o f v a r i a b l e s i s w h e th e r o r n o t t o d e f l a t e . By j t h i s i s meant w h eth er o r n o t t o d i v id e th ro u g h by a p r i c e in dex so d a t a a r e e x p re s s e d i n term s which a re in d e p e n d e n t j o f p r i c e c h a n g e s .11 The n e x t problem i s t o d e c id e which p r i c e d e f l a t o r s e r i e s t o a p p ly t o th e d i f f e r e n t v a r i a b l e s . I TO DEFLATE OR NOT TO DEFLATE j I t may seem s t r a n g e t o q u e s tio n w h e th er d e f l a t i o n i I i s n e c e s s a r y o r d e s i r a b l e . The q u e s t io n a r i s e s , how ever, b ecau se th e p ro c e s s of d e f l a t i o n can i n j e c t b i a s i n t o o t h - j e rw is e pu re d a t a . Jo h n s to n s t a t e s t h a t such b i a s i s im p u te d , w ith th e b i a s b e in g e i t h e r p o s i t i v e o r n e g a tiv e and i n c r e a s i n g f o r l a r g e r d i s t a n c e s from th e b a se y e a r . 12 Fur-: th e rm o re , s in c e a l l in d e x e s a r e w e ig h te d a v erag e com posites: j o f p r i c e s o f com ponents, i t i s a p p a re n t t h a t some d e g re e ofj e r r o r can be i n j e c t e d b e c a u se o f w e ig h tin g problem s even if| b i a s i s a b s e n t . T his i s t r u e w h e th er t h e P aasche o r th e L asp ey res method o f index number c o n s t r u c t i o n i s i i p . E. C ro x to n , D. J . Cowden, and S. K le in , A pplied G en eral S t a t i s t i c s (3 rd e d . ; Englewood C l i f f s , N. J . : P r e n t i c e - H a l l , I n c . , 1967) , p. 226. 12J . J o h n s to n , S t a t i s t i c a l Cost A n a ly sis (New York: McGraw-Hill Book Company, I n c . , i 9 6 0 ) , p . 17 . V ; used.-1 -^,!^ i ; I : i A ls o , a l l f o r e c a s t s w i t h i n th e Firm a re d e v elo p ed j I i in c u r r e n t ( i . e . , n o m in a l) d o l l a r s . Thus, i t would be | j i : s im p le s t t o I m i t a t e t h i s p o l i c y by com puting a l l r e g r e s - I i j : s io n s in term s o f c u r r e n t d o l l a r s . T h is i s th e s t r o n g e s t argument a g a i n s t d e f l a t i n g , s i n c e t h e p r e s e n t overh ead mo- i d e l i s t o be v a l i d a t e d by com paring i t s r e s u l t s w ith a s u b j e c t i v e f o r e c a s t . S in ce t h i s s u b j e c t i v e f o r e c a s t i s in c u r r e n t d o l l a r s , t h e o n ly t r u l y v a l i d com parison would be t o compute th e m o d e l’ s f o r e c a s t i n c u r r e n t d o l l a r s a l s o . The a l t e r n a t i v e i s t o d e f l a t e a l l v a r i a b l e s b e fo r e com p u tin g th e r e g r e s s i o n e q u a t i o n s , b u t th e n i t would be n e c - ; e s s a r y t o f o r e c a s t t h e t r e n d s i n p r i c e s t o d e f l a t e th e s u b j e c t i v e f o r e c a s t so i t i s c o m p a tib le w ith th e m o d el’s f o r e c a s t . T h is i s a d i f f i c u l t t a s k b e c a u se t h e r e i s no s u re way o f knowing what s o r t o f e x p e c te d p r i c e t r e n d was used by th o s e who p r e p a r e d th e s u b j e c t i v e f o r e c a s t . On th e o t h e r h an d , a c u r r e n t - d o l l a r f o r e c a s t c o n ta in s what R obinson c a l l s an i m p l i c i t f o r e c a s t . ^ ; i j 1^ K arl A. Fox, I n t e r m e d i a t e Economic S t a t i s t i c s j (New York: John W iley and S o ns, I n c . , 1968) , p. 127* I lZ*G. T i n t n e r , M athem atics and S t a t i s t i c s f o r E c o n o m is ts'(New York: H o l t , R i n e h a r t , and W inston, 1966) , pp. 303-304. ^ C o l i n R o b in so n , "Some P r i n c i p l e s o f F o r e c a s t i n g j in B u s in e s s ," J o u r n a l o f I n d u s t r i a l E conom ics, XIV j (November, 1 9 6 5 ), pp. 1 -2 . T his i m p l i c i t f o r e c a s t i s t h a t p r i c e e s c a l a t i o n w i l l con tin u e as i t has i n t h e p a s t . A lthough p e rh a p s v a l i d a t tim e s , t h i s p r e s e n t l y i s a s t r o n g a ssu m p tio n s in c e t h e l a s t few y e a r s have r e s u l t e d i n a n y th in g b u t "norm al" p r i c e e s c a l a t i o n b ecau se o f th e V ie t Nam War. For exam ple, th e GNP p r i c e l e v e l r o s e an a v e ra g e o f 1.4$ p e r y e a r betw een 1959 and 1964, but i t a v e ra g e d 2 . 8 % p e r y e a r s in c e (T able 1 2 ) . 16 I t t h e r e f o r e would a p p e a r d e s i r a b l e t o r e p l a c e such an i m p l i c i t f o r e c a s t by an e x p l i c i t f o r e c a s t . T his w i l l a llo w th e a n a l y s t t o s e l e c t any d e s i r e d f o r e c a s t f o r e s c a l a t i o n to c o n v e rt h i s c o n s t a n t d o l l a r f o r e c a s t i n t o c u r r e n t d o l l a r s . W hile h i s " d e s i r e s " may n o t be very good ( s in c e i n f l a t i o n i s p a r t i c u l a r l y h a rd t o f o r e c a s t 1? ) , a t l e a s t th e y would be open t o t h e view and c r i t i c i s m o f th o s e u sin g th e m odel. The v ie w e rs can t h e n s u b s t i t u t e t h e i r g u e sse s sh o u ld th e y so d e s i r e , which i s an o p tio n t h a t i s a b sen t when u n d e f l a te d d a ta a r e u se d . As m entioned ab o v e, such an app roach r e q u i r e s t h a t th e c o m p arativ e s u b j e c t i v e f o r e c a s t be d e f l a t e d — a d i f f i c u l t and u n d e s i r a b l e s t e p . However, t h e a l t e r n a t i v e s., P r e s i d e n t , Economic R eport o f th e P r e s i d e n t: 1969 (W ash ing ton , D. C .: U. S. Government P r i n t i n g O f f i c e , 196 9) , p. 2 3 6 . •^B. G. Hickman, Q u a n t i t a t i v e P la n n in g o f Economic P o lic y (W ashington, D. C .: -The B rookings I n s t i t u t i o n , 1965), p. 16. 74 | I | open t o us i s even more u n d e s i r a b l e . T h is a l t e r n a t i v e I ! c o n s i s t s o f u s in g c u r r e n t d o l l a r s t h r o u g h o u t. T h is would 1 j p e rm it a v a l i d com parison betw een t h e hand f o r e c a s t and i j th e m o d el’s f o r e c a s t . However, p r i c e e s c a l a t i o n i s a v a r - j i a b l e t h a t u l t i m a t e l y must be h a n d le d e x p l i c i t l y b e cau se i t i s so depen dent on n a t i o n a l c o n d i t i o n s . T hus, th e n o m in a l - d o l l a r a l t e r n a t i v e would mean t h a t a l l o f th e r e - I g r e s s i o n e q u a tio n s would have t o be d e r iv e d t w i c e — once i n : c u r r e n t d o l l a r s and once i n r e a l d o l l a r s . I t i s f e l t t h a t t h i s i s n o t an a c c e p ta b le a l t e r n a t i v e i n th e p r e s e n t stu d y .: The d e c i s i o n was t h e r e f o r e t o d e f l a t e a l l d o l l a r v a r i a b l e s i n t h e a n a l y s i s . The d i s c u s s i o n now t u r n s t o the- s e l e c t i o n o f t h e p r i c e in d e x e s t o u se i n d e f l a t i n g . . WHICH PRICE DEFLATORS TO USE There a re f i v e c l a s s e s o f d o l l a r d a t a in th e overhead model: o v erh ead c o s t s , d i r e c t l a b o r d o l l a r s , pro-; f i t s , s a l e s , and f i x e d a s s e t s . I t i s p o s s i b l e t o use one o r more in d e x e s t o d e f l a t e each o f t h e s e c l a s s e s . In p a r - ; t i c u l a r , th e o v erhead c o s t s i n c l u d e numerous s u b a g g r e g a te s j t h a t r e p r e s e n t d i f f e r e n t components o f n a t i o n a l incom e; ■ I p resu m ab ly , each a cc o u n t sh o u ld be d e f l a t e d s e p a r a t e l y by ! th e a p p r o p r i a te p r i c e in d e x . T h is can be se en from A lle n : j " S t r i c t l y s p e a k in g , each a g g re g a te and in d e e d , v a r io u s sub-| i a g g r e g a te s w i t h in i t , sh o u ld be d e f l a t e d by a d i f f e r e n t ! index o f p r i c e s , e . g . , consum ption by v a r i o u s in d e x e s o f | : th e p r i c e s o f consumer goods and s e r v i c e s , in v e s tm e n t by i v a rio u s in d e x e s o f p r i c e s o f c a p i t a l g o o d s . | E x i s t i n g macroeconomic m odels o f t e n have been j b a sed on t h i s a p p ro a ch . F o r exam ple, th e " I m p l i c i t P r ic e D e f l a t o r o f th e C o n sta n t D o lla r GNP S e r i e s " was u sed t o o b t a i n a m easure o f th e g e n e r a l p r i c e l e v e l t o d e f l a t e i n come flow s in t h e K le in -G o ld b e rg e r m o d e l. ^ However, cap i t a l consum ption a llo w a n ce s a re d e f l a t e d by an in d e x o f c a p i t a l equipm ent p r i c e s . They u se an i m p l i c i t p r i c e i n dex o f d is p o s a b l e p e r s o n a l income t o d e f l a t e p e r s o n a l con sum ption e x p e n d i tu r e s , and th e U. S. D epartm ent o f L a b o r 's i w h o le s a le p r i c e in d e x t o d e f l a t e governm ent p u r c h a s e s . O th er in d ex e s a l s o a re u se d : th e U. S. D epartm ent o f Com merce com posite c o n s t r u c t i o n in dex was a p p lie d t o new con s t r u c t i o n e x p e n d i t u r e s , an in d ex o f w h o le s a le p r i c e s f o r m achinery and m otive p r o d u c ts was a p p l i e d t o e x p e n d itu r e s f o r p r o d u c e r s ’ d u ra b le eq u ip m en t, and th e w h o le s a le p r i c e in dex was a p p lie d t o th e n e t change i n b u s in e s s in v e n t o r i e s . Im port and e x p o rt p r i c e d e f l a t o r s a l s o were u s e d . 20 ; i S i m i l a r l y , i n th e B ro o k in g s' Q u a r te r ly Model o f ! i — . . | 18r . g. D. A l l e n , M a th e m a tic a l Economics (2nd e d . ; London: M acm illan, 19 5 9 ), p . 43. ■^l . R. K le in and A. S. G o ld b e rg e r, An Econom etric! Model o f th e U n ite d S t a t e s : 1929 - 1952 (Amsterdam: N o rth -H o llan d P u b lis h in g C o ., 1 9 6 4 ), p . 115. i 20K le in and G o ld b e rg e r, o£. c i t . , p . 137. j th e U. S . , p r o f i t s and c a p i t a l e x p e n d i tu r e s were d e f l a t e d by w eig h te d GNP a cc o u n t i m p l i c i t p r i c e d e f l a t o r s f o r " o th - j e r new c o n s t r u c t i o n " and " p r o d u c e r s ’ d u r a b le e q u ip m e n t." ' j S a le s i n d u r a b le s and n o n d u ra b le s were g e n e r a l l y d e f l a t e d by th e a p p r o p r i a t e w h o le s a le p r i c e in d e x e s . R e t a i l s a l e s j p*1 were d e f l a t e d by th e consumer p r i c e in d e x . x The Ja p a n e se m edium -term m acro-m odel c o n ta in s s i x j p r i c e in d e x e s : p r i c e s o f consumer g o o d s, in v e s tm e n t goo ds, r e s i d e n t i a l c o n s t r u c t i o n , w h o le s a le g o o d s, e x p o r t s , and i m p o r t s . 22 In c o n t r a d i s t i n c t i o n t o t h e s e m o d els, t h e r e i s a s t r o n g argum ent f o r u s in g a s i n g l e in d e x f o r a l l p r i c e s , s i n c e i t i s much s im p le r t o m a n ip u la te th e f o r e c a s t s o f a s i n g l e index r a t h e r th a n a number o f in d e x e s . A lle n i n d i c a t e s t h a t " t o s im p li f y th e model w ith o u t re d u c in g i t s e s s e n t i a l s i g n i f i c a n c e , t h e a ssu m p tio n i s t h a t a l l s e c t o r i p r i c e s move i n p a r a l l e l so t h a t each a g g re g a te can be r e g a rd e d as d e f l a t e d w ith one and th e same i n d e x . " 23 T his t r e a tm e n t can p r e v a i l as lo n g as t h e r e i s a good c o r r e l a t i o n betw een t h a t s i n g l e in d ex and o t h e r in d e x e s t h a t could! be a p p lie d i n d i v i d u a l l y . A l t e r n a t i v e l y , t h i s means t h a t 2 1 j. S. D u e se n b erry , et^. a l . , The B rookings : Q u a r te r ly E conom etric Model o f th e U n ite d S t a t e s CChlcago: i Rand McNally and C o ., 1 9 6 5 ), pp. 99-10 0. 22J a p a n , Economic P la n n in g Agency, 0£ . c i t . , p. 2lJ 2 3 A lle n , oj>. c i t . , p. ^3. changes in r e l a t i v e p r i c e s betw een d i f f e r e n t a g g re g a te s a re i g n o r e d . 2* * While such a t r e a t m e n t can be q u e s tio n e d in m acro- economic m o d e l s , 25 i t would a p p e a r t o be v a l i d f o r th e p r e s e n t overhead m odel. The movement o f a l t e r n a t i v e p r i c e in d e x e s i s so f a r removed from th e i n t e r e s t o f th e Firm t h a t t o i n c o r p o r a t e numerous in d e x e s i n t o th e model f o r th e sake o f p r e c i s i o n ( o r p u rism ) i s u n c a lle d f o r . Given t h a t t h e use o f a s i n g l e in d ex i s v a l i d , th e n e x t s te p i s t o s e l e c t t h e in d ex t h a t p ro v id e s th e n e c e s s a r y p r e c i s i o n i n a l l d o l l a r c a t e g o r i e s . As f a r as th e overhead e x p e n d itu r e s a r e c o n c e rn e d , one i s im m ed iately a t t r a c t e d t o t h e consum er p r i c e in d e x . T h is i s b e ca u se a s u b s t a n t i a l p o r t i o n o f o v e rh e ad ex p en se s a r e l a b o r o r l a b o r - a s s o c i a t e d c o s t s , and l a b o r c o s t s o f t e n a re .r e l a t e d t o th e p r i c e l e v e l o f consum er g o o d s . 2^ T ip p e r s t a t e s t h a t "from 65 p e r c e n t t o 85 p e r c e n t o f th e t o t a l c o s t i n o v e r head f u n c tio n s i s r e l a t e d t o p e o p l e . " 2? A c u rs o ry i n s p e c t i o n o f t h e F irm ’ s o v e rh e a d e x p e n d itu r e s i n 1968 i n d i - : c a t e s t h a t around 70% o f t h e t o t a l c o s t s a r e l a b o r - o r i e n t e d 2**Allen, o£. c i t . , p . 32. 2^ C arl F. C h r i s t , "A ggregate E co n o m etric M odels," American Economic Review , XXXXVI (J u n e , 1 9 5 6 ), p . 396. 2^ C ro x to n , Cowden, and K le in , 0£ . c i t . , p . 227. 27Harry T ip p e r , J r . , C o n t r o l l i n g O verhead (New York: American Management A s s o c i a t i o n , 1966) , p . 29. C a rry in g t h i s i n s p e c t i o n a l i t t l e f u r t h e r , how e v e r , r e v e a l s t h a t a b o u t 5% o f th e 1968 c o s ts p ro b a b ly sh o u ld be d e f l a t e d by th e w h o le s a le p r i c e in d e x . These c o s t s r e p r e s e n t e x p e n d i tu r e s f o r s u p p l i e s , p e r i s h a b l e t o o l s , e t c . An a d d i t i o n a l h% o f c o s t s a r e in v e stm e n t item s ( d e p r e c i a t i o n ) and t h e r e f o r e sh o u ld be d e f l a t e d u s in g an in v e s tm e n t in d e x . The re m a in in g 20% o f c o s ts a re more o r l e s s n o n d e s c r i p t v a lu e s t h a t would b e s t be d e f l a t e d u s in g th e GNP i m p l i c i t p r i c e d e f l a t o r . T u rn in g t o t h e o p e r a t i n g v a r i a b l e s , i t i s a p p a re n t t h a t d i r e c t l a b o r d o l l a r s a r e l a b o r c o s t s . S i m i l a r l y , s a l e s and p r o f i t d o l l a r s a r e m o stly l a b o r c o s ts ( e i t h e r th e F irm ’s or a n o th e r f i r m s ' whose components t h e Firm p u r c h a s e s ) . Only th e f i x e d - a s s e t d a t a would app ear t o be unique and r e q u i r e an in v e s tm e n t in d e x . B e a rin g t h e s e c o n s i d e r a t i o n s i n mind, i t was de cid e d t o d e f l a t e a l l d o l l a r f i g u r e s by th e GNP i m p l i c i t p r i c e in d e x . T h is p e rh a p s s u r p r i s i n g c o n c lu s io n was rea ch e d by way o f t h e f o llo w in g r e a s o n in g : T here i s a very c lo s e c o r r e l a t i o n (0 .9 9 9 7 ) betw een th e GNP d e f l a t o r and th e consumer p r i c e in d e x d u r in g t h e p a s t 10 y e a r s . C o r r e l a t i o n d o e s n 't t e l l th e whole s t o r y , however, s in c e th e a b s o l u te l e v e l s o f t h e two in d e x e s a ls o must be compared. T able 12 shows t h i s c o m p a ris o n .2® I t can be 2®U. S . , P r e s i d e n t , Economic R eport o f th e P r e s i - d e n t : 1969 (W ashington, D. C . : U. S. Government P r i n t i n g O f f i c e , 1969), pp. 230 and 280. TABLE 12 PRICE TRENDS YEAR GNP IMPLICIT PRICE DEFLATOR PERCENTAGE VALUE CHANGE CONSUMER PRICE INDEX 1959 101.6 1 . 6 % 101.5 I960 103.3 1 .7 103.1 1961 104.6 1 .3 104.2 1962 105.8 1 .1 105.4 1963 107.2 1 .3 106.7 1964 108.8 1.5 108.1 1965 110.9 1.9 109.9 1966 113.8 2 .6 113.1 1967 117.3 3.0 116.3 1968 121.8 3 .8 120.9 Source: U. S. Economic R epo rt o f th e P r e s i d e n t : 1969 (W ashington: U. S. Government P r i n t i n g O f f i c e , 1 9 6 9 )j pp. 230 and 280. seen t h a t t h e GNP in d e x a p p a r e n t l y h as r i s e n s l i g h t l y f a s t e r th a n t h e consum er p r i c e in d e x : th e in d e x e s were alm ost i d e n t i c a l i n 1959> b u t th e y d i f f e r by 0 .9 o f a p o in t by 1968, a d i s p a r i t y o f 0 . 75S- Over 90$ o f t h e o v erhead c o s t s and a l l b u t one o f th e o p e r a t i n g v a r i a b l e s can c o r r e c t l y be d e f l a t e d by ap p l y in g e i t h e r t h e GNP i m p l i c i t p r i c e in d ex o r t h e consum er p r i c e in d e x , and s i n c e th e y a r e so h ig h ly i n t e r c o r r e l a t e d , one can be more o r l e s s i n d i f f e r e n t betw een th e tw o. The GNP d e f l a t o r i s p r e f e r a b l e t o t h e consumer p r i c e in d e x , how ever, s i n c e th e GNP in d e x c o n ta in s w e ig h te d components t o r e f l e c t th o s e ite m s n o t c o n ta in e d i n th e consum er p r i c e in d ex ( e . g . , w h o le s a le p r i c e s and p r i c e s on in v e s tm e n t i te m s ) . The GNP in d e x was t h e r e f o r e s e l e c t e d as t h e b e s t s i n g l e in d e x t o a p p ly t o a l l d o l l a r d a t a . S in c e th e GNP d e f l a t o r s e r i e s a re p u b l is h e d w ith 1957 - 1959 as t h e b a se p e r i o d , i . e . , th e in d ex f o r 1958 i s a p p ro x im a te ly 100, t h e d a t a i n t h i s stu d y were d e f l a t e d t o t h a t y e a r ’s d o l l a r s . Any y e a r ’s r e a l d o l l a r s c o u ld have been u s e d , as d e s i r e d , b u t i t i s a p p a r e n t t h a t th e d a t a can be tra n s fo r m e d i n t o a n o th e r y e a r ’s r e a l d o l l a r s m ere ly by a p p ly in g a c o n s t a n t a d ju s tm e n t f a c t o r y t o th e r e g r e s s i o n c o e f f i c i e n t s and i n t e r c e p t . CHAPTER IV DERIVATION OF MODEL Now t h a t th e p r e l i m i n a r y problem s have been done away w i t h , th e d i s c u s s i o n can t u r n t o th e overhead model i t s e l f . T h is d i s c u s s i o n w i l l b e g in w ith an e x p la n a t i o n o f th e p ro c e d u re s fo llo w e d i n d e v e lo p in g th e m odel. Then th e model i t s e l f — e q u a t i o n s , s t a n d a r d e r r o r s , e t c . — w i l l be p r e s e n t e d i n th e l a t t e r p o r t i o n o f t h i s c h a p te r . I . PROCEDURE USED IN DEVELOPING MODEL AGGREGATION OF ACCOUNTS I t was n o t c o n s id e re d f e a s i b l e n o r d e s i r a b l e to o b t a i n r e g r e s s i o n e q u a tio n s f o r a l l 250-280 overhead a c c o u n ts . F e a s i b i l i t y was la c k in g b e ca u se some i n d i v i d u a l a c c o u n ts behave e r r a t i c a l l y and t h e r e f o r e a re v i r t u a l l y im p o s s ib le t o e s t im a t e (w hereas i n c o n c e rt th e e r r a t i c n a t u r e s o f t e n c a n c e l o u t ) . D e s i r a b i l i t y was la c k in g s i n c e a model b a se d on few er e q u a tio n s te n d s t o be more conven i e n t t o u se th a n one w ith many e q u a t io n s . T hus, some form o f acco u n t a g g re g a tio n was d e s i r e d . I t , t h e r e f o r e , was d e c id e d t o a g g re g a te a lo n g th e l i n e s o f th e F ir m ’ s e x i s t i n g s u b j e c t i v e f o r e c a s t i n g m ethods. W hile t h i s s t i l l r e s u l t e d i n a l a r g e e f f o r t (o v e r 80 p o t e n t i a l 81 82 e q u a t i o n s ) , t h i s c o r r e l a t i o n o f th e two f o r e c a s t i n g methods p e r m its a com parison o f r e s u l t s t h a t would be a b s e n t o th e r w i s e . The r e s u l t a n t a g g re g a te d a c c o u n ts — 82 o f them— a re l i s t e d in Appendixes A, B, C, and D, t o g e t h e r w ith th e t e n - y e a r s ’ d a ta used i n th e a n a l y s i s . DERIVATION OF EQUATIONS The te c h n iq u e used h e re i s a s ta n d a r d s te p w is e m u l t i p l e r e g r e s s i o n program a d ap ted f o r u se w ith th e GE 325 d i g i t a l c o m p u ter.^ The program p ro v id e s e q u a tio n s o f th e f o llo w in g form: z = a + bu + cv + dw + ex + . . . where z i s an endogenous v a r i a b l e and u, v, w, x , . . . a r e in d e p e n d e n t v a r i a b l e s . The program a ls o p r o v id e s s t a n d a r d e r r o r s f o r each r e g r e s s i o n c o e f f i c i e n t as a g u id e f o r d e te rm in in g how many term s a re to be in c lu d e d in each equa t i o n . 2 In g e n e r a l , c o e f f i c i e n t s were r e j e c t e d u n le s s s i g n i f i c a n t a t th e 95# l e v e l ( o n e - t a i l e d t e s t ) . 3 T h is means t h a t t v a lu e found by d i v i d i n g th e r e g r e s s i o n c o e f f i c i e n t by i t s s t a n d a r d e r r o r was around 1 .9 o r g r e a t e r . ^ However, ^N. R. D raper and H. S m ith, A p plied R e g re s s io n A n a ly s is (New York: John W iley and Sons, I n c . 7 1 9 ^ 6 ), pp. 171-172. 2M ordecai E z e k ie l and K a rl A. Pox, Methods o f C o r r e l a t i o n and R e g re s s io n A n a ly sis (New York: John W iley and S o n s, I n c . , 1967) , p. 502. ^ C arl F. C h r i s t , "A ggregate Economic M od els," Am erican Economic R eview , XXXXVI (Ju n e , 1956) , p. 391. 83 o f t e n was n e c e s s a r y t o r e l a x t h i s e n d ea v o r i n o r d e r t o e s t im a t e some o f th e i n t r a c t a b l e a c c o u n ts . T h is u n f o r t u n a te f e a t u r e i s a d i r e c t r e s u l t o f t h e few y e a r s f o r which d a ta a r e a v a i l a b l e . Form o f R e g re s s io n E q u a tio n s The p ro c e d u re f o r s e l e c t i n g th e a p p r o p r i a t e in d e pen d en t v a r i a b l e s was f a c i l i t a t e d by th e a c c o u n ts them s e l v e s . 5 The e n g in e e r in g ov erhead a c c o u n ts , f o r exam ple, g e n e r a l l y a r e r e l a t e d to e n g in e e r in g a c t i v i t y v a r i a b l e s . The same i s t r u e o f most o f th e f a c t o r y a c c o u n ts . The a d m i n i s t r a t i v e a c c o u n ts were u s u a l l y found t o be r e l a t e d to th e sum o f e n g in e e r in g and f a c t o r y a c t i v i t y v a r i a b l e s , a lth o u g h some e x c e p tio n s d id show up. The s m a ll s p a r e s p o o l was e a s i e s t o f a l l t o e s t i m a t e , b e in g r e l a t e d p r i m a r i l y t o s p a r e s s a l e s , and s e c o n d a r i ly t o s p a r e s d i r e c t p e r s o n n e l . In o r d e r t o be c o n s i s t e n t w ith e c o n o m e tric t h e o r y , i t was n e c e s s a r y t o e s tim a te e q u a tio n s when th e y were in red u c ed form . T h is means i t was n e c e s s a r y t o av o id u se o f 5t . C. Koopmans., Three E ssays on th e S t a t e o f Economic S c ie n c e (New York: McGraw H i l l Book C o ., I n c . , 1 9 5 7 ), P. 201. 6 c a r l C h r i s t , "A T e s t o f an E conom etric Model f o r th e U n ite d S t a t e s : 1921-1947," C onference on B u sin e ss C ycles (New York: N a tio n a l Bureau o f Economic R e s e a rc h , 19 5 1 ), P. 42. some v a r i a b l e s t h a t a re endogenous from th e p o i n t o f view o f th e overhead m o d e l.? The v a r i a b l e s t h a t were u sed a l l were ju d g e d t o be exogenous, s in c e t h e y do n o t depend on th e o verhead a c c o u n ts i n any way. T hese v a r i a b l e s , such as d i r e c t p e r s o n n e l o r d i r e c t wage r a t e s a l l a r e e s tim a te d e x t e r i o r t o th e ov erhead model and s u p p l i e d t o th e model in t r u e exogenous f a s h i o n . In o t h e r w o rd s, o v e rh e ad amounts a re lin k e d t o d i r e c t c o s t s r a t h e r th a n t o o v e rh e ad c o s t s . B ecause t h i s i s th e c a s e , th e model a v o id s a l l o f th e problem s a s s o c i a t e d w ith sim u lta n e o u s s o l u t i o n s f o r i n t e r r e l a t e d e q u a t i o n s .^ In g e n e r a l , a d e f i n i t e e f f o r t was made t o i n s u r e t h a t t h e o v erhead acco u n t was lin k e d t o a t l e a s t one a c t i v i t y v a r i a b l e . T hus, e q u a tio n s which i n c lu d e d o n ly a wage term o r a t r e n d term were av oid ed i f p o s s i b l e . A few e q u a tio n s c o n ta in i n g only TREND were a c c e p te d whenever i t was o th e r w is e im p o s s ib le t o p ro v id e a m e a n in g fu l e q u a tio n and f o r e c a s t , b u t t h e s e were f e l t t o be j u s t i f i a b l e on o t h e r grounds as w e l l. S i m i l a r l y , th e i n i t i a l e q u a tio n s were e s tim a te d on t h e b a s i s o f e i g h t o r n in e y e a r s , w ith lag g e d d a t a f o r 7g . H. O r c u t t , "Views on S im u la tio n Models o f S o c i a l S eptem s," Symposium on S im u la tio n M odels: Method o lo g y and A p p lic a tio n s t o th e B e h a v io ra l S c i e n c e s , ed. by A. C. H oggatt and P. E. B a ld e r s to n ( C i n c i n n a t i : S o u th - W estern P u b l i s h i n g C o., 1963) , p . 230. ^K arl A. Pox, I n t e r m e d i a t e Economic S t a t i s t i c s (New York: John W iley and S on s, I n c . , 1 9 6 8 ), p . 3^6. e i t h e r two o r one y e a r s . I t was fo u n d , how ever, t h a t v e r t i c a l l y a l l e q u a tio n s co uld b e s t be e s t im a t e d w ith o u t u s in g la g g e d v a r i a b l e s . F u rth e rm o re , th e e q u a tio n s t h a t d id c o n ta in lagged v a r i a b l e s c o n ta in e d o nly lag g e d v a r i a b l e s , and t h i s was u n a c c e p ta b le on th e b a s i s o f th e f o llo w in g re a s o n in g : 1. In th e use o f m acroeconomic m o d els, t h e r e i s some j u s t i f i c a t i o n f o r t h e u se o f la g g e d v a r i a b l e s . GNP, f o r exam ple, can be e s tim a te d a c c u r a t e l y u s in g d i f f e r e n c e e q u a t i o n s , and t h i s i s l o g i c a l l y c o r r e c t as w e l l . W e e x p e c t GNP t o i n c r e a s e g e n tl y each y e a r , and even th e p r e s e n c e o f r e c e s s i o n s d o e s n ’ t d e t e r t h e t r e n d s i g n i f i c a n t ly b e c a u se o th e r i n f l u e n c e s a r e a l s o p r e s e n t . 9 2. I t i s easy t o p o s t u l a t e t h a t t h i s y e a r ’ s e x p en ses f o r an overhead acco u n t a r e r e l a t e d t o l a s t y e a r ’ e x p e n s e s — P a r k i n s o n 's Law h o ld s i n firm s j u s t as i t does e ls e w h e re . In the c ase o f t h e F irm , how ever, i t i s not r e a s o n a b le to allow such a d i f f e r e n c e e q u a tio n t o p ro v id e a f o r e c a s t f o r an a c c o u n t. The r e a s o n i s t h a t th e in d e p en d en t v a r i a b l e s i n th e Firm a re much more v a r i a b l e th a n th o s e f o r th e economy. P r o f i t s and t h e work f o r c e can s h r i n k o r expand v i o l e n t l y , w h ile d i r e c t h o u rs can f l u c t u a t e s i g n i f i c a n t l y b e ca u se o f o v e rtim e b ro u g h t about 9w. C. Hood and T. C. Koopmans, S tu d ie s i n Econo- m e tr ic Method (New York: John W iley and S o n s, I n c . , 19 5 3 ), P. 23. by p r i o r i t y c o n t r a c t s . Changes o f t h i s ty p e w i l l o v e r whelm any " i n e r t i a " i n th e F irm , o r a t l e a s t a re more l i k e l y t o do so th a n a r e changes i n th e n a t i o n ’s economy. I t was t h e r e f o r e d e c id e d t o e l i m i n a t e a l l lag g e d overhead v a r i a b l e s , which p e r m i tt e d th e use o f th e f u l l t e n y e a r s ’ d a ta f o r a l l a c c o u n ts . Not o nly does t h i s g e n e r a l l y g u a ra n te e s m a lle r s t a n d a r d e r r o r s , b u t a l s o h o ld s prom ise t h a t more i n f l u e n c e s w i l l show up i n th e d a t a . USE OF SUBJECTIVE FORECAST A s e r i o u s problem d e v e lo p e d when t r y i n g to s e l e c t t h e " b e s t" r e g r e s s i o n e q u a t io n . The problem was sim ply t h a t t h e e q u a tio n p ro d u c in g th e b e s t f i t t o th e d a t a o f t e n produced an u n re a s o n a b le f o r e c a s t . T his u n d o u b ted ly was due p r i m a r i l y to th e s h o r t d a ta s e r i e s t h a t was a v a i l a b l e f o r e s t i m a t i o n . Because o f t h i s p ro b lem , i t was d e c id e d t o u se th e l a s t "hand-made" f o r e c a s t as a g e n e r a l check f o r r e a s o n a b l e n e s s . 10 T h is s u b j e c t i v e f o r e c a s t does have th e a d v a n ta g e o f b e in g p re p a re d by know ledg eab le a n a l y s t s who know a t l e a s t i m p l i c i t l y how most o f t h e s e a cc o u n ts b ehave. T hus, i f th e r e g r e s s i o n e q u a tio n p ro d u ce d a f o r e c a s t t h a t was s u b s t a n t i a l l y d i f f e r e n t from t h e hand-made or 10F. M o d ig lia n i, " D is c u s s io n o f M a n ag e rial Econo m ics: A New F r o n t i e r ? " American Economic Review, LI (May, 1961), p. 157- s u b j e c t i v e f o r e c a s t , t h i s was i n t e r p r e t e d t o mean t h a t a t l e a s t one a s p e c t o f th e t r u e s i t u a t i o n had been o v e r loo k ed . H A new s e a r c h was th e n begun f o r a d i f f e r e n t e q u a tio n which would p ro v id e b o th a good f i t and a r e a s o n a b le f o r e c a s t . The problem o f u n re a s o n a b le f o r e c a s t s became p r o nounced when w orking w ith th e f a c t o r y p o o l b ecau se o f th e l a r g e e x p e c te d i n c r e a s e i n r e l a t i v e l y u n s k i l l e d l a b o r . T his r e a l l y i s a s t r u c t u r a l change b e ca u se th o s e u n t r a i n e d p e rs o n n e l w i l l p e rfo rm d i f f e r e n t t a s k s th a n most o f th e p r e s e n t em ployees, and th e t a s k o f t e n d i c t a t e s th e ty p e s of overhead e x p e n d itu r e s i n v o l v e d . 12 T his d i f f i c u l t y a l s o a f f e c t e d th e a d m i n i s t r a t i v e p o o l t o some e x t e n t . SELECTION OF REGRESSION EQUATIONS A c u rio u s f e a t u r e o f th e p r e s e n t s u b j e c t i v e method o f f o r e c a s t i n g i s th e a t t e n t i o n t o d e t a i l . W e f in d e x q u i s i t e d e t a i l g iv e n t o a c c o u n ts t h a t a re q u i t e m in i s c u l e . T hat i s , an a c c o u n t r e c e i v e s v i r t u a l l y th e same a t t e n t i o n w h eth er i t i s l a r g e o r s m a ll. T his does n o t seem t o be r e a s o n a b le s i n c e e r r o r s i n th e l a r g e f o r e c a s t s comp l e t e l y dw arf any p r e c i s i o n i n th e s m a lle r a c c o u n ts . ^ A r n o l d Z e l l n e r , "D e c isio n R ules f o r Economic F o r e c a s t i n g ," E c o n o m e tric a , XXXI ( J a n u a r y - A p r i l , 1963) , P. 157. i 2 N. R. D rap er and H. Sm ith, op. c i t . , pp. 2*10- 2*tl. 88 To be more r e a l i s t i c i n th e p r e s e n t o v erh ead m odel, th e " s a t i s f i c i n g ” t h r e s h o l d was p la c e d a t a low er l e v e l on th e s m a ll e r a c c o u n ts as compared t o th e l a r g e r a c c o u n ts . T h is r e f e r s t o th e p ro c e s s o f s e l e c t i n g th e " c o r r e c t " r e g r e s s i o n e q u a tio n out o f a s e r i e s o f p o t e n t i a l c a n d i d a t e s .13 p0r th e s m a lle r a c c o u n ts , any r e a s o n a b ly good f i t was a c c e p te d and f u r t h e r work s to p p e d . F o r th e l a r g e r a c c o u n ts , how ever, more c are was ta k e n t o s e l e c t a good e x p la n a to r y e q u a t io n , w ith a d d i t i o n a l e q u a tio n s d ev elo p ed t o p ro v id e s a t i s f a c t i o n t h a t no b e t t e r f i t i s a v a i l a b l e . TEST FOR AUTOCORRELATION Each p o t e n t i a l e q u a tio n was t e s t e d f o r a u t o c o r r e l a t i o n . The p r i n c i p a l s t a t i s t i c used i n t h i s t e s t in th e l i t e r a t u r e i s th e D urbin-W aston s t a t i s t i c . 1^ 15 However, u p p e r and low er bounds f o r t h e D urbin-W atson t e s t have n o t been computed f o r sample s i z e s o f l e s s th a n 15. C o n se q u e n tly , i t was n e c e s s a r y t o e x t r a p o l a t e back t o a 1 3 c a r l F. C h r i s t , "A ggregate Economic M o dels," American Economic R eview , XXXXVI (Ju n e , 1 9 5 6 ), p. *100. l ^ J . D urbin and G. S. W atson, " T e s tin g f o r S e r i a l C o r r e l a t i o n i n L e a s t S quares R E g ression: P a r t I , " B io- m e t r ik a , XXXVII (December, 1 9 5 0 ), pp. 409-428. 1 5 j. D urbin and G. S. Watson, " T e s tin g f o r S e r i a l C o r r e l a t i o n i n L e a s t S quares R e g re ss io n : P a r t I I , " B io- m e t r ik a , XXXVIII (Ju n e , 1 9 5 1 ), pp. 159-178. sample s i z e o f 10 (an a d m itte d ly r i s k y o p e r a t io n ) t o o b t a i n a p p ro x im ate up per and low er bounds. The v a lu e s so o b ta in e d a r e 0.70 and 1 .6 0 , r e s p e c t i v e l y , f o r 10 o b s e r v a t i o n s and two in d e p e n d e n t v a r i a b l e s . T h i s i s a f a i r l y wide i n t e r v a l , and t h i s makes th e D urbin-W atson t e s t somewhat weak s in c e th e t e s t i s i n c o n c lu s iv e when th e s t a t i s t i c f a l l s betw een th e low er and upper bounds. A second t e s t f o r a u t o c o r r e l a t i o n t h e r e f o r e was added. T his was th e Von Neumann s t a t i s t i c , which i s •11# g r e a t e r t h a n th e D urbin-W atson s t a t i s t i c ( f o r a sample s i z e o f 10) b e cau se i t i s d iv id e d by t h e r a t i o (n - l ) / n . ^ The a d v an tag e o f t h i s t e s t i s t h a t e x a c t l i m i t s a re a v a i l a b l e t o d e c id e w h e th er p o s i t i v e (o r n e g a t iv e ) a u to c o r r e l a t i o n i s p r e s e n t . The c r i t i c a l v a lu e f o r t h i s s t a t i s t i c i s 1 .1 8 f o r a sample o f 10 and a 95# c o n fid e n c e l e v e l . T h is Von Neumann t e s t ag re ed w ith th e D urbin-W atson t e s t i n a l l i n s t a n c e s t h a t th e l a t t e r was c o n c l u s i v e , and i n a d d i t i o n , was a b le t o make a judgm ent w henever th e l a t t e r was i n c o n c l u s i v e . Only i n c a se s where p o s i t i v e a u t o c o r r e l a t i o n was p r e s e n t was t h e r e f e l t to be grounds f o r e l i m i n a t i n g a l 6 j . D urbin and G. S. W atson, " T e s tin g f o r S e r i a l C o r r e l a t i o n i n L e a st S quares R e g re s s io n : P a r t I I , " B io- m e t r ik a , XXXVII (Ju n e , 1 95 1 ), p . 162. l ^ E z e k i e l and Pox, op. c i t . , p . 3*11. 90 p o t e n t i a l e q u a t io n . A few c a s e s o f m odest n e g a tiv e a u to c o r r e l a t i o n were u n c o v e re d , b u t t h e s e were f e l t t o be due t o random f l u c t u a t i o n s i n th e d a t a . A p o t e n t i a l case can be made f o r e l i m i n a t i n g an e q u a t io n b e c a u se o f n e g a tiv e a u t o c o r r e l a t i o n , e . g . , "ex p e n se s a r e h ig h t h i s y e a r b e - . cause th e y were low l a s t y e a r . " However, such a p o lic y seems g e n e r a l l y u n l i k e l y i n th e Firm u n d er s tu d y . TEST FOR HETERO SCEDASTICITY The e q u a tio n s a l s o were t e s t e d f o r h e t e r o s c e d a s t i - c i t y . A lthough no t e s t s a r e u n i v e r s a l l y a c c e p te d , th e t e s t a d o p ted was d e v is e d by G o ld f e ld and Quandt (and w i l l 1 O be a b b r e v i a t e d GQ i n s u b s e q u e n t p a g e s ) . ° The t e s t i s made by f i r s t o r d e r in g th e d a t a by s i z e and th e n o b ta in in g s e p a r a t e r e g r e s s i o n e q u a tio n s (and r e s i d u a l s ) f o r the up p er and low er p o r t i o n s o f t h e d a t a . The r a t i o o f th e sum i s th e sq u a re s o f th e r e s i d u a l s i s th e n d i s t r i b u t e d as F, so a s t r a i g h t f o r w a r d v a r i a n c e t e s t i s u t i l i z e d . In t h i s s t u d y , th e 95% l e v e l o f s i g n i f i c a n c e was u t i l i z e d . The t e s t h e re u n d o u b te d ly i s q u i t e weak. T his stem s from th e sm a ll number o f o b s e r v a t i o n s a v a i l a b l e , s in c e a t most only f i v e p o i n t s can be used i n th e upper and low er g r o u p s . T h is le a v e s e i t h e r two o r t h r e e d e g re es ^ S t e p h e n m. G o ld fe ld and R ic h a rd E. Quandt, "Some T e s ts f o r H o m o s c e d a s tic ity ," J o u r n a l o f th e American S t a t i s t i c a l A s s o c i a t i o n , LX ( J u n e , 1 9 6 5 ), PP* 539-5^1. 91 of freedom a f t e r th e d a t a a r e f i t w ith e q u a tio n s w ith e i t h e r t h r e e o r two c o e f f i c i e n t s . The F s t a t i s t i c s f o r two o r t h r e e d e g re e s o f freedom s a r e l a r g e , i . e . , 19.00 and 9 -55 i r e s p e c t i v e l y .^9 Note t h a t th e "p" o f G o ld fe ld and Quandt has been s e t t o z e r o — a f e a t u r e n e c e s s i t a t e d by th e sm a ll sam ple. T his number r e p r e s e n t s th e number o f ,,m id d le ', o b s e r v a t i o n s e li m in a te d b e f o r e com puting t h e r e g r e s s i o n s f o r t h e low er and u p p er p o r t i o n s o f th e d a t a . S ince th e s t r e n g t h o f th e GQ t e s t i s d ep en d e n t on th e s i z e o f p , a p o f z e ro te n d s t o make th e t e s t somewhat w eak. 20 An a l t e r n a t i v e r e g r e s s i o n was sou ght in th o s e i n s t a n c e s where h e t e r o s c e d a s t i c i t y was d is c o v e r e d . When t h i s f a i l e d , th e e q u a tio n was tra n s fo rm e d by d i v i d i n g a l l th e v a r i a b l e s by one o f th e in d e p e n d e n t v a r i a b l e s . T his tr a n s f o r m a tio n - im p lie s t h a t t h e v a r ia n c e i s p r o p o r t i o n a l t o th e v a lu e o f th e in d e p e n d e n t v a r i a b l e . 21 DEFLATION OF SUBJECTIVE FORECAST In th e f i g u r e s accom panying th e t e x t f o r each ov erhead a c c o u n t, th e m o d e l's f o r e c a s t s w i l l be compared w ith b o th th e h i s t o r i c a l d a ta and th e s u b j e c t i v e 1 9 c ro x to n , Cowden, and K le in , op. c i t . , p. 679. 20G o ld fe ld and Quandt, op. c i t . , p. 5^1. 2lEdward J . Kane, Economic S t a t i s t i c s and Econo- m e tr ic s (New York: H arp er and Row, P u b l i s h e r s , 1968) , P. 374'. f o r e c a s t . F or p u rp o se s h e r e , i t was n e c e s s a r y t o d e f l a t e th e s u b j e c t i v e f o r e c a s t t o th e 1958 p r i c e l e v e l . The assumed p r o g r e s s i o n o f th e GNP i m p l i c i t p r i c e in d ex i s shown In T ab le 13, as i s th e p e rc e n ta g e change y e a r by y e a r . I t can be se en t h a t th e p e rc e n ta g e i n c r e a s e in th e in d ex d ro p s from 6% p e r y e a r i n 1969 to 2% i n 1978. T his may have been somewhat to o h ig h a r a t e o f i n f l a t i o n in l i g h t o f th e r e p o r t e d 4.7# a c t u a l i n c r e a s e f o r I 9 6 9 .22 However, most o f th e e f f o r t c o n ta in e d i n th e s e g rap h s was p r e p a r e d b e f o r e th e 1970 economic d a ta were com piled. S in ce t h e s u b j e c t i v e f o r e c a s t i s used o n ly t o o b t a i n a rough i d e a o f th e t r e n d p r e d i c t e d by th e s u b j e c t i v e f o r e c a s t o r , i t was n o t f e l t t h a t g r e a t p r e c i s i o n was needed. I f th e r e a d e r f e e l s t h a t a low er r a t e o f I n f l a t i o n i s more l i k e l y , he can m e n ta lly a d j u s t s l i g h t l y upward th e s u b j e c t i v e f o r e c a s t s . ABBREVIATIONS In o r d e r t o f a c i l i t a t e th e d i s c u s s i o n , th e v a r i a b l e s in c lu d e d i n th e e q u a tio n s have been a b b r e v i a t e d . Many o f t h e s e a re o b v io u s: FASSETS s ta n d s f o r f i x e d a s s e t s (a v e ra g e f o r y e a r ) , PROFIT f o r p r o f i t , LOGPROFIT f o r th e lo g a rith m o f p r o f i t , and TREND f o r a tim e v a r i a b l e t h a t i s 22U. S . , P r e s i d e n t , Economic R ep o rt o f th e P r e s i d e n t: 1970 (W ashington, D.CTl U\ Si Government P r i n t i n g O f f i c e , 1 9 7 0 ), p. 180. 93 TABLE 13 FORECAST FOR G.N.P. IMPLICIT PRICE INDEX YEAR IMPLICIT PRICE INDEX PERCENT CHANGE 1969 129.1 6% 1970 135.6 5 1971 142.3 5 1972 148.0 4 1973 154.0 4 197^ 158.6 3 1975 163.3 3 1976 166.6 2 1977 170.0 2 1978 173.3 2 e q u a l t o 1 i n 1959 th ro u g h 20 i n 1978. The ones t h a t a re n o t o bvio u s a r e : p D i r e c t P e rs o n n e l (av e rag e f o r y e a r ) w Average Wage Rate DLD D ir e c t L abor D o lla r s DLH D ir e c t L abor Hours INCOSLS In tercom pan y S a le s TSALES T o t a l S a le s SPSALES S p ares S a le s The l e t t e r s E, F, A, and S p re c e d e th e s e codes t o d en o te th e a p p r o p r i a t e p o o l. T hus, EP s ta n d s f o r e n g in e e r in g d i r e c t p e r s o n n e l , w h ile EW s ta n d s f o r e n g in e e r in g wage. The a v e ra g e d i r e c t wage f o r th e whole Firm , i n c i d e n t a l l y , i s a b b r e v i a t e d EFW, and o t h e r Firm -w ide v a r i a b l e s a re n o te d s i m i l a r l y . O verhead a c c o u n ts f o r th e t h r e e l a r g e p o o ls w i l l be d i s c u s s e d t o g e t h e r . T his d i s c u s s i o n i s broken up i n t o s e c t i o n s which d e a l f i r s t w ith l a b o r - o r i e n t e d a c c o u n ts and l a t e r w ith t h e re m a in in g a c c o u n ts . F o llo w in g t h i s i s a d i s c u s s i o n o f th e s p a r e s p o o l, and f i n a l l y a d i s c u s s i o n as t o why s e v e r a l a c c o u n ts co uld n o t be e s t i m a t e d . I I . EQUATIONS FOR LABOR-ORIENTED ACCOUNTS A number o f a c c o u n ts a r e e a s i l y i d e n t i f i e d as b e in g r e l a t e d t o l a b o r . These in c lu d e v a c a tio n and h o l i 95 day p a y , e x p e n d itu r e s f o r s o c i a l s e c u r i t y , r e t i r e m e n t , and group in s u r a n c e p l a n s , and c o s ts o f i n d i r e c t l a b o r . I t was o r i g i n a l l y f e l t t h a t th e way t o e s t im a t e t h e s e a c c o u n ts was to f i r s t e s t im a t e th e number o f i n d i r e c t p e r s o n n e l . The c o s t s would th e n be e s tim a te d as a f u n c t i o n o f i n d i r e c t p e r s o n n e l a lo n e o r th e sum o f b o th i n d i r e c t and d i r e c t p e r s o n n e l. An a p p a r e n t p o or r e l a t i o n s h i p betw een d i r e c t and i n d i r e c t p e r s o n n e l p re v e n te d t h i s a p p ro a ch . In e n g in e e r i n g , th e was only 0 .1 4 , w h ile i n th e f a c t o r y i t was 0 .3 9 . I t was t h e r e f o r e d e c id e d t o u se only d i r e c t p e rs o n n e l i n th e r e g r e s s i o n s . Here i t i s r e c o g n iz e d t h a t an i m p l i c i t f o r e c a s t i s made, i . e . , i t i s assumed t h a t th e number o f i n d i r e c t p e rs o n n e l w i l l p a r a l l e l th e number o f d i r e c t p e r s o n n e l . T his i s ad eq u a te as long as th e number o f i n d i r e c t p e r s o n n e l rem ain f a i r l y sm a ll as compared to th e number o f d i r e c t p e r s o n n e l. INDIRECT LABOR The i n d i r e c t l a b o r acco u n t i n a l l t h r e e p o o ls i s used t o a ccu m u late expenses f o r th o s e w o r k e rs ' s a l a r i e s who a r e n o t c h a rg in g d i r e c t l y t o a c o n t r a c t . I t would be e x p e c te d t h a t a wage v a r i a b l e sh o u ld a p p e a r In th e f i n a l e q u a t io n , p lu s some v a r i a b l e t h a t l i n k s i n d i r e c t l a b o r to th e o v e r a l l a c t i v i t y o f th e Firm . Examples o f th e s e l a t t e r v a r i a b l e s a re d i r e c t l a b o r d o l l a r s , d i r e c t h o u r s , and d i r e c t p e rs o n n e l. The r a t i o n a l e h e re i s t h a t th e number o f i n d i r e c t w orkers i s d i r e c t l y r e l a t e d t o th e number o f d i r e c t w orkers (o r t h e i r manhours o r d i r e c t l a b o r e x p e n s e s ) , and t h e i r s a l a r i e s a re com parable. E n g in e e rin g I n d i r e c t Labor A good f i t (0 .8 0 ) was o b ta in e d w ith e n g in e e r in g wage and h ours as th e in d e p e n d e n t v a r i a b l e s . The r e s u l t a n t f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t , a lth o u g h somewhat h ig h e r (F ig u re 2 ). EINDIRECT = -5*12 + 162.91 EW + 0. 3693 EH (5 2 .9 4 ) (0.1 513 ) R2 = 0 .7 9 5 ; VN = 1 .5 8 ; GQ = 9-31 A com parable f i t can be o b ta in e d u s in g wage and p e rs o n n e l as th e in d e p e n d e n t v a r i a b l e s . F a c to ry I n d i r e c t Labor F a c to ry d i r e c t wage (FW) and h o u rs (FH) were used as th e in d e p e n d e n t v a r i a b l e s i n t h i s l a r g e a c c o u n t. The f i t w ith th e s e v a r i a b l e s i s good (0 .8 9 ) and i s c o n s i d e r a b ly b e t t e r th a n w ith th e wage and p e r s o n n e l v a r i a b l e s . The r e s u l t a n t f o r e c a s t compares very w e ll w ith th e s u b j e c t i v e f o r e c a s t u n t i l 1973» b u t exceeds i t beyond t h a t p o i n t (F ig u re 3)» I t would seem l i k e l y t h a t th e s u b j e c t i v e f o r e c a s t may be a l i t t l e d e f l a t e d beyone 1973 ( i n l i g h t o f th e n e a r - p e r f e c t agreem ent b e f o r e ) . T his problem i s f a i r l y c o n s i s t e n t in many a c c o u n ts i n th e f a c t o r y p o o l. C o s t ( $ / 0 o o) I f 6 0 r IhOQ I f o o 1 2 0 0 l o o o %oo boo foo zo o 0 EINDIRECT = -542 + 162.91 EW + 0.3693 EH (5 2 .9 4 ) (0 .1 5 1 5 ) R2 = 0.795 VN = 1 .58 GQ = 9.31 .• * ^ .O * * • ° P * X * o Q'" x * x O.. Q .-' O o o ST 6 0 (ot- fey 66 6> i 70 73- 7Y 7 < o 7 g ~ FIGURE 2.— ENGINEERING INDIRECT LABOR COST ( $ / 6 6 6 ) 1 0 0 0 FINDIRECT = -2149 + 916.84 FW + 1.2783 FH %G00 (204 .98) (0.1951) R2 = 0-891 t7 6 0 0 \ VN = 1.33 GQ = 2.19 ( o O O O I - . X"-— x * 5~000 id d c ) .0 -. x * Sooo o-.... .o" X---- P'* ° o 0 . „ • v 600 / 0 6 0 •x x x * X JC X O » ■ « * « » ■ 1 1 « ■ - r a 6 0 & -J- 6V 66 6 T 7 d 7S^ 7 K 7 ^ FIGURE 3.— FACTORY INDIRECT LABOR FINDIRECT = -2149 + 916.84 FW + 1.2783 PH (204.98) (0.1951) r2 = 0.891; VN = 1.33; GQ = 2.19 A d m in is tr a tiv e I n d i r e c t Labor An e x p e c te d l a r g e i n c r e a s e In Firm com m ercial s a l e s cau se s problem s i n th e a n a l y s i s o f t h i s a d m i n i s t r a t i v e a cc o u n t (and i n many o t h e r a d m i n i s t r a t i v e a c c o u n ts ) . The d i f f i c u l t y a r i s e s becau se th e number o f f a c t o r y p e rs o n n e l i s e x p e c te d t o r i s e d r a m a t i c a l l y . T h is l a r g e i n c r e a s e w i l l o c c u r p r i m a r i l y among f i n a l a s s e m b le r s , and th e s e w orkers a re r e l a t i v e l y u n t r a i n e d and , c o n s e q u e n tly , lo w e r- p a id . I t i s n o t s u r p r i s i n g , t h e r e f o r e , t o f i n d t h a t th e a v erag e f a c t o r y wage i s e x p e c te d t o d e c l i n e f o r s e v e r a l y e a r s . A lso , th e a v erag e Firm wage ( i . e . , th e w eig h ted a v erag e o f th e e n g in e e r in g and f a c t o r y wage) a ls o i s e x p e c te d to d e c l i n e even thoug h e n g in e e r in g wages a re b u o y a n t. The i m p l i c a t i o n s f o r t h e a d m i n i s t r a t i v e p o o l a re c l e a r : a d m i n i s t r a t i v e s a l a r i e s w i l l n o t undergo a d i l u t i o n ( a t l e a s t n o t as much a d i l u t i o n ) as f a c t o r y o r FIRM s a l a r i e s . The only p a th s t i l l open i s to assume t h a t a d m i n i s t r a t i v e s a l a r i e s w i l l p a r a l l e l e n g in e e r in g s a l a r i e s . T h is i s n ’t p a r t i c u l a r l y u n re a s o n a b le s in c e many o f th e a d m i n i s t r a t i v e p e r s o n n e l a r e as w e ll t r a i n e d as th e e n g i n e e r s , so th e s a l a r i e s sh o u ld move more o r l e s s t o g e t h e r . 100 The b e s t r e g r e s s i o n e q u a tio n f o r th e l a r g e a d m in i s t r a t i v e i n d i r e c t l a b o r i s b ased on e n g in e e r in g d i r e c t wage (EW) and e n g in e e r i n g p lu s f a c t o r y d i r e c t p e r s o n n e l (EFP). The f i t i s good (0 .8 0 ) and th e r e s u l t a n t f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t ( a lth o u g h more o p t i m i s t i c beyond 1 9 7 1 ), as shown i n F ig u re AINDIRECT = -1437 + 338.99 EW + 1.0751 EFP (16 2.06 ) (0 .641 7) R2 = 0 .7 9 6 ; VN = 1 .7 4 ; GQ = 1.72 A second p o s s i b i l i t y c o n ta in s as v a r i a b l e s e n g in e e r in g p lu s f a c t o r y p e r s o n n e l (as above) p lu s e n g in e e r in g and f a c t o r y wage. The f i t i s b e t t e r ( 0 . 9 2 ) , b u t th e r e g r e s s io n c o e f f i c i e n t s a re l e s s s i g n i f i c a n t , and th e f o r e c a s t has some downward b i a s . HOLIDAYS The h o lid a y a c c o u n ts e v id e n c e th e a p r i o r i im p re s s io n t h a t h o lid a y pay i s a f u n c t i o n o f th e wage r a t e and th e number o f p e r s o n n e l c o l l e c t i n g t h a t wage r a t e . Mote, how ever, t h a t th e d a t a a re a l l c o n s i s t e n t in term s o f th e number o f h o l id a y s g r a n te d i n 1969, namely t e n . I f th e number o f g r a n te d h o lid a y s i s e x p e c te d to i n c r e a s e , t h i s v /ill have a b u o y an t e f f e c t on th e f o r e c a s t . (See F ig u r e s 5, 6, and 7 .) Such an o c c u rre n c e can be in c o r p o r a te d i n t o th e overhead model m erely by a d j u s t i n g th e r e g r e s s i o n f o r e c a s t a p p r o p r i a t e l y . CO ST 7 0 0 0 r 7ooo &000 &000 ^joao 3o do 2-060 1 060 AINDIRECT = -1437 + 338.99 EW + 1.0751 EFP (1 62.0 6) (0 .6 41 7) R2 = 0.796 VN = 1.74 GQ = 1.72 x n * O X , x X •' x x x x -0—0 ..... ST 60 6 2 - 6Y 6 6 6 f 70 72- ~ * Y 7 *“ Y ^ y tn , FIGURE 4.---ADMINISTRATIVE INDIRECT LABOR C o s t (J> 1 0 0 6 ) EHOLIDAY = -142 + 27.81 EW + 0.4339 EP (5 .9 8 ) (0.037 4) r2 = o.984 VM =2.45 6 6 o l- GQ = 6 ,5 8 S d o 3(>o • x .O’* 0 - 6 v x ^ * 2-00 /d O ..©• "0F -G -0 ’ re 6o f o x f c * 6 6 fo r 70 7 3 L . 7 ? 70, 7 r Y SAK FIGURE 5.— ENGINEERING HOLIDAYS 7 0 0 Zoo 7oo 600 FHOLIDAY = R VN G Q 2 _ 83 + 0.0*1835 FDLD (0.0 082 9) 0.809 1.72 1.20 S ’ O O C O S T @ / o o o ) ‘ lOO 3 o o zo o x x / o * * * # .*0 * © " /o o S 8 60 62 6? 66 6 8 70 7*- 79 76 77 FIGURE 6.---FACTORY HOLIDAYS 103 COST Q iodo) goo 7oo i&o M oo 300 ^00 m AHOLIDAY = 2 + 0.00783 EFDLD ( 0 . 00128 ) R2 = 0.824 VN = 2.26 GQ = 1.85 v x - ~ X ' X x X X £& GO 62- & i 6 6 6 f f *3 7 2 . 7 ^ 7 s 7 9 FIGURE 7.— ADMINISTRATIVE HOLIDAYS 105 EHOLIDAY = - 142 + 27.81 EW + 0.4339 EP (5 -9 8 ) (0 .037 4) R2 = 0 .9 8 4 ; VN = 2 .4 5 ; GQ = 6.58 FHOLIDAY = 83 + 0.04835 EDLD ( 0 . 01 2 1 0 ) R2 = 0 .8 0 9 ; VN = 1 .7 2 ; GQ = 1.20 AHOLIDAY = 2 + 0.00783 EFDLD ( 0 . 00128 ) R2 = 0 .8 2 4 ; VN = 2 .2 6 ; GQ = 1.85 VACATIONS The v a c a t i o n a c c o u n ts a re q u i t e s i m i l a r t o th e h o lid a y a c c o u n ts . The t o t a l pay g iv en t o em ployees depends p r i m a r i l y on th e number o f employees and th e wage r a t e e a rn e d . A lso p r e s e n t a r e e f f e c t s from o t h e r f a c t o r s such as changes i n lo n g e v i t y ( s in c e s e n i o r employees a re g r a n te d lo n g e r v a c a t i o n s ) and t u r n o v e r (w h erein employees l o s e t h e i r v a c a ti o n p r i v i l e g e s ) b u t t h e s e c o u ld n ’t be i d e n t i f i e d . The computed f o r e c a s t s compare w e ll w ith th e su b j e c t i v e f o r e c a s t , e s p e c i a l l y in th e e n g in e e r in g and a d m i n i s t r a t i v e p o o l s . ( F ig u re s 8, 9, and 1 0 .) The low er s u b j e c t i v e f o r e c a s t i n th e f a c t o r y p o ol could be a sim p le u n d e r e s tim a tio n o r an i m p l i c i t d e g r a d a tio n due t o r e c o g n i t i o n o f th e i n f l u x o f l e s s s e n i o r em ployees. EVACATION = -260 + 70.92 EW + 0.4364 EP (2 7 .0 2 ) (0 .1 691 ) R2 = 0 .8 5 8 ; VN = 2 .6 9 ; GQ = 10.83 C O S T 900 n o 760 ( boo soo 9oo 2 0 0 2 60 / OQ EVACATION = -260 + 70.92 EW + 0.4364 EP (2 7 .0 2 ) (0.169 1) R2 = 0.858 VN = 2.69 GQ = 10.83 X * X 9" " O ' ..O ’ ' • ••••• *•* JS' o o •© n.** ^ * * * v x o o < io fay 64 6 r 70 7Y ?r Y&M FIGURE 8.— ENGINEERING VACATIONS 106 I Zoo cosy ( $ / o o o ) IGOO lioo 1200 looo 8 00 Goo loo 200 FVACATION = -936 + 292.51 FW + O.5083 FP ( 6 8 . 16) (0.19 21) R2 = 0.848 VN = 1.58 GQ = 15.18 x * .'X Q . . ’o ...*o SB 60 6a. Cf 66 68 7 0 12 76 7£ y e * * . FIGURE 9.--FACTORY VACATIONS C o s T l boo) JOOr $00 700 Goo £ 0 0 ¥ 6 0 3 6 0 0-60 J60 AVACATION = -1^7 + 30.68 EW + 0.0759 EFP ( 7 - 22 ) ( 0 . 0286 ) R2 = 0.929 VN = 1.6 8 GQ = 6 .37 . * " * * * * * * x ..- x -• ■a o ...............‘ S’ S L O 6 ,2 . 4 / 6 6 7o 73- 7 ^ 7q , 7 f y FIGURE 10.— ADMINISTRATIVE VACATIONS 108 109 FVACATION = -936 + 292.51 PW + 0.5083 FP ( 6 8 . 1 6 ) ( 0 . 1921 ) R2 = 0 .8 4 8 ; VN = 1 .5 8 ; G Q . = 15.18 AVACATION = -147 + 30.68 EW + 0.0759 EFP ( 7 . 22 ) ( 0 . 0286 ) R2 = 0 .9 2 9 : VN = 1 .6 8 GQ = 6 .37 GROUP INSURANCE Group in s u r a n c e premiums a re p r i m a r i l y r e l a t e d to th e number o f p e o p le i n t h e i n s u r a n c e p l a n . In f a c t , th e s u b j e c t i v e f o r e c a s t was made by a p p ly in g a r a t e p e r p e rso n t o th e f o r e c a s t number o f w o rk ers i n each p o o l. I t would a p p e a r, how ever, t h a t th e r e l a t i o n s h i p i s more complex th a n t h a t , s in c e th e c o r r e l a t i o n s a r e a l i t t l e low, e s p e c i a l l y i n th e f a c t o r y p o o l ( 0 . 4 5 ) . Even th e s e r e g r e s s io n e q u a tio n s i n d i c a t e f u r t h e r c o m p lex ity s in c e th e i n t e r c e p t term s a re a l l l a r g e , im p ly in g more i s in v o lv e d th a n h e a d -c o u n t. C lose s c r u t i n y r e v e a l e d t h a t a l l fo u r group i n s u r ance a c c o u n ts showed a marked i n c r e a s e In p e r c a p i t a expenses betw een 1962 and 1 9 6 3. T h is i n c r e a s e was a r e s u l t o f a change in Firm p o l i c y w h erein em ployees no lo n g e r were r e q u i r e d to pay p a r t o f th e group in s u r a n c e premiums. R e g re s s io n e q u a t i o n s , t h e r e f o r e , were o b ta in e d on th e b a s i s o f th e d a ta f o r th e l a s t s i x y e a rs o n ly . These r e g r e s s i o n s were n o t t e s t e d f o r h e t e r o s c e d a s t i c i t y b e ca u se o f th e sm all sample s i z e . 110 I j I t was found t h a t th e o n ly c o n s i s t e n t and r e a s o n - i i a b le e q u a tio n s were th o s e in which p e r c a p i t a group I in s u r a n c e c o s t s were r e l a t e d t o th e lo g a r ith m o f TREND. ! Such a r e l a t i o n s h i p i s r e a s o n a b l e i f i t i s assumed t h a t th e l a r g e i n c r e a s e s i n in s u r a n c e c o s t s have a lr e a d y o c c u r re d and only m oderate i n c r e a s e s w i l l o c c u r i n th e f u t u r e . The r e s u l t a n t f o r e c a s t s compare w e ll w ith th e | s u b j e c t i v e f o r e c a s t s , as shown i n F ig u r e s 11, 12, and 13. j EGROUP/EP = 0.1026 + 0.2798 LOGTREND (0 .0 8 0 4 ) | R2 = 0 .7 5 2 ; VN = 4.22 I FGROUP/FP = 0.0390 + 0.3605 LOGTREND ! (0 .1 3 1 5 ) ; R2 = 0 .6 5 3 ; VN = 2 .1 3 I AGROUP/EFP = 0.00079 + 0.0545 LOGTREND | ( 0 . 0192 ) | R2 = 0 .6 6 7 ; VN = 2.06 ! RETIREMENT Funds ch arged t o th e r e t i r e m e n t p la n have very l i t t l e t o do w ith th e number o f em ployees a c t u a l l y r e t i r e d . Most o f th e s e funds a r e s e t a s i d e f o r f u t u r e r e t i r e e e s and c o n s e q u e n tly a re r e l a t e d t o em ployees in each p o o l and t h e i r wages. O th e r f a c t o r s which sh o u ld be p r e s e n t a re a v e ra g e age and s e n i o r i t y o f em ployees. | 900r c o s t Ciiooo') eoo 100 600 5 0 0 m 3 0 0 200 too EGROUP/EP = 0.1026 + 0.2798 LOGTREND (0.0804) R2 = 0.752 VN = 4.22 X V X .." y . •••• • - \ y •—-x ..... * X - X ' K 0 - a " ° o - o " 58 60 6 Z 69 66 68 70 72- 79 76 7 £ Y f * * FIGURE 11.— ENGINEERING GROUP INSURANCE 111 COST C $rooo) 1600 m o 1200 1000 800 600 voo 200 FGROUP/FP = 0.0371 + 0.3605 LOGTREND (0.1315) R2 = 0.653 VN = 2.13 * * * x x ...... ...-o’ O O . •• w o o o ■ 5 * 8 60 62 6H 66 68 70 7Z T*t 76 7B Y E A R FIGURE 12.— FACTORY GROUP INSURANCE ?60 C O S T Q$ /ooo) 200 7 00 boo 500 H O O 300 200 100 AGROUP/EFP = 0.00079 + 0.05^5 LOGTREND (0.0192) R2 = 0.667 VN = 2.06 O o o o Q . . a - o - o “ 'a X * - ' x * K A C * * X X " SB 60 62. 67 66 6<r TO 72 77 76 78 Y e m FIGURE 13.— ADMINISTRATIVE GROUP INSURANCE I l l i | ;E n g in e e rin g and A d m i n is tr a t iv e R e tire m e n t Good f i t s were o b ta in e d f o r th e e n g in e e r in g and a d m i n i s t r a t i v e p o o ls by u s in g wage and p e rs o n n e l v a r i a b l e s . The f o r e c a s t s compare very w e ll w ith th e s u b je c t i v e f o r e c a s t s ( F ig u r e s 14 and 15). ERETIRE = 1355 + 267.19 EW + 1.1834 EP ( 51 . 0 0 ) ( 0 . 3192 ) r2 = 0 .9 4 7 ; VN = 3 .1 1 ; GQ = 1.02 ARETIRE = -579 + 128.01 EW + 0.1064 EFP (3 3 .1 0 ) (0 .0 659 ) R2 = 0 .8 6 5 ; VN = 2 .2 1 ; GQ = 1.07 F a c to ry R e tire m e n t The f a c t o r y a cc o u n t was e x tre m e ly i n t r a c t a b l e . S e v e ra l e q u a tio n s were o b ta in e d w ith good f i t s (o v er 0.80) b u t t h e r e alw ays was a flaw e i t h e r i n term s o f wrong s i g n , low s i g n i f i c a n c e , a u t o c o r r e l a t i o n , o r very u n re a so n a b le f o r e c a s t . T y p i c a l l y , th e wage term domin a te d th e s e e q u a t i o n s , so r e t i r e m e n t payments were f o r e c a s t to d e c l i n e w henever wage r a t e s d e c l in e d . The r e a s o n b e h in d th e d i f f i c u l t i e s l i e s i n th e f a c t t h a t t h i s p o o l i s dom inated by a la r g e number of s e n i o r em ployees. Because o f t h i s , h igh r e t i r e m e n t e x p en d ig u res a r e a n t i c i p a t e d in th e n e a r f u t u r e , and th e s e r e s u l t i n h ig h p r e s e n t a l l o c a t i o n s o f fu n d s. As th e s e em ployees r e t i r e , s m a ll e r amounts w i l l be needed p e r a c t i v e employee i n o r d e r t o meet th e commitments. IQoo COST (£ /O O o ) I Goo IH oo l2oo /ooo 800 Goo Hoo "loo ERETIRE = -1355 + 267.19 EW + 1.1834 EP ( 5 1 . 0 0 ) ( 0 . 3 19 2 ) R2 = 0.947 VN = 3 - 1 1 GQ = 1.02 X'"X x y * < ? * * ‘* X x x 9"o 0 / o ..- - o o : ■ O se 60 6* . 6 8 70 7 2 . 7y 7* 78 FIGURE 14.— ENGINEERING RETIREMENT C o s t ($• /ooo_) ?00 $00 7oo coo S ’ O O io o 300 zoo m ARETIRE = -579 + 128.01 EW + 0.1064 EFP (33.10) (0.0659) R2 = 0.865 VN = 2.21 GQ = 1 .0 7 X X * * O ..••O ’-" * ■ “ x o * y .-6 o Q ’ - d-. o : O S'S Co &Z. G>¥ (o(* C f 7 o * 7 3 L 7 $ 76 Y e a a FIGURE 15.— ADMINISTRATIVE RETIREMENT 116 I t was t h e r e f o r e f e l t t h a t more work i s r e q u i r e d Ion t h i s a c c o u n t. T h is work would c e n t e r around p r o v id in g and u s in g age and s e n i o r i t y v a r i a b l e s i n e s t i m a t i n g th e a c c o u n t. Note t h a t s i m i l a r v a r i a b l e s would improve th e u n d e rs ta n d in g o f th e o t h e r t h r e e r e t i r e m e n t a c c o u n ts . However, t h e s e r e p r e s e n t no problem a t p r e s e n t becau se th e work f o r c e i s more h e te ro g e n e o u s i n age and s e n i o r i t y . SOCIAL SECURITY As w ith o t h e r l a b o r - o r i e n t e d a c c o u n ts , th e s o c i a l s e c u r i t y e x p en ses seem t o be r e l a t e d t o p e rs o n n e l numbers and wages. E n g in e e rin g S o c i a l S e c u r i t y Payments As w ith a lm o st e v ery o t h e r a c c o u n t, i t was easy to d e r iv e a good f i t f o r th e e n g in e e r in g s o c i a l s e c u r i t y a c c o u n t. The f i t was good (0 .9 1 ) and th e r e s u l t a n t f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t , a lth o u g h somewhat h i g h e r th ro u g h o u t (F ig u re 16 ). ESOCIAL = - 37 + 0.05086 EDLD ( 0 . 00536 ) R2 = 0 .9 1 9 ; VN = 1 .8 5 ; GQ = 1.14 Fa c t o r y S o c i a l S e c u r i t y The f i t f o r th e f a c t o r y a cco u n t was f a i r l y good (0 .7 9 ) when f a c t o r y wage and p e r s o n n e l a re th e e x p la n a to r y v a r i a b l e s . The f o r e c a s t , how ever, compares p o o rly w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 1 7 ). In t h i s c a s e , i t i s 900 600 :7oo 600 ESOCIAL = -37 + 0.05086 EDLD (0.00535) R2 = VN = GQ = 0.919 1.85 1.14 500 Co s t 3oo Zoo /00 O : 0 X x*. 'X'X X •o -o ' ° . O .6 -•.Q' 5B £ 0 £ 2 6V £6 6 8 7 0 72. 7 ^ 7 6 7 8 y e a * FIGURE 16.— ENGINEERING SOCIAL SECURITY 118 CO ST ( $ / 0 0 oN > IS 0 0 IG O Q HOO I2Q 0 1000 8oo G O O VOQ 2P0 PSOCIAL = -1107 + 230.70 PW + 0.8097 FP (8 9 .3 6 ) (0.251 9) R2 = 0.792 VN = 2.09 GQ = 2.19 ;x .0........ . 0 o o ..6 0 * X * x S3 6 0 6 y 6 f 7 < j 7 2 . 7 K 7 6 7 ^ FIGURE 17---FACTORY SOCIAL SECURITY 120 n e a r ly c e r t a i n t h a t th e s u b j e c t i v e f o r e c a s t i s to o low s in c e s o c i a l s e c u r i t y paym ents a re q u i t e n e a r ly p r o p o r t i o n a l t o p e r s o n n e l. The h i g h e r f o r e c a s t m erely r e f l e c t s th e l a r g e i n c r e a s e i n f a c t o r y em ployees. PSOCIAL = -1107 + 230.70 PW + 0.8097 FP (8 9 .3 6 ) (0 .2 5 1 9 ) R2 - 0 .7 9 2 ; VN = 2 .0 9 : GQ - 2.19 A d m in is tr a tiv e S o c i a l S e c u r i t y The a d m i n i s t r a t i v e s o c i a l s e c u r i t y account i m i t a t e s o th e r a c c o u n ts d e s c r i b e d abo ve. A good f i t (0 ,8 7 ) was o b ta in e d w ith e n g in e e r in g and f a c t o r y d i r e c t la b o r d o l l a r s as th e s i n g l e e x p la n a to r y v a r i a b l e . The r e s u l t a n t f o r e c a s t d iv e r g e s from th e s u b j e c t i v - f o r e c a s t , how ever, and ends up o v e r 100# g r e a t e r th a n th e s u b j e c t i v e f o r e c a s t by 1978 (F ig u re 1 8 ). The computed f o r e c a s t i s f e l t t o be s u p r e i o r in t h i s case b e c a u se o f i n c r e a s e d p e r s o n n e l r e q u ire d t o h a n d le th e l a r g e r w o rk lo ad . I t i s alm ost in c o n c e iv a b le t h a t s o c i a l s e c u r i t y payments (and t h e r e f o re p e r s o n n e l) would o n ly r i s e 23# when t o t a l s a l e s amost q u a d ru p le . T his i s b e ca u se th e number o f a d m in is tr a -i t i v e p e r s o n n e l must expand in o r d e r to a d m i n i s t e r th e i n c r e a s e d s a l e s ( a lth o u g h p e rh a p s n o t p r o p o r t i o n a t e l y ) . ! | A f o r e c a s e b a se d on a l i n e a r r i s e in p e rs o n n e l i s even j f u r t h e r above t h e s u b j e c t i v e f o r e c a s t , so i t i s f e l t t h a t ! th e s e l e c t e d r e g r e s s i o n f o r e c a s t i s r e a s o n a b le . T his i s ; e s p e c i a l l y t r u e in l i g h t o f th e o t h e r l a b o r - o r i e n t e d Joo C O S J ( $ /0 O O ) Qoo 7oo GOO Soo y 60 3oo 2 4 0 /O q ASOCIAL = -i|8 + 0.01315 EFDLD ( 0 . 00180 ) R2 = 0.869 VN = 2.48 GQ = 2.69 O X * X X * « « p _ O'*© ■ t...........I.... I ,1....... I JT3 6 0 6 * - * 6 f e e 7 -2 79 7 6 v 'J ' yevH? FIGURE 18.— ADMINISTRATIVE SOCIAL SECURITY 121 122 a c c o u n ts whose a c c e p t a b l e r e g r e s s i o n f o r e c a s t s a re b ased on an i m p l i c i t i n c r e a s e i n a d m i n i s t r a t i v e p e r s o n n e l. ASOCIAL = - 48 + 0.01315 EFDLD (0.00 18 0) R2 = 0 .8 6 9 ; VN = 2 .6 9 ; GQ = 2.48 I I I . EQUATIONS FOR OTHER MAJOR-POOL ACCOUNTS SUPPLIES The term " s u p p l i e s '' r e a l l y r e f e r s to a t o t a l o f th e amoungs c o n ta in e d i n th e fo llo w in g a c c o u n ts , o f which only a p o r t i o n a r e c o n ta in e d i n a s i n g l e p o o l: a. Shop Supplies b. Perishable Tools c. Perishable Factory Equipment d. Low Value Factory Equipment e. Perishable Office Equipment f. Low Value Office Equipment g- Returnable Conatiners h. Gasoline i. Postage J. Badges and Identification k. Blueprint and Photography 1. Printing and Art Because t h e s e a r e so d i v e r s e , th e a g g re g a te d a c c o u n ts a re r e l a t i v e l y h a rd t o f i t . E n g in e e rin g S u p p lie s T h is a g g re g a te d a c c o u n t i s r e l a t i v e l y s m a ll, and i t i s s u r p r i s i n g to d i s c o v e r t h a t t h e r e i s alm ost no c o r r e l a t i o n betw een i t and th e e x p e n d itu r e o f e n g in e e r in g l a b o r . T his i s b e ca u se some o f th e a c c o u n ts w i th in th e t o t a l a re v a r i a b l e and depend on th e s ta g e o f e f f o r t . For exam ple, th e p r i n t i n g and a r t acco u n t depends on w h ether many of th e e n g ie e r s a re w orking on p r o p o s a ls i n an a tte m p t t o o b t a i n new b u s i n e s s o r w orking on o l d e r l i n e s o f b u s i n e s s . A com prehensive s e r i e s o f r e g r e s s i o n s were run on th e d a ta f o r t h i s a c c o u n t, and th e o nly one t h a t seemed w orthw hile i s th e f o llo w in g f u n c t i o n . ESUPPLZ = H 2 + 8.31 LOGPROFIT = 1 . 6 7 TREND (3 .1 5 ) (1 .4 1 ) R2 = 0 .5 1 7 ; VN = 2 .2 0 ; GQ = 2.10 The f i t i s n ’t to o good and th e s i g n i f i c a n c e l e v e l on th e tr e n d v a r i a b l e i s p o o r. However, i t a p p ea rs t h a t s u p p l i e s : are a t l e a s t somewhat lin k e d to p r o f i t s . T his p ro b ab ly would n o t be s u r p r i s i n g t o an employee who has l i v e d I th ro u g h s e r i o u s c u tb a c k s when p r o f i t s were low. Such c a re in expending s c a r c e funds re a c h e s t o th e r e s e a r c h b u d g e ts ! from which come some o f th e funds t h a t p ro c u re equipm ents J j t a b u l a t e d in th e su p p ly a c c o u n ts . ! I While a n o th e r e q u a tio n c o n ta in in g an a c t i v i t y > v a r i a b l e would have been p r e f e r r e d , th e s e l e c t e d e q u a tio n j 124 does seem t o f i t th e h i s t o r i c a l d a t a f a i r l y w e ll. T h is e q u a tio n a l s o p r o v id e s a r e a s o n a b l e f o r e c a s t (F ig u re 19). I t could be t h a t a d d i t i o n a l d i s a g g r e g a t i o n i s r e q u i r e d b e f o r e a r e a l l y d e s i r a b l e f u n c t i o n can be d ev elo p ed . F a c to ry S u p p lie s C o n sid e rin g th e d i f f i c u l t y a s s o c i a t e d w ith th e e n g in e e r in g su p p ly a c c o u n t, th e f a c t o r y a cco u n t a t f i r s t seemed q u i t e s t r a i g h t f o r w a r d to e s t i m a t e . A good f i t (0 .8 1 ) can be o b ta in e d w ith f a c t o r y d i r e c t l a b o r d o l l a r s , and a f i t o f 0.60 can be o b ta in e d w ith f a c t o r y d i r e c t h o u rs . However, th e i n f l u x o f f i n a l assem bly w orkers i n d i c a t e s a s t r u c t u r a l change i n t h i s a c c o u n t. T his i s b e ca u se a sse m b le rs d o n ’ t "consume" as much p e r i s h a b l e e q u ip m e n t-y -e tc ., as th e re m a in in g f a c t o r y p e r s o n n e l. T h u s, a f o r e c a s t b ased on a s t r i c t t o t a l f a c t o r y d o l l a r s o r h ou rs r e l a t i o n s h i p w i l l o v e r e s t i m a t e th e e x p e n d itu r e s f o r s u p p l i e s . U n f o r t u n a t e ly , t h e r e a r e no o t h e r v a r i a b l e s t h a t p ro v id e b o th a good f i t and a good f o r e c a s t . What must be done i s to d i s a g g r e g a te th e f a c t o r y p o o l i n t o f u n c t i o n a l l a b o r groups and use th e n o n -a s s e m b le r group f o r f i t t i n g and f o r e c a s t i n g . I t was im p o s s ib le t o do t h i s f o r th e p r e s e n t stu d y p r i m a r i l y b e c a u se no manhour o r d o l l a r f o r e c a s t e x i s t s e x c e p t f o r th e f a c t o r y b ran c h as a whole. In o r d e r to d e v elo p a u s a b le f o r e c a s t , a sim ple e q u a tio n was used which c o n ta in e d o n ly TREND. The f i t i s COST ( 5 ? / O Q o ) fO ESUPPLY = H2 + 8.31 LOGPHOFIT - I .67 TREND 9 (3 .1 5 ) (1 .4 1 ) - R2 = 0.517 VN = 2.20 GQ = 2.10 70 ^ o G O o , . / 0 •O 70 ID 10 ■1-, 1 x X x jr $ ... : o :- * X x 7 r • \ X X «J3 60 6 z- fcy -7 V 7 C . 7 ? VGA* FIGURE 19.— ENGINEERING SUPPLIES 125 126 poor b u t r e p r e s e n t a t i v e o f th e d a t a ( 0 . 32) , and th e f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 20). FSUPPLIERS * 213 + 13.90 TREND (7 .1 9 ) R2 = 0 .3 1 9 ; VN = 1 .7 4 ; GQ = 6.49 In p a s s i n g , n o te t h a t t h i s i s p ro b a b ly a c o n s e rv a t i v e e s t i m a t e . The a sse m b le rs w i l l u t i l i z e some s u p p l i e s , so th e f i n a l t r e n d sh o u ld l i e somewhere above th e t r e n d i n d i c a t e d i n th e f i g u r e . A d m in is tr a tiv e S u p p lie s The a d m i n i s t r a t i v e s u p p l i e s acco unt was e s t im a t e d on th e b a s i s o f an e q u a tio n c o n ta in i n g e n g in e e r in g and f a c t o r y d i r e c t l a b o r d o l l a r s . T h is v a r i a b l e s u f f e r s from th e same d i f f i c u l t y as th e f a c t o r y s u p p l i e s a cc o u n t i n t h a t an o v e r e s t i m a t i o n i s l i k e l y . T his i s because a d m i n i s t r a t i v e n eed s p ro b a b ly w i l l n o t expand p r o p o r t i o n a l l y t o th e i n c r e a s e in f a c t o r y w o rk e rs. The f i t , how ever, i s f a i r l y good (0 .5 9 ) and th e r e s u l t a n t f o r e c a s t compares re a s o n a b ly w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 21 ). ASUPPLIES = - 7 + 0.03373 EFDLD (0.0 099 6) R2 = 0 .5 8 9 ; VN = 3-16; GQ = 5-19 SERVICES CHARGED The " s e r v i c e s c h arg ed " a cc o u n ts t a b u l a t e c h a rg e s i n c u r r e d by o t h e r groups o r companies and s u b s e q u e n tly COST (J> /oocd 960 $6 0 PSUPPLY = 213 + 13-90 TREND (7-19) r y , R2 = 0.319 7°° ’ VN = 1.7ft GQ = 6.49 (oOO £00 * X X X . # » ! • o ° ........... x 3oo o 0/V . cr" ° * o /JO O O o^-** . • 6 0 6 2 &V 66 6 r 7o 72- 7Y 2$ 7f FIGURE 20.— FACTORY SUPPLIES 127 ?oo r Co st & /o o o ) 700 700 6 00 SdO VO 0 3 0 0 2-do /O O 0 ASUPPLY = -7 + 0.03373 EFDLD ( 0 . 00996 ) R2 = 0.589 VN = 3.16 GQ = 5.19 X * / X .© ..o 0/ 0 O 0 * 0 S'F 6 ,0 6z UY & ( , 6 f 70 7 J L 7* 76 7 f Ve/h/^ FIGURE 21.— ADMINISTRATIVE SUPPLIES 128 ; 129 b i l l e d t o th e Firm . The o v e rh e ad e x p en ses I n c u r r e d by con t r a c t l a b o r p e rs o n n e l a l s o a r e c h arg ed t o th e e n g in e e r in g and f a c t o r y p o o ls . A ll t h r e e a c c o u n ts a r e v e ry s m a ll, and any e q u a tio n p r o v id in g a r e a s o n a b l e f o r e c a s t i s a c c e p t a b l e . In th e e n g in e e r in g p o o l , th e a c c o u n t was e s tim a te d j w ith e n g in e e r in g h o u rs and TREND. The f i t i s n ’ t to o good j ( 0 . 6 0 ) , b u t p ro b a b ly good enough f o r such a v a r i a b l e a c c o u n t. The r e s u l t a n t f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 2 2 ). The very sm a ll f a c t o r y a c c o u n t was e s t im a t e d w ith j only a TREND term . The f o r e c a s t i s q u i t e a c c e p ta b le (F ig u re 23 ). The low 122 i s a r e s u l t o f t h e a lm o st com- | p l e t e la c k o f s lo p e i n th e f i t t i n g e q u a t io n , s in c e v i r t u a l l y no v a r i a t i o n i n y can be e x p la in e d by TREND when | 23 i th e c o e f f i c i e n t i s so s m a ll. j | The a d m i n i s t r a t i v e a c c o u n t was e s tim a te d w ith only I i j e n g in e e r in g d i r e c t la b o r d o l l a r s . The computed f o r e c a s t j l i e s above th e s u b j e c t i v e f o r e c a s t (F ig u re 2 4 ), b u t i n : l i g h t o f th e h i s t o r i c a l d a t a , t h e computed f o r e c a s t i s ! i c e r t a i n l y a c c e p t a b l e . j ECHARGE = -23 + 0.0644 EH - 2 .9 8 TREND (0.0 204 ) ( 1 .1 4 ) R2 = 0 .5 9 6 ; VN = 3 .8 1 ; GQ = 2 .3 5 2% o r d e c a i E z e k ie l and K arl A. Fox, op. c i t . p. 191. COST CP/000) 70 L o SO H O 30 ZO 10 -10 -ZO ECHARGE = 2 _ = VN GQ -2 3 + 0.0644 EH - 2.98 TREND (0 .0 2 0 4 ) (1 .1 4 ) 0.596 3.81 2.35 * a- • o '. o; o * 'P .-* j < X X X X X X X 66 UZ 70 72. 77 76 7S FIGURE 22.— ENGINEERING SERVICES CHARGED 130 C o s t C 4 > looo) f o fo • FCHARGE = 3.3 - 0.08 TREND ( 0 . 08 ) 16 R2 = 0.109 VN = 2.56 ( J O Sb H O 30 20 lb GQ = 1.57 x 9..-O--0...Q..P.. ... . X . . . x V fl 6 0 < o 2 . (oi Ub bg 70 72. 7H 76 7* 'i£A-R FIGURE 23.— FACTORY SERVICES CHARGED CoS7* ( j£/ood) 90 80 70 60 so H O 30 20 J0 ACHARGE = - 8 .4 + 0.00311 EDLD (0.0 006 9) R2 = 0.715 VN = 2.28 GQ = 2.36 * •« •• • . •* 0.- * . * . . . . . \ - °.-’o ° *'X’ XX XX .X X- X’ Y fll n ' ' ^ ' 1 1 \ . r .. I .1 SB '"'Co 62. cy C 6 > C8 70 7 2 - 79 76 7a FIGURE 24.— ADMINISTRATIVE SERVICES CHARGED 132 ! 133 :PCHARGE - 3 .3 - 0.08 TREND j (0 . 08) R2 = 0 .1 0 9 ; VN = 2 .5 6 ; GQ = 1 .5 7 - 1ACHARGE = - 8 . 4 + 0.00311 EDLD (0.0 006 9) R2 = 0 .7 1 5 ; VN = 2 .2 8 ; GQ = 2.36 TRAINING In a d d i t i o n t o t r a i n i n g done w i t h in t h e c o n f in e s o f th e F irm , some t r a i n i n g i s p u rch a se d from o u t s i d e . These e x p e n d i tu r e s a re q u i t e s m a ll i n th e e n g in e e r in g p o o l, b u t do t o t a l t o a s i g n i f i c a n t amount in th e a d m in i s t r a t i v e p o o l. S ince most o f th e s e expenses a r e i n c u r r e d j i in t r a i n i n g e n g in e e r s (no m a t t e r in which a cc o u n t t h e c o s t s j a re t a b u l a t e d ) , e n g in e e r in g a c t i v i t y v a r i a b l e s p ro v id e th e b e s t f i t f o r b o th a c c o u n ts . I E n g in e e rin g T r a in in g ! | The e n g in e e r in g account uses e n g in e e r in g d i r e c t j l a b o r d o l l a r s as th e s i n g l e v a r i a b l e t o o b t a i n a good f i t | ( 0 .9 0 ) . The r e s u l t a n t f o r e c a s t i s m in is c u le b u t s t i l l s f 1 compares w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 2 5 ). ETRAIN = - 0 . 3 + 0.00045 EDLD (0.00005) R2 = 0 .9 0 5 ; VN = 2 .5 0 ; GQ = 2.79 A d m in is tr a tiv e T r a in in g The c o e f f i c i e n t o f d e te r m in a tio n i s 0.76 f o r th e 1 a d m i n i s t r a t i v e t r a i n i n g account when th e lo g a r ith m of t r e n d i s u se d as th e s i n g l e in d ep e n d en t v a r i a b l e I n 10 COST @ /o o o ) fO 70 ETRAIN = - 0 .3 + 0.00045 EDLD (0.00005) R2 = 0.905 VN = 2.50 (oO GQ = 2.79 SO </0 3° 3 0 /O Q - o . ^ - O - e r - O - e - y - O - ? " S~T Go 6 i_ 6V i> (o 6<T 7 0 7s*. 7K 7” 6 FIGURE 25.— ENGINEERING TRAINING 'e x p l a i n i n g t r a i n i n g c o s t s p e r e n g in e e r . T hat p ro b a b ly i s i o igood enough s i n c e t h i s a cc o u n t te n d s t o e v id e n c e some v a r i a b i l i t y due t o th e a r b i t r a r y n a t u r e o f e x p e n d i tu r e s . The r e s u l t a n t f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t in th e n e a r and f a r te r m , b u t t h e r e i s some d iv e rg e n c e betw een 1972 and 1976 (F ig u re 2 6 ). ATNG/EP = 0.00448 + 0.05220 LOGTREND ( 0 . 01032 ) R2 = 0 .7 6 2 ; VN = 2 .9 4 ; GQ = 2.12 SERVICES PURCHASED j Each m ajor p o o l has an a cc o u n t l a b e l e d " s e r v i c e s p u r c h a s e d " . I t I s w i t h in t h e s e a c c o u n ts t h a t e x p en ses f o r ; non-F irm employees a re t a b u l a t e d . In th e e n g in e e r i n g p o o l,; t h i s a cc o u n t r e p r e s e n t s paym ents t o c o n s u l t a n t s and o t h e r ; p r o f e s s i o n a l s e r v i c e s . In th e f a c t o r y p o o l , th e l a r g e s t i item s a re t r a s h pickup and c le a n i n g s e r v i c e s , w ith some i c o n s u l t a n t e x p e n se s. L egal and a u d i t i n g f e e s , r e t i r e m e n t j and sa v in g s p la n management f e e s , and some com puter p r o - i gramming expenses a re t a b u l a t e d in th e a d m i n i s t r a t i v e p o o l.! E n g in e e rin g S e r v ic e s P u rch ased The e n g in e e r in g a c c o u n t i s r e l a t e d t o t o t a l e n g in e e r in g p e r s o n n e l , a lth o u g h th e f i t i s p o o r ( 0 .2 9 ) . I t was n o t p o s s i b l e to d e r i v e a m e a n in g fu l e q u a tio n w ith any o f th e u s u a l v a r i a b l e s such as wage r a t e s , l a b o r d o l l a r s , t r e n d , o r p r o f i t s . T h is i s such a s m a ll a cco u n t t h a t a d d i t i o n a l e f f o r t does n o t seem t o be w a r r a n te d , cos7" (f/ooa) 90 r 80 70 60 so ¥0 30 - 20 - 10 ATNG = 0.00448 + 0.0522 LOGTREND (0.0 1 0 3 ) R2 VN GQ 0.762 2.94 2.12 * X X ■ s ' X .-•X X o / ° .-•O o & 0/ 1 _______I 58 6 0 (A £9 66 68 7 0 72. 7 9 7 t > y ^ M 7 8 FIGURE 26.— ADMINISTRATIVE TRAINING I e s p e c i a l l y s in c e th e computed f o r e c a s t compares so w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 2 7 ). ESERVICE = -4 + 0.0168 EP (0.0093) R2 = 0 .2 8 9 ; VN = 2 .0 8 ; GQ = 2.7 1 FACTORY SERVICES PURCHASED S e r v ic e s p u rc h a se d and a c c o u n te d f o r i n th e f a c t o r y p o o l r e l a t e p r i m a r i l y to h o u se k e e p in g f u n c t i o n s . T h is i s r e l a t e d to th e amount o f f a c i l i t i e s to be look ed a f t e r , which i n t u r n a re r e l a t e d t o th e work b e in g done i n ; th e f a c t o r y ( s in c e f a c i l i t i e s f o r th e o t h e r b ra n c h e s ; rem a in more o r l e s s f i x e d ) . F a c to ry d i r e c t l a b o r d o l l a r s i and wages were found to p ro v id e th e b e s t f i t ( 0 . 6 2 ) , and th e r e s u l t a n t f o r e c a s t compares w e ll w ith th e s u b j e c t i v e : f o r e c a s t (F ig u re 2 8 ). ; FSERVICE = -45 + 13.06 FW + 0.00 372 FDLD 1 ( 6 . 9 3 ) ( 0 . 00201 ) R2 = 0 .6 2 1 ; VN = 2 .1 0 ; GQ = 1.74 Admi n i s t r a t i v e S e r v ic e s P urchased I t was n o t p o s s i b l e t o f i n d a good f i t f o r t h i s j j a c c o u n t when any o f th e o p e r a t in g v a r i a b l e s were used i n I th e r e g r e s s i o n e q u a tio n . P a r t o f th e problem was found t o j be th e p re s e n c e o f a s p u rio u s d a ta p o i n t f o r 1968, b ro u g h t | i a b o u t by an u n u su a l amount o f p u rc h a se d o u t s i d e a s s i s t a n c e . ! T h is was d is c u s s e d w ith th e a cc o u n t f o r e c a s t o r who i n d i c a t ed t h a t th e d a ta would be more c o n s i s t e n t i f th e s e u n u su a l expenses were e li m in a te d . When t h i s i s done, th e C O S T ( j / o o o ) 90 ?0 ESERVICE = -4 + 0.0168 EP * (0.0 0 9 3 ) ^ * R2 = 0.289 VN = 2.07 6£>L GQ = 2.71 S'O .</0 36 'io / o - O . . - X -x ..... .....--- V— *C" "’ o x x * x x X x x « 1 ■5T 62. 6 / 66 6 T 7 o 72. 7 J ' 76. 7<T FIGURE 27.— ENGINEERING SERVICES PURCHASED lo C o s t ( $ / 0003 go 70 60 ^0 Vo 3o 2 o / 0 FSERVICE = -45 + 13.06 FW + 0.00372 FDLD (6 . 93 ) ( 0 . 00201 ) R2 = 0.621 VN = 2.10 GQ = 1 . 7 4 * X * / X o . . . o o &' o o 'O o ' • * 1 ■ 1 1 ■ 1 Sff 66 62. Ot Lt> i 8 7 0 7 2 . 7¥ 76 7 8 FIGURE 28.— FACTORY SERVICES PURCHASED 139 140 TREND v a r i a b l e p r o v id e s a f a i r f i t ( 0 . 3 5 ) , and is. l o g i - j j c a l l y c o n s i s t e n t as w e l l . Such t h in g s as a u d i t i n g f e e s , i l e g a l f e e s , and s a v in g s and r e t i r e m e n t p la n management fe e s can be e x p e c te d t o d r i f t upward more o r l e s s i n d e p en d en t o f th e s i z e o f th e Firm . The f o r e c a s t which i s j b ased on th e TREND v a r i a b l e compares q u i t e w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 2 9 ). ASERVICE = 39 + 2 .6 6 TREND ( 1 .2 9 ) R2 = 0 .3 4 6 ; VN = 1 .9 4 ; GQ = 2.80 ENTERTAINMENT An e n te r ta i n m e n t a c c o u n t a p p e a rs i n b o th e n g in e e r i n g and a d m i n i s t r a t i v e p o o ls . Because o f r e c e n t D efense D epartm ent p o l i c i e s , th e s i z e o f t h e s e a c c o u n ts has d e c lin e d c o n s i d e r a b ly d u rin g th e p e r i o d under a n a l y s i s . E n g in e e rin g E n te r ta in m e n t T h is a c c o u n t i s s m a ll th ro u g h o u t th e 1 0 -y e a r h i s t o r y , n e v e r e x c e e d in g $ 4 ,0 0 0 . A sim p le f o r e c a s t was o b ta in e d w ith TREND and la g g e d e n te r t a i n m e n t . However, j th e p re s e n c e o f h e t e r o s c e d a s t i c i t y i n d i c a t e d a tr a n s f o r m a - I I i t i o n was r e q u i r e d . T h is c o n s i s t e d o f d i v i d i n g th ro u g h by j th e lag g ed e n te r ta i n m e n t v a r i a b l e . The f i t i s p o or ( 0 . 4 6 ) , j b u t th e f o r e c a s t compares w e ll w ith th e s u b j e c t i v e | f o r e c a s t (F ig u re 30). lo o C o s t ( 4 / 000) f o o 7 60 ASERVICE = 39 + 2 .6 6 TREND (1 .2 9 ) R2 = 0.346 VN = 1.94 GQ = 2.80 3 o o zo o O...J0L...O- -O—Or- 'd " o ’ * o " Q * * FIGURE 29.--ADMINISTRATIVE SERVICES PURCHASED T t y i 9 0 t Coer ( p t e o ) 8 6 76 CO SO V O 3 6 20 JO EENT(t) = n + 2.1866 1 ( E E N T (t-l) ’ E E N T (t-l) (0 .9 1 3 9 ) (( R2 = 0.461 VN = 2.68 GQ = 4.74 o ° o & " " Q ......." ’j..........-X -X . X X . V £0 Lt- t y U 68 7o 72. 7 / 76 yeA (\ .1589 TREND E E N T (t-l) .0647) JL. 78 FIGURE 30.— ENGINEERING ENTERTAINMENT SlTl 1*13 EENT ( t ) EENT ( t - 1 ) = 0.2610 + 2.1866 (0 .9 1 3 9 ) ----------------- -0 1589------------------- EENT ( t - 1 ) EENT ( t - 1 ) (0.061*7) R2 = 0.1*61; D W = 2.1*2; GQ = 1*. 71* A d m in is tr a tiv e E n te r ta in m e n t The h i s t o r i c a l d a ta f o r t h i s a c c o u n t show a p r o nounced downward t r e n d (F ig u re 2 1 ). A p r e l i m i n a r y r e g r e s s i o n e q u a tio n c o n ta in e d o nly th e TREND v a r i a b l e w ith e x t r a p o l a t i o n o f t h i s e q u a tio n r e a c h i n g z e ro i n 1973 s i . e . , one y e a r l a t e r th a n e n g in e e r in g . e v e r , i n d i c a t e d t h a t a s a l e s v a r i a b l e sh o u ld be added. A good f i t (0 .9 3 ) was o b ta in e d u s in g b o th TREND and t o t a l Firm S a le s (TSALES). The r e s u l t a n t f o r e c a s t compares q u i t e w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 31)• AENTERTAIN = 13 + 0.000233 TSALES - 1 .6 2 TREND R2 = 0 .9 3 1 ; VN = 1 .5 8 ; GQ = 1.92 COMPANY AIRCRAFT The company owns o r l e a s e s a i r c r a f t which a re used i n b o th th e e n g in e e r in g and a d m i n i s t r a t i v e p o o ls . Both a cc o u n ts were b e s t d e s c r ib e d by d i r e c t l a b o r d o l l a r v a r i a b l e s . Both computed f o r e c a s t s seem r e a s o n a b l e , b u t only th e a d m i n i s t r a t i v e f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t s . Because o f th e o u t s t a n d i n g f i t t o some h ig h ly v a r i a b l e d a t a , th e computed f i t i s f e l t to be a c c e p ta b le (F ig u re s 32 and 33)• A com parison w ith th e s u b j e c t i v e f o r e c a s t , how- (0.000 69) (0 .1 7 ) ? 0 ?0 60 SO COST (}t/aoo) 30 2 0 /O AENTERTAIN = R VN GQ 2 _ 13 + 0.000233 TSALES + 1, ( 0 . 000069) ( 0 , 0.931 1.58 1.92 O * * x X / © •• x 6*..o * Sg Co 61 69 6C c r 7o 73. 79 'ieAtK 62 TREND 17) x X ■ -7 C 7 / FIGURE 31.— ADMINISTRATIVE ENTERTAINMENT COST C $>/ooo) ?0 70 70 ■ G o SO 30 2o EAIRCRAPT = -32 + 0.14128 EDLD ( 0 . 01872) R2 = 0.877 VN = 3.0 1 GQ = 3.23 V o l . ° / ? . . • * X x X X /'• • ' /o \ • • • V o / \o • I n / V 6‘b i i > SS 6 0 U Z - (.Y L(, Qg 70 7*, 7K Z T y e /M FIGURE 32.— ENGINEERING COMPANY AIRCRAFT 1 0 0 2oo 7oo fooo C o s t £ 0 0 ( $ / a o o ) tfoo 3 0 0 Zoo JOo 0 AAIRCRAFT = R2 = VN = GQ = -137 + 0.01855 EFDLD (0.00472) 0.658 1.28 4.16 O ....Q..... .•••’ .*0 FIGURE 33.— ADMINISTRATIVE COMPANY AIRCRAFT EAIRCRAFT = -25 + 0.01413 EDLD (0.0 018 7) R2 = 0 .8 7 7 ; VN = 3 .0 1 ; GQ = 3.23 AAIRCRAFT = 137 + 0.01855 EFDLD (0.0 047 2) R2 = 0 .6 5 8 ; VN = 1 .2 8 ; GQ = 4.16 REPAIR AND MAINTENANCE Each pool contains an account for accumulating expenditures for repairing and maintaining facilities under the pool's jurisdiction. These are relatively difficult accounts to fit because much of the expenditures are arbitrary in timing. An attempt to account for this was made by utilizing a profit variable, but none of the resultant equations were reasonable, while the use of fixed assets as an explanatory variable resulted in extremely high forecasts which were discarded. It was not possible to discover an equation for estimative factory repair and maintenance that was also free of autocorrela tion . Both of the other two regression equations are based on direct labor expenditures. A trend variable was added to the engineering equation to improve the fit. Both of the resultant forecasts compare well with the subjective forecasts at least until 1975( Figures 34 and 35). EREPAIR = 15 + 0.01217 EDLD + 48.73 LOGTREND (0 .0 0 6 8 2 ) (2 2 .2 9 ) R2 = 0 .8 3 1 ; VN = 3 .0 6 ; GQ = 1.11 COST C$1000) 1 0 0 m 700 w o SbO 100 300 260 m EREPAIR = -137 + 35-36 EW + 0.1515 EP (1 2 .7 6 ) (0.0 799 ) R2 = 0.831 VN = 3-06 GQ = 1.11 .Q-"*............................------- * a . .» ■ ■ ................... o* *-O 58 60 62- bl 66 7d 7£ / / 76 7g FIGURE 3^.— ENGINEERING REPAIR AND MAINTENANCE COST ($/<?oo) 70 % o I d [pO SQ f a lb o AREPAIR = -30 + 0.00595 EFDLD (0.00229) / R2 = 0.459 X * x x VN = 2 .3 1 * ' " * GQ = 1.14 X t O o / 3d * /* ° o/ • - ,t / 0 O * -1 — . . « . FIGURE 35-— ADMINISTRATIVE REPAIR AND MAINTENANCE AREPAIR = -30 + 0.00595 EFDLD (0.00229) r 2 = 9 . 4 5 9 ; VN = 2 .3 1 ; GQ = 1.14 TRAVEL The e n g in e e r in g and f a c t o r y t r a v e l a c c o u n ts were found to r e l a t e w e ll t o e n g in e e r i n g d i r e c t l a b o r d o l l a r s . The r a t i o n a l e h e re i s t h a t most t r a v e l f o r th e p o o ls i s a s s o c i a t e d w ith p ro d u c t d e v elo p m en t, and r e l a t i v e l y l i t t l e w ith s u s t a i n i n g e f f o r t (such as p r o d u c t i o n ) . While th e a d m i n i s t r a t i v e p o o l a ls o r e l a t e d w e ll t o e n g in e e r in g d i r e c t l a b o r d o l l a r s (R2 = 0 . 6 5 ) s an e q u a t io n i n v o lv in g t o t a l d i r e c t l a b o r d o l l a r s was s e l e c t e d s i n c e a d m i n i s t r a t i v e t r a v e l p e r s i s t s th ro u g h o u t th e p r o d u c tio n s t a g e . I t was r * n e c e s s a r y to d iv id e t h e ,.f a c t o r y e q u a tio n by e n g in e e r in g d i r e c t la b o r d o l l a r s and o b t a i n a new f i t in o r d e r t o e li m in a te h e t e r o s c e d a s t i c i t y . The f i t s a r e a l l good and th e r e s u l t s compare q u i t e w e ll w ith th e s u b j e c t i v e < 5 f o r e c a s t s (F ig u re s 36 , 37,"an d 38) . ETRAVEL = 12 + 0.01974 EDLD (0.00293) R2 = 0 . 850 ; VN = 1 .4 8 ; GQ = I .13 FTRAVEL/EDLD = O.OI63 - 29.622 1 EDLD (9 .4 7 7 ) R2 = 0 .6 2 1 ; VN = 1 .6 0 ; GQ = 1.08 CRATING C r a tin g expenses a re t a b u l a t e d in a sm all f a c t o r y a c c o u n t. These expenses were found t o r e l a t e w e ll to C o ^ T C $ /to o ? ■> ?00 %0O % 0 L to S to io o 3oo ZOO Zoo ETRAVEL = 12 + 0.01974 EDLD (0.00293) R2 = 0.850 VN = 1.48 GQ = 1.13 S t 60 &-i- *Y 66 i>K 70 73^ 7 Y 7(0 'TE 4R FIGURE 36.— ENGINEERING TRAVEL 151 C o s t C$1000) 90 so 70 G O SO 70 30 20 to a--' * * • .o r • ' O 0 FTRAVEL/EDLD = 0.01632 - \ 0 R2 = 0.551 0 VN = 2.00 GQ = 4.98 (9 .4 8 ) SB & 0 6 2 - 6 Y 66 63 VeA-% 7 * > 72. 7</ 76 7 g FIGURE 37.— FACTORY TRAVEL 1/EDLD 152 C O S T ( g /O U f a o Z do 700 ioCO 57)0 3 00 2 - 6 0 / 6 0 ATRAVEL = 25 + 0.00674 EPDLD ( 0 . 00186 ) R2 = 0.621 VN = 1.60 GQ = 1.08 - * X x X o _ ........- • * * ' ®* * -© ■ ' O o -5T 6 0 6 2 - 6 / 66 ?0 7#- 7 K 7<b 7<T y^v*/^ FIGURE 3 8.— ADMINISTRATIVE TRAVEL 153 s p a r e s s a l e s , s in c e only s p a r e s ite m s need t o be c r a t e d . A good f i t (O .83) was o b t a i n e d , and th e r e s u l t a n t f o r e c a s t compares r e a s o n a b ly w e ll w ith th e s u b j e c t i v e f o r e c a s t , e s p e c i a l l y in th e e a r l y and l a t e y e a r s o f th e f o r e c a s t . However, th e p re se n c e o f a u t o c o r r e l a t i o n s u g g e s te d th e use o f f i r s t d i f f e r e n c e s r a t h e r th a n th e a b s o l u t e a m o u n ts. T h is f i t was 0.71, and th e f o r e c a s t was q u i t e s i m i l a r to th e o r i g i n a l f o r e c a s t , a lth o u g h s t i l l somewhat below th e s u b j e c t i v e f o r e c a s t (F ig u re 39). DELFCRATE = -0 .3 2 7 6 + 0.001115 DELSPLS ( 0 . 000270 ) R2 = 0 .7 1 0 ; VN = 1 .6 6 ; GQ = 2.3 8 PRODUCTION ANALYSIS T his sm a ll f a c t o r y a cc o u n t r e f l e c t s th e r e s e a r c h and t r o u b l e - s h o o t i n g a s p e c t s o f p r o d u c t i o n . C o n v e rsa tio n s w ith o v erhead a n a l y s t s have i n d i c a t e d t h a t e x p e n d itu r e s te n d to be somewhat a r b i t r a r y , so a p r o f i t v a r i a b l e was s u g g e s te d . A f te r a number o f a t t e m p t s , a f i t was found which c o n ta in e d p r o f i t and th e lo g a r ith m o f t r e n d . The r e s u l t a n t f o r e c a s t seems r e a s o n a b le in l i g h t o f r e c e n t e x p e r i e n c e , b u t i t compares somewhat p o o rly w ith th e s u b j e c t i v e f o r e c a s t (F ig u re *J0). However, some i n c r e a s e o v e r p r e s e n t l e v e l s i s l i k e l y b e c a u se f u t u r e r e s e a r c h i s l i k e l y t o be i n c r e a s e d . A lso , some i n c r e a s e i s c e r t a i n l y i n d i c a t e d b e cau se o f i n c r e a s e d p r o d u c tio n d i f f i c u l t i e s a s s o c i a t e d w ith th e i n c r e a s e d p r o d u c t i o n . On th e o t h e r # C O ST /Ooo) <f0 So 70 Co So ¥0 3d 2o /D DELFCRATF, = 0.3276 + 0.001115 DELSPARSLS ( 0 . 000270 ) R2 = 0.710 VN = 1.66 GQ = 2.38 o * X o- o o o "o"" " X 1 \ &3 Co CZ a U 68 70 72. 7? 76 7Q FIGURE 39.— FACTORY CRATING 155 COST (* tooo) Ho ?o 7* (oO ■ SD Ho 3 0 2o /0 0 x: X X X X X a-"* X o : o :Q PANALYSIS = 17 + 42.09 LOGTREND + 0.00389 PROFIT (1 5 .1 5 ) (0.00320) 0 ? ’ R2 = 0.762 * # # VN = 1.66 GQ = 2.39 SB 6 0 £>z. 6 / 6 6 6<f 7 o 7a 7 V 7 6 7 ? FIGURE 40.— PRODUCTION ANALYSIS 157 ! hand , t h e combined r e s u l t o f t h e s e two e f f e c t s w i l l p ro b a b ly n o t be p r o p o r t i o n a l t o t h e in c r e a s e d work done by th e f a c t o r y . T h is i s b e c a u se p r o d u c tio n can i n c r e a s e m an y -fo ld a f t e r th e u s u a l problem s have been s o lv e d j u s t once. In l i g h t o f t h i s , i t c o u ld w e ll be t h a t t h e s u b j e c t i v e f o r e c a s t i s to o low, c o n s i d e r i n g th e l a r g e e x p e c te d i n c r e a s e i n s a l e s p r e s e n t l y a n t i c i p a t e d . The e q u a tio n below sh o u ld be a c c e p ta b le f o r such a sm a ll and a r b i t r a r y a c c o u n t, even though th e s i g n i f i c a n c e l e v e l on th e p r o f i t v a r i a b l e i s low. ( t = 1 .2 ) FANALYSIS = 17 + 42.09 LOGTREND + 0.00389 PROFIT (1 5 .5 1 ) (0 .00 320 ) R2 = 0 .7 6 2 ; VN = 1 .6 6 ; GQ = 2.39 FREIGHT A ll f r e i g h t expenses a re charg ed t o t h e f a c t o r y p o o l. These ex p en se s a re p r i m a r i l y th e r e s u l t o f i n t e r company s a l e s , i . e . , work done f o r a n o th e r d i v i s i o n o f th e c o n g lo m era te c o r p o r a t io n and sh ip p ed t h e r e on c o m p le tio n . The f i t i s f a i r l y good w ith o n ly t h a t v a r i a b l e ( 0 . 7 4 ) , and th e r e s u l t a n t f o r e c a s t compares f a i r l y w e l l w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 41). FREIGHT = 75 + 0.00343 INCOMSLS (0 .0 007 1) R2 = 0 .7 4 4 ; VN = 2 .1 7 ; GQ = 3.67 HEAT, LIGHT, WATER, AND POWER T h is u t i l i t y a cco u n t r e p r e s e n t s a f a i r l y l a r g e a c c o u n t t h a t c o r r e l a t e s very w e ll w ith TREND p lu s COST Q f /ooo} fo o t %0o » 7 oo • (o b O S D O tfoo 3 60 Zoo (0 0 n 51 C o FPREIGHT = 75 + 0.00343 INTCOSLS (0.00071) R2 = 0.744 VN = 2.17 GQ = 3-67 y FIGURE 4l.— FREIGHT 159 f a c t o r y d i r e c t h o u r s . FUTILITY = 90 + 11.03 TREND + 0.03009 FDLH (0 .7 6 ) R2 = 0 .9 7 1 ; VN = 2 .8 8 ; GQ = 3.07 REAL PROPERTY TAXES A ll r e a l p r o p e r ty t a x e s a re c h arg ed t o t h i s acc o u n t In th e f a c t o r y p o o l. I t i s n o t s u r p r i s i n g t h a t r e a l p r o p e r ty ta x e s seem to fo llo w th e amount o f f i x e d a s s e t s , w ith an 0.88 c o e f f i c i e n t o f d e te r m i n a ti o n b e in g a c h ie v e d u s in g t h i s s i n g l e v a r i a b l e . The a d d i t i o n o f f a c t o r y d i r e c t l a b o r d o l l a r s l i n k s t h i s t a x a cc o u n t to th e s c a l e o f b u s i n e s s . With th e two v a r i a b l e s , th e f i t i s q u i t e good and th e c o e f f i c i e n t s s i g n i f i c a n t a t th e 99% l e v e l . FREAL = -2 + 0.02*18*1 FASSETS + 0.00917 FDLD ( 0 . 0 0 2 W (0 . 002*12) r2 = 0 .9 5 9 ; VN = 1 .8 6 ; GQ = 1.15 The r e s u l t a n t f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t , a lth o u g h th e l a t t e r l i e s somewhat below th e form er (maximum d i s p a r i t y i s abou t 3 0 $ ), as shown in F ig u re > 13. BUILDING AND PROPERTY RENTALS A ll b u i l d i n g and p r o p e r ty r e n t a l expenses a re t a b u l a t e d in th e f a c t o r y p o o l. T h is would a p p e a r t o be a c o n t r a d i c t i o n s in c e r e n t s were found to be c l o s e l y r e l a t e d t o e n g in e e r in g p e r s o n n e l and wage r a t e s . In o t h e r w ords, r e n t a l s o ccur i n re s p o n se t o e n g in e e r in g C O S T Qt/ooo) J o o TOO 70o ( d OO 5D 0 7 o o 3o o 2-dO / O o FUTILITY = 90 + 0.03004 FH + 11.03 TREND ( 0 . 01156 ) ( 0 . 7 6 ) R2 = 0.971 ' VN = 2.88 GQ = 3.07 x- K x x * O '* x , , . / 6 o 6?- <y 6 ? Vo 72- 7K 74 7 ^ FIGURE 42.— HEAT, LIGHT, WATER, AND POWER 160 CO S T C ^/ooo) 7oo $ 0 0 700 ( d6 o S b o iO o 3 o o Z o o / o o FREAL = -2 + 0.00917 FDLD + 0.0248 ASSETS (0.0 024 3) (0 .002 4) R2 = 0.959 VN = 1.86 GQ = 1.15 / * * x x * X X x . 0 - 0 / * * S f Go 62- 6Y 66 7 o 72- 76 7 ? FIGURE 43.— REAL PROPERTY TAXES 162 ; n e e d s , w hereas f a c t o r y needs a re u s u a l l y met th ro u g h use o f ; owned b u i ld i n g s and p r o p e r t y . The f i t i s good (0 .9 0 ) and th e r e s u l t a n t f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 4 4). FRENT = -232 + 44.89 EW + 0.3234 EP (1 5 .1 1 ) (0 .094 6) R2 = 0 .9 0 1 ; VN = 1 .9 4 ; GQ = 5-96 TELEPHONE AND TELEGRAPH T elephone and t e l e g r a p h ex p en se s r e l a t e w e ll w ith a l l p la n t- w id e a c t i v i t y m e a su re s, w ith th e v a r i a b l e " e n g i n e e r in g p lu s f a c t o r y d i r e c t l a b o r d o l l a r s " h a v in g th e b e s t c o r r e l a t i o n ( 0 .8 8 ) . The a d i t i o n o f th e t r e n d v a r i a b l e r e f l e c t s p ro b a b le i n c r e a s e d dependence on t h i s mode o f com m unication, b u t th e s i g n i f i c a n c e o f th e c o e f f i c i e n t s i s below th e 90% l e v e l . The r e s u l t a n t f o r e c a s t w ith the s i n g l e l a b o r d o l l a r v a r i a b l e compares w e ll w ith th e s u b j e c t i v e f o r e c a s t , a lth o u g h th e com parison i s u n u su a l (F ig u re 4 5 ). ATEL = -36 + 0.02174 EFDLD (0.00420) R2 = 0 .7 7 0 ; VN = 2 .0 5 ; GQ = 2.32 MISCELLANEOUS EMPLOYMENT EXPENSE The M i s c e lla n e io u s Employment Expense Account a p p ea rs only in th e a d m i n i s t r a t i v e p o o l and r e p o r t s ex p e n ses in c u r r e d i n r e c r u i t i n g new em ployees. I t c o n ta in s b o th th e a d v e r t i s i n g ex p en se s and th e moving expenses in c u r r e d f o r new em p loy ees, b u t n o t f o r i n t r o - c o r p o r a t i o n COST C4 /ooo) %60 loo Goo S d o Voo 3 o o 2 -o o / o o FRENT = -232 + 44.89 EW + 0.3234 EP (1 5 .1 1 ) (0.094 6) R2 = 0.901 VN = 1.94 GQ = 5.96 0..-0 J_____ I_____ 1 _____ I_____ I_____ I_____ I_____ 1 _____ L . FIGURE 44.— BUILDING AND PROPERTY RENTALS C o s t J o o 8 00 70o Goo s o o io o 3 o o 2 Oo / o o ATEL = -36 + 0.0217** EPDLD ( 0 . 00 * 120) R2 = 0.770 VN = 2.05 GQ = 2.32 * * v ........ * * X sc ■ Y X X o y ..•O ■••••Q..P’ • O -O ire 6 0 6 z- 4y 66 7o 7-Z 7K 76 78 Y ersM FIGURE * 15. — TELEPHONE AND TELEGRAPH 165 t r a n s f e r e e s . Of a l l th e o p e r a t i n g v a r i a b l e s , th e b e s t f i t i s o b ta in e d w ith th e v a r i a b l e t o t a l d i r e c t l a b o r d o l l a r s . A d d itio n a l v a r i a b l e s such as wage r a t e s o r t r e n d degrade ! th e s i g n i f i c a n c e l e v e l e x c e s s i v e l y . AMISC = -58 + 0.01178 EFDLD (0.00457) r2 - 0 .H54; VN = 2.-49; GQ = 1-09 A lthough th e R2 i s low (0 .4 5 )» th e r e g r e s s i o n v a lu e s do • ap p ro x im ate th e h i s t o r i c a l d a t a f a i r l y w e l l . The r e s u l t a n t f o r e c a s t compares q u i t e w e ll w ith th e s u b j e c t i v e f o r e c a s t th ro u g h o u t th e f o r e c a s t p e r i o d , a lth o u g h some s l i g h t d iv e rg e n c e o ccu rs i n l a t e r y e a r s (F ig u re 46). : EMPLOYEE MORALE j I The company expends some funds i n an a tte m p t to i | p ro v id e b e t t e r o v e r a l l w orking c o n d i t i o n s . These expenses- in c lu d e moneys f o r r e c r e a t i o n a l a c t i v i t i e s , employee c o u n s e lin g , and even a s i b s i d y t o th e c a t e r e r t h a t o p e r a t e s in company c a f e t e r i a s . A ll ex p en se s a re accum ulated in th e a d m i n i s t r a t i v e p o o l. A f a i r l y good f i t (0 .6 5 ) can be o b ta in e d u sin g only t o t a l d i r e c t la b o r d o l l a r s as th e e x p la n a to ry v a r i a b l e . The a d d i t i o n o f o t h e r v a r i a b l e s , however, I | r e s u l t s e i t h e r in poor s i g n i f i c a n c e l e v e l s o r wrong s ig n s I 1 | on th e c o e f f i c i e n t s . | The f o r e c a s t d e riv e d w ith th e t o t a l d i r e c t l a b o r I d o l l a r v a r i a b l e seems c r e d i b l e in l i g h t o f r e c e n t I CO ST C i /0 O o ) foo . g o o . yoo 6>6o S b o ¥60 3(50 260 /60 AMISC = -58 + 0.01178 EPDLD (0.00457) R2 = 0.454 VN = 2.49 GQ = 1.09 — . X .Xl~x— f f " " ' x * * x x x o a x p p . - ......... - ............ -V -' 0 v- « r - * o -1 - v i .... — i . _ . I................... i ..1 S 8 60 (oz. w 66 6 S 70 7 0 . 7 ^ 7 6 FIGURE 46.— MISCELLANEOUS EMPLOYMENT EXPENSE 166 167 e x p e r ie n c e . However, th e f o r e c a s t d iv e r g e s r a p i d l y from th e s u b j e c t i v e f o r e c a s t (F ig u re ^7)- T his would a p p e a r to be an i n s t a n c e o f an a r t i f i c i a l s u b j e c t i v e f o r e c a s t t h a t i f p r e d i c t s an a b s o l u te l e v e l i n g o f f o f e x p e n d itu r e s a t th e ! 1968 l e v e l , which seems t o be u n r e a l i s t i c in l i g h t o f th e 1 e x p e c te d l a r g e i n c r e a s e in th e number o f p e r s o n n e l . I An a l t e r n a t i v e r e g r e s s i o n f o r e c a s t i s b ased s o l e l y j on th e t r e n d v a r i a b l e . T h is has some c r e d i b i l i t y , s in c e 9 1 a p p a r e n t l y e x p en ses have been r i s i n g w ith tim e (R^ i s 0.9*Oj I While t h i s f o r e c a s t l i e s c l o s e r to th e s u b j e c t i v e f o r e - ! i I c a s t , th e o r i g i n a l f o r e c a s t b ased on l a b o r d o l l a r s would ] I I a p p e a r t o be s u p e r i o r b e cau se i t i s lin k e d t o th e s c a l e o f j o p e r a t i o n (and t h e r e f o r e p e r s o n n e l ) . ! AMORALE = -29 + 0.00^25 EFDLD ! (0.00111) | I r 2 = 0 . 6 M6 ; VN = 1.36 ; GQ = 1.39 ; CORPORATE ALLOCATION A whole a l l o c a t i o n to th e c o r p o r a t i o n i s expensed i n th e a d m i n i s t r a t i v e p o o l. The a p r i o r i im p re s s io n o f t h i s a c c o u n t i s t h a t t h e expense i s r e l a t e d t o some a c t i - j v i t y v a r i a b l e , p lu s p e rh a p s a t r e n d v a r i a b l e t o r e f l e c t ! i n c r e a s e d b u re a u c ra c y a t th e c o r p o r a te l e v e l . The c o e f - j I f i c i e n t s o f d e te r m in a tio n f o r th e b e s t t h r e e a c t i v i t y v a ri-: 1 a b le s l i e betw een 0.60 and 0 .7 0 , and a d d i t i o n a l v a r i a b l e s i d e g rad e th e s i g n i f i c a n c e e x c e s s i v e l y . j The s i n g l e v a r i a b l e s e l e c t e d was t o t a l d i r e c t I COST $/oac£> 9 0 So 7 o so H o 3 0 2 o /O AMORALE = -29 + 0.00*125 EPDLD ( 0 . 0 0 1 1 1 ) R2 = 0.6*16 VN = 136 GQ = 1.39 ° / X o o o o 9 - o . I_______* _______I SB 60 6z 6V 66 68 70 72. 7¥ 76 ~re ysA % FIGURE *17.— EMPLOYEE MORALE 168 ; 169 h o u r s , a lth o u g h t h i s had th e w o rs t f i t o f th e b e s t t h r e e . The o t h e r two v a r i a b l e s were f a c to r s ' v a r i a b l e s , and i t I j I would a p p e a r more r e a s o n a b le t o i n c o r p o r a t e a c t i v i t y f o r j j t h e whole o f th e Firm r a t h e r th a n f o r a s i n g l e b ra n c h . I F u rth e rm o r e , th e t o t a l d i r e c t h o u rs v a r i a b l e p ro v id e d th e i j b e s t com parison t o th e s u b j e c t i v e f o r e c a s t , and t h i s com- | p a r i s o n i s q u i t e good (F ig u re 4 8 ). ; ACORP = 109 + 0.06928 EFDH I (0.01978) R2 = 0 .6 0 5 ; VN = 1 .4 7 ; GQ = 1.35 1 iPROPOSAL EXPENSES j ■ — ■ - ■ . . . - ' E x p e n d itu re s f o r p r o p o s a ls t o o b t a i n new b u s in e s s I a re accum ulated in th e a d m i n i s t r a t i v e p o o l. Such e x p e n d i- i ; t u r e s a r e q u i t e a r b i t r a r y a t t im e s , and viere e x p e c te d to ; be d i f f i c u l t t o e s t i m a t e . None o f th e o p e r a t in g v a r i a b l e s had c o r r e l a t i o n s in e x c e ss o f 0 .4 0 , and i t was n o t p o s s i b l e t o combine s e v e r a l t o o b t a i n m ea n in g fu l c o e f f i c i e n t s !o f d e te r m in a tio n . I t was t h e r e f o r e d e c id e d t o make an 1 i e x c e p tio n o f norm al p o l i c y and use o n ly lo g a rith m o f t r e n d | ; t o f i t t h i s a c c o u n t. The t r e n d v a r i a b l e i s more a c c e p t - i a b le h e re th a n e lse w h e re b e ca u se o f th e n a tu r e o f th e !p r o p o s a l e x p e n se s. These e x p e n se s te n d t o re a c h a more : o r l e s s ste a d y s t a t e y e a r a f t e r y e a r , w ith some e s c a l a t i o n jb e c a u se o f i n c r e a s e d c o m p e titio n and improved c o n t r a c t - i s s u i n g p ro c e d u re s by c u sto m e rs. I t seems l i k e l y t h a t f u t u r e p ro p o s a l e x p en ses co u ld fo llo w a lo n g a lo g a r ith m C 0S7“ ($ /0O t>) 900 800 lo o ACORP = 103 + 0.06928 EPH ( 0 . 01978 ) R2 = 0.605 VN = 1 . 4 7 600 GQ = 1.35 S ' O O f o o O x . 3 6 0 . ° o ° -O’ * ........... * X ^ O P . - 0 2-66 1 0 0 -c? 5B 6 0 62 . 6 y 6 6 6 g 70 7Z. 7 ? 7-6 7 £ FIGURE 48.— CORPORATE ALLOCATION 171 t r e n d l i n e , and th e a c c e p t a b l e com parison w ith th e su b j e c t i v e f o r e c a s t b e a r s t h i s out (F ig u re 49). APROPOSAL = 196 + 200.11 LOGTREND j (8 2 .9 1 ) ! R2 = 0 .4 2 1 j VN = 2 .1 4 ; GQ = 1.24 j ADVERTISING EXPENSES A ll a d v e r t i s i n g expenses a re a cc o u n ted f o r i n th e ! i a d m i n i s t r a t i v e p o o l. These in c lu d e e x p e n d itu r e s f o r ; a d v e r t i s i n g f o r em ployees, s a l e s p ro m otio n and p u b l i c j i r e l a t i o n s ex p en se . The a p r i o r i im p re ss io n was t h a t t h e s e ! I ex p en se s would be c a u s a l l y lin k e d to p r o f i t s , b u t no such { t r e l a t i o n s h i p was u n c o v ered . A f a i r f i t (0 .6 3 ) was o b t a i n - j ed u s in g e n g in e e r in g p e rs o n n e l (EP) as th e s i n g l e e x p la n a to r y v a r i a b l e . The r a t i o n a l e h ere i s t h a t many o f t h e s e i i i e x p en ses a r e in c u r r e d d u rin g p ro d u ct d evelop m ent, and t h a t i s when th e e n g in e e r in g s t a f f i s e n la r g e d . The r e s u l t a n t f o r e c a s t l i e s below th e s u b j e c t iv e f o r e c a s t , b u t o n ly s i g n i f i c a n t l y so i n 1972-1975 (F ig u re 5 0 ). T h is a c c o u n t has a s t r o n g a r b i t r a r y e le m e n t, so a b e t t e r f i t and b e t t e r j i f o r e c a s t s a re u n d o u b ted ly d i f f i c u l t t o o b t a i n on t h e i | i b a s i s o f Firm o p e r a t in g v a r i a b l e s . I j i A second f o r e c a s t which was b ased on e n g in e e r i n g j d i r e c t l a b o r d o l l a r s had ro u g h ly th e same f i t (0 .5 9 ) b u t { i th e f o r e c a s t was s l i g h t l y worse in com parison t o t h e su b - | I j e c t i v e f o r e c a s t . C o s t fco 7oo S00 Hoo 360 2-60 J o o APROPOSAL = 196 + 200.11 LOGTREND (8 2 .9 1 ) R2 = 0.421 VN = 2.04 GQ = 1.24 0 O c x .••* 0 o .0 o ........... * o o $ 7 co 6 2 . ay 4 6 ?o -7«- 7 ^ 7 6 FIGURE 49.— PROPOSAL EXPENSES C O S T ($/OO0^ y o o t o o 7 0 0 GOo Sdo i o o 3 °o ZO o J 6 0 AADVERT = -67 + 0.2998 EP (0.08 17) R2 = 0.627 VN = 1.90 GQ = 3.61 x ^ - X X X * * X X X - ST 60 6* _ cy 66 6 T 7o 70. 7K 76 7.T Y S ^ FIGURE 50.— ADVERTISING EXPENSES 173 AADVERT = -67 + 0.2998 EP (0 .0 8 1 7 ) R2 - 0 .6 2 7 ; VN = 1 .9 0 ; GQ = 3-61 i FRANCHISE TAX The a d m i n i s t r a t i v e p o o l a l s o c o n ta in s an account f o r f r a n c h i s e t a x , i . e . , s t a t e c o r p o r a t e income t a x . T his acc o u n t o b v io u sly i s lin k e d t o p r i o r p r o f i t s . The b e s t r e g r e s s i o n e q u a tio n c o n ta in s p r o f i t s lag g e d b o th one y e a r and two y e a r s , and th e f i t i s good ( 0 . 8 4 ) , a lth o u g h i t te n d s t o u n d e re s tim a te v a r i a t i o n s somewhat. The r e s u l t a n t f o r e c a s t , how ever, compares q u i te p o o rly w ith th e s u b j e c t i v e f o r e c a s t , i n t h a t th e s u b j e c t i v e f o r e c a s t g r e a t l y exceeds th e computed v a lu e (F ig u re 51). S in ce th e C a l i f o r n i a income t a x r a t e p r e s e n t l y i s a s t r a i g h t 4% ( i . e . , n o n - p r o g r e s s i v e ) , i t would ap p ea r t h a t th e p r e p a r e r o f th e s u b j e c t i v e f o r e c a s t i s a n t i c i p a t i n g an o v e r a l l i n c r e a s e i n t h e r a t e a t which th e income ta x i s t o be a p p l i e d . 2* * »25 i t seems r e m a r k a b le , how ever, t o a n t i c i p a t e an i n c r e a s e which would d o u b le t a x e s p a i d , so th e < s u b j e c t i v e f o r e c a s t co uld be to o h ig h . A l t e r n a t i v e l y , t h e r e could be s i g n i f i c a n t c o m p le x itie s i n t h e ta x law t h a t would r e s u l t in a g r e a t e r t h a n p r o p o r t i o n a l in c id e n c e 24a. M. Sharp and B. F. S l i g e r , P u b lic Finance (Homewood: The Dorsey P r e s s , 1 9 6 4 ), p. 2 6 5 ' . 25r . w. Lindholm , P u b lic F in a n ce and F i s c a l P o lic y (New York: Pitm an P u b lis h in g C o r p ., 1950)> P* 519. C o s t C ^ /o o o ) QQO ' APRANCHISE(t ) = 50 + 0.0390 PROFIT(t-1) ( 0 . 0090 ) 1 00 . + 0.0140 PROFIT(t-2) (0.0 0 9 1 ) * 7 0 0 ■ R2 = 0.844 VN = 1.87 Goo S 0 0 H 60 3 o o ZOO 10Q GQ = 2.75 O r ° o -o o ■ 9* ■ - -'.1 -------- 1 ---------1 --1 —X—ft— --------------L . .5 3 *> * ..0 /6 2 . C y 6t 4 F 7 o 7 * 7 F 7* 7f FIGURE 51. "FRANCHISE TAX 175 176 o f t a x e s . In any e v e n t , h i s t o r y a p p a r e n tly i s a poor d e s c r i p t i o n o f th e f u t u r e f r a n c h i s e t a x e s . APRANCHISE ( t ) = 50 + 0.03887 PROFIT ( t - 1 ) + 0.01420 PROFIT (0 .0 0 8 9 7 ) (0.0 091 0) ( t - 2 ) r 2 = o .8 4 4 ; VN = 1 .8 7 ; GQ = 2.75 DUES AND DONATIONS The dues and d o n a tio n s a cco u n t i n th e a d m i n i s t r a t i v e p o o l i s f a i r l y s m a ll and somewhat v a r i a b l e . A some what p o or f i t ( 0 .3 5 ) was o b ta in e d w ith th e e n g in e e r in g p lu s f a c t o r y d i r e c t l a b o r d o l l a r s as th e s i n g l e in d e p e n d e n t v a r i a b l e . The r e s u l t a n t e q u a tio n compares w e ll enough w ith th e s u b j e c t i v e f o r e c a s t , c o n s i d e r i n g th e a r b i t r a r y n a tu r e o f b o th th e a cc o u n t and th e s u b j e c t i v e n a t u r e o f th e f o r e c a s t f o r t h i s ty p e o f a cco u n t ( F ig u r e 52). ADUES = 0.00294 EFDLD ( 0 . 00138 ) R2 = 0 .3 5 4 ; VN = 2 .2 3 ; GQ = 8.80 OTHER EXPENSES The c a te g o r y la b e le d " o t h e r ex p en se s" c o n ta in s th e r e s i d u e o f a c c o u n ts t h a t have n o t been t a b u l a t e d e ls e w h e re . The f a c t o r y c a te g o r y i s q u i t e s m a ll , w hereas th e e n g in e e r in g and a d m i n i s t r a t i v e a c c o u n ts a re l a r g e enough t o cause c o n ce rn . A ccounts such as t h e s e , o f c o u rs e , a re d i f f i c u l t t o e s t im a t e b e ca u se o f th e random n a tu r e of th e s m a ll a c c o u n ts c o m p risin g t h e t o t a l . The f a c t o r y a cc o u n t was ex tre m e ly s m a ll and t h e r e f o r e was n o t e s t im a t e d . C o s t ( 3 loao) 90 YD 76 (>0 so f t 30 2 o ADUES = 0.00294 EFDLD ( 0 . 00138 ) R VN GQ 0.354 2.23 7.80 .0 • • • . . . Q'' O • • • O x .... K X JO JL S T 6 0 6 Z 0 9 C.6 6>% -7 6 - 7 2 ^ ~7Y 7 6 7 f y * A R FIGURE 52.— DUES AND DONATIONS 178 ! Other Engineering Expenses The major Items comprising this category in the engineering pool are test models, relocation expenses, books and magazines, and state disability insurance. It i was found that a surprisingly good fit (0.82) could be obtained using engineering wage and direct labor dollars as the explanatory variables. The forcast compares fairly well with the subjective forecast, shown in Figure 53* EOTHER = - 23 + 12.34 EW + 0.00385 EDLD ( 4 .8 7 ) (0.00226) R2 = 0 .8 2 4 ; VN = 3-05; GQ = 4.08 Other Administrative Expenses Contained within this category are such items as medical and food service expenses, some relocation ex penses, and especially blueprint expenses. These were found to relate womewhat (0 .4 5 ) to engineering and factory ; direct labor dollars. The resultant forecast is good (Figure 5 4 ). AOTHER = 40 + 0.01296 EFDLD (0.00504) R2 = 0 .4 5 2 ; VN = 1 .2 0 ; GQ = 7.91 REDISTRIBUTION As discussed previously, the redistribution accounts represent the mechanism whereby costs are shuttled between overhead pools. This procedure permits the Firm to originally tabulate some expenses in a single pool (such as taxes or plant maintenance) but then to make C o s t ($/0OO> ?0o - %00 EOTHER = -23 + 12.34 EW + 0.00385 EDLD ( 4 .8 7 ) (0.00226) 700|* R2 = 0.824 VN = 3.05 GQ = 4.08 <£>00 S~oo H oo 3 oo •zo o / O O ■ x X 0 _ A Q x ........... 43 60 62. « / ££ LT 7a ?3L y y 7& 7 ? FIGURE 53.— OTHER ENGINEERING EXPENSES 179 <joo 800 700 GOd COST &oo ( .i/n o ) H o o 300 260 loo AOTHER = -40 + 0.01296 EFDLD (0-00504) R VN GQ 2 _ 0.452 1.20 7.91 x .. V , ..........................-X v . -L JL SB 6 0 62 . 6V U (* % 70 7Z 7 7 7 C . 7& FIGURE 54.— OTHER ADMINISTRATIVE EXPENSES 180 : i 8 i j i a f i n a l a d ju s tm e n t t o r e f l e c t th e t r u e l i a b i l i t y . The m ajor item s t h a t a r e r e d i s t r i b u t e d a re i n s u r a n c e , t a x e s , ! m a t e r i a l , p l a n t e n g i n e e r i n g , u t i l i t i e s , d a ta p r o c e s s i n g , i and a d m i n i s t r a t i v e s e r v i c e s . The e n g i n e e r i n g , a d m i n i s t r a t i v e , and s p a r e s r e d i s t r i b u t i o n a c c o u n ts ( th e l a t t e r d is c u s s e d i n th e s e c t i o n on s p a r e s ) a l l a re r e l a t i v e l y e asy t o e s t im a t e d . For e n g in e e r i n g , a good f i t (0 ,8 5 ) was a c h ie v e d u s in g e n g in e e r i n g d i r e c t l a b o r d o l l a r s and TREND. The a d m i n i s t r a t i v e acco u n t was f i t u s in g e n g in e e r i n g p e r s o n n e l , w ith a n e a r p e r f i t f i t b e in g a c h ie v e d (0 .9 9 )* The r a t i o n a l e h e re i s t h a t 50-70# o f th e r e d i s t r i b u t e d expenses t h a t o r i g i n a l l y a re t a b u l a t e d i n th e a d m i n i s t r a t i v e a cc o u n t a r e th e r e s u l t : o f e n g in e e r in g w ork, so e n g in e e r i n g v a r i a b l e s a re a c c e p t- p a b le . In th e s p a r e s p o o l, and R o f 0.69 was o b ta in e d u s in g s p a r e s s a l e s as th e o n ly in d e p e n d e n t v a r i a b l e . See F ig u re s 5 5 , 56, and 57 f o r a com parison betw een th e com p u te d and s u b j e c t i v e f o r e c a s t s . The f a c t o r y r e d i s t r i b u t i o n a c c o u n t, how ever, i s v i r t u a l l y im p o s s ib le t o f i t and s t i l l o b t a i n an a c c e p t a b le f o r e c a s t . T h is le d t o an i n v e s t i g a t i o n o f th e method ; used i n p r e p a r i n g th e s u b j e c t i v e f o r e c a s t . T h is f o r e c a s t : I p re p a re d as a r e s i d u a l a f t e r a c c o u n tin g f o r th e o t h e r r e d i s t r i b u t e d fu n d s . T hat i s , th e r e d i s t r i b u t i o n a c c o u n ts i can be r e p r e s e n t e d by th e f o llo w in g i d e n t i t y : i EREDIST + FREDIST + AREDIST + SREDIST + CREDIST = 0 i I so o t Co s t { $ lo o o ) 1600 m oo 1 2 0 0 1 0 0 0 800 G o o H O 0 Zoo EREDIST = -148 + 0.12303 EDLD + 16.04 TREND (0.0 536 7) (1 8 .2 4 ) R2 = 0.846 VN = 1 .5 1 GQ = 5.80 x x x . ■ o O Q ** * . .0 58 G O 61 Qt 66 10 7Z 11 16 78 FIGURE 5 5 .--ENGINEERING REDISTRIBUTION I I 182 C o s T c p o o o ) $00 7oo 606 500 io o 3 0 0 Zoo lO o FREDIST = 192 + 15.25 TREND (8 .5 7 ) R2 = 0.284 VN = 1 .1 8 GQ = 5.83 .O"-" O * o * X 5 8 <£o 62. 6 V 6 6 6 6 7o 7 2 7 7 75 7 8 FIGURE 5 6.— FACTORY REDISTRIBUTION -10001 COST C fiooo) -gooo -'jooo -0,000 ~5oo0 -H M -3000 -2000 -1000 AREDIST = 6 3 0 - 147.41 E¥ - 1.9547 EP (2 1 .4 9 ) (0 .134 5) R2 = 0.991 VN = 3.14 GQ = 1.55 x x x X x X x x ____ _ - ........... S3 GO GZ G1 U 68 70 1Z 71 7b 7 / yeftK FIGURE 57-— ADMINISTRATIVE REDISTRIBUTION 185 I where CREDIST r e f e r s t o c h a rg e s made by th e c o r p o r a t io n and r e d i s t r i b u t e d a lo n g w ith th e F i r m 's o v e rh e ad c h a rg e s . A f te r e s t i m a t i n g EREDIST, AREDIST, and SREDIST, th e s u b j e c t i v e f o r e c a s t o r p ic k e d a s i n g l e v a lu e f o r CREDIST and th e n found FREDIST as th e r e s i d u a l . T his p rodu ced th e f o r e c a s t which i s found i n F ig u re 56 . In th e y e a r s 1969-1972, f a c t o r y d i r e c t l a b o r e x p e n d itu r e s a r e e x p e c te d t o r i s e to 135$ o f th e 1968 l e v e l . In s p i t e o f t h i s , th e f o r e c a s t f o r FREDIST shows a d e c l i n e o f 60$ d u r in g t h i s p e r i o d . T his does n o t seem r e a s o n a b l e , and th e blame l i e s w ith th e u t i l i z a t i o n o f a r e s i d u a l t o p ro v id e th e f o r e c a s t . A much b e t t e r way i s t o e s t im a t e each r e d i s t r i b u t i o n a c c o u n t i n d i v i d u a l l y . Even i f th e f i v e r e d i s t r i b u t i o n a c c o u n ts do n o t sum to z e r o , th e i m p l i c i t e r r o r s a re d i s t r i b u t e d i n a l l f i v e a cc o u n ts r a t h e r th a n i n one r a t h e r sm a ll a c c o u n t. I t I s b a sed on th e above r e a s o n i n g t h a t th e computed f o r e c a s t p r e s e n te d In F ig u r e 56 i s f e l t to be s u p e r i o r to th e s u b j e c t i v e f o r e c a s t . A lthough b ased on a poor f i t ( 0 .2 8 ) , i t seems more r e a s o n a b le th a n a d e c l i n i n g f o r e c a s t when th e l a r g e r i s e in f a c t o r y a c t i v i t y i s c o n s id e r e d . I t i s n o t a good f o r e c a s t , b u t u n le s s a sub s t a n t i a l amount o f d i s a g g r e g a t i o n i s done so as to p e rm it f u l l e r u n d e rs ta n d in g o f th e a c c o u n t, i t i s as good as can ; be d e riv e d u s in g eco n o m etric m ethods. EREDIST = -148 + 0.12303 EDLD + 16.04 TREND (0 .0 530 7) (1 8 .2 4 ) r2 = 0 .8 4 6 ; VN = 1 .5 1 ; GQ = 5.80 186 FREDIST = 42 + 15.25 TREND (8 .5 7 ) R2 = 0 .2 8 4 ; VN = 1 .1 8 ; GQ = 5.83 AREDIST = -630 + 147.41 EW + 1.9547 EP (2 1 .4 9 ) (0 .1 3 4 5 ) R2 = 0 .9 9 1 ; VN = 3-1 4 ; GQ = 1.55 IV. EQUATIONS FOR SPARES POOL The s p a r e s o v e rh e ad p o o l I s s m a ll and somewhat u n iq u e. The p r i n c i p a l e x p la n a to r y v a r i a b l e i s s p a re s s a l e s (SPARSLS). S p ares d i r e c t p e r s o n n e l (SP) a ls o con -, t r i b u t e s to th e e x p l a n a t i o n o f some o f th e overhead a c c o u n ts . The p e r c e p t i v e r e a d e r may have d e t e c t e d a d e f e c t in th e use o f s p a r e s s a l e s as an e x p la n a to r y v a r i a b l e . T his re a s o n in g i s v a l i d b e c a u se s p a re s overhead c o s t s r e p r e s e n t a p o r t i o n o f t o t a l c o s t s , and s a l e s t y p i c a l l y a re a f u n c t i o n o f c o s t s p lu s some f e e . I t t h e r e f o r e would a p p ea r t h a t s p a r e s s a l e s r e a l l y i s an endogenous v a r i a b l e . On th e o t h e r hand, th e sim p le o n e - s ta g e l e a s t sq u a re s te c h n iq u e presum es re d u c e d -fo rm e q u a t i o n s , i . e , no endo genous v a r i a b l e s on th e r i g h t s id e o f th e e q u a l s i g n . 2^ Thus, o u r f i r s t im p r e s s io n I s t h a t we would v i o l a t e econo m e tr ic th e o ry i f we were to o b t a i n l e a s t s q u a re s 2^M. J . B rennan, P re fa c e t o Ec o n o m e tric s (C in c in n a t i : S ou th -W estern P u b l i s h i n g C o ., 1965)> P* $03- 187 | ! e s t im a t o r s t h a t a re b a se d on th e a ssu m p tio n t h a t s p a re s s a l e s i s an exogenous v a r i a b l e . However, a c a r e f u l lo o k a t th e v a r i a b l e " s p a r e s s a l e s " r e v e a l s t h a t i t r e a l l y i s an exogenous v a r i a b l e — a t l e a s t o p e r a t i o n a l l y i f n o t s t r i c t l y t h e o r e t i c a l l y . F o re c a s t s f o r s p a re s s a l e s a re n o t b a sed on a c o m p ila tio n of c o s ts p lu s th e f e e , b u t a r e b a se d on o t h e r s a l e s . For exam ple, i f th e Firm i s e s t i m a t i n g s a l e s o f some ite m a t $ 1 0 ,0 0 0 ,0 0 0 , th e f o r e c a s t i n g a n a l y s t w i l l re c o g n iz e t h a t an a d d i t i o n a l amount (say 20$) must be p rodu ced to p ro v id e rep la ce m e n t p a r t s o r " s p a r e s . " Such a s a l e s e s t im a t e t r u l y i s exogenous from th e p o i n t o f view o f th e overhead odrol, and can be used c o r r e c t l y in a re d u c e d -fo rm l e a s t sq u a re s r e g r e s s i o n . INDIRECT LABOR A good f i t f o r i n d i r e c t l a b o r (0 .9 8 ) was o b ta in e d u s in g s p a re s s a l e s and Firm wage as th e in d e p e n d e n t v a r i a b le s . The a d d i t i o n o f s p a r e s p e rs o n n e l r e s u l t e d i n un- a c c e p ta b ly low s i g n i f i c a n c e f o r th e r e g r e s s i o n c o e f f i c i e n t s . The f o r e c a s t b ased on t h i s e q u a tio n compares v e ry w e ll i w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 58 ). I SINDIRECT = -84 + 0.01920 SPARSLS + 56.03 EFW (0.001 16) (1 9 .3 5 ) R2 = 0 .9 8 2 ; VN = 1 .4 0 ; GQ = 13.88 FRINGE BENEFITS Since th e s p a r e s p o o l i s so s m a ll, f i v e overhead COST (J> /0 0 o ) ?<M> 8 0 0 700 < 6 o D S~00 *fc>0 3oo 2-00 /oo SINDIRECT = -84 + 0.0192 SPARSLS + 56.03 EFW ( 0 . 0016 ) ( 1 9 - 35 ) R2 = 0.982 VN = 1 . 4 0 GQ = 13.88 o • • A • '-P x x X x X •’••G b o ’ * • . x x O . P . . O ....... o S ? 60 62 - <>¥ 66 6 ? 70 7z_ 7 y 7 6 FIGURE 5 8.— SPARES INDIRECT LABOR 188 189 a c c o u n ts were a g g re g a te d p r i o r to d e te rm in in g th e r e g r e s s io n c o e f f i c i e n t s . The f i v e a re s p a r e s s a l a r y and h o u rly v a c a tio n and h o lid a y pay p lu s s p a r e s management i n c e n t i v e com pen satio n . The r e s u l t a n t a g g r e g a tio n (SPRINGE) i s s t i l l s m a ll, n e v e r e x c e e d in g $50,000 d u rin g th e 1 0 -y e a r h i s t o r i c a l p e r i o d . SPRINGE = 8 + 0.001599 SPARSLS + 0.2691 SP + 1 .2 5 TREND ( 0 . 000132 ) ( 0 . 1378 ) ( 0 . 88 ) R2 = 0 .9 9 2 ; VN = 1 .7 8 ; GQ = 9.28 The t r e n d v a r i a b l e h e re r e p r e s e n t s c o n s i d e r a t i o n of an e s c a l a t i o n o f b e n e f i t s as tim e goes on— a v a l i d a ssu m p tio n . T his e q u a tio n a l s o p r o v id e s a f o r e c a s t t h a t i s c l o s e r to th e s u b j e c t i v e f o r e c a s t th a n th e e q u a tio n w ith o u t th e t r e n d term (F ig u re 5 9 ). SOCIAL SECURITY Both s p a r e s s a l e s and s p a r e s p e r s o n n e l v a r i a b l e s were needed t o o b t a i n a good f i t f o r th e s p a re s s o c i a l s e c u r i t y a c c o u n t. The f i t i s good ( 0 .8 7 ) , b u t th e e q u a tio n e x h i b i t s h e t e r s c e d a s t i c i t y . The u s u a l t r a n s f o r m a ti o n e l i m i n a t e s t h i s , and th e r e s u l t a n t f o r e c a s t compares f a i r l y w e ll w ith th e s u b j e c t i v e f o r e c a s t (a lth o u g h somewhat: h ig h e r th ro u g h o u t th e 1 0 -y e a r p e r i o d , as shown i n F ig u re 60). ' SSOCIAL/SPARSLS = 0.0012 + 0.8024 SP - 7.45 1 j SPARSLS SPARSLS ! ( 0 . 1100 ) ( 2 . 78 ) r2 = 0 . 967 ; VN = 2 .9 3 ; GQ = 1.92 COST ( $ / o o o ) 70 f> 70 6 0 SO 7o 30 2 0 / o SFRINGE = 8 + 0.00160 SPARSLS + 0.2691 SP + 1 (0 .00 013 ) (0 .1 3 7 8 ) (0 R VN GQ 2 _ 0.992 1.78 9.28 X 'X 0- ..a O’ .O ’ j O " ST b o 6*- 6 Y 6 >b &T ?o 9 ^ . 7^ 7 $, 7 f y s /h /S FIGURE 59.— SPARES FRINGE BENEFITS .25 TREND . 28) 190 Co s t ($ /0 0 o ) H o 86 7o 60 So H o 30 1£> 10 SSOCIAL/SPARSLS = 0.0012 + 0.8024 SP/SPARSLS - 7.45 ( 0 . 1010 ) ( 2 . 78 ) R2 = 0.967 VN = 2.93 GQ = 1 . 9 2 o / o P. o o / ° -•■p rO.....-* 1 1 ' SQ 60 6a. 6 / 66 66 To 72- 76 78 FIGURE 60.— SPARES SOCIAL SECURITY 1/SPARSLS » 191 192 Note t h a t th e n e g a t iv e s ig n on th e r e c i p r o c a l o f SPARSLS i s n o t a problem s in c e t h i s becomes th e i n t e r c e p t term when th e e q u a tio n i s m u l t i p l i e d by SPARSLS. RETIREMENT The r e t i r e m e n t acco u n t in th e s p a r e s p o o l was found to r e l a t e w e ll t o b o th s p a re s p e rs o n n e l and t r e n d (R2 = 0,7*0- In i t s o r i g i n a l form , t h i s e q u a tio n showed ev id e n ce o f h e t e r o s c e d a s t i c i t y , b u t d i v i d i n g th ro u g h by s p a r e s p e r s o n n e l was s u c c e s s f u l in e l i m i n a t i n g i t . The r e s u l t a n t f o r e c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 6 1 ). SRETIRE -------------- = 0.4679 + 1-9302 T_ + 5.2 1 SP SP SP (0 .4 3 9 4 ) R2 = 0 .7 3 8 ; VN = 2 .2 8 ; GQ = 3.64 GROUP INSURANCE The b e s t f i t t h a t co uld be o b ta in e d f o r t h i s a cc o u n t was 0 . 58 , u s in g s p a re s s a l e s as th e only in d e p e n d e n t v a r i a b l e and s i x - y e a r s ' d a ta (due to th e change m entioned e a r l i e r ) . The agreem ent betw een th e r e g r e s s i o n f o r e c a s t and th e s u b j e c t i v e f o r e c a s t i s n o t to o good, b u t a c c e p t a b l e f o r such a sm a ll acco u n t (F ig u re 6 2 ). SGROUP = -1 + 0.00082 SPARSLS + 1.19 TREND ( 0 . 00022 ) ( 0 - 55 ) SUPPLIES T h is s i n g l e v a r i a b l e " s p a r e s s a l e s " i s a d e q u a te to d e s c r i b e t h i s very sm all a c c o u n t, and th e r e s u l t a n t f o r e - 9 0 $o 7& 60 SRETIRE/SP = 0.4679 + 1.9302 T/SP + 5.2 1/SP (0 .4 3 9 4 ) (2 .6 ) R VN GQ 2 _ 0.738 2.28 3.64 x x x X X X X X COST ( $ / 0 0 o ) SO V O 30 ■ 2. 0 /0 .-*o o..-6 I -I SB 6 0 * > Z 66 68 70 Y & K 72. 7 / 76 7 8 FIGURE 61.— SPARES RETIREMENT 90 CO S T C $ /O 0 o ) 8 0 70 60 5b 90 30 2.0 /0 SGROUP = -1 + 0.00082 SPARSLS + 1 . 1 9 TREND ( 0 . 00022 ) ( 0 . 55 ) R2 = 0.834 VN = 2.26 * * * * X * * x JC x ° \ 0 . ........ •' •' ■ 1 « - 1 SQ < o O fa 69 db 66 70 7 * - 7¥ 7 6 7 Q Y & bI FIGURE 62.— SPARES GROUP INSURANCE 1 — 1 VO £r 195 c a s t compares w e ll w ith th e s u b j e c t i v e f o r e c a s t (F ig u re 63 ). SSUPPLIES = 1 + 0.0001*19 SPARSLS ( 0 . 000026) r2 = 0 .8 0 7 ; VN = 1 .3 7 ; GQ = 1.3 5 PACKING AND CRATING A rem ark ab ly good f i t (0 .8 1 ) was o b ta in e d f o r t h i s acc o u n t i n s p i t e o f th e f a c t t h a t th e h i s t o r i c a l d a ta a re q u i t e v a r i a b l e . The b e s t f i t was b a sed on b o th s p a r e s s a l e s and t r e n d , w ith a n e g a t iv e s ig n on th e t r e n d v a r i a b l e . Whether o r n o t th e t r e n d v a r i a b l e i s in c lu d e d , th e r e s u l t a n t f o r e c a s t te n d s t o u n d e re s tim a te f u t u r e v a r i a t i o n s , a t l e a s t i f we can a c c e p t th e s u b j e c t i v e f o r e c a s t as t r u e (F ig u re 6*1). The f o r e c a s t com parison i s s l i g h t l y b e t t e r w ith th e t r e n d v a r i a b l e i n c l u d e d , however. SPACK = 37 + 0.00222 SPARSLS - I . 5H TREND (0 .0 006 3) (1 .1 1 ) R2 = 0 .8 1 1 ; VN = 1 .8 8 ; GQ = 3-*»3 OTHER EXPENSES The r e s i d u a l c a te g o ry " o t h e r e x p e n s e s ” i s s m a ll — alw ays betw een $6,000 and $ 17,0 0 0 . A r e a s o n a b ly good f i t (0 .6 0 ) was o b ta in e d w ith s p a r e s s a l e s as th e only v a r i a b le . S0THER = 7 + 0.000597 SPARSLS ( 0 . 000172 ) R2 = 0 .6 0 2 ; VN = 1 .6 1 ; GQ = 1.52 W hile c e r t a i n l y n o t p e r f e c t , t h i s d e g re e o f f i t i s a c c e p t a b le f o r a c a t c h - a l l c a te g o r y such as t h i s . The r e s u l t a n t C o s t C.i'/occ) ? 0 1 0 10 60 SO ¥ 0 30 l o JO SSUPPLY = 1 + 0.000149 SPARSLS ( 0 . 000026 ) R2 = 0.807 VN = 1.37 GQ = 1.35 S B t O 6z. 6 ? 6 6 6 g 7 o 7 a 7 ? 7 6 7 ? Y € 4 « FIGURE 63.— SPARES SUPPLIES COST C&/000) H O 80 70 (oO S O H O 3 0 Z O SPACK = 37 + 0.00222 SPARSLS + 1 . 51 * TREND (0.0 006 3) (1 .1 1 ) 0 R2 = 0.811 VN = 1 .8 8 * o / \ GQ = 3 .4 3 x o / O' o • 10 1 1 s e t o 62. t i 70 72. V6> 7 / 76* 7% EIGURE 64.— SPARES PACKING AND CRATING f o r e c a s t compares f a i r l y w e ll w ith th e s u b j e c t i v e f o r e c a s t , a lth o u g h i t i s somewhat h i g h e r th a n th e s u b j e c t i v e f o r e - i c a s t a f t e r 1972 (F ig u re 65 ) . S in c e th e a b s o lu te amount j 1 in v o lv e d i s s m a ll, th e d i s p a r i t y does n o t a p p e a r t o be j J f s e r i o u s . j REDISTRIBUTION j i The r e d i s t r i b u t i o n a cc o u n t i n th e s p a r e s p oo l p e r - j t forms th e same f u n c t i o n as o t h e r r e d i s t r i b u t i o n a c c o u n t s ; j namely t o s h u t t l e ex p en ses betw een p o o l s . The r e g r e s s i o n j e q u a tio n s e l e c t e d h e re c o n ta in s b o th s p a re s s a l e s and j J t r e n d , w ith th e R^ f o r t h i s e q u a tio n b e in g 0.95* ! SREDIST = - 69 + 0.02015 SPARSLS + 18.89 TREND (0.0 0 1 6 7 ) (2 .9 5 ) r2 = 0 .9 5 4 ; VN = 2 .0 7 ; GQ = 7.58 j V. ACCOUNTS NOT ESTIMATED | I t was n o t p o s s i b l e to d e te rm in e v a l i d r e g r e s s i o n e q u a tio n s f o r s e v e r a l a c c o u n ts . These a c c o u n ts f e l l i n t o f i v e g ro u p s: ta x e s and i n s u r a n c e , r e n t e d eq uip m en t, j I 1 management i n c e n t i v e , com pensation d e p r e c i a t i o n , and s e r v i c e s c r e d i t e d . TAXES AND INSURANCE While v a l i d e s t im a t e s were o b ta in e d f o r s e v e r a l j i t a x a c c o u n ts , th e u se t a x , p e r s o n a l p r o p e r t y t a x , and ! i in s u r a n c e a c c o u n ts c o u ld n o t be e s t im a t e d . These ta x e s and in s u r a n c e a re n o t p a id on goods s o ld t o th e U. S. governm ent n o r on t o o l s used to make such goods. However, Co s f ( $ J 0 O 6 ) 10 r 80 10 60 S'b VO 30 20 /0 0 SOTHER = 7 + 0.000597 SPARSLS ( 0 . 000172 ) R2 = 0.602 VN = 1 .6 1 GQ = 1.52 S 3 6o 62 6V i t 6 8 70 72. 7 i 7b 78 y ^ / f FIGURE 65.--OTHER SPARES EXPENSES 199 < ? 0 0 £60 7oo SREDIST = -69 + 0.02015 SPARSLS + 18.89 TREND (0.0 016 7) (2 .9 5 ) R2 = VN = GQ = 0 .954 2.07 7-58 c o s t sm ( $ / o o o ) 300 zoo /oo •• o o 0 o '•6-“0r............... 1 1 1 5 9 60 6*. & * / fcb 6g ?0 72. 7Y 76 VSAR n FIGURE 66.— SPARES REDISTRIBUTION 200 c o m m e r c ia l- o r ie n te d t o o l s and goods a re c h arg ed i n th e u s u a l m anner. In o rd e r t o e s t im a t e t h e s e a c c o u n ts , a j more com plete u n d e rs ta n d in g i s r e q u i r e d o f what i s ta x a b le j o r i n s u r a b l e , th e le n g th o f le a d - ti m e s on com m ercial i j p r o d u c t s , e t c . A d d itio n a l in d e p e n d e n t v a r i a b l e s w i l l be j r e q u i r e d t o make th e s e f o r e c a s t s . j RENTED EQUIPMENT ! i D uring th e h i s t o r i c a l p e r i o d , r e n t e d equipm ent J te n d e d t o fo llo w th e t r e n d i n f i x e d a s s e t s . However, as j i | more f i x e d a s s e t s a re p u rc h a s e d , few er r e n t e d ones sh o u ld j be r e q u i r e d . S in ce th e only re a s o n a b ly good r e g r e s s i o n I s I e q u a tio n c o n ta in e d only TREND, I t was f e l t t h a t i t would j I be b e s t n o t to f o r e c a s t t h e s e a c c o u n ts u n t i l i t was p o s- i I | | s i b l e t o dev elo p a f u l l e r u n d e rs ta n d in g o f th e u n d e r ly in g i n f l u e n c e s . T his i s e s p e c i a l l y t r u e s i n c e e x p e n d itu r e s f o r t h i s a cco u n t te n d to be somewhat a r b i t r a r y . MANAGEMENT INCENTIVE COMPENSATION Management i n c e n t i v e com pen sation i s d is b u r s e d i J i n an a tte m p t t o s t i m u l a t e m anagers to improve th e p r o f i t p i c t u r e th ro u g h b e t t e r u t i l i z a t i o n o f r e s o u r c e s . The amounts d is p e n s e d i n th e p a s t have been l i n k e d somewhat j i c l o s e l y t o c u r r e n t p r o f i t s , w ith c o e f f i c i e n t s o f d e t e r - J m in a tio n o f around 0 .7 in th e t h r e e m ajor p o o l s . The j ' j ! a d d i t i o n o f some v a r i a b l e t h a t r e f l e c t s f o r e c a s t p r o f i t im proves th e f i t about 0 .1 more. 202 U n f o r t u n a t e ly , h e t e r o s c e d a s t l c i t y i s p r e s e n t i n two o f th e e q u a t io n s , and th e u s u a l tr a n s f o r m a ti o n s a r e u n s u c c e s s f u l i n rem oving i t . F u rth e rm o re , th e s u b j e c t i v e f o r e c a s t i s low and c o n s t a n t th ro u g h o u t th e f o r e c a s t i i i p e r io d (in c u r r e n t d o l l a r s ) . Such a f o r e c a s t i s a r t i f i c i a l ! i ! i b u t un dou b ted ly deemed p ru d e n t by a management t h a t j d o e s n 't want to a p p e a r t o be ro b b in g th e Firm . The ! c o n s ta n t f o r e c a s t i s p a r t i c u l a r l y u n r e a l i s t i c in l i g h t o f th e d r a s t i c changes i n p r o f i t s t h a t a re f o r e c a s t to j \ i o c c u r, s in c e l a r g e p r o f i t s u n d o u b te d ly mean l a r g e r manage- j ment i n c e n t i v e paym ents. T h is i s e s p e c i a l l y t r u e s in c e i ) j j s e v e r a l bad p r o f i t y e a r s p re c e d e th e good y e a r s , and j I management must be rew ard ed f o r i t s p a ti e n c e d u rin g th e | y e a rs when th e paym ents a r e s m a ll. i The c o n s ta n t s u b j e c t i v e f o r e c a s t s do p o in t out one im p o rta n t f a c e t o f t h i s problem which i s t h a t th e acco u n t amounts a re h ig h ly a r b i t r a r y . T his i s a w arning t h a t eco n o m etric f o r e c a s t s a re l i k e l y t o be u n a c c e p ta b le even i f th ey do u n co v er some o f th e u n d e rly in g elem ents which a f f e c t th e e x p e n d i t u r e s . U n t i l more d a ta a re a v a i l a b l e , a p ru d e n t s u b j e c t i v e f o r e c a s t un doubtedly i s p r e f e r a b l e to an e c o n o m e tric f o r e c a s t . DEPRECIATION I — ———— — — t D e p r e c ia tio n ex p en se s i n th e f a c t o r y pool were | found to fo llo w f i x e d a s s e t s q u i t e w e l l. However, th e ac c o u n ts f o r e n g in e e r in g and a d m i n i s t r a t i o n were not so 203 e a s i l y e s t im a t e d . T here a r e two p r i n c i p a l re a s o n s beh in d t h i s . 1. D e p r e c ia t io n i s ch arg ed t o th e v a r io u s p o o ls i n an a r b i t r a r y m anner. T hus, even though t o t a l d e p r e c i a - i | t i o n fo llo w s th e t r e n d o f f ix e d a s s e t s , a s i n g l e p o o l ’s | !expenses can be u n r e l a t e d or v a r i a b l e . i J 2. Tax law s now p ro v id e f o r r a p i d w r i t e o f f o f ! many ty p e s o f d e p r e c i a b le a s s e t s . Such expenses a re I t y p i c a l l y u n c o r r e l a t e d w ith a c t u a l d e p r e c i a t i o n , and |t h e r e f o r e u n r e l a t e d t o p o o l o r Firm a c t i v i t y . U n t i l a more th o ro u g h knowledge can be dev eloped o f b o th t a x law and th e a l l o c a t i o n o f ex penses to th e o v e r head p o o l s , i t w i l l n o t be p o s s i b l e to d e te rm in e v a l i d e s t im a t e s f o r t h e s e a c c o u n ts . SERVICES CREDITED i j The s e r v i c e s c r e d i t e d a c c o u n ts a re used t o repay th e o v erh ead p o o ls f o r expenses t h a t a re charg ed d i r e c t l y t o c o n t r a c t s . These e x p en ses a re o r i g i n a l l y charg ed on a p o ol b a s i s t o f a c i l i t a t e a c c u m u la tio n . For exam ple, assume a group o f p e r s o n n e l w orking a t some rem ote i n s t a l l a t i o n use some s e r v i c e s o r goods which a re charged to th e F irm ’s o v e rh e ad a c c o u n ts . At th e end o f th e y e a r , ithe custom er re p a y s t h i s group f o r th e s e e x p e n s e s , and th e amounts used to d e f r a y th e o v e rh e ad a c c o u n ts a p p e a r as c r e d i t s i n th e o v e rh e ad summary. The m agnitudes o f th e s e e x p e n d itu r e s were found t o be c o m p le te ly in d e p e n d e n t o f th e ' ' 20^ a c t i v i t y v a r i a b l e s f o r th e Firm . While th e amounts te n d t o be s i g n i f i c a n t , i t was a p p a r e n t t h a t a d d i t i o n a l in d e p e n d e n t v a r i a b l e s would be needed i n o r d e r to f i t th e a c c o u n ts . Since th e s e v a r i a b l e s a re n o t now p r e p a r e d in th e u s u a l f o r e c a s t p r o c e s s , i t was f e l t t h a t t h e s e a c c o u n ts sh o u ld be ig n o re d i n th e p r e s e n t s tu d y . CHAPTER V VALIDATION OF MODEL Now t h a t th e e q u a tio n s c o m p risin g t h e model have been d e r i v e d , i t i s p o s s i b l e t o f i n d out w h e th er i t was a l l w o rth t h e e f f o r t . A number o f t e c h n iq u e s have been used t o v a l i d a t e e c o n o m e tric m od els, and s e v e r a l o f t h e s e w i l l be used i n t h i s s tu d y . No model can be e x p e c te d t o f i t d a t a — h i s t o r i c a l o r f u t u r e — e x a c t l y . The q u e s tio n t h a t must be answ ered i s "w h e th e r th e r e s i d u a l e r r o r s a re s u f f i c i e n t l y s m a ll t o be t o l e r a b l e and s u f f i c i e n t l y u n s y s te m a tic t o be t r e a t e d as ra n d o m ... We have no a d e q u a te s t a t i s t i c a l t h e o r y t o p r o v id e c r i t e r i a f o r ju d g m en t, but we can a t l e a s t compute and examine th e e rr o r s ." - ^ I . TECHNIQUES FOR VALIDATING A MODEL T here a r e a number o f te c h n iq u e s t h a t have been u sed i n e s t i m a t i n g th e v a l i d i t y o f m acroeconomic econom et r i c m o dels. One o f t h e s e i s b a se d on t h e goodness o f f i t o f t h e i n d i v i d u a l e q u a t i o n s . 2 T h is method o f e v a l u a t i o n I s ■ L J . S. D u e se n b e rry , e t . a l . , The B rookings Quar t e r l y E cono m etric Model o f th e U n ite d S t a t e s (C hicago : Rand McNally and C o ., 1 965 ), p. 639. 2L. R. K le in and A. S. G o ld b e rg e r, An E con o m etric Model o f th e U n ited S t a t e s : 1929-1952 (Amsterdam: N o rth - H ollan d P u b l i s h i n g C o ., 1 9 6 4 ), pp. 93-110. 205 206 so i n t e r t w i n e d w ith th e p ro c e s s o f e q u a tio n s e l e c t i o n t h a t was d i s c u s s e d i n th e l a s t c h a p t e r t h a t no f u r t h e r comments w i l l be made h e r e . Two o t h e r te c h n iq u e s t h a t have found w id e sp re a d use a re com parisons b a sed on ex p o s t and ex a n te f o r e c a s t s . 3 EX POST FORECAST The ex p o s t method c o n s i s t s o f a com parison b e tween v a lu e s p r e d i c t e d by th e model and a c t u a l d a t a . Since a c t u a l d a ta a r e used h e r e , th e t r u e v a lu e s f o r a l l o f th e exogenous and endogenous v a r i a b l e s a r e known a t th e tim e th e com parison i s made. T his means t h a t " d i s c r e p a n c i e s betw een th e v a lu e s f o r e c a s t f o r th e endogenous v a r i a b l e s and th o s e a c t u a l l y observed a re t h e r e f o r e a t t r i b u t a b l e to th e model p r o p e r . T here a re two p o s s ib l e ways o f p r o v i d in g a c t u a l d a t a f o r th e endogenous v a r i a b l e s . The f i r s t method con s i s t s o f " s a v in g " p a r t o f th e o r i g i n a l d a t a , i . e . , u s in g o nly a p o r t i o n o f the a v a i l a b l e d a ta t o d e r i v e th e r e g r e s s i o n c o e f f i c i e n t s . The m o d el’s f o r e c a s t th e n can be compared t o d a t a which were n o t used i n d e r i v i n g th e model. 3l . R. K lein and A. S. G o ld b e rg e r, oj). c l t . , pp. 78- 8 8 . ^A. S. G o ld b e rg e r, Im pact M u l t i p l i e r s and Dynamic P r o p e r t i e s o f th e K le ln -G o ld b e rg e r Model (Amsterdam: N o rth -H o lla n d P u b lis h in g C o ., 19 5 9 ), P* 9. 207 A ccording t o C h r i s t , t h i s te c h n iq u e i s i n c o r r e c t ” . . . b e cause th e b e s t one can a cco m p lish i s t o d e v is e a p l a u s i b l e model t h a t e x p la in s w e ll a l l o f th e r e l e v a n t d a t a , and i t makes l i t t l e d i f f e r e n c e w h eth er t h i s i s done by f i t t i n g th e model t o a l l o f th e d a t a , o r by f i t t i n g i t t o p a r t o f them and d i s c o v e r i n g a fte r w a r d t h a t i t e x p l a i n s th e r e s t o f them w e l l . "5 While t h i s may n o t be u n i v e r s a l l y a c c e p te d , s e t t i n g a s id e some o f th e d a t a f o r th e econom et r i c o v erh ead model was u n th in k a b le b e c a u se an n u al d a ta f o r o n ly te n y e a r s were a v a i l a b l e . Each o f th o s e p ie c e s o f d a t a was much to o v a lu a b le t o s e t a s i d e b e ca u se o f th e e f f e c t on s t a n d a r d e r r o r s . ^ F u rth e rm o re , a s m a ll e r sample c o n s i s t e n t l y would have ru n i n t o d i f f i c u l t i e s b e c a u se o f l a c k o f a v a i l a b l e d e g re es o f freedom when u s in g m u lt i - te r m r e g r e s s i o n e q u a tio n s . The second method o f u s in g ex p o s t f o r e c a s t s to e v a l u a t e v a l i d i t y i s to use th e e n t i r e s e t o f a v a i l a b l e d a t a t o d e r iv e th e r e g r e s s i o n e q u a t i o n s . The a n a l y s t th e n compares some o r a l l o f th e s e same d a t a p o i n t s w ith th e v a lu e s p r e d i c t e d by th e m o d e l.7 I t may be s t r a n g e to "check" a model u s in g th e same d a t a t h a t was u t i l i z e d i n ^C arl F. C h r i s t , "A ggregate E co nom etric M odels," American Economic R eview . XXXXVI (J u n e , 1 9 5 6 ), p. ^02. ^K arl A. Fox, I n te r m e d ia te Economic S t a t i s t i c s (New York: John Wiley and Sons, I n c . , 1 9 6 8 ), p . 17^. 7 c a r l F. C h r i s t , op. c i t . , p. 402. 208 d e r i v i n g th e m odel. However, i t i s q u i t e e n l i g h t e n i n g t o do t h i s b e ca u se th e f i t may be p o o r e r th a n r e c o g n iz e d . F u rth e rm o re , i t i s p r o f i t a b l e t o compare p r e d i c t i o n s w ith r e a l i t y f o r a l l e q u a tio n s ta k e n t o g e t h e r . T his i s b e cau se " i t i s q u i t e r e a s o n a b le f o r t h e i n d i v i d u a l e q u a t i o n s . . . t o f i t r e a s o n a b ly w e l l , b u t when a l l th e e q u a tio n s a re so lv e d j o i n t l y , e r r o r s may a cc u m u late and a bad f i t may be ob t a i n e d . "8 T h is does n o t a p p ly t o th e p r e s e n t o verhead m odel, how ever, s in c e i t r e f e r s t o problem s a s s o c i a t e d w ith s im u lta n e o u s s o l u t i o n o f a l l e q u a t i o n s , and each overhead e q u a tio n i s in d e p e n d e n t o f th e o t h e r s . A v a r i a n t t o t h i s te c h n iq u e i s t o compare th e a c c u ra c y o f th e r e g r e s s i o n model w ith a n a iv e m o d e l.9 With such a m odel, we can d e te rm in e w h e th er th e e f f o r t e n t a i l e d i n d e r i v i n g th e e c o n o m etric model was w o rth w h ile as f a r as p r o v id in g a d d i t i o n a l p r e c i s i o n ( t h i s same te c h n iq u e a ls o i s used i n th e ex a n te f o r e c a s t com parisons d is c u s s e d b e lo w ). EX ANTE FORECAST The r e a l t e s t o f an e c o n o m e tric model i s i t s a b i l i t y to f o r e c a s t i n t o a p e r i o d f o r which d a ta do n o t 8 j . S. D u e se n b e rry , et^. al^ ., op. c i t . , p. 639. ^ C arl F. C h r i s t , A T e s t o f an E conom etric Model f o r th e U n ite d S t a t e s : 1921-19^7 (New York: N a tio n a l Bureau o f Economic R e s e a rc h , 1951)» PP. 56-57. 209 e x i s t . •'•0 G o ld b e rg e r s t a t e s t h a t " i t i s on i t s ex a n te f o r e c a s t i n g r e c o r d t h a t an e c o n o m e tric model s ta n d s o r f a l l s in c o m p e titio n w ith a l t e r n a t i v e p r e d i c t i v e p r o ced u res . U s u a lly , one w a i ts f o r s e v e r a l y e a r s and th e n compares a c t u a l r e s u l t s w ith p r e d i c t e d r e s u l t s . U n fo rtu n a t e l y , t h i s te n d s t o re d u c e s u b s t a n t i a l l y th e v a lu e o f such a model (even th oug h i t may be found t o be a good p r e d i c t o r a t some p o i n t in th e f u t u r e ) . The model i s meant t o f o r e c a s t and any d e la y d e t r a c t s from i t s u s e f u l n e s s . T his tim e l i m i t a t i o n , w h ile s i g n i f i c a n t i n an academ ic e n v iro n m e n t, i s c r u c i a l i n a b u s in e s s en v iro n m en t. T h is i s p a r t i c u l a r l y t r u e in th e a e ro sp a c e i n d u s t r y , w here change o c c u rs a t phenomenal sp eed. In u s in g t h i s m ethod, a n a l y s t s have tu r n e d to " n a iv e " models as a means o f v a l i d a t i n g t h e i r s o p h i s t i c a t e d m odels. Two such n a iv e m odels have been used t o v a l i d a t e th e K le in -G o ld b e rg e r m acroeconom ic m odel: one which assumes t h a t no change w i l l o c cu r i n th e endogenous v a r i a b l e s and a second which assumes t h a t th e endogenous 10C a rl P. C h r i s t , "A ggregate E conom etric M o d e ls,” American Economic R eview , XXXXVI (J u n e , 19 5 6 ), p . 402. ^-lA. S. G o ld b e rg e r, o p . c i t . , p. 9« 210 v a r i a b l e s w i l l change by th e same a b s o l u te amount as th ey d id i n th e p r e v io u s y e a r . 12 A t h i r d p o s s i b i l i t y i s to assume th e v a r i a b l e s change by th e same p e r c e n ta g e amount as th e p r e c e d in g y e a r . I I . VALIDATING THE OVERHEAD MODEL By th e tim e th e model was d e v e lo p e d , an a d d i t i o n a l y e a r ’ s d a ta had become a v a i l a b l e , and th e s e d a ta were used in th e v a l i d a t i o n . Both th e ex p o s t and th e ex a n te checks were made i n t h i s v a l i d a t i o n . However, th e ex a n te com pari son i s somewhat w eaker th a n when used w ith ’’c lo s e d " m o dels, s in c e a l l o f th e a c t i v i t y v a r i a b l e s a re exogenous. T hat i s , i f th e s e exogenous a c t i v i t y v a r i a b l e s a re i n e r r o r , th e model lik e w i s e w i l l be in e r r o r , b u t t h i s may n o t mean th e model i s p o o r. The ex p o s t com parison d o e s n ’t s u f f e r from t h i s drawback s i n c e th e t r u e v a lu e s f o r th e a c t i v i t y v a r i a b l e s a r e known b e f o r e th e f o r e c a s t i s made. COMPARING ACTUAL AND FORECAST ACTIVITY VARIABLES I t i s i n t e r e s t i n g to compare th e a c t u a l and f o r e c a s t v a lu e s f o r t h e a c t i v i t y v a r i a b l e s , as i s done i n T able 14. I t can be seen t h a t most of th e a c t i v i t y v a r i a b le s were f o r e c a s t s u r p r i s i n g l y w e l l . Ten o f them were f o r e c a s t w i t h in H % o f th e a c t u a l v a lu e , and t h r e e more 12C a rl F. C h r i s t , A T e s t o f an E conom etric Model f o r th e U n ited S t a t e s : 1 9 2 1-194 7, (New York: N a tio n a l Bureau o f Economic R e s e a rc h , 19 5 1 ), p. 56. 211 TABLE 14 ACTUAL VS. FORECAST VALUES FOR ACTIVITY VARIABLES D o l l a r F ig u re s A d ju ste d t o 1958 P r i c e L ev el ACTUAL FORECAST PERCENT VALUE VALUE DIFFERENCE P e rso n n e l E n g in e e rin g 751 692 8 - 5 5 6 * F a c to ry 969 985 - 1 .6 S p a res 31 32 - 3 .1 D ir e c t Labor D o l l a r s ($1000s) E n g in e e rin g $7718 $7127 8.3 F a c to ry 5484 5418 1 .2 D ir e c t Labor Hours (1000) E n g in e e rin g 1498 1390 7-8 F a c to ry 1562 1562 0.0 Wage R ates E n g in e e rin g $5.15 $5.13 0.4 F a c to ry 3.51 3.47 1.2 Firm 4.31 4.25 1.4 S a le s ( $ M illio n s ) T o ta l S a le s $30.50 $31.74 - 3 .9 S p ares S a le s 5.19 5 .2 5 - 1 . 1 Intercom pany S a le s 4.32 4.27 1 .2 P r o f i t ( $ M illio n s ) $ -2 .5 5 $ -0 .3 6 - 6 0 8 .3 F ix ed A s s e ts ( $ M illio n s ) 9.59 7.7 8 2 3 .3 212 ( a l l e n g in e e r in g ) w i t h in 9%. However, th e p r o f i t p i c t u r e was much more b le a k th a n a n t i c i p a t e d , and f i x e d a s s e t s grew more r a p i d l y th a n s c h e d u le d . MODEL VALIDATION In p e rfo rm in g th e v a l i d a t i o n , th e m o d e l's f o r e c a s t was compared t o fo u r o t h e r f o r e c a s t s : (1) th e s u b j e c t i v e f o r e c a s t ; (2) a f o r e c a s t b ased on no change from 1968; (3) a f o r e c a s t b ased on th e same a b s o l u t e change as i n 1968; and (4) a f o r e c a s t b ased on th e same p e r c e n ta g e change as i n 1968. The r e s u l t s o f t h e s e com parison s a re shown i n T ab les 15, 16, 17, and 18. The r e s u l t s a re sum m arize d i n T ab le 19• The a b s o lu te e r r o r s a r e compared in t h e s e t a b l e s , and s ig n i s ig n o re d t o p r e v e n t c a n c e l l i n g o f e r r o r s . ^3 While p e rc e n ta g e e r r o r s c o u ld be u t i l i z e d , i t was f e l t t h a t th e w e ig h tin g o f th e l a r g e r a c c o u n ts i n c o r p o r a t e d i n th e a b s o l u te com parison was an im p o r ta n t f a c e t i n th e v a l i d a t i o n . One c o n c lu s io n t h a t can be made from t h e s e t a b l e s i s th e a p p a re n t e x c e lle n c e o f th e s u b j e c t i v e f o r e c a s t . T h is f o r e c a s t has an a v erag e e r r o r o f 40-50$ l e s s th a n th e m o d e l's f o r e c a s t , and, o f c o u rs e , i s s i g n i f i c a n t l y b e t t e r th a n any o f th e n a iv e f o r e c a s t s . At th e Firm l e v e l , th e e c o n o m e tric model seems t o 13h . T h e i l , Economic F o r e c a s t s and P o lic y (Amsterdam: N o rth -H o llan d P u b lis h in g C o ., 1 9 6 l ) , p . 26. TABLE 15 ENGINEERING FORECAST ERRORS ACCOUNT 1969 ACTUAL AMOUNT $1000s ABSOLUTE ERROR IN FORECAST < & - H O O O s) ECONOMETRIC MODEL EX POST EX ANTE SUBJECTIVE FORECAST NAIVE MODELS NO CHANGE SAME CHANGE SAME PERCENT CHANGE I n d i r e c t Labor $ 735 $115 $ 72 $-49 $-65 $ -7 $ 2 H olidays 238 89 S3 69 30 77 87 V a c a tio n s 440 -7 34 — >21 -59 5 18 Group In s u ra n c e 298 -2 -25 23 -53 9 34 R e tire m e n t 778 131 57 39 -13 167 222 S o c i a l S e c u r i t y 259 97 67 -8 -24 7 12 S u p p lie s 48 -24 -24 7 -2 4 5 S e r v ic e s Charged 61 -21 -27 -6 -28 -18 115 T r a in in g 2 1 1 1 0 1 1 S e r v ic e s P urchased 6 3 2 , 0 -2 -5 -3 E n te rta in m e n t 1 0 0 0 0 -1 0 Company A i r c r a f t 44 33 25 0 2 6 6 R e p a i r , M aintenance 95 64 5^ 62 52 96 115 T ra v e l 169 -17 -7 -20 -44 -19 -13 O ther 62 -9 5 57 3 13 16 R e d i s t r i b u t i o n 1068 -90 -163 -40 -257 -84 -38 Average 253.4 43.9 39 .1 2 5 .1 39.6 32.4 42.9 TABLE 16 FACTORY FORECAST ERRORS ACCOUNT 1969 ACTUAL AMOUNT $1000s ABSOLUTE ERROR IN FORECAST C$10001s) ECONOMETRIC MODEL EX POST EX ANTE SUBJECTIVE FORECAST NAIVE MODELS NO CHANGE SAME CHANGE SAME PERCENT CHANGE I n d i r e c t Labor $3468 $-399 $-439 $-189 $-578 $-999 $-948 H o lid ay s 398 -50 -54 12 -44 -70 -68 V a ca tio n s 582 2 -3 -62 -43 -50 -50 Group In s u ra n c e 443 -43 -37 56 -32 -9 -8 S o c ia l S e c u r i t y 460 28 32 10 -12 -70 -63 S u p p lie s 388 -22 -22 -36 -174 -369 -275 S e r v ic e s Charged 2 0 0 3 0 1 2 S e r v ic e s P u rch ased 29 -8 -9 -3 -8 -3 -1 T ra v e l 63 33 23 -6 -22 -27 -27 C ra tin g 27 -7 -5 -10 -7 -7 -7 P r o d u c tio n A n a ly sis 52 -1 8 -1 -3 -24 -18 F r e i g h t 122 -32 -32 -37 -26 -50 -45 H e a t, L ig h t , Power 260 -2 -2 16 -17 -24 -23 R eal P r o p e r ty Tax 181 105 64 5 -15 -8 -6 B u ild in g R e n ta ls 265 -23 -43 -23 -46 14 36 R e d i s t r i b u t i o n 265 95 95 -65 -7 -41 -37 Average 457 53.2 54.3 32.8 64.6 110.3 100.9 TABLE 17 ADMINISTRATIVE FORECAST ERRORS ACCOUNT 1969 ACTUAL AMOUNT $1000s ABSOLUTE ERROR IN FORECAST ($1000* s) ECONOMETRIC MODEL EX POST EX ANTE SUBJECTIVE FORECAST NAIVE MODELS NO CHANGE SAME CHANGE SAME PERCENT CHANGE I n d i r e c t Labor $2432 $274 $329 $ -5 $-128 $280 $348 H o lid ay s 108 -3 -8 -10 -14 -6 -1 V a c a tio n s 152 -10 -15 -8 -13 3 6 Group In s u ra n c e 114 -14 -17 15 -18 1 6 R e tire m e n t 310 -47 -54 -23 -16 36 47 S o c i a l S e c u r i t y 110 16 7 9 -25 -26 -26 S u p p lie s 461 -23 -46 -17 -73 65 136 S e r v ic e s Charged 8 8 6 -3 3 9 14 T r a in in g 19 25 22 29 9 -4 0 S e r v ic e s P urchased 39 29 30 84 21 10 12 E n te r ta in m e n t 7 -6 -5 3 2 2 2 Company A i r c r a f t 125 -17 -29 17 -23 10 26 R e p a ir , M aintenance 59 -10 -14 -4 -22 -16 -15 T r a v e l 135 -21 -26 -34 -30 -19 -18 T elep h o n e , T e le g ra p h 283 -32 -46 -2 -66 -46 -45 M ie s. Employ. Expense 64 34 25 1 10 42 66 Morale 21 6 2 -2 -1 2 2 C o rp o ra te A l l o c a ti o n 326 11 18 -1 -53 -78 -76 Bid and P ro p o s a l 249 155 155 -17 161 146 147 215 TABLE 17— Continued ACCOUNT 1969 ACTUAL AMOUNT $1000s ABSOLUTE ERROR IN FORECAST ($ 1 000 ’ s) ECONOMETRIC MODEL EX POST EX ANTE SUBJECTIVE FORECAST NO CHANGE NAIVE MODELS SAME SAME PERCENT CHANGE CHANGE A d v e r tis in g $ 82 $ 7 6 $ 59 $ 50 $ 55 $108 $128 F r a n c h is e Tax 0 87 87 6 127 19 69 Dues and D onations 34 5 3 16 5 16 20 O ther 182 51 59 56 -38 8 29 R e d i s t r i b u t i o n -1587 10 -108 -88 -274 -118 -102 Average 276.3 40.4 48.7 20.8 49.5 44.6 55.9 TABLE 18 SPARES FORECAST ERRORS ACCOUNT 1969 ACTUAL AMOUNT $1000s ABSOLUTE ERROR IN FORECAST o o o i —i s) ECONOMETRIC MODEL EX POST EX ANTE SUBJECTIVE FORECAST NO CHANGE NAIVE MODELS SAME SAME PERCENT CHANGE CHANGE I n d i r e c t Labor $ 236 $ 21 $ 19 $ 12 $-19 $-35 $-35 F rin g e -43 -4 -4 16 -9 -6 -6 S o c i a l S e c u r i t y 19 5 6 7 -2 0 0 R e tire m e n t 51 -10 -6 1 -11 -3 -1 Group I n s u ra n c e 21 -5 -5 5 -5 -1 0 S u p p lie s 3 -1 -1 1 -1 -1 -1 P a c k in g , C r a tin g 28 1 4 8 -2 -18 -12 O th e r 13 -3 -3 -3 -5 -3 -2 R e d i s t r i b u t i o n 225 19 19 6 -7 4 5 Average 71.0 7.7 7 .4 6 .6 CO • VO 7-9 6.9 217 TABLE 19 AVERAGE ACCOUNT ERRORS WITH VARIOUS FORECASTING METHODS D o lla r Amounts i n Thousands NAIVE MODELS ECONOMETRIC MODEL SUBJECTIVE NO SAME SAME PERCENT POOL EX POST EX ANTE FORECAST CHANGE CHANGE CHANGE E n g in e e rin g $43.9 $39.1 $25.1 $39-6 $ 32.4 $ 42.9 F a c to ry 53.2 54 .3 32.8 64.6 110.3 100.9 A d m in is tr a tiv e 40.4 48.7 20 .8 49.5 4 9 .6 55.9 S p ares 7.7 7.4 6 .6 6 .8 7.9 6.9 E n t i r e Firm 39.9 42.0 22.9 44.8 52.7 57.0 219 do b e t t e r th a n any o f th e n a iv e m o d els, a lth o u g h n o t s i g n i f i c a n t l y b e t t e r th a n th e "no change" m odel. The m o d el’s a b s o l u te e r r o r s a re c o n s id e r a b ly l e s s th a n th e " c o n s t a n t change" and " c o n s ta n t p e rc e n ta g e change" m o d els, however. The im provem ents a re betw een 25# and 43#. At th e p oo l l e v e l , th e r e s u l t s a r e somewhat more m ixed. G e n e r a lly , th e e c o n o m e tric m o d e l's f o r e c a s t s a re a p p ro x im a te ly as good o r b e t t e r th a n th e n a iv e m o d els' f o r e c a s t s . The only s i g n i f i c a n t e x c e p ti o n i s th e e n g in e e r in g ex p o s t f o r e c a s t which had an a v e ra g e e r r o r o f $ 4 3 ,9 0 0 , w hereas th e " c o n s ta n t change" model a v e ra g e d only $3 2,40 0. I t sh o u ld be p o in te d o u t t h a t co m p arison s o f th e ty p e j u s t d e s c r ib e d may n ot r e v e a l a g r e a t d e a l . K le in s t a t e s "one y e a r 's t e s t t e l l s us p r a c t i c a l l y n o th in g i n a s t a t i s t i c a l se n se about th e m e r i ts o f e c o n o m e tric t e c h n iq u e s . . .A b s o lu te ly no s c i e n t i f i c c o n c lu s io n s can be drawn u n t i l many f o r e c a s t s have been made u n d e r r e a l i s t i c f o r e c a s t i n g c o n d itio n s w ith e f f i c i e n t m e t h o d s . I f t h i s i s t r u e , th e r e s u l t s p r e s e n te d above s h o u ld be a c c e p te d as a ty p e o f p a s s iv e a p p ro v a l. T hat i s , we c an n o t p ro v e t h a t th e model i s good, b u t we may p ro v e t h a t i t i s n ' t b ad . The ex p o s t and ex a n te com parisons seem to i n d i c a t e t h a t th e model i s n ' t bad. R. K le in , "Comment on A T e s t o f an Economet r i c Model f o r th e U n ited S t a t e s : 1 9 2 1 -1 9 4 7 ," C on ference on B u sin e ss C ycles (New York: N a t io n a l Bureau o f Economic R e se a rc h , 1 9 5 1 ), PP. 121-122. 220 I t i s i n t e r e s t i n g to s p e c u l a t e on what would happen i f th e e c o n o m e tric model co u ld be compared t o th e same n a iv e models f o r th e n e x t t e n y e a r s . We would e x p e c t th e n a iv e models t o do f a i r l y w e ll as lo n g as n o th in g u n u su a l h ap p en s, b u t t o become i n a c c u r a t e as b u s in e s s c o n d itio n s change. S in ce th e e c o n o m e tric model i s a b le t o ta k e i n t o a cc o u n t a t l e a s t some o f th e dynamic elem en ts u n d e rly in g th e F ir m 's o p e r a t i o n , i t would seem re a s o n a b le to assume t h a t th e m o d e l's a cc u ra c y sh o u ld improve when compared t o th e n a iv e models o v e r lo n g e r f u t u r e p e r i o d s . In a l l h o n e s ty , how ever, t h i s m erely c o u ld be th e b i a s e d optim ism o f an a n a l y s t t h a t sim ply knows t h a t h i s model i s good j u s t b e ca u se he has become so in v o lv e d w ith i t . CHAPTER VI NEED FOR UPDATING MODEL Anyone who has worked w ith e c o n o m e tric models r e c o g n iz e s th e need t o u p d ate th e e q u a tio n s as new d a ta becomes a v a i l a b l e . H olt i n d i c a t e s t h a t we must resp o n d to th e new knowledge by r e v i s i n g our f o r e c a s t s . ^ K le in warns t h a t a macroeconomic e c o n o m etric model b ased on r e l a t i v e l y s h o r t tim e s e r i e s must be r e v i s e d "ev e ry two o r t h r e e y e a r s . . . t o keep i t up t o d a t e . " 2 K le in and G o ld b erg er s t a t e " e s t im a t e s from r e l a t i v e l y sm a ll sa m p le s, such as th e 20-25 a n n u al o b s e r v a t i o n s f r e q u e n t l y used i n e c o n o m etric model c o n s t r u c t i o n , w i l l som etim es be s e n s i t i v e t o sm a ll changes i n o b se rv e d d a t a . . . The b e s t p r a c t i c e i n f o r e c a s t i n g from e c o n o m e tric models i s t o r e c a l c u l a t e a l l p a ra m e te r e s t im a t e s from th e l a t e s t r e v i s e d s e t o f d a t a . "3 ^ C h arles C. H o lt, " Q u a n t i t a t i v e D e c isio n A n a ly sis and N a tio n a l P o lic y : How Can We B ridg e th e Gap?" Q u a n ti t a t i v e P la n n in g o f Economic P o l i c y , ed. B. G. Hickman (W ashington, D .C .: The B rookings I n s t i t u t i o n , 1965), p. 261. 2L. R. K le in , I n t r o d u c t i o n t o E cono m etrics (E ngle wood C l i f f s , N . J . : P r e n t i c e - H a l l , I n c . , 1962) , p. 2 6 9. ^L. R. K le in and A. S. G o ld b e rg e r, An E conom etric Model o f th e U n ited S t a t e s : 1929-1952 (Amsterdam: N orth- H o lland P u b lis h in g C o ., 196*0, p. 8 9 . 221 222 Because o f t h e s e a d m o n itio n s , an a n a l y s i s was u n d e rta k e n t o d e te rm in e how s e n s i t i v e th e a cc o u n t f o r e c a s t s a r e t o th e a d d i t i o n o f new d a t a . T h is stu d y c o n s i s t e d o f o b t a i n i n g a s e r i e s o f r e g r e s s i o n e q u a tio n s when e i t h e r one, tw o, o r t h r e e ''new" y e a r ’s d a t a w ere added t o th e o r i g i n a l s e r i e s . These new d a ta were assumed to f a l l e x a c t l y on th e f o r e c a s t t r e n d and a l s o 10$, 20$, and ^10$ above th e tr e n d ( i t was f e l t t h a t th e r e s u l t s would be a p p ro x im a te ly sy m m etrica l so t h e r e was no n eed t o p r o v id e f o r v a lu e s f a l l i n g below th e t r e n d ) . Com parisons were th e n made betw een th e o r i g i n a l f o r e c a s t v a lu e f o r 1978 and each o f th e r e v i s e d f o r e c a s t s b a sed on th e expanded s e r i e s . T h is p ro c e d u re was fo llo w ed f o r f i v e a c c o u n ts , w ith a t l e a s t one a cc o u n t b e in g s e l e c t e d from each m ajor p o o l. An a tte m p t was made t o s e l e c t e q u a tio n s which c o n ta in e d d i f f e r e n t in d e p e n d e n t v a r i a b l e s in o r d e r to be a b le t o j u s t i f y some s o r t o f m ea n in g fu l c o n c l u s i o n s . N ote, how ever, t h a t o n ly th e v a r i a b l e s c o n ta in e d i n th e o r i g i n a l e q u a tio n were a llo w e d t o a p p e a r i n th e new e q u a tio n s . T h is must be view ed as a l i m i t a t i o n , b u t i t was n e c e s s a r y i n o r d e r to j u s t i f y c o n c l u s i o n s . T hat i s , i f th e e n t i r e e q u a tio n was a llo w e d t o ch an ge, i t i s d o u b tf u l t h a t any g e n e r a l i z a t i o n s a t a l l would be p o s s i b l e u n l e s s a very l a r g e sample o f a c c o u n ts were in v o lv e d . The r e s u l t s o f t h e s e com parisons a re p r e s e n t e d in 223 T able 20, and th e y a p p e a r t o be e n c o u ra g in g . They show t h a t a 10# d i s p a r i t y betw een th e a c t u a l and p r e d i c t e d v a lu e s f o r 1969 sh o u ld r e s u l t i n an a v erag e change o f l e s s th a n 5# i n th e 1978 f o r e c a s t . More s i g n i f i c a n t , even i f t h i s d i s p a r i t y c o n tin u e s f o r one o r two more y e a r s , th e 1978 f o r e c a s t sh o u ld be a f f e c t e d by l e s s th a n 9#. F or d i s p a r i t i e s o f g r e a t e r th a n 10#, th e r e s u l t s a re n o t so e n c o u ra g in g . I f th e 1969 v a lu e i s 20# above i t s p r e d i c t e d v a lu e , th e r e v i s e d 1978 f o r e c a s t would be 8# above i t s o r i g i n a l l e v e l . T h is p ro b a b ly would s t i l l be a c c e p t a b l e . However, i f t h i s 20# d i s p a r i t y p e r s i s t s f o r two o r t h r e e y e a r s , th e f o r e c a s t w i l l be a l t e r e d by 13# and 19#, r e s p e c t i v e l y . F or d i s p a r i t i e s o f 40#, th e s h i f t s a re even more pronounced. I t i s a p p a re n t t h a t a v e ra g e s h i f t s do n o t t e l l th e whole s t o r y , i . e . , we sh o u ld lo o k a t th e i n d i v i d u a l a c c o u n ts f o r o u r answ er. The c o n c lu s io n s s t a t e d above, how ever, a r e j u s t as v a l i d when th e i n d i v i d u a l a c c o u n ts a re c o n s id e r e d . Thus, we f i n d t h a t a 10# d i s p a r i t y betw een f o r e c a s t and a c t u a l d a t a i n 1969 r e s u l t s i n s h i f t o f l e s s th a n 9# i n th e a c c o u n t s ’ f o r e c a s t s . Even i f t h i s d i s p a r i t y p e r s i s t s f o r one o r two y e a r s l o n g e r , t h r e e o f th e f i v e a c c o u n ts would be s h i f t e d by l e s s th a n 10#, and a l l o f them by l e s s th a n 14#. In th e case o f m acroeconomic m o d els, s h i f t s o f th e m agnitude d e s c r ib e d above p ro b a b ly a re n o t a c c e p t a b l e . TABLE 20 FORECAST SENSITIVITY TO NEW DATA YEARS * DATA ADDED TO SAMPLE DISPARITY BETWEEN PREDICTED AND ACTUAL VALUE FOR ADDITIONAL YEARS PERCENT DISPARITY BETWEEN ORIGINAL AND REVISED FORECAST FOR 1978 ENGINEERING FACTORY ADMINISTRATIVE AVERAGE OF TRAVEL REAL PROPERTY TAXES UTILITIES CORPORATE ALLOCATION SUPPLIES ABSOLUTE VALUE OF DISPARITY 1969 0# 10 20 40 0.0% 5.H 10.7 21.5 0.6# 4.2 7-5 10 .1 0 .2 % - 1 .6 - 3 .5 - 6 .7 - 0 .4 # 8.7 17.9 35-8 - 0 .4 # 0.7 1 .1 1.5 0.3# 4 .1 8.1 13.1 1969- 0 0.0 - 0 .3 - 0 .3 1.5 - 0 .4 0.5 1970 10 6 .7 3.6 6.4 14.1 1 .1 6 .4 20 13-4 7-2 13.8 29.6 2.6 13-3 H O 26.9 14.6 27-2 60.6 3.7 26.6 1969- 0 0.0 0.6 0 .2 - 1 .1 - 0 .4 0 .5 1971 10 7 .4 8.1 1 2 .2 13.6 1 .8 8.6 20 1 4 .8 14.9 24.0 38.2 3-3 19.0 H O 29.5 17-6 37.4 57.3 5.1 29-4 225 The c o n c lu s io n s o f t h i s c h a p t e r can be summed up as f o llo w s : th e m o d el’s e q u a tio n s sh o u ld be r e v i s e d when new d a ta becomes a v a i l a b l e . However, i f t h i s i s n o t p r a c t i c a b l e , t h e s e new d a ta s h o u ld be compared w ith th e f o r e c a s t s f o r th e new d a t a . A d i s p a r i t y o f 10# can be e x p e c te d t o a f f e c t th e t e n t h y e a r ’ s f o r e c a s t by som ething l e s s th a n 10#, even i f th e d i s p a r i t y p e r s i s t s f o r s e v e r a l y e a r s . A lso , d i s p a r i t i e s o f 20# can p e rh a p s be t o l e r a t e d as lon g as th ey do n o t p e r s i s t beyond one y e a r . Of c o u r s e , th e s e e s t im a t e s r e f e r t o exp e c te d e f f e c t s , whereas th e changes to i n d i v i d u a l a c c o u n ts may be g r e a t e r t o some e x t e n t . CHAPTER V II SUGGESTIONS FOR FURTHER RESEARCH In any com prehensive stu d y such as t h i s , th e a n a l y s t must f e e l a k in t o a d e s e r t e x p lo r e r who t h in k s th e whole a r e a i s dead u n t i l he t u r n s o v e r a few r o c k s . In t h i s s tu d y , a number o f problem s m a n ife s te d th e m s e lv e s , and a number o f a l t e r n a t e t r e a tm e n ts had to be abandoned upon due c o n s i d e r a t i o n o f th e i m p l i c a t i o n s . I t i s w ise a t t h i s tim e to m ention some p o s s i b l e r e f in e m e n ts t h a t could be made to th e above stu d y so t h a t f u t u r e a n a l y s t s m ight a v o id some o f th e p i t f a l l s t h a t were to o w e ll h id d en a t th e b e g in n in g o f t h i s s tu d y . I . FURTHER VALIDATION OF THE MODEL F u r t h e r v a l i d a t i o n o f th e model w i l l be p o s s i b l e as a d d i t i o n a l d a t a a r e d e v elo p ed by th e Firm . Each new y e a r b rin g s w ith i t more d a t a , and th e s e d a ta can be used f o r o b t a i n i n g u s e f u l e s t i m a t e s o f th e m o d e l's f o r e c a s t i n g a b i l i t y in an ex p o s t e n v iro n m e n t.^ When th e model s y s t e m a t i c a l l y u n d e r e s t i m a t e s o r o v e r e s tim a te s a p a r t i c u l a r ^L. R. K le in and A. S. G o ld b e rg e r, An E conom etric Model o f th e U n ite d S t a t e s : 1929-1952 (Amsterdam: N o rth - H o lland P u b lis h in g C o ., 196*0, p. 78 226 227 v a lu e , t h i s i s e v id e n ce t h a t th e r e g r e s s i o n e q u a t io n i s o v e rlo o k in g some a s p e c t o f th e F ir m 's o p e r a t i o n . I t i s a r e l a t i v e l y sim p le m a t t e r t o compare each new y e a r 's d a ta w ith t h e p r e d i c t e d v a lu e t o d e te rm in e i f any such b i a s e x i s t s . I I . USING THE MODEL One c r i t i c i s m o f t e n l e v e l e d a t f o r e c a s t i n g models i s th e l a c k o f use t o which th e model i s p u t i n s p i t e o f th e s u b s t a n t i a l e f f o r t r e q u i r e d t o d e riv e t h e m od el.^ Such use i s v i t a l s in c e models te n d t o become o b s o l e s c e n t r a p i d l y a f t e r developm ent u n le s s m o d if i c a t io n s a r e m ad e.3 Such m o d i f i c a t i o n s a re r e q u i r e d b e ca u se th e env iro nm ent which was to be e x p la in e d by th e model te n d s t o vary in tim e b e c a u se o f complex dynamic ele m e n ts c o n ta in e d w i t h in th e d a t a b u t o v e rlo o k e d i n th e model. Use o f t h i s model i s p r e d i c a t e d on th e assu m p tio n t h a t no s t r u c t u r a l changes w i l l o c c u r which w i l l i n v a l i d a t e th e r e g r e s s i o n e q u a t io n s . O fte n , how ever, t h e a n a l y s t can a n t i c i p a t e a s t r u c t u r a l change and m odify e i t h e r th e ^George D. I r w in , "A Com prative Review o f Some Firm Growth M odels," A g r i c u l t u r a l Economics R ese arch XX: J u l y , 1 96 8 ), p. 95. 3w. J . Fabrycky and P. E. T o r g e r s e n , O p e ra tio n s Economy (Englewood C l i f f s , N. J . : P r e n t i c e - H a l l , I n c . , 1966 ) , "p. 24. 228 e q u a tio n i t s e l f o r th e h i s t o r i c a l d a t a and th e n d e r iv e a new r e g r e s s i o n e q u a t io n . Such a p ro c e d u re im p lie s more o r l e s s c o n ti n u a l u p d a tin g o f t h e model as new in f o r m a tio n b e comes a v a i l a b l e . F o r t u n a t e l y , t h e c o s t o f such e f f o r t s te n d t o be sm a ll b e ca u se most o f th e work i n th e p r e s e n t stu d y i s s t i l l v a l i d (p e rh a p s w ith a sm a ll amount o f a d j u s t i n g ) . 5 I I I . INCORPORATING UNWIELDLY ACCOUNTS The i n i t i a l i n t e n t o f th e model was one o f p r o v id in g a r e l a t i v e l y sim ple o v e rh e ad m odel. I t i s now a p p a re n t t h a t i t i s n o t p o s s i b l e t o d e r i v e v a l i d r e g r e s s i o n e q u a tio n s f o r a l l o f th e o v e rh e ad a c c o u n ts u n le s s a d d i t i o n a l in d ep e n d en t v a r i a b l e s a re u t i l i z e d . U n f o r t u n a t e ly , t h i s i s much h a r d e r th a n i t m ight seem, even though only a r e l a t i v e l y few number o f a c c o u n ts s t i l l need t o be e s tim a te d . The in s u r a n c e a c c o u n ts and most o f th e t a x a cc o u n ts a re lin k e d i n an e x tre m e ly complex way to com m ercial p ro d u c t s . Not only a re th e l in k a g e s com plex, b u t th e lon g le a d - tim e a s s o c i a t e d w ith com m ercial p r o d u c tio n te n d s to d i s t r i b u t e expenses i n such a way t h a t i t i s im p o s s ib le t o i d e n t i f y th e e f f e c t s even w ith la g g e d r e g r e s s i o n v a r i a b l e s . ^ I rw in , op_. c i t . , p . 95 5Fabrycky, o£. c i t . , p . 2k. 229 The remaining accounts can be categorized as arbi trary, in that their magnitudes tend to depend on seemingly arbitrary decisions of management. Such decisions are based on present, past, and future profits and sales plus certain trends that are difficult to establish. It could well be that these are the most difficult of all accounts to estimate. In general, however, It should be possible to estimate relationships for these difficult accounts by further disaggregation. This must be true because the analysts preparing the subjective forecasts have been able to forecast these accounts, and this implies that a com puted solution is at least possible if not practicable. It may be wise to ask whether such disaggregation is worthwhile. This question is asked because it may not be worthwhile to disaggregate further if an additional forecast for at least one exogenous variable is needed In order to provide a forecast for each overhead account. The answer to the above question is undoubtedly that we don't know until the disaggregation has been done and the addi tional regression equations derived. It would seem reasonable to expect that several of the difficult accounts could be estimated from common exogenous variables, so the process of disaggregation should be worthwhile. 230 IV. CLOSING THE MODEL As presently constituted, the overhead model depends on certain operating variables that are supplied by an estimator outside the model. An ideal model would internalize this estimator and perform all the calcula tions needed for the whole forecast. Such a model would accept expected sales for each year as the only exogenous input. An econometric relation ship would then translate sales values into the other activity variables: direct labor dollars, hours, and personnel, profit and fixed assets, etc. Other relation ships would translate these activity variables into overhead account amounts. The summary of such a model would contain forecasts for most of the financial and operational variables for the Firm. While such a model is entirely within reason, it should be borne In mind that it represents a significant step forward In terms of effort required for development. The principal reason for this complexity is the dynamic nature of the interrelationships between sales and the operating variables. This year’s sales depend not only on this year's personnel and fixed assets, but also on last year's personnel and fixed assets, and also on the values for the years prior to that. With such dynamic diffi culties, it probably will take a series of data that is 231 longer than ten years In order to develop these interrela tionships . Furthermore, the relationships undoubtedly vary with product line. That is, a commercial product will have a different profit and manhour expenditure profile than a military product. Also, there probably are variations between alternative military products as well. It would be surprising if the Firm had enough consistent historical data to discriminate between these different product profiles. However, it should be possible to derive some reasonable valid profile for use in fore casting. This conclusion rests on the observation that current forecasting methods are predicated on mental pro files, and the econometrician should be able to do at least as well as a subjective forecastor. Of course, this assumes that the econometrician understands the interrela tionships as well as the subjective forecastor and such an understanding may be hard to develop. In spite of the above comments, it is clear that development of a closed model can and should be undertaken to provide a valid, comprehensive Firm forecast. It should be pointed out that some of the work done in developing the overhead model would have to be redone if further expansion of the model is undertaken. This is because the one-st'age least-squares technique used in deriving the regression equations is predicated on the 232 assumption that all stochastic effects are associated with the dependent variable. This means that the fitted equa- r tions are all in reduced form. If the model is closed up, the operating variables will be endogenous rather than exogenous, so the overhead account equations will contain stochastic terms on either side of the equal sign. To avoid this problem, it is necessary to rederive the equations using predicted values rather than actual values for the operating variables. This is what is known as two-stage least squares tech nique . 7 Of course, even though this would be necessary, all of the data used in this study would still be valid, so the derivation of the revised equations should be relatively straightforward. V. USING THE PROBABILISTIC EQUATIONS The deterministic model was developed because of limitations in time and the lack of ability to program the model on a computer. However, a definite trend is now established in industry to utilize probabilistic equations ^M. J. Brennan, Preface to Econometrics (Cincin nati: South-Western Publishing Co., 1965), P* 401. ?Karl A. Pox, Intermediate Economic Statistics (New York: John Wiley and Sons, Inc., 1968), p. 388. 233 ; rather than deterministic equations.® Such equations are utilized in an attempt to recognize the inherent uncertain ty associated with most of the forecasts generated by a firm. This uncertainty is made explicit by using a fore cast that consists of not only an expected value, but also a standard deviation associated with that value.9 In the overhead model, such uncertainty would involve the estimates for company sales and profits. Also involved are the estimates for personnel, manhours, and wage rates associated with producing the salable products. The overhead accounts themselves have uncertainty associ ated with the fitted equations (i.e., the standard error terms). If these all can be incorporated into the model, the resultant forecast will consist of an expected value plus a standard error term that describes uncertainty around the central expected value. Unfortunately, it is only now becoming possible to manipulate such probabilistic terms, and then only on a computer. However, granted access to such a computer, it would be relatively easy to adapt the results of the present overhead model to a probabilistic environment. If ®Donald H. Words, "Improving Estimates that Involve Uncertainty," Harvard Business Review, XXXXIV (July-August, 1966), pp. 96-97. 9C. A. Bliss, "Absolutism in the Realm of Uncer tainty," California Management Review, XI (Spring, 1969), p. 39. . 234 the model were ’ ’closed" as described above, forecasts for most of the financial and activity variables could be developed in terms of the expected value plus fiduicial bands above and below the expected trend. In closing, it is worthwhile saying that all of the above refinements can capitalize significantly on the present overhead study. 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Planning, Production, Inven tories, and Work Force. Englewood Cliffs, N. J.: Prentice-Hall, Inc., i96 0. Hood, W. C., and Koopmans, T. C. Studies in Econometric Method. New York: John Wiley and Sons, Inc., 1953* Hurwicz, L. "Prediction and Least Squares." Statistical Inference in Dynamic Economic Models. Edited by Tjailing C. Koopmans. New York: John Wiley and Sons, Inc. , 1950. Johnston, J. Econometric Methods. New York: McGraw-Hill Book Company, 1963. Johnston, J. Statistical Cost Analysis. New York: McGraw- Hill Book Company, i96 0. Kane, Edward J. Economic Statistics and Econometrics. New York: Harper and Row, Publishers, 1 9 6 8. Klein, L. R. "Comment on 'A Test of an Econometric Model for the United States: 1921 - 19^7.'" Conference on Business Cycles. New York: National Bureau of Economic Research, 1951. Klein, L. R. Introduction to Econometrics. Englewood Cliffs, N. J.: Prentice-Hall, Inc., i9 6 0. Klein, L. R., and Goldberger, A. S. An Econometric Model of the United States: 1929 - 1952. Amsterdam: North-Holland Publishing Co., 1964. Koopmans, T. C. Three Essays on the State of Economic Science. New York: McGraw-Hill Book Co., 1957* Lindholm, R. W. Public Finance and Fiscal Policy. New York: Pitman Publishing Corp., 1950. Noah, J. W., and Smith, R'. W. Cost-Quantity Calculator. Santa Monica: The Rand Corporation, 1962. Orcutt, G. H. "Views on Simulation and Models of Social Systems." Symposium on Simulation Models: Method ology and Applications to the Behavioral Sciences. Edited by A. C. Hoggatt and P. E. Balderston. Cin cinnati: South-Western Publishing Co., 1963. Purcell, W. R., Jr. Commercial Profits from Defense-Space Technology. Boston: The Shur Company, 1964. Sharp, A. M., and Sliger, B. P. Public Finance. Homewood, Illinois: The Dorsey Press, 1964. Stedry, A. C. Budget Control and Cost Behavior. Englewood Cliffs, N. J.: Prentice-Hall, Inc., i9 6 0. Steiner, G. A. Top Management Planning. London: The Macmillan Company, 1969• Stekler, Herman 0. The Structure and Performance of the Aerospace Industry. Berkeley: University of Cali fornia Press, 1965. Theil, H. Economic Forecasts and Policy. Amsterdam: North-Holland Publishing Co., 1961. Tinbergen, J. Econometrics. New York: The Blakiston Company, 1951. Tintner, G. Mathematical Statistics for Economists. New York: Holt, Rinehart, and Winston, 1966. Tintner, G. Methodology of Mathematical Economics and Econometrics. Chicago: University of Chicago Press 1968. Tipper, Harry, Jr. Controlling Overhead. New York: American Management Association, 1966. Warren, E. K. Long Range Planning: The Executive View point . Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1966. B. GOVERNMENT PUBLICATIONS Armed Services Procurement Regulation. Washington, D. C.: U. S. Government Printing Office, 1968. Japan. Economic Planning Agency. Econometric Models for Medium-Term Economic Plan: 196^4 - 1968, 19 65. U. S. President. Economic Report of the President: 196,9. Washington, D. C.: U. S. Government Printing Office 1969. 241 U. S. President. Economic Report of the President: 1970. Washington, D. C.: U. S. Government Printing Office, 1970. C. PERIODICALS Baloff, Nicholas. "The Learning Curve— Some Controversial Issues." Journal of Industrial Economics, XIV (July, 1966), 275 - 282. Bliss, C. A. "Absolutism in the Realm of Uncertainty." California Management Review, XI (Spring, 1969), 35 - 42. Christ, Carl F. "Aggregate Econometric Models." American Economic Review, XXXXVI (June, 1956), 385 - 408. Durbin, J., and Watson, G. S. "Testing for Serial Correla tion in Least Squares Regression: Part I." Biometrika, XXXVII (December, 1950), 409 - 428. Durbin, J., and Watson, G. S. "Testing for Serial Corre lation in Least Squares Regression: Part II." Biometrika, XXXVIII (June, 1951), 159 - 178. Goldfeld, Stephen M., and Quandt, Richard E. "Some Tests for Homoscedasticity." Journal of the American Statistical Association, LX (June, 1965), 539 - 547* Hammond, R. A. "Making OR Effective for Management." Business Horizons, V (Spring, 1962), 73 - 82. Hirschmann, W. B. "Profit from the Learning Curve." Harvard Business Review, XXXXII (January - February, 1964), 125 - 139. Irwin, George D. "A Comparative Review of Some Firm Growth Models." Agricultural Economics Research, XX (July, 1968), 82 - 100. Modigliani, F. "Discussion of ’Managerial Economics: A New Frontier?’" American Economic Review, LI (May, 1961), 156 - 159. Robinson, Colin. "Some Principles of Forecasting in Business." Journal of Industrial Economics, XIV (November, 1965), 1 - 13* Shubik, Martin. "Economics, Management Science, and Operations Research." Review of Economics and Statistics, XL (August, 1958), 214 - 220. "The Fortune Directory of the 500 Largest U. S. Industrial Corporations." Fortune Magazine, June 15, 1968, 186 - 217. Wagner, H. M. "Practical Slants on Operations Research." Harvard Business Review, XXXXI (May - June, 1963), 61 - 71. Woods, Donald H. "Improving Estimates that Involve Uncertainty." Harvard Business Review, XXXXIV (July - August, 1966), 91 - 98. 2^3 Zellner, Arnold. "Decision Rules for Economic Fore casting." Econometrica, XXXI (January - April, 1963), H I - 130. D. NEWSPAPERS Lawrence, John F. "C-5A: Boondoggle— or Good Deal?" Los Angeles Times, June 8, 1969, P* H-10. APPENDICES APPENDIX A ENGINEERING ANNUAL OVERHEAD ACCOUNT DATA Thousands of 1958 Dollars ACCOUNT 1959 I960 1961 1962 1963 1964 1965 1966 1967 1968 Indirect Labor $272 $278 $441 $499 $550 $502 $559 $606 $611 $670 Vacations 154 256 191 235 241 239 282 331 317 381 Holidays 127 130 153 179 170 169 191 223 221 268 Management Incentive 28 0 38 64 70 63 65 64 49 0 Social Security 80 93 104 155 156 126 142 230 204 235 Group Insurance 71 77 72 76 133 127 158 182 181 245 Retirement 179 177 195 246 387 360 523 606 585 765 Repair and Maintenance 54 63 72 72 85 112 98 122 103 147 Travel 58 52 73 99 92 74 84 103 100 125 Entertainment 2 2 3 4 4 2 1 1 1 1 Training 1 1 1 1 1 1 2 2 2 2 Supplies 49 32 54 59 65 55 68 70 40 46 Taxes and Insurance 2 3 4 5 6 6 8 3 2 1 Depreciation 133 136 134 120 187 214 184 171 189 159 Rented Equipment 96 96 119 171 184 218 244 234 209 212 Company Aircraft 3 4 6 24 18 10 18 34 42 46 Professional Services 1 1 2 5 7 4 3 2 8 4 Services Charged 10 22 13 35 3 2 9 14 3 23 Services Credited -14 -17 -76 -100 -114 -185 -204 -190 -172 -112 Other 40 42 32 40 54 41 49 58 55 65 Redistribution 255 241 272 363 308 297 344 475 634 809 APPENDIX B FACTORY ANNUAL OVERHEAD ACCOUNT DATA Thousands of 1958 Dollars ACCOUNT 1959 I960 1961 1962 1963 1964 1965 19 66 1967 1968 Indirect Labor $2512 $2312 $2698 $3167 $3054 $2716 $2635 $3014 $3311 $2890 Vacations 354 313 347 419 446 451 462 516 546 539 Holidays 296 274 298 351 345 347 341 375 380 354 Management Incentive 14 0 20 24 30 33 36 36 33 1 Social Security 267 257 276 403 440 374 352 487 506 448 Group Insurance 208 188 167 172 327 299 340 354 388 411 Retirement 304 226 231 305 439 480 582 708 790 1021 Repair and Maintenance 343 310 369 399 517 584 654 700 572 561 Travel 12 10 21 32 28 18 35 67 46 41 Supplies 222 186 228 305 316 316 316 385 407 214 Real Property Tax 113 109 117 124 130 133 141 150 159 166 Personal Property Tax 410 362 296 288 182 99 78 70 70 88 Miscellaneous Taxes 54 64 67 105 53 52 52 90 109 118 Insurance 45 45 46 49 47 47 55 .50 42 40 Depreciation 237 308 355 350 305 394 438 434 525 580 Rented Equipment 10 10 12 15 8 8 10 10 16 10 Heat,Light,Water,Power 147 155 175 198 203 206 231 223 250 243 Packing and Crating 28 30 36 40 31 20 20 22 20 20 Freight 81 68 77 101 88 86 76 96 120 96 Rented Property 74 78 81 92 107 119 138 138 159 219 Production Analysis 21 22 30 40 55 47 70 79 70 49 Professional Services 8 6 9 14 21 16 12 17 16 21 Services Charged 4 2 3 3 3 3 4 4 1 2 Services Credited -88 -97 -110 -77 -74 -89 -128 -174 -170 -247 Other 3 2 3 3 3 3 1 3 3 3 Redistribution 237 234 207 160 234 291 428 419 292 258 9 4 2 APPENDIX C ADMINISTRATIVE ANNUAL OVERHEAD ACCOUNT DATA Thousands of 1958 Dollars ACCOUNT 1959 I960 1961 1962 1963 1964 1965 1966 1967 1968 Indirect Labor $1320 $1287 $1393 $1550 $1662 $1592 $1685 $1874 $1896 $2304 Vacations 73 71 78 91 103 102 114 124 123 139 Holidays 60 58 63 72 70 74 60 84 86 94 Management Incentive 27 1 29 42 42 39 48 46 37 2 Social Security 39 48 52 88 64 64 72 103 86 85 Group Insurance 36 36 32 32 62 58 68 73 77 96 Retirement 83 74 75 90 154 146 199 208 242 294 Repair and Maintenance 10 10 9 15 38 36 13 33 31 37 Travel 84 73 65 78 89 80 84 101 94 105 Entertainment 24 18 17 22 19 14 12 12 9 9 Training 2 4 9 12 23 18 20 24 41 28 Supplies 218 218 256 321 308 284 310 401 252 388 Personal Property Tax 5 5 5 6 10 10 6 4 5 6 Franchise Tax 50 0 -13 56 141 141 127 168 235 127 Insurance 165 82 114 62 ^7 20 24 24 20 24 Depreciation 20 22 18 19 34 36 34 38 39 44 Rented Equipment 128 144 172 163 189 179 194 152 194 217 Advertising 73 35 34 73 69 51 81 72 84 137 Telephone and Telegraph 128 113 108 153 184 149 161 176 197 217 Miscellaneous Employ- 38 17 45 72 29 10 60 86 42 74 ment Expense APPENDIX C— Continued ACCOUNT 1959 I960 1961 1962 1963 1964 1965 19 66 1967 1968 Dues and Donations $ 22 $ 13 $ 24 $ 27 $ 24 $ 32 $ 33 $ 23 $ 28 $ 39 Employee Morale 0 1 0 4 5 12 15 14 17 20 Corporate Allocation 255 2 66 268 332 307 283 295 293 298 273 Company Aircraft 0 0 9 12 11 19 30 39 69 102 Bid and Proposal 204 235 265 268 478 428 314 249 425 410 Professional Services 46 49 47 53 44 42 45 48 44 60 Services Charged 0 0 0 1 1 2 6 4 6 12 Services Credited -458 -408 -499 -580 -582 -533 -572 -706 -340 -88 Other 68 56 53 56 56 71 81 82 98 144 Redistribution -<586 -671 -760 -923 -947 -854 -964 -1092 -1157 -1313 APPENDIX D SPARES ANNUAL OVERHEAD ACCOUNT DATA Thousands of 1958 Dollars ACCOUNT 1959 I960 1961 1962 1963 1964 1965 1966 1967 1968 Indirect Labor 247 280 346 468 433 284 202 223 233 217 Fringe Benefits 26 28 35 49 47 33 27 29 31 34 Social Security 9 12 15 25 27 16 10 15 15 17 Group Insurance 8 9 8 10 18 13 11 11 12 16 Retirement 12 12 13 20 29 25 23 25 32 40 Supplies 2 1 2 4 4 2 1 2 2 2 Personal Property Tax 15 13 11 10 7 3 2 2 2 4 Packing and Crating 53 57 69 76 60 38 27 47 42 26 Services Credited -24 -31 -48 -68 -60 -65 -45 -62 -75 -115 Other 16 13 17 16 15 15 9 8 6 8 Redistribution 152 149 239 374 395 223 149 156 207 218 APPENDIX E SUBJECTIVE FORECAST FOR ENGINEERING POOL Thousands of 1958 Dollars ACCOUNT 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 Indirect Labor $ 686 $ 601 $ 542 $ 573 $ 5^8 $ 583 $536 $ 627 $ 723 $ 682 Vacations 419 391 364 375 381 447 384 490 545 498 Holidays 307 289 248 255 252 288 248 316 349 317 Management Incentive 0 33 31 30 29 28 27 27 26 26 Social Security 251 253 215 211 212 230 188 230 242 209 Group Insurance 321 292 243 256 241 261 229 277 291 265 Retirement 817 780 747 749 749 812 771 890 937 939 Repair and Maintenance 157 123 98 101 102 82 116 96 117 104 Travel 149 128 98 89 89 76 98 96 110 100 Entertainment 1 1 1 1 1 0 0 1 0 0 Training 3 2 2 2 1 2 1 2 2 1 Supplies 55 53 46 46 42 38 36 42 43 41 Taxes and Insurance 1 1 1 1 1 1 1 1 1 1 Depreciation 151 213 257 243 223 228 253 279 303 320 Rented Equipment 291 303 426 423 410 424 463 458 466 368 Company Aircraft 44 43 42 42 41 42 42 42 43 43 Professional Services 6 5 4 4 4 4 4 4 5 4 Services Charged 339 54 5 5 6 6 6 6 6 6 Services Credited -50 -48 -46 -44 -42 -41 -40 -39 -38 -38 Other 119 102 81 68 68 63 87 72 93 88 Redistribution 1028 1060 1040 1037 1000 1018 999 1037 1050 1052 250 APPENDIX F SUBJECTIVE FORECAST FOR FACTORY POOL Thousands of 1958 Dollars ACCOUNT 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 Indirect Labor $3279 $3546 $4393 $5184 $5957 $5092 $5309 $5349 $5717 $5821 Vacations 520 580 780 863 858 866 884 916 1006 1027 Holidays 410 459 632 708 709 715 731 752 818 828 Management Incentive 0 18 17 16 15 15 15 14 14 14 Social Security 470 584 879 983 1025 970 953 907 938 902 Group Insurance 499 565 810 983 956 906 964 915 946 979 Retirement 1085 1282 1446 1620 1820 1890 1828 1581 1522 1369 Repair and Maintenance 713 656 729 822 766 728 796 765 847 836 Travel 57 52 51 58 63 57 64 56 61 59 Supplies 352 340 410 456 463 448 497 513 555 560 Real Property Tax 186 242 281 283 281 284 278 273 270 265 Personal Property Tax 76 101 105 111 107 104 101 99 97 95 Miscellaneous Taxes 73 90 106 143 107 136 173 172 167 178 Insurance 333 340 410 456 464 448 496 512 545 558 Depreciation 929 1757 1544 1412 1367 1313 1113 1103 1059 998 Rented Equipment 19 23 33 36 36 28 28 24 25 24 Heat,Light,Water,Power 276 354 309 353 330 314 313 310 323 318 Packing and Crating 17 23 34 43 45 41 41 36 38 36 Freight 85 103 113 130 136 130 125 111 112 107 Rented Property 242 250 232 266 248 236 236 233 239 239 Production Analysis 51 68 70 78 75 66 64 54 53 52 Professional Services 26 30 37 48 50 45 45 40 41 40 Services Charged 6 3 2 2 2 2 2 2 2 2 Services Credited -218 -111 -106 -101 -97 -95 -92 -90 -88 -87 Other 43 7 4 -3 -3 -2 2 10 9 9 Redistribution 209 162 151 108 196 227 241 292 382 393 APPENDIX G SUBJECTIVE FORECAST FOR ADMINISTRATIVE POOL Thousands of 1958 Dollars ACCOUNT 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 Indirect Labor $2427 $2552 $2779 $2880 $2882 $2872 $2958 $3119 $3409 $3381 Vacations 144 181 200 217 222 224 215 219 220 219 Holidays 98 118 131 141 144 146 140 143 144 143 Management Incentive 1 23 22 21 20 20 19 19 18 18 Social Security 119 108 119 117 122 115 111 108 113 104 Group Insurance Retirement 129 127 131 137 133 127 130 126 132 130 307 305 376 420 442 436 432 414 414 407 Repair and Maintenance 55 73 80 81 77 76 82 80 79 78 Travel 101 107 128 155 159 149 136 127 132 128 Entertainment 10 12 14 17 18 16 16 15 16 15 Training 48 33 40 48 50 46 46 42 44 42 Supplies 444 511 513 527 494 457 448 453 460 462 Personal Property Tax 33 104 339 935 1456 1403 1318 1256 1021 787 Franchise Tax 6 0 0 0 538 753 792 957 799 892 Insurance 38 134 371 974 2028 2193 2150 2253 1858 1718 Depreciation 60 84 84 74 68 62 48 40 36 34 Rented Equipment 321 465 488 510 490 468 499 489 496 488 Advertising 132 147 152 148 175 158 153 147 143 144 Telephone and Telegraph 281 303 353 406 422 377 348 342 340 326 Miscellaneous Employment 65 111 131 158 162 152 149 139 145 137 Expenses IV) VJI ro APPENDIX G— C on tin u ed ACCOUNT 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 Dues and Donations $ 50 $ 59 $ 66 $ 68 $ 61 $ 56 $ 52 $ 50 $ 46 $ 41 Employee Morale 19 20 20 20 20 20 20 20 20 20 Corporate Allocation 325 386 484 526 464 455 434 428 437 447 Company Aircraft 142 222 217 215 219 220 220 222 226 228 Bid and Proposal 232 420 380 480 487 480 465 444 430 438 Professional Services 123 76 68 72 74 70 71 70 69 72 Services Charged 5 5 5 5 4 4 4 4 4 4 Services Credited -784 -793 -874 -822 -797 -782 -746 -749 -712 -696 Other 238 151 173 190 186 183 169 203 191 126 Redistribution -1499 -1506 -1478 -1436 -1482 -1537 -1527 -1626 -1733 -1746 r u VJ1 LO APPENDIX H SUBJECTIVE FORECAST FOR SPARES POOL Thousands of 1958 Dollars ACCOUNT 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 Indirect Labor $ 248 $ 256 $ 299 $ 309 $ 345 $ 391 $ 349 $ 358 $ 367 $ 377 Fringe Benefits 46 46 54 55 62 63 57 58 58 58 Social Security 26 22 26 25 29 28‘ 24 23 22 21 Group Insurance 26 23 26 27 29 29 26 25 24 24 Retirement 52 49 57 57 66 68 66 63 58 58 Supplies 4 4 3 3 3 4 4 4 4 3 Personal Property Tax 2 2 9 22 21 21 20 20 20 19 Packing and Crating 36 25 32 37 56 54 74 69 54 44 Services Credited -171 -190 -210 -213 -224 -206 -161 -158 -140 -128 Other 10 8 8 8 8 8 8 8 8 7 Redistribution 231 249 250 254 251 258 254 264 267 269

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Creator Eberhardt, Duane Orrin (author)

Core Title An Econometric Overhead Model Of An Aerospace Firm

Degree Doctor of Philosophy

Degree Program Economics

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Economics, Finance,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Tintner, Gerhard (committee chair), Niedercorn, John H. (committee member), White, C. Michael (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-423607

Unique identifier UC11361027

Identifier 7025021.pdf (filename),usctheses-c18-423607 (legacy record id)

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Document Type Dissertation

Rights Eberhardt, Duane Orrin

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Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

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Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA