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Demoeconomic dynamics: Evidence from historic Europe

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Demoeconomic dynamics: Evidence from historic Europe

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Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, M l 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NOTE TO USERS This reproduction is the best copy available. UMI' Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DEMOECONOMIC DYNAMICS: EVIDENCE FROM HISTORIC EUROPE by Oleg V. Pavlov A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment o f the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) May 2000 © 2000 Oleg V. Pavlov Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3018026 ___ _ ® UMI UMI Microform 3018026 Copyright 2001 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIVERSITY OF SOUTHERN CALIFORNIA T H E GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 9 0 0 0 7 This dissertation, w ritten by under the direction of /l.£ .s . ____ Dissertation Committee, and approved by a U . its members, has been presented to and accepted by The Graduate School in partial fulfillm ent of re- quirements for the degree of DOCTOR OF PHILOSOPHY OLEG PAVLOV Date Ma£ 22 ’ 2000 DISSERTATION COMMITTEE Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Oleg V. Pavlov Richard H. Day DEMOECONOMIC DYNAMICS: EVIDENCE FROM HISTORIC EUROPE This work proposes a model o f fertility, mortality and economic development. As in its precursor, the General Evolutionary Model (GEM) o f Day, this model includes one sector production, increasing infrastructure, merging and splitting o f economies, and regime switching. Fertility is a function o f income, child costs, evolving family preferences and fecundity. Mortality is inversely related to income and depends on health technology and crowding. Mortality shocks are used to mimic the apparent random nature o f epidemics; however, this non-linear, multiple-phase model is capable o f producing complex dynamic patterns even in the absence o f epidemic shocks. The model, which I call GEM Europe, is calibrated to explain the European experience using the methodology o f qualitative econometrics. According to this approach, when data are scarce, the primary concern o f the researcher is to discover mechanisms that generate qualitative properties o f the historical reality. The model can explain salient aspects o f the European experience, such as: (i) very slow demographic growth for a prolonged period o f time; (ii) an accelerated population growth after the Neolithic Revolution with raising mortality and fertility rates circa 10000 years ago; (iii) a recent demographic transition (falling mortality and fertility rates starting in the last century); (iv) long run production growth; (v) intertemporal production fluctuations; (vi) switching between socioeconomic regimes. Furthermore, a series o f experiments shows that adapting economic agents who adjust their fertility to the socioeconomic environment may avoid a system collapse either by locking into cycles or converging to a demographic equilibrium. Experiments also suggest that Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mortality decline alone may not be sufficient to slow down population growth and need to be accompanied by economic development. Additional simulations look at the effects o f family planning programs, a possible future population decline, and environmental policies. To develop a computer implementation o f the model, I turn to the methodology and tools of System Dynamics. The regular system analysis is appended with the causal sign rule that affords model simplifications that may be desirable under certain conditions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To my A m erican family, R obert and M argrit Cheeseboro Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A c k n o w le d g m e n ts I th a n k Professor Richard H. Day. my teacher, research advisor and dissertation com m ittee chairm an, for his guidance of my studies in economics th roughout my graduate school years. He raised im p o rtan t questions, provided many insights, an d instilled in me a sense of enthusiasm for th e projects I undertook. I am also thankful to him for introducing me to system dynam ics an d supporting my sim ulation efforts. I am grateful to Professors Anthony M ichaels and Linwood P endleton who took tim e from their busy schedules to serve on my dissertation com m ittee. T hey provided me w ith m any con stru ctiv e com m ents and criticism s. In addition, B arb ara Gordon-Day was m ost helpful in answ ering m y numerous questions regarding form atting and typesetting. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV Contents D ed ica tio n s A ck n o w le d g m e n ts 1 In tro d u ctio n 2 A B r ie f H isto r y o f S tru ctu ra l D e v e lo p m e n t 2.1 Hunting an d G athering ..................................................................................... 2.2 Settled A g r ic u ltu r e ................. .............................................................................. 2.3 Complex Societies and U rban C ivilization (The C ity S t a t e ) .............. 2.4 Trading E m p i r e s ................................................................................................... 2.5 Industrial E c o n o m ie s ............................................................................................ 2.6 Global Inform ation Economies ....................................................................... 3 P r o d u c tio n F u n c tio n 3.1 I n fra s tru c tu re .......................................................................................................... 3.2 Social s p a c e .............................................................................................................. 3.3 Production .............................................................................................................. 3.4 R eplication a n d integration of e c o n o m ie s..................................................... 3.5 E nvironm ental s p a c e ............................................................................................ 3.6 E p o c h s......................................................................................................................... 3.7 Learning by D o i n g ............................................................................................... 3.8 Production p a ra m e te rs ......................................................................................... ii iii 1 5 6 6 8 y 10 u 12 12 13 13 15 16 17 18 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C O N TEN TS v 4 D y n a m ic F e r tility 24 4.1 D em ographic tra n s itio n s ................................................................................................ 24 4.2 How is the desired fertility fo rm e d ?........................................................................... 25 4.3 M ortality e f f e c t................................................................................................................. 27 4.4 L im ited fe rtility ................................................................................................................. 30 4.5 F ertility param eters ...................................................................................................... 32 5 A H isto r y o f M o r ta lity 37 5.1 G eneral observations on m ortality ........................................................................... 37 5.2 R andom ness of death in h is to ry .................................................................................. 38 5.3 Im provem ents in health te ch n o lo g y ........................................................................... 41 5.4 A relationship to social s l a c k ..................................................................................... 43 5.5 N utritional effects .......................................................................................................... 43 5.6 T h e M ortality Causal C h a in ......................................................................................... 47 5.7 M ortality e q u a t i o n ......................................................................................................... 49 5.8 M ortality p a ra m e te rs ...................................................................................................... 52 5.9 Epidem ic shocks ............................................................................................................. 53 6 A S im u la tio n o f W orld D evelop m en t 57 6.1 T he dynam ic structure of GEM E u r o p e ................................................................ 57 6.2 A num erical sim ulation ............................................................................................... 58 7 C o n d itio n a l S cen a rio s 70 7.1 A history w ithout epidemic s h o c k s ........................................................................... 70 7.2 Possible future sc e n a rio s ............................................................................................... 72 7.2.1 Im pact of family planning p r o g r a m s ......................................................... 73 7.2.2 The Black D eath in 2075 ............................................................................... 76 7.2.3 Environm ental c o n c e rn s .................................................................................. 78 7.2.4 Im pact of lowered m o rta lity ........................................................................... 78 8 C o n c lu sio n 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C O N TEN TS VI B ib lio g ra p h y 81 A p p en d ic es 86 A G lo ssa ry o f M a th e m a tic a l N o ta tio n 86 B C o m p u ter Im p le m e n ta tio n 87 B.l System Dynamics: Introduction.......................................................................... 87 B.2 System Dynamics: the L an gu age...................................................................... 88 B.3 D iagram s................................................................................................................ 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 Chapter 1 Introduction D espite years of research, th ere is still no clear understanding of th e m echanism s th a t underlie dem ographic grow th and fluctuations. O ne of the prom inent indications of such m isunderstanding is th a t betw een 1994 an d 1998 the UN P opulation Division revised three tim es its world population projections for 2050 (Haub 1998). E rroneous views on population dynam ics can lead to inadequate pension, foreign aid an d national security program s and many other negative policy consequences. In an effort to add to th e understanding of the issue, I propose a m odel of fertility, m ortality and economic developm ent th a t utilizes an evolutionary m odeling approach to dem ography (Olshansky and Carnes 1994). Following the evolutionary view, I a tte m p t to uncover intrinsic causal links th a t have been present in the dem ographics over th e past 100,000 years of hum an existence. T he m odel extends the General Evolutionary Model (GEM) of Day (1999), from which it inherits the basic structure, as well as the production com ponent. The production consists of one sector and exhibits dim inishing returns to labor. These are com m on features found in models that take a long view approach to studying dem ographics an d production (other exam ples, besides G EM , include Lee 1988 and K rem er 1993). However, following G EM , this model includes elem ents th a t are seldom seen in other models, such as: increasing infrastructure, regim e sw itching and m erging and splitting of economies. G EM has served as a foundation for a num ber of studies. Zou (1991) adapted the model to sim ulate more closely the developm ent of capitalist econom ies during th e past four hundred years. W ith th a t purpose in m ind, he introduced capital as a new variable into G EM , neglecting th e dem ographic com ponent of the model. Powell (1994) also concentrated on m odifications to the production function. He endogenized infrastructure (which he called ’’adm inistrative technology” ). Being set as a m ultiplication factor in the production function infrastructure in effect acted as a constraint on production. Also, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H AP TER 1. IN TRO D U C TIO N o arguing th a t capital was not a significant factor during the early days of hum anity, the production function of the hunter-gathering regime takes only labor as in p u t. Unlike Zou and Powel, m y m odifications to G EM are aimed at th e dem ographic sector. To recreate the com plexity of fertility and m ortality patterns observed in history, th e sim ple M althusian population m odule of G EM is replaced with a m ore complete sector th a t explicitly includes m ortality and fertility. T he m ortality function is adopted w ith som e modifications from Jones (1999). It still inversely relates m ortality to income, bu t it also includes health technology and crowding effects. M ortality shocks are retained from Jones to account for the ap parent random n atu re of epidemics; however, rather th a n being additive, a random shock in this m odel enters th e m ortality equation as a m ultiplier. M ultiplication of effects rath e r than their sum m ation em phasizes th a t other factors, such as health knowledge, o r low population density m ay substantially reduce the severity of an epidemic. Also, using m ultiplication reduces the excessive dependence on shocks th a t were required in Jones’ design to produce the historic p attern s of mortality. In fact, I show th a t the model is capable of producing com plex dynamic p attern s even in th e absence of epidemic shocks. T he fertility sector is based on the work by D ay et al. (1989). which however was not included in th e original GEM m odel. I am end their fertility function w ith a m ortal ity effect as there has been wide evidence suggesting th a t fertility adjusts to m ortality (E asterlin 1996). Thus, th e new model, which I call G EM Europe as it is applied to th e European history, com bines the relative com plexity of the G EM production function w ith a com prehensive dem ographic sector. As a result, the m odel can explain salient aspects of the E uropean experience, such as: (i) very' slow dem ographic grow th for a prolonged period of tim e; (ii) an accelerated population grow th after th e N eolithic Revolution w ith raising m ortality and fertility rates circa 10000 years ago: (iii) a recent dem ographic transition (falling m ortality and fertility rates sta rtin g in the last century); (iv) long ru n production grow th; (v) intertem poral production fluctuations; (vi) sw itching between socioeconomic regim es. Furtherm ore, it shows th a t adapting economic agents who adjust their fertility Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 1. IN TRO D U C TIO N 3 to the socioeconomic environm ent m ay avoid a system collapse either by locking into cycles or converging to a dem ographic equilibrium . This work also addresses m ethodological issues of economic m odeling. To develop a com puter im plem entation of the m odel. I tu rn to the m ethodology and tools of System Dynam ics, a field th a t was originated in the late 1960s by Jay Forrester. R egrettably, the field has made few inroads in Econom ics. T here are still very few works on traditional econom ic topics th a t take advantage of the methodology, and alm ost all of th em were w ritten by system dynam ics researchers them selves, rather th an econom ists (see Forrester 1982, Sterm an 1985, Bach and Saeed 1992). I am aware of only one rare exception which is a 1974 article by Day. T his situation is unfortunate, as the m odular m ethodology and graphical software of system dynam ics are well suited for economic m odeling and analysis and can help alleviate the developm ental and analytical difficulties present in sophisti cated economic models. T he m odular approach also facilitates utilization of disparate expert findings and cooperation between researchers. I append regular system analysis w ith the causal sign rule th a t identifies th e sign of th e relationship between variables th a t are not directly linked in a causal graph. T he rule affords model sim plifications th a t m ay be desirable under certain conditions. To calibrate the m odel I tu rn to th e m ethodology of qualitative econometrics (Day 1999). According to this approach, w hen d a ta are scarce, the prim ary concern of the researcher is to discover m echanism s th a t generate qualitative properties of the historical reality. While hardly a potent m ethodology for the exact disciplines such as physics or engineering, it is quite a viable one for Economics, which relies on aggregate d a ta and indices. Indeed, it has been said th a t econom ic models are like caricatures of th e world, rath e r th an a precise p o rtraits of it (K rugm an 1993 and private com m unication w ith D ay). A brief historical overview of E urope is given in C hapter 2. C hapters 3 th rough 5 describe the general stru ctu re of the m odel and explain the choice of param eter values. R esults are presented in C hapter 6. C h ap ter 7 looks at conditional scenarios. C hapter 8 concludes with a sum m ary of the stu d y and suggestions for further research. To guide th e reader through a m aze of notation, I prepared a glossary of no tatio n in A ppendix A. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H AP TER 1. IN TRO D U C TIO N A ppendix B explains com puter im plem entation. T he model code is available from au th o r upon request. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 Chapter 2 A Brief History of Structural Development We m ay identify a num ber of epochs in the history of E urope th a t are distinct in produc tion technology, organizational infrastructure, fam ily preferences and ways o f life. Day (1999) offers th e following division: 1. H unting and G athering 2. Settled (Village) A griculture 3. C om plex Societies and U rban Civilization (th e C ity State) 4. T rading Em pires 5. Indu strial Economies 6. G lobal Inform ation Econom ies Regions w ithin E urope passed these epochs a t various tim es. Moreover, som etim es an advance to th e next evolutionary stage was no t successful and the society reversed back to th e previous regime. Such fluctuations betw een stages could repeat several times before a stage got firmly established. D ay considers these broad regimes for th e world as a whole. In this stu d y I narrow the focus to the E u ro p ean experience. Correspondingly, relying heavily on R oberts (1996) for historical facts, I give an outline of each of the m acro cultures below as they relate to Europe. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 2. A B R IE F H IS T O R Y OF STRU C TU RAL D E V E LO P M E N T 6 2.1 Hunting and Gathering T his period is the longest one of all six regimes. It started about 100,000 years ago with the emergence o f th e m odern m an. Homo sapiens sapiens, and ended w ith adoption of agriculture ab o u t ten m illennia ago. Traces of these early people are found virtually throughout E urope. It is not com pletely clear w hat social organization they had. But m ost likely they lived in bands th a t m ade survival in the harsh conditions of the Ice Age possible. Som etim es these groups were forming alliances and even m erging or splitting into sm aller groups. R oberts suggests th a t bands were ra th e r isolated as th ere were very few people at th e tim e. Also, archeologists have identified fluctuations in the number of people and econom ic conditions. Such fluctuations were caused by exogenous stres sors such as w eather and availability of food. However, as G EM Europe dem onstrates, endogenous dem oeconom ic forces were capable of contributing to such fluctuations too. Living conditions were very prim itive. T hey found shelter in caves which helped them to survive th e cold. T hey were getting their food by hunting, fishing, and foraging. D uring those early years people m ade a number of inventions and discoveries th a t allowed them to modify their environm ent. These were the knowledge of how' to m ake fire, drills to make holes in stone axe-heads, bone harpoons for fishing and needles to make simple clothes out of anim al skins. T hey perfected such tasks as killing the gam e, processing food, and fabricating clothes. 2.2 Settled Agriculture A bout 8,000 years ago, at the tim e when the last Ice Age draw to a close, inhabitants of Europe began adopting a new form of production. They sta rte d living in som ew hat larger groups in villages, tending to crops an d dom esticated anim als. T he tran sitio n was not a sudden one, b u t rath e r lasted over m any millennia and was possibly driven by pressures from expanding population and difficulties in supporting greater num bers of people by hunting and food foraging (Boserup 1983). There were also changes in flora and fauna, as th a t was the tim e when m egaanim als such as, for exam ple, the m am m oth becam e extinct. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CH APTER 2. A B R IE F H IS T O R Y OF STR U C T U R A L D E V E LO P M E N T i The earliest neolithic sites were found in Greece an d Balkans. W heat was grown near the site of Knossos in C rete in 6000 BC. Aurochs, a predecessor of m odem cattle, were first dom esticated on C rete also about th a t tim e. M odern day radio-carbon dating indicates th a t from Greece agriculture spread up the D anube valley, arriving into th e Low Countries (Belgium, the N etherlands, and Luxem bourg) som etim e around 5000 BC and then advancing fu rther to Scandinavia and the British Isles d uring th e next few hundred years. R oberts suggests th a t by about 4000 BC farm ing spread all around Europe w ith occasional reversions to the previous regime. Besides husbandry and agriculture the innovations o f th a t period were improved stone tools, skin-scrappers, chisels, pottery, and weaving. W hether invented in E urope or borrowed from the N ear E ast, by 5000 BC Europeans h a d som e rudim entary metallurgy'. A t first, tools were m ade out of copper by ham m ering. L ater on. using the plentiful wood resources, sm elting developed. O ne of the first b o ats found in E urope dates back to seventh m illennium and it was found in Denm ark. R em ains of textiles and baskets were found in the Swiss sites d ating back to 5000 BC. D uring th a t period C entral Europeans invented th e pitched roof, which was much better for th e clim ate of the N orthern Europe th an the flat roofs of the M editerranean. A griculture allowed surplus production of food thus providing for people to do other things than being involved directly in production. T h e early indicators of social orga nization of some com plexity can be seen in the m egalithic sites found in Europe. T he m ost ancient exam ples are cham ber tom bs in Spain an d B rittany' th a t date to 4000 BC. T he most famous later exam ple is Stonehenge in so u th ern E ngland, which dates back to about 2000 BC. T here are speculations th a t such sites indicate ancient religious beliefs. Religion is one of a num ber of social institutions, which are incorporated abstractly in the model under a nam e of infrastructure. This was the age w hen th e European civilization was being born. The new life style allowed faster population grow th. However, for a long time E urope was still a p retty em pty place as seen from the fact th a t early Neolithic sites had no defensive buildings. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 2. A B R IE F H IST O R Y OF ST R U C T U R A L D E V E LO P M E N T 8 2.3 Complex Societies and Urban Civilization (T h e C ity S ta te) A bout th ree millennia ago some villages in E u ro p e m erged into th e first little towns. T he process began in the M editerranean, where m ild clim ate and the w arm seas of the region m ade tra d e and com m unication easy. T he M inoan society on C rete was the first one in E urope to develop all m ain attrib u tes of a civilization: literacy, com plex social structure, m onum ental architecture, and it engaged in diplom acy with outsiders and was exercising its naval superiority. D uring its 600 years of existence the civilization created the earliest E uropean writings. T hese were tablets used for adm inistration o r accounting. Cretans grew w heat, olive and vine, had dom esticated c a ttle and sheep th a t were used for export of wool. A fter being w eakened by a powerful earthquake and an eru p tio n th a t destroyed the palace a t Knossos, th e civilization was overtaken by the invaders from Greece. L ater, some of the sm all fortified sites in G reece grew into cities. Among them were A thens, M ycenae and Syracuse. These city sta te s were run as m ini-nations: self-governing societies w ith formal political structures for people to participate in collective decision m aking. Usually there were periodic councils a t which deliberations on public issues took place. Mycenae h ad a staff of bureaucrats involved in an extensive record keeping. Syracuse was the w ealthiest and most influential am ong all the cities. It was formed in 733 BC by the colonists from Corinth. It h ad th e best harbor in Sicily and in time it becam e a dom inant pow er in the M editerranean. A m ore complex political structure was tested when a num ber of cities formed a loose league. T hese were early signs of em ergence of the notion of a nation, a distinction betw een ” us” , speaking G reek and sharing Hellenic culture, and "th em ". non-Hellens. T he wars of th a t period between the Greeks a n d th e Persians co n trib u ted to the formation of th a t nationalistic sp irit, as Greeks felt them selves to be a group of civilized men fighting an inferior group of barbarians. They were form ing the ground for th e G reek civilization. T he G reek self-consciousness allowed them to hold th e first panhellenic gam es in 776 BC. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 2. A BRIEF H IST O R Y OF STR U C T U R A L D E V E LO P M E N T 9 2.4 Trading Empires T he M inoan civilization of C rete was a precursor of the later trading em pires. Lydians1 invented m oney around 700 BC. greatly sim plifying trade. Previously th e Greeks were using iron goods as a rudim entary form of currency. By the fifth cen tu ry BC, trade was flourishing. Greek city states were trading extensively, im porting grain from the M editerranean, and Egypt. This was accom panied by growing population and scientific progress. In the fourth century BC, two M acedons2, Phillip II and later his son Alexander th e G reat, united the Greeks in another w ar against Persia. T he legendary military successes of A lexander created a huge em pire spreading the G reek influence to areas th a t had never felt it before. At the same tim e, the empire ad o p ted a bureaucratic and governm ent machine transplanted from M esopotam ia and Egypt. A lexander's wars released great am ounts of precious objects which stim ulated economy, patronage of the a rts and enabled him to m aintain standing arm ies and bureaucracies. However, soon after the d eath of Alexander his em pire disintegrated into several sm aller kingdoms. It was not long before another em pire was born. According to a legend, Rome was form ed by Rom ulus in 753 BC. It stayed under the rule of the T arquin family of the E truscan royal house until circa 500 B.C. T h at year the family was overthrow n and the R om an R epublic was established. D uring the tim e of A ugustus, who ruled from 27 B.C. to 14 A.D., th e Roman Republic was succeeded by an empire. At its greatest extent it controlled territories stretching from B ritain and Germ any to N o rth Africa and the Persian Gulf. U nity was brought to a large area allowing many cultures living side by side to contribute to the cosmopolitan whole. Rom an upper-class boys were learning Greek classics and people were travelling across the M editerranean m ore easily. As Roberts w rites: ” power brought the peace..." The Rom an Em pire created a new world order in w estern Asia, the M editerranean, w estern Europe and N orth Africa. R om an system 1 Lydia was an ancient country of west-central Asia M inor on the Aegean Sea in present-day northwest Turkey. It was noted for its wealth and the magnificence o f its capital, Sardis (T h e American Heritage D ictionary 1992). ' M acedon was an ancient kingdom at the North of Greece. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 2. A B R IE F H IS T O R Y OF STR U C TU R A L D E V E LO P M E N T 10 sprang, formed and th en eventually adopted the new religious dogm a, the C hristianity, th a t shaped the rest of th e European history. Religious w ritings in Greek an d L atin created during the early days of C hristianity were read by the Europeans through the years to come. A fter 395 the R om an Em pire was split into the B yzantine E m pire and the W estern R om an Em pire. The la tte r rapidly digressed into anarchy under th e attacks of barbarian invaders from the north and east. T he last em peror of th e em pire. Romulus A ugustus (born c. 461), was dethroned by the G oths in 476, the traditional d ate for the end of the R om an Em pire. A successful attem p t to reunite at least some of th e territories formerly in th e em pire was m ade by Charlem agne, also known as C harles th e G reat, who was king of the Franks 768-814. O n C hristm as D ay of 800 he was crowned the em peror of th e West by Leo III, whom Charlem agne restored to the papacy. T h a t event established th e Holy R om an Em pire, which was a legitim ate successor to the R om an Em pire (T he Concise C olum bia Encyclopedia). T he em pire was virtually dissolved in the Peace of W estphalia (1648) th a t ended the T h irty Years W ar and recognized the independence of all th e states of the empire. 2.5 Industrial Economies T h e term industrialization implies a change from small scale production to large enter prises, such as factories, shipyards th a t use new power technologies. Industrialization calls for revolutionary different attitu d es to wealth to satisfy its need for capital: people m ust be willing to invest. Once production takes off, it leads to higher incomes and higher consum ption, which creates greater m arkets. This leads to even more invention an d more w ealth flowing into production. Thus once industrialization starts, a totally new socioeconomic system is born (Pollard 1998). T his is a description of a process th a t unfolded in Europe startin g in the IS th century. T h e change was so drastic th a t a special term was coined for it, the Industrial R evolution. Industrialization sta rte d in G reat B ritain and then spread to the C ontinental E urope. At first it was only a sim ple steam engine invented by Newcomen in 1712. It was prim arily Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CH APTER 2. A B R IE F H IS T O R Y OF S T R U C T U R A L D E V E LO P M E N T 11 used to remove w ater from mines. In 1769. while repairing one of the Newcomen engines, W att im proved on the design. As more im provem ents were made, a rudim entary engine becam e a p o te n t power source th a t created unprecedented possibilities in many fields. T he steam ship was invented in 1803 and first railroad was built in 1814. The steam engine transform ed textile mills into factories as we know them today, m aking the G reat B ritain a w orld leader in cotton m anufacturing and textiles. 2.6 Global Information Economies B y the end o f th e tw entieth century many new innovations in technological and political fields created a world which significantly differs from th e preceding ind u strial economies. T he New Inform ation Age reduced the im portance of boundaries, created new wealth and possibilities. T h is is th e age th a t saw the b irth of th e Internet, the end of the Cold W ar and collapse o f th e dual power system after the Soviet U nion disintegrated. This is th e system we live in today. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 Chapter 3 Production Function A production function determ ines aggregate output based on the population level. The production function for G EM Europe is taken w ithout m odifications from th e original G E M model; therefore, this chapter draw s heavily on D ay (1999). 3.1 Infrastructure Any society possesses institutions th a t are not directly involved in any production process. A prem odem tribe m ight have h ad a council of elders th a t was adjudicating disputes and m ade decisions of th e concern of th e entire group. T here was also m ost likely som e sort of a religious leader, a sham an, who was guiding religious life of the society. L ater societies developed courts, governm ents, universities, police, political parties, etc. th a t all together have been contributing to cohesion and cooperation of o th e r productive activities. Such infrastructure also train s and encultures the labor force. G EM assumes th a t population, x . consists of households, each having two adults. T his assum ption poses m ethodological difficulties in estim atin g param eters as a popula tion consists of people of various age groups, some adults never marry, and som e of those who do form couples are barren. To avoid these difficulties, unlike GEM , this m odel mea sures population in th e num ber of individuals. The population divides its tim e between work in infrastructure and production. The am ount of w ork-hours spent on activities in infrastructure is M . T hen, tim e spen t in the labor force on productive activities is: L — x - M . (3.1) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 3. PRO D U C TIO N FU NCTIO N 13 3.2 Social space Each given technology ” produces" social space. N . which is defined as a m axim um num ber of people th a t a current socioeconomic order can support. T hen th e social slack, S, for a given econom ic unit is the difference betw een th e social space a n d th e current level of population of th a t unit: S — N - x (3.2) 3.3 Production We assum e the following production function: Y := BG(L, S ), L > 0, 5 > 0 . (3.3) T his equation implies th a t production is a function of the technology level, B , labor input. L, and social slack, S. We assum e that w ith respect to the labor in p u t the production function has th e following properties Q Q G(L,0) = 0 and lim = oo . (3.4) l—o oL T he production function is also continuous in S and satisfies the conditions: Q Q G(0, S) = 0 and lim = oo (3.5) v 5— 0 dS These assum ptions say th a t labor and social slack are required for positive production and both have declining m arginal productivities. The effect th a t social slack has on production can be understood from considering a hypothetical exam ple of a hunting and gathering band. A t first there is plenty of food in the neighborhood of the band. To increase production the group only needs to spend more w ork-hours on food collection. However, as the band grows, it depletes the anim al and plant foods in the area, decreasing th e productivity of the search (example is taken from Day 1999). A real life case th a t Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 3. PRO D UCTIO N FU N C TIO N 14 exem plified such, production dynam ics was the one of E aster Island (M iller 1996: see more on E aster Island in section 7.2). S ubstitu tin g (3.1) for L an d (3.2) for 5 . production function (3.3) can be w ritten as . 0 . i ? (A/. N) H (x ):= { ■ (3.6) B G { x — M , A — x ), x 6 (A/, N ) T he param eters M and N are th e lim its th at perm it or prevent the use of a particular technology. Conditions (3.4) and (3.5) im ply that lim H'{x) = co x—A / lim H'(x) - — oo x— » A r and th a t for all x e (M . N ), H"(x) < 0, so H(.) is strictly concave on [A/, iV'j (Figure 1). X N K Figure 1: Production function w ith infrastructure and social space. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 3. P R O D U C TIO N FU NCTIO N 15 3.4 Replication and integration of economies As internal diseconom ies of social space becom e felt by the population, it may choose to split into a n um ber of sm aller economies w ith th e sam e technology. Such a split will result in an increase in the aggregate welfare. T he ancient G reeks were the m asters of such strategy of replication. As m ainland Greece was becom ing too small for the growing population, th e G reeks began forming settlem ents around th e Aegean and Ionian seas, the Black Sea a n d in th e M editerranean. R oberts w rites: W hen a city grew too big for its resources, or its in h ab itan ts felt th a t it had done so. a com pany of em igrants made up of whole families and households would set o u t to find a suitable place overseas for a new settlem ent. Suitability was a m a tte r of being able to pursue a G reek way of life w ith as little change as possible, and given the M editerranean shape and clim ate, this was not usually too difficult. T he result was the G reek diaspora consisting of m ore th an 1000 colonies. M any cities survived to the present day. For example, M arseilles in southern France is the descendant of an earlier G reek colony M assilia. Sometimes form ing a larger economy through m ergers of autonom ous economic units m ay be beneficial (recall the cases of A lexander’ s or R om an em pires). Such mergers allow to economize on infrastructure. In the model, each generation decides on the optim al num ber of econom ic units, j E {2l,l € = { 1 ,2 ,4 ,8,....} , which maximizes the to tal output: j = J {x ) = arg m ax 2l~ l H ( x /2 l~ l ) . Such population would have 2J" economies each of them locally efficient for the population of size x/2U T h en th e aggregate production function is K (x ) = 2j H { x /2 j ) (3.7) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 3. PRO D U C TIO N FU NCTIO N 16 3.5 Environmental space We assum e th at a geographic region can su p p o rt a lim ited population given a particular production technology and infrastructure conditions. Such limit is called an environm en tal capacity, x. T he difference between the cu rrent population level and th e environm ental capacity is the environm ental slack, E: E := x — x . T h e environm ental slack acts on the production through a damage function: g (x - x) - = 1 , x = 0 > 0 , x € (0,x ) = 0 . x = x (3.8) w here for all x € E [0.x], < 0, lim = 0 . an d lim d x x— '0 dx x— * x dx — oo A pplying function (3.8) as a dimensionless m ultiplier to production (3.7) gives the envi ronm entally constrained production function: K {x ) = 2j H { x /2 j )g (x - x) (3.9) This form ulation implies th a t dim inishing environm ental slack has a negative effect on production. Following D ay (1999), I use th e following form ulation for th e dam age func tion: g ( x - x ) = ( f c i ) = ( l - l )4 • (3.10) Defining G {L ,S ) := L ^ S 1- 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 3. PRO D U CTIO N FU N C TIO N 17 equation (3.9) can be w ritten as < s K (x ) = ( 1 - | ) B t ( x - 2 l l M ) 0 (2 l lN - x ) 1- 0 ' (3-11) Figure 2 displays an exam ple of the environm entally constrained production function K { x ). H orizontal axis shows population in logs. Each of the humps in th e direction from th e vertical axis corresponds to the distinct value of param eter I : 1. 2, 3. etc., which determ ines th e num ber of economies to be 2/_1, th a t is 1, 2. 4. 8. 16. etc. T h e growing population eventually reaches the environm ental space level, x , at w hich point production falls to zero. K ( X , r \ Figure 2: An environm entally constrained production function. 3.6 Epochs T h e m odel has six distinct socioeconomic regim es (Table 1) as outlined in C hapter 2, each characterized by its particular param eter values. Each epoch represents distinct adm inistrative and production technologies, different family values, a n d ways of life. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P TE R 3. PR O D U C TIO N FU N C TIO N T a b le 1. The M acro System s in W orld H istory IS A pproxim ate D uration Initial E n try Index D escription D uration (years) (generations) (generations ago) 1 H unting b an d 100,000-8,000 BC 3680 4080 2 Village agriculture 8,001-3,500 BC 180 400 3 C ity-state 3501-500 BC 120 220 4 Trading em pires 501 BC-1750 AD 90 100 5 Industrial societies 1751-1975 AD 9 10 6 Global inform ation economy 1976-present AD o 2 Source-, adapted from R ichard D ay 1999: 271 In each generation, people choose th e optim al system for the current population and technology out of a set of possible production functions, th a t is: K ( x ) = m ax {K „ (x)\ . p={L,2,...,6} P ' (3.12) w here K v {x) is a production function (3.11) th a t uses param eters of epoch p. T hen the production function becomes: K (x ) — max p={l,2,...,6} 1 — — m ax x p J IGX++ B t,P (x - 2l- l M p) 0p (2 l~ l N p - x ) (3.13) 3.7 Learning by Doing We think of each production regim e as having a technological potential, B . P roduction experience accum ulates w ithin an active system according to th e following rule: Ht+i — B t ( B — B t \ T - = p hr-J T his form ulation im plies th a t th e rate of change is proportional to some learning para- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 3. PRO D U C TIO N FU N C TIO N 19 m eter p and relative efficiency gap between the current level of technology, B t, and th e p o te n tial technology, B . T h a t equation can be rew ritten as a learning by doing rule: w here 0 < p < 1 ensures convergence of the process to B . W hen a given regime is entered for th e first time, the technology param eter assum es some initial value Bo, which satisfies 0 < B q < B . The rate of grow th is the greatest when the initial level is low and the p o ten tial is high resulting in a large technology gap. T he rate of grow th declines, as the technology level asym ptotically approaches its potential. Figure 3 illustrates the process of technology converging to its potential value. (3.14) 3 I Figure 3: Dynamics of technology improvement. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CH APTER 3. PRO D U C TIO N FUNCTIO N 20 We assume th a t a t any particular period only th e technology of th e governing regime improves for only then can experience increase practical knowledge. If i is the index of the dom inant regime, then n i n , pH 3 !)2 3 t-rl — 1" P )3 t --------j p ---- 3 L i = B{ , j # i. Figure 4 shows how the technological knowledge acquisition governed by equation (3.14) responds to increases in th e learning rate, p. G reater values of p im ply faster tech nological progress, th a t is a faster approach to th e m axim um potential value of technology B (the upper right com er of the graph). 3c.: 0 FigU ie 4. Pdashed ^ Psolid 3.8 Production parameters Production function as it is specified in (3.13) is extrem ely complex to analyze due to the m ultitude of effects each individual param eter has on it. Additionally, th e dynam ic Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 3. PRO D UCTIO N F U N C TIO N 21 n atu re of th e technology param eter. B , com plicates th e m a tters even further. In Figure 5 and Table 2 I attem p ted to sum m arize som e of the effects th a t production param eters have on production function (3.11). K ( X ) I /VVVVVYY\ L o g i x ) Figure 5: Effects that param eters have on th e production function. P aram eter values for the production function were chosen such as to cap tu re stylis tically the historical facts from Europe. Values for the environm ental space, x , which signifies th e m axim um population level of a socioeconom ic regime, were set to th e popu lation estim ates from Livi-Bacci (1996) for th e tim e of a regim e sw itch. For exam ple, in 1750 (period 4069 in th e model — see section 6.2) population of Europe was a.bout 111 million. S ettin g xq to th a t number ensures th a t a t the tim e of the switch to the In d ustrial regim e the sim ulated population is at the historically plausible level of 111 m illion. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 3. PR O D U C TIO N FU NCTIO N T a b le 2: Some shifts to the production function 22 Effect P aram eter change E xplanation A A n increase the slope o f the left edge o f the graph M i Lowering infrastructure requirem ent allows sm aller populations to use a p articular technology B A shift to the right o f the left edge o f the graph M T Raising inffustructure requirem ent means th a t only larger populations can use a technology X t G reater environm ental space increases social slack, thus reducing the negative effects of the dam age function g(x — x) C A n upward shift o f the graph M i Lower infrustructure requirem ent allows m ore people to be involved in production N T G reater social space delays the internal diseconom ies 3 T G reater 3 means greater m arginal prouductivity of labor B r B etter technology implies greater productivity x T G reater environm ental space delays diseconom ies associated with it D .4 reduction in the slope o f decent near the x n Lowering this param eter reduces the effect th e environm ental dam age function has on production E A shift to the right o f the right edge of the graph x t G reater environm ental space allows greater populations to use the sam e production function Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 3. PRO D U C TIO N FU NCTIO N 23 For the sake of sim plicity this model, following G EM , assumes th a t countries th a t a system consists of are of equal size. Therefore, at best th e choice of values for the social space, N . and infrastructure, AI. can capture the stylistic fact th at more advanced coun tries could support greater populations and required larger infrastructure. Thus, Table 3 shows th a t num bers for N and A I progressively increase through the system s. The sam e principle was used for selecting values of the technology acquisition rate, p. and the potential technology, B . This means th a t technological progress of m ore advanced regimes is faster and the potential technology level is greater. In practice, the param eter values were selected through the application of the grid search (Greene 1993). This is the m ethod th a t had been used to find param eters for G EM and is com m only applied to m any other models (exam ples are Forrester 1971 an d Ivremer 1990). Table 3 presents param eter values adopted for the production function for each of the system s. T a b le 3: Production P aram eter Values (Note: K = 1000) P aram eter System 1 Hunting System 2 Village System 3 C ity-state System 4 Trading System 5 Industrial System 6 Inform ation econom y Bo 2.97 2.15 2.41 2.0 2.0 300 B 7.0 10.0 12.0 16.0 120.0 3000.0 P 0.0003 0.012 0.09 0.2 0.4 0.99 (3 0.9 0.6 0.6 0.6 0.6 0.4 AI 5.0 250.0 250K 2.5K2 20K2 39SK2 N 30 2000.0 IK 2 10K2 350K2 900K2 8 0.1 0.1 0.1 0.1 0.1 0.1 X 1.6K2 6K 2 19K2 11 IK 2 o i w o o - x t * 900K2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4 Dynamic Fertility 24 I tu rn now from production technology to th e relevant aspects of dem ography. 4.1 Demographic transitions T here were two dem ographic transitions in th e history of E urope. O ne was a fertility3 hike after adoption of agriculture. Bently e t al. (July 1993) found th a t in general sede- ta ry agriculture is m ore congenial to higher b irth rates than a hunter-gathering system. T h ey surveyed th e literature on 57 natural fertility populations'1 a n d showed that average fertility for non-agriculturalists was 5.5 b irth s per female, while th a t for agriculturalists was around 6.6. D uring the second dem ographic transition, which started aro u n d the end of the last century and com pleted by th e tim e of W W II, fertility declined from about six children per wom an to around 2 (see Table 4). T a b le 4. Average num ber of children p er woman for 1750-1950 C ountry 1750 1775 1800 1825 1850 1875 1900 1925 1950 Sweden 4.21 4.34 4.68 4.4 4.28 3.51 1.9 2.05 1.98 E ngland and Wales 5.28 5.87 5.54 5.05 4.56 3.35 1.96 2.15 2.0 G erm any - - - - 5.17 3.98 2.0S 2.06 1.65 France - - - 3.42 3.27 2.6 2.14 2.59 2.13 T he N etherland - - - - 4.98 3.98 2.86 2.76 1.85 Spain - - - - - 4.64 3.38 2.51 2.18 Italy - - - - 4.67 4.5 3.14 2.27 1.9 Source-. A dopted from Livi-Bacci 1997: 134 3 Fertility refers to the number o f children born by a woman during her lifetim e. 'A natural fertility population is a society that d oes not practice modern forms of contraception. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 4. D Y N A M IC F E R T IL IT Y 25 4.2 How is the desired fertility formed? T here is still no clear answer to the question of how desired fertility is formed. Due to the m ultifaceted n atu re of the issue w ith m any interactions and feedbacks, there is still no single fertility theory in spite of the m any years of research in various disciplines. In an extensive review article on the fertility theory as applied to th e second fertility transition Voland (1998) w rites th a t "experts do not agree on what changes in which independent variables have ultim ately introduced this transform ation." However, we do know some of th e factors th a t affect th e dem and for children. They include income, cost of raising children, social and cultural customs, and expected child m ortality. T h e cost of raising a child is a com bination of direct costs of child-rearing, economic o p p o rtu n ity costs for parents, economic constraints imposed by dow ry for daughters, the health o f the m other which is affected by each childbearing and birth, etc. W om en’ s education and her opportunity cost of staying a t home also have effect on fertility — if women custom arily do not work, then fertility tends to be higher (Schultz 1993). A w elfare-transfer effect has also been identified as a factor in fertility decisions. If the econom ic w ealth flow theory of fertility, originated by Becker, is correct, children must have a positive net econom ic value for their parents (Reher 1995). A child is seen as an investm ent th a t parents hope will be repaid. According to Caldwell (1976), in extended families th ere is an intergenerational w ealth transfer from th e younger generation to the elders. For exam ple, it has been suggested th a t am ong possible reasons for greater num ber of children in th e agricultural household was th e need for children as sources of ex tra labor (B entley Ju ly 1993). B ut evolutionary reproductive ecologists disagree with th a t view suggesting th a t rare organism s exploit th eir offsprings; therefore, they argue th a t the net intergenerational w ealth flow is from parents to the children, and not vice versa. For exam ple, Schofield (1991) suggested th a t th e economic value of children in the English speaking world was negative. Indeed, it appears th a t today in m any nuclear families of the developed societies th e flow is from parents to the children. T he disagreem ent on the net econom ic value of children in history is possible because inform ation about the production and consum ption patterns of children in historic E urope is scarce (Reher). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 4. D Y N A M IC F E R T IL IT Y 26 Nevertheless, there has been a well docum ented relationship between production out p u t and fertility. For th e longest period of tim e fertility was positively related to income, and it is only recently th a t th e trend in E urope was in the opposite direction. Since th e last century, every country in Europe passed through a transition in which fertility declined as people becam e b etter off (Livi-Bacci 1997, Kremer, 1993). D ay et al. (1989) studied a birth function th a t depends on family preferences, con sum ption, subsistence income, and costs of child rearing: rx(cj) = < 0. ai(uj— T ] )a2- 0 < U < T] U J > T ] (4.1) Here ui is the average welfare, q is the cost of childrearing, a is the preference for children, 7 7 is th e welfare threshold; a i, ao , < 2 3 are some param eters. Figure 6 shows the function. £ (w) w n Figure 6: A desired fertility function. Confirming the theorem th a t virtually any regular behavior can be rationalized (Day 1994), this particular b irth function satisfies an indirect utility function of the following Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P TE R 4. D Y N A M IC F E R T IL IT Y 27 form: T,, . f u(w). 0 < U < T ] V (q ,u ) - - < [ W (q,u:), u > q where v{u>) := K \ ujk , and W (q ,u ) := K itjk 4- ai(u> — q)a3 4- ao • Param eters th a t enter function (4.1) c ap tu re the adaptive nature of the reproduc tive process. E volutionary reproductive ecology implies th a t over the years reproductive preferences evolve through stages in a D arw inian way (Van de Walle 1992). An optim al reproductive strateg y is determ ined over tim e by the society through some sort of cost benefit analysis perform ed over the statistically average household. Once a perception of an ideal family size is formed, it becomes a p a rt of culture, spreads across the society and is passed down from generation to generation. Thus women in the m odern W estern culture form the perception of an ideal fam ily size long before marrying (Van de Walle). Voland writes th a t in prim itive societies th e kin exerts influence on the reproductive de cisions of its m em bers, enforcing what is th o u g h t an optim al reproductive strategy. Such constraints as m ate selection, matrimony, a n d so on are all adjusted to fit the strategy. 4.3 Mortality effect Function (4.1) does not yet account for m ortality. T hroughout the anim al world m ortality plays a m ajor role in shaping the reproductive strateg y of species. Biologists identify two extrem es of reproductive behavior. O ne, called r-reproduction, is characteristic of organism s th a t live in very hostile or uncertain environm ents, and therefore have to take every opportunity to m ultiply, bringing as m any offsprings as possible in the hopes th a t som e of them will survive to adulthood. E xam ples are frogs and rabbits. A nother extrem e is having only few offsprings and taking care of them . T his is the so called K -strategy, usually typical of large animals, such as elephants. All organisms fall somewhere in betw een these two extrem es. Though far from following the r-reproduction, in environm ents w ith high m ortality rates hum ans m ay opt for high fertility, ra th e r th a n quality of children. Demographic Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A PTE R 4. D Y N A M IC F E R T IL IT Y 28 studies have show n th a t num ber of births is positively correlated w ith m o rtality rate (see Sah 1991 and Schultz 1993). An increase in infant m o rtality after adoption o f agriculture has been suggested as a contributing factor to th e increased fertility after th e Neolithic revolution (B entley et al. July 1993). Also, there has been a long trad itio n in population research th a t advocates th a t decline in child and infant m o rtality was th e m ajor reason th a t swayed people to have fewer children and caused th e second dem ographic transition (see Gillis et al. 1996, R eher 1995, E asterlin 1996 an d m any other works). T he chain of events might have been as follows. M odernization lead to an adult and child m ortality decline, followed by th e infant m ortality decline. As the survivability of children increases, m ore th an desired num ber of children survive. E ventually parents s ta rt to internalize the new' reality into th eir reproductive behavior: they plan th e num ber of children w ith the num ber of children they expect to survive in m ind. T hus, low' rates of child and infant deaths bring ab o u t lower fertility. However because the m ortality effect is not th e only one influencing fertility, it is not surprising th a t som etim es fertility declined prior to the fall of m ortality. As a result, some studies (for exam ples see Van de Walle) did not find any convincing evidence based on local European d a ta th a t the decline in infant deaths led to the fertility decline. How'ever, in an extensive review article Palloni and R afalim anana (1999) conclude th a t even though th e m agnitude of th e effects of m ortality on fertility varies across E uropean countries and tim es it is consistently positive for m ost of the cases. M ortality acts on fertility through a num ber of m echanism s. T here is a physiological effect of the in fan t’ s d eath to fertility (Palloni and R afalim anana 1999). T erm ination of breast-feeding w ith the child’s d eath causes resum ption of menses an d ovulation and thus increases chances of conception. This m echanism is particularly stro n g in countries w here contraceptive use is not pervasive and breast-feeding is com m only practiced. T he lag between the child m ortality changes and fertility change due to th e m echanism is betw een one and two years. T here is also a replacement effect, which expresses itself w hen parents strive to a tta in a desired num ber o f surviving children at the end of their reproductive cycle. Some suggest (Caxey and Lopereato 1995) th a t we have form ed a ” two-child psychology” under which Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 4. D YN A M IC F E R T IL IT Y 29 the hum an reproductive goal has long evolved to the level o f two surviving offsprings: others (Reher) think th a t ”on average all couples will have enough births to guarantee th a t a t least three children will survive to their fifth birthday” . T he lag between infant's or child’s d eath an d replacem ent can be as short as for the physiological effect as parents may cease to use contraception and resum e sexual intercourse right away or as long as 35 years as they m ight wait until la ter years in their reproductive period to have a ’ ’replacem ent” child. O ften physiological and replacem ent effects can not be empirically distinguished (O lsen 1980). T he insurance (hoarding) effect shows itself in parents having m ore children than they would have had in the absence of m ortality. T he effect is m ore likely to be strong in societies th a t rely on the kinship old-age support networks and th a t stress the im portance of the reproduction of the lineage for th e purposes of inheritance. Fertility responds to the perceived child m ortality, and because such perceptions are difficult to measure, the m echanism is rath er elusive from detection in the available d ata. A nother factor that prevents th e m echanism from being easily detected is its spread over the entire reproductive period of a couple. Additionally, the perception m ay be changing over the reproductive years and thus hoarding m argin m ay be different a t different times. A ccounting for the death rate effect, th e relationship for desired fertility (4.1) may be rew ritten as: n(u>) — + i a i t y —T))a3 ~a l -raoq~“ t y —r / ) “ ■ a^d U! < T] otherw ise (4-2) where d is the d eath toll in the previous generation. Such form ulation implies that reproductive strateg y adjusts to the d eath rate w ith some lag. Figure 7 shows function (4.2) and various effects param eters have on it. A more detailed sensitivity analysis of this function is given in a later section on param eters. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 4. DYNAiVHC F E R T IL IT Y 30 D e s i r e d f e r t i l i t y C h i l d c o s t s i n c r e a s e o r , . M o r t a l i t v d e c r e a s e s . I a c o m e e l a s t i c i c 4 o r c h i l a r e n I i n c r e a s e s t h r e s h o l d r a i s e s I n c o m e Figure 7: Shifts to th e desired fertility function. 4.4 Limited fertility Desired fertility m ight be constrained due to biological lim itation. T he biological b irth ceiling is set by th e length of the reproductive period of a w om an. T he earliest the re productive period can begin is the age of puberty, which is th e earliest possible age of childrearing. Theoretically, the period ends at the age when biologically the last preg nancy is possible. However, in most of th e societies th a t d o n ’t practice birth control th e last child is born betw een the ages of 38 and 41 (Easterlin). A ssum ing th a t the first child is born at 16 and th e last one at 41, the w om an’s reproductive period is 25 years. If the m inim um time betw een births is 1.5 years (Livi-Bacci), then the m axim um num ber of births is: 25-year reproductive period , „ „ , . , f - - — : ---= 16.7 births. 1.5-year birth interval T he length of th e reproductive period and thus the upper bound on fertility is changing over tim e. For exam ple, nowadays pub erty and menopause com e a t different ages th a n Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P TE R 4. D YN AM IC F E R T IL IT Y 31 in historic Europe, thus theoretically increasing the potential num ber of children a woman can have. However, in reality, the upper bound in fertility is rarely reached. It can for example, be caused by poor nutrition. H ausm an an d W ilmsen (1984) notice th a t conceptions am ong the IKung are m ore often at the tim es of food abundance. Rose Frisch (1978) observed th a t in societies th a t do not practice contraception leaner women had longer intervals between births as com pared to fatter women. Taking into account the upper bound on fertility, F . th e fertility function may be rew ritten as: f(ui) = m in(F ,n(oj)) . (4.3) T he graph is shown in Figure 8. F e r t i l i t y I n c o m e n Figure 8 : F ertility lim ited by fecundity. C ausal fertility links discussed in this chapter form a causality graph of Figure 9. A plus sign on a link m eans th a t th e relationship is positive. A m inus sign implies a negative relationship. Notice th a t there is no sign on the Incom e-D esired Fertility link as its m odality varies. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 4. D Y N A M IC F E R T IL IT Y 32 Child Costs W elfare Elasticity o f < ► D esired Fertility Income Fecundity Welfare ThreSi^iu. / Fertility Mortality Figure 9: A fertility causal chain. 4.5 Fertility parameters As for the production param eters, I found the best param eter values for th e fertility function (4.3) by applying a grid search procedure. T he search is assisted by perform ing the sensitivity analysis for the fertility function w ith respect to changes in param eter values as shown in Figures 10 and 11. The analysis is extrem ely helpful in calibration efforts as, for example, it shows th a t, a has a very sm all effect at low income levels (say, around 3 income units); however, q has very stro n g effect a t small income levels. Note th a t in these graphs th e threshold param eter q is set equal to the values in Table 5. Day, Easterlin, Van de Walle and many o th e r researchers note th a t preferences of people evolve over tim e. For exam ple, the fam ily preference param eter, a , m ost likely decreases for each succeeding epoch. Preference for children may be decreasing due to b e tte r income opportunities for parents and b e tte r pension systems th a t elim inate the safety m otif in parents w anting to have children (Gillis 1996). Fecundity, F , also does not stay constant over th e years: as has been m entioned in the previous section, variables such as nutritional quality affect the maximum possible biological level of fertility. In this m odel I assum e th a t fecundity m ay be greater for m ore advanced regimes. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 4. D YN A M IC F E R T IL IT Y 33 4 0 3 7 . 5 35 3 2 . 5 3 0 2 7 . 5 25 2 2 . 5 w 60 30 4 0 50 70 8 0 1 0 2 0 a) C hange in a (solid line: a = 0.1 : dashed line: a = 0.01) 3 7 . S 35 3 2 . 5 30 2 7 . 5 25 2 2 . 5 w 40 80 30 5 0 7 0 1 0 20 b) Change in q (solid line: q = 1.1: dashed line: q = 2) n (w> 4 0 3 2 . 5 3 0 2 7 . 5 2 5 2 2 . 5 50 3 0 4 0 7 0 80 20 1 0 c) Change in 7 7 (solid line: 7 7 = 0.7; dashed line: 7 7 = 5) Figure 10: Sensitivity analysis of the fertility equation w ith respect to the variable param eters. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P TE R 4. D YN A M IC F E R T IL IT Y 34 n(w > 4 0 3Sf new ) 4 0 ; 3 2 . S 30 2 7 . 5 2 5 2 2 . 5 : SO 70 1 0 20 30 50 4 0 a) C hange in ai (solid line: a i = 0.3; dashed line: a i = 0.6) 3 2 .5 1 2 7 .5 } 25 2 2 . 5 ' 5 0 70 1 0 SO 2 0 30 4 0 b) C hange in ao (solid line: a9= 210:dashed line: ao= 100) n (v) 4 0 r 35 3 2 . 5,1 30 2 7 . Si 25 2 2 . 5 SO 70 S O 10 20 30 50 4 0 c) C hange in a3 (solid line: < 2 3 = 2.4;dashed line:a3 = 3.0) n;wi 40 r 35 r 3 2 .5 1 30 2 7 25 22 .5 w 60 10 S O 70 S O 20 4 0 30 d) C hange in a4 (solid line:a4=0.7877:dashed line:a4= 0.7) Figure 11: Sensitivity analysis of th e fertility equation w ith respect to invariant param eters. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 4. D Y N A M IC F E R T IL IT Y T a b le 5: F ertility Param eter Values 35 P aram eter System 1 H unting System 2 Village System 3 C ity-state System 4 T rading System 5 Industrial System 6 Inform ation economy ai 0.3 0.3 0.3 0.3 0.3 0.3 a.2 210.0 210.0 210.0 210.0 210.0 210.0 03 2.4 2.4 2.4 2.4 2.4 2.4 G 4 0.78 0.78 0.78 0.78 0.78 0.78 F 35.57 46 46 140 260 260 Q 0.9 O.S 0.8 0.8 0.5 0.4 9 0.224627 0.23 0.248 0.258 0.13 0.1 V 0.2 0.3 0.4 0.41 1 0.7 However, I assum e th a t some param eters, uam ely a i, ao , < 23, and < 24, are invariant through th e socioeconom ic systems. These param eters establish the basis for the reproductive behavior th a t was formed in the early days of hum anity. Param eters th a t do change cap tu re th e ad ap tatio n s that the basic reproductive behavior undergoes in response to variations in environm ents. Table 5 gives a sum m ary of param eter values. It is im p o rtan t to stress th a t a num ber o f sim plifying assum ptions render this model to be a highly stylistic one. Among such assum ptions are th e ones th a t param eter values do not change w ithin a given epoch and th a t all agents are homogenious in their preferences. In reality, not only the cost of child rearing varies from one household to another, but there is often an unequal care for children even w ithin one fam ily based on gender, perceived ability of th e child, socioeconomic conditions, etc. (see Voland 1998 for a review). A nother ab stractio n comes from th e tim e unit chosen for GEM and adopted for G E M Europe, which is one generation, or 25 years. A ssum ing population sta rts w ith xq m em bers and th a t th e reproductive ra te of the ad u lt population in the year t is bt the population dynam ics within a generation of 25 years is expressed as follows: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 4. D YN A M IC F E R T IL IT Y 36 Xi = xq ( 1 4 - b \ ) — 2:1(1 4 - 62 ) = 2:0(1 4- £>i) (1 4- bo) * 3 = 2 : 2 ( 1 - 1 - 6 3 ) = - - = 2 :0 (1 4- 60(1 4 - 6 2 ) ( l - r 6 3 ) x-25 = 2:24(1 -1 - 623) = ...= :r0( l 4- 6x)(l 4- 62)(1 4- 63)...(1 4- 625) = x 0N ■where N = ( l 4-6x)(l4-62) (l 4-63)...( l4- 625) denotes a generational fertility rate. A ssum ing th a t the reproductive rate stays constant and is equal to 6 for the entire generation. N = (1 4- 6)25. At the tim e ju st before the latest dem ographic transition the b irth rate was about 40 births per one thousand of population (E asterlin 1996). If all new borns were to survive to adulthood, th a t w ould im ply th a t 6 = 0.04. U nder such circum stances th e generational b irth rate, iV, could have been as high as N = (1 4- 0.04)2° ~ 2.67. C onverting it back to births per a th o u san d of population, gives an N = 2,670, which can be thought of as a m axim um possible fertility level per generation in a perfect world w ithout infant and child deaths. This num ber scaled by 10 (to account for the fact that not all newborns survive) is about th e u pper level on fertility, F , set for the Ind u strial and Inform ation Economy regimes of th e model (see Table 5). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 Chapter 5 A History of Mortality Let us now look a t the history of m ortality. 5.1 General observations on mortality As historic census d a ta are scarce, researchers m ust rely on estim ates for m ost of European history. Such estim ates come from the analysis of prehistoric cem eteries and population densities th a t can be sup p o rted by particular environm ents (Livi-Bacci). T he estim ates are very approxim ate as there are many sources of errors for such reasons, among many, as the practice o f infanticide and killing of the elderly and infirm th a t were common to many societies in the world (M eindl 1998). However, this is w hat we know for the m ortality p a tte rn s over the longest period. The average life expectancy m ust have been around 30 years, as this is the average life span th a t is required for a successful hum an reproduction (O lshanscy and C arnes 1994). Livi- Bacci estim ates th a t for the period between 1 A .D . and 1750, m ortality rates possibly averaged 40 per 1000. This agrees well w ith the rep o rt th a t life expectancy at birth for the English upper class from the 13th to early 18th centuries was always between 20 and 40 years w ith som e fluctuations over the years (Lee 1980). T h a t life expectancy approxim ately corresponds to the crude death rate o f 25 to 50 per 1000. In the 18th century, a dram atic change in the m o rtality patterns began that was later dubbed T he M ortality Revolution. Even though, m o rtality rate varied by the social class and geographical location (Blum, Houdaille a n d Lam ouche 1990), it universally fell. Average expectancy a t b irth increased between 1740 and 1840 from 33 to 40 years in England; from 25 to 40 in France; from 37 to 45 in Sweden; and from 35 to 44 in D enm ark. Table 6 shows th a t since the 18th century life expectancy m ore than doubled for m ajor E uropean countries. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H ISTO R Y O F M O R T A L IT Y 38 T a b le 6: Life expectancy in several W estern E uropean countries (1(50-1985) C ountry 1750-9 1800-9 1S50-9 1S80 1900 1930 1950 1993 England 36.9 37.3 40.0 43.3 48.2 60.8 69.2 76.2 France 27.9 33.9 39.8 42.1 47.4 56.7 66.5 77.4 Sweden 37.3 36.5 43.3 48.5 54.0 63.3 71.3 78.1 G erm any - - - 37.9 44.4 61.3 66.6 76.2 Italy - - - 35.4 42.8 54.9 65.5 77.7 T he N etherlands - 32.2 36.8 41.7 49.9 64.6 71.S 77.0 Source: ad ap ted from Livi-Bacci 1997: 121 C an life expectancy be increased even further? O lshansky and Carnes (1994) suggest th a t th e m axim um possible life expectancy for the hum an population is betw een 85 and 100 years. T he num bers can be increased if significant im provem ents to h ealth can be m ade through genetic m odifications. However, even then the possible life expectancy is difficult to predict due to th e still unknow n effects of aging. T h e life expectancy of 100 years corresponds to about 11.77 deaths in a year per a 1000 of the population. 5.2 Randomness of death in history M ortality is affected by m any factors, such as nutritional level, sanitation, available med ical technologies, etc. However, som etim es changes in m ortality are fast an d dram atic w ithout any change in any of the above factors. These are th e m ortality hikes due to epidem ics. T he m ost devastating epidem ic disease of all was plague, the B lack D eath. T here were a few well recorded waves of plagues in E urope through the history. There was an o u tbreak of plague in 80 AD, during the reign of th e Rom an em peror Titus (Wells 1984). E ighty seven years later, in 167, a victorious arm y of the em peror Marcus retu rn ed from the Asian em pire of P a rth ia (geographically, th e region of m o d em Iran and A fghanistan) bringing back am idst the spoils of the victory th e bubonic plague. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 5. A H IS T O R Y OF M O R T A L IT Y 39 Then there were alm ost four centuries of absence. Plague reappeared in Italy again in th e 6th century terrorizing the region from 541 to 600 (Livi-B acci). More than 600 years later, in 1347. the first wave of a series of new catastrophic plague epidemics began. It started in Sicily and by 1352 it had affected all Europe, spreading as far north as Norway and as far E ast as R ussia. Later waves of plague were in 1360-3. 1371-4. 1381-4, 1388-90 and 1398-1400. For som e regions in Italy between 1340 and 1400, there was a m ortality crisis with deaths increasing at least sevenfold once every 11 years. If we assume th a t the m ortality was about 35 per thousand , then a tenfold increase in m ortality would have wiped out about one-third of the population. Fivefold increase would have elim inated one-sixth of the population. A nd it did cause a lot of devastation. E uropes population around the 14th cen tu ry of about 80 m illion was reduced to 50 m illion by 1400. There were less violent outbreaks through the fifteenth century'. Between 1400 and 1450 there were fivefold increases in m ortality on average every 13 years. For 1450-1500 th e average crisis happened every 37 years w ith m ortality increasing four times. Over the following centuries th e frequency and ferocity of these attack s declined further. They were also happening in a more localized m anner. During the plague of 1630 the epidemic was limited to M ilan only, though half of the city died; the sam e happened to Genoa and Naples during the epidem ic of 1656. T he last outbreak of plague in Europe th at covered a large area was in 1663-70. The areas involved were England, n o rth ern France, the Low Countries (Belgium, th e N etherlands, and Luxembourg) and th e R hine valley. The experience o f Europe showed th a t m ortality crises due to epidemics were largely independent of living standards or nutritional status and m ust be treated as exogenous to the population system . Their appearance was affected by som e biological and environ m ental factors. The ease w ith w hich the epidem ic spread and vicious efficiency w ith which it struck ■w as due to the way it was transm itted. T he schematic description of the bubonic plague transm ission is the followdng. T he bacillus (yersinia pestis) th a t causes plague is trans m itted by fleas th a t axe carried by mice and rats. W hen th e Eea bites a person, the lym ph glands of th e neck, underarm s, and groin swell. A fter a brief incubation period, the person gets high fever, coma, cardiac failure, and inflam m ation of internal organs. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 5. A H IS T O R Y OF M O R T A L IT Y 40 The disease is lethal for ab o u t two-thirds of those w ho contract it. T here is no natural im m unity to plague and those who survive acquire only a sh ort-term resistance to it. Also, neither prior nor during th e Medieval epidem ics th e cure o r preventive measures were discovered. Therefore, m ost likely the severity of th e disease declined over the years not due to the widely acquired im m unity to the disease by the population, but due to the evolution of the p arasite th a t enabled parasites from com pletely destroying the hosts. W ithout such an ad ap tatio n , th e plague would have killed th e entire hum an population of Europe. Sim ilar biological adjustm ent between parasites a n d th e hosts seem ed to be at least partially responsible for th e lesser virulence of infectious diseases an d the decline of mor tality in Europe after 1750 (M okyr 1993). Though, d e a th was still very unpredictable and random , over the years swings in m ortality rates atten u ated . Table 7 shows varia tions in the m ortality rates for 25 year periods caused by various crises (epidemics, wars, droughts, etc.). T a b le 7: M axim um and m inim um death rates (per 1000) in France and Sweden (18th-20th centuries) Sweden France Period M axim um M inim um Difference M axim um M inim um Difference 1736-49 43.7 25.3 1S.4 48.8 32.3 16.5 1750-74 52.5 22.4 30.1 40.6 29.5 11.1 1775-99 33.1 21.7 11.4 45.2 27.1 18.1 1800-24 40.0 20.8 19.2 34.4 24.0 10.4 1825-49 29.0 18.6 10.4 27.7 21.1 6.6 1850-74 27.6 16.3 11.3 27.4 21.4 6.0 1875-99 19.6 15.1 4.5 23.0 19.4 3.6 1900-24 18.0 11.4 6.6 22.3 16.7 5.6 1925-49 12.7 9.8 2.9 18.0 15.0 3.0 1950-74 10.5 9.5 1.3 12.9 10.5 2.4 Source: Livi-Bacci 1997, p. 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P TE R 5. A H IST O R Y OF M O R T A L IT Y 41 U nfortunately, there is little hope th a t we have com pletely elim inated the th re a t of terrific infectious epidemics. Epidem iologists say th a t viral evolution is next to im possible to predict (T he Econom ist 1999). M oreover, changing life-styles may induce appearance of diseases not known before. M alaria, em erged as a consequence of irrigation th a t cam e w ith agriculture (Livi-Bacci). C holera has been a problem in Europe only since th e last century (O gden 1998). The latest newcom er into the fam ily of virulent epidemics is AIDS. 5.3 Improvements in health technology B etter sanitation and greater m edical knowledge reduce the im pact diseases m ay have on a population resulting in lower m ortality. T he significance of better health technology m ay be seen in exam ples of im poverished LDCs th a t were able to substantially increase their life expectancy w ithout great advances in production but mainly due to th e health technology expertise received as aid from the developed countries (Preston 1980). Looking at E uropean his to n ', great leaps in life expectancy occurred between W W I and W W II am idst th e worst economic crisis, but im proving san itatio n and medical care availability (E asterlin). It is believed that vaccinations and public w orks played a decisive role in the decline of infectious diseases th a t sta rte d in the 18th century. T here were m any inventions and discoveries th a t led to the decline. For exam ple, C rapper invented flush toilets in the last century in E ngland contributing to the im prove m ents in sanitation th a t cities around E urope began in th e 1850s. Interestingly, cleaning of the tow n streets began due to the erroneous m iasm atic theory th a t saw diseases as being caused by bad vapors raising from th e sewers. T h e 1854 discovery of Jo h n Snow and W illiam F arr th a t infected w ater causes cholera prom pted authorities throughout Europe to clean w ater supplies. T h at act not only reduced incidence of cholera, b u t also of typhoid and dysentery. Those who opposed the change paid for their shortsightedness dearly. H am burg in Germany resisted w ater filtration and food-preparation education. As the result H am burg suffered a cholera epidemic in 1892. However, Brem en, which is not far from H am burg to the southw est, did not have th e sam e fate as it had im plem ented Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H IS T O R Y OF M O R T A L IT Y 42 san itary m odifications (M okyr). Table 8 sum m arizes the im pact th a t m edical knowledge and health practices had on health startin g in th e last century. T a b le 8: Disease Im pact of Public H ealth an d M edical Innovations Period Innovation Disease Affected 1850s on S an itatio n (supervision of w ater, food, pasteurization of milk) Cholera, dysentery, typhoid fever, hookworm, diarrhea, scarlet fever, measles, whooping cough 1880s on Im m unization D iphtheria, typhoid fever, smallpox, tuberculosis, whooping cough, scarlet fever 1890s on P revention of communicable diseases through education, clinics, dispensaries D iarrhea, measles, tuberculosis 1900s on C ontrol of m osquitoes (pest poisons, sw am p drainage) M alaria, yellow fever 1900s on C ontrol of rodents Plague Source: E asterlin 1996, 161 As E urope succeeded in prolonging lives o f its inhabitants, new diseases appeared. As a person gets older, he becomes affected by age-related diseases, such as various forms of cancers. M ost of these degenerative diseases were previously unim portant or even not known. In th e future, these diseases may becom e more im portant th a n th e infectious diseases (E asterlin). Evolutionary theory postulates th at increased m orbidity due to aging is inevitable in all organism s th a t live longer than the reproductive age: therefore, no m edical technology, modified physical environm ent, or im proved life-style will be able to elim inate som atic dam age caused by the genom e itself, which inevitably leads to death (O lshansky and C arnes 1994). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H IST O R Y OF M O R T A L IT Y 43 5.4 A relationship to social slack Etiology of diseases is not incorporated by this model. However, the notion of social space introduced in th e chapter on production captures a positive relationship between popu lation density and incidence of diseases. Indeed, aro u n d 8,000 years ago, th e Neolithic R evolution brought about a change in settlem ent p attern s. Settled habitation created good conditions for parasites an d infections. In m odern preagricultural populations in fectious diseases are rare, and therefore hunters die a t later ages as com pared to farmers (Livi-Bacci). Sim ilar effects could have been observed in E urope going through industrialization. U rbanization was the marked feature of the Industrial R evolution (Easterlin). T h e British census of 1801 indicated th at population of M anchester, which was a textile center, had increased tenfold in 25 years. As urban population grew, urban m ortality worsened. In France of th e 1800-60 the life expectancy at birth for women was lower by 6 to 7 years for th e districts th a t included such urb an centers as P aris, M arseilles and Lyon. ShoSeld and R eher put forw ard an argum ent th a t a tem porary lack in m ortality im provem ent around th e m id of th e last century was due to the rapid urbanization at th a t time. Lack of ad equate sewage disposal, prevalence of rodents, poor air quality and work at factories all contributed to th e poor epidemiological situation. However, gradually im proving living and w orking conditions turned th e situation for the b etter. 5.5 Nutritional effects Since the earliest times of economic analysis food availability was thought of as a m ajor check to th e population grow th. Indeed, Schults (1993) found th a t com bined calorie intake of a fam ily is one of the m ost im portant determ inants in the child’s chances to survive. M cKeown (1983), who originated the n u tritio n al hypothesis, writes: ’’...the slow grow th of th e hum an population before the eighteenth century was due m ainly to lack of food, and th e rapid increase from th a t tim e resulted largely from improved n u trition.” Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A PTE R 5. A H IS T O R Y OF M O R T A L IT Y 44 A comprehensive Worlds model (M eadows and Meadows 1973) shows th e relationship betw een food per capita in calories and. life expectancy obtained from a cross sectional stu d y as a non-linear function w ith dim inishing returns. W hen food is scarce, the m arginal retu rn to food increase is great. P resto n (1980) suggested th a t th ere is a quadratic relationship between calories and m ortality, w ith no marginal benefits above 3,400 calories per day. There are also m arginal costs for consum ption above th a t level. T he minim um daily calorie requirem ent is about 1,500. T here were two tim es in hum an h istory when there were su b stan tial changes in food consum ption patterns. Archeological records show th a t during th e tim e of the Ne olithic Revolution about 10,000 years ago there was a reduction in body size, height and thickness of bones (Livi-Bacci). H eight and weight are two of a num ber of adap tations that the hum an body goes through in response to th e changing energy intake. In fact, both of these variables are com bined by health professionals into an index th a t m easures the health sta tu s of an individual. T he body mass index, or BM I, is defined as: ■nvfT __ height in m otors w e ig h t in k ilo g r a m s '- It has been shown th a t when th e BM I is below 21 and above 29, the age-specific m ortality increases. T he curve relating BM I and m ortality is called the W aaler curve and has a U-shape. T he m echanism th a t generates this relationship have not been discovered (Strauss and Thom as 1998). Reductions in body height and w eight indicate that at least at the beginning stage of th e Neolithic revolution th ere was a reduction in nutritional quality. T hough this m aybe a counterintuitive proposition, specialists in the field tell us th a t it m ight have some m erit. Even though, agriculture and dom estication of animals allowed a m ore regular supply of food than in previous tim es, th a t food was less diverse nutritionally as it was heavily dependent on grains. H eavy reliance on grains reduced intake of proteins, vitam ins, and minerals, th a t were m ore plentiful in wild game and vegetable foods. T h a t lead to som e nutritional deprivation. Sim ilar body changes were also found in th e m odern-day Sudanese Nubian populations th at only recently adopted agriculture (C ohen 1989 and Livi-Bacci 1997). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P TE R 5. A H IS T O R Y OF M O R T A L IT Y 45 T he second change in food consum ption happened during th e In d u strial Revolution. Industrialization brought ab o u t b etter nutrition th a t eventually resulted in lower m or tality. Among new agricultural products of th a t period was p o ta to th a t came from th e New W orld. From a given p lo t of land, it could feed the population of up to three tim es as com pared to the grain. T able 9 shows the im provem ents in h ealth startin g in the 18th century as indicated by th e height. Height itself is positively related to nutrition. Indeed, during th e war in V ietnam , th e statu e of V ietnam ese males sto p p ed increasing unlike in preceding years, which was a result of economic hardship (Strauss and Thom as). T a b le 9: R ate of Increase in S tature of M en during Selected Periods, Six E uropean Countries (centim eters per century) Betw een T hird Q u arter of th e 18th and 19th C enturies Between T h ird Q uarter of 19th a n d 20th Centuries Average 1.1 7.7 ■ G reat B ritain 3.4 5.7 France 3.5 6.4 Norway 4.7 9.7 Sweden 1.4 8.1 D enm ark -0.5 10.7 H ungary -6.0 5.4 Source: E asterlin 1996, p. 82 B etter nutrition played a role in the m ortality decline in E u ro p e from 1750 to 1875 as the decline occurred before treatm ents for m any infectious diseases were discovered or widely used (see chapter on H ealth Technology). According to th e nutritio n al hypothesis, im proved nutrition during th e Industrial R evolution led to the increase in natural resis tance to diseases (M okyr). T here is a num ber o f diseases th a t are affected by nutritional statu s (Stinson 1992). N u tritio n below adequate levels results in increased prevalence of infections by means of th e following mechanisms (see R otberg an d R abb 1983): Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CH APTER 5. A H IS T O R Y OF M O R TA LITY 46 (i) Reduced production of hum oral antibodies (ii) Im paired cell-m ediated im m unity (iii) Less effective phagocytosis (iv) W eakened epithelial barriers (v) Lower lysozyme production (vi) Various o th er non-specific effects0 Table 10 shows schem atically relationships between diseases and nutrition: T a b le 10: N utritional Influence on M orbidity and M ortality of Infections D efinite Variable M inim al Measles Typhus Sm allpox Diarrheas Diphtheria M alaria Tuberculosis Staphylococcus Plague M ost R espiratory Infections Streptococcus T yphoid Pertussis Influenza T etanus M ost Intestinal Parasites Syphilis Yellow Fever Cholera Systemic W orm Infections E ncephalitis Leprosy Poliom yelitis Herpes Source: R otberg and R abb 1983 In m ost of th e world, including historic Europe, calorie intake has been positively related to income: and prices have been shown to have had an im p o rtan t influence on determ ining m ortality (Ravallion 1997, Schofield 1989, and m any others). For example, in response to grain price increases in the sixteenth century Siena it experienced a m ortality hike (Livi-Bacci). T h a t was happening because higher prices lowered real incomes th a t positively correlated w ith food consum ption. ^Phagocytes fight m icroorganism s. Epithlial barriers are a protective covering on internal and external surfaces. A lysozyme is a basic protein in body fluids that functions as an antibiotic. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 5. A H IST O R Y OF M O R T A L IT Y 4 7 5.6 The Mortality Causal Chain A com bination of causal links discussed above results in a com plete m ortality causal chain of Figure 12. T here is a num ber of reasons why we may w ant to sim plify this causal flow. F irst of all there are no reliable d a ta available for two of the variables. H ealth is one of such variables. H ealth m easurem ent is still heavily d e b a te d and there has not been a uniform decision reached on how to m easure it. One o f th e recent articles th a t reviews m easuring health is by Strauss an d T hom as (1998). T h ey rep o rt th a t there are m any possible ways to do th a t, each of th e indicators differing in degree of observability. As proxies for health one could use height, body mass, disease incidence and physical functioning. Income M ortality 9 + Health Technology Social Slack. Epidemics Figure 12: A com plete m ortality causal chain. Moreover, because it is not financially feasible to conduct a com prehensive clinical evaluation of health statu s, health surveys usually rely on self-evaluations, such as general health sta tu s (GHS). In GHS a person is asked to rate his h e a lth on a four or five-tier scale: from poor to excellent. Thus it is th e perception of health th a t is recorded, rath e r th an the actu al health status. As a result, people may rate th e sam e level of health variously since, as a rule, there are no clear guidelines about th e scale. Self reporting results in ” paradoxes” as, for example, th a t people who use h e a lth care facilities report Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H IST O R Y OF M O R T A L IT Y 48 worse health th an those who do not use the facilities and really are in th e sam e health statu s. In th e surveys com ing o u t of LDCs, th e poorest som etim es ap p ea r th e healthiest because of th e self reporting error. Thus, the h ealth d a ta are not reliable. A nother variable th a t we do not have reliable d a ta on is nutrition. Indeed, as changes in m ortality p attern during the N eolithic tran sitio n indicate the nutritional effect is not purely a function of the q u an tity of food, but also of its quality. T he su b ject of how to m easure nutritional quality is still debated. We can simplify the causal chain of Figure 8 by noticing th a t for th e adjacent causal links th e following causal sign rule holds: 4- A — = — -f- A 4- = 4- - A - = + This table is a mnemonic device th a t draw s a parallel w ith the well know n arithm etic rule of how to determ ine the sign of a product of two signed num bers. In th e context of causal links the rule m eans th a t m ultiplying m odalities o f two adjacent links gives the m odality of the com bined effect. For example, in F igure 8 . the effect of Incom e on N utri tion is positive and the effect of N utrition on M o rtality is negative: therefore, using the above sign rule, the effect of Incom e on M ortality is 4- A — = — , th a t is negative. In other words, the Incom e-N utrition-M ortality chain has been reduced to Incom e-M ortality chain w ith a negative relationship. In the same m anner, the chain Incom e-N utrition-H ealth- M ortality becom es another negative Incom e-M ortality relationship. Therefore, two orig inal relationship chains are equivalent to one negative Incom e -M ortality relationship. U nder these conventions th e g raph of Figure 12 reduces to th a t in F igure 13. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H IS T O R Y OF M O R T A L IT Y 49 Income Health Technology ► M ortality 7 Social Slack Epidemics Figure 13: A simplified m ortality chain. 5.7 M ortality equation For the sim ulation purposes, the m ortality relationship of F igure 13 needs to be put into a m athem atical form. O ne of the possible form ulations is: T h is m ortality function implies th at no one survives if incom e, u t „ falls below a certain level, 7 r; therefore, m ortality D is the m axim um possible d e a th rate. Such an assum ption of a threshold is quite common in the economic literature (see for examples, Ravallion an d Jones). For incomes above the threshold, kt is the ran d o m epidem ic shock, Ct is the crow ding param eter, h t measures the im pact of the h ealth technology, function z(.) is decreasing in income and captures the trend of th e observed d ata, d is the lowest possible d e a th rate. M ultiplication of param eters represents the synergy am ong the factors as th e y strengthen each o th ers’ effects. For th e functional form of z(.), we may tu rn to the w ork by Jones (1999). He as sum es th a t the m ortality rate depends inversely on consum ption. Substituting income for consum ption and adding the threshold param eter 7 r an d p aram eter 7 * 4, Jones’ function D , Lu't < 7t ktcL h tz{uJt) 4- d , uit > 7 T (5.1) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H ISTO R Y OF M O R T A L IT Y 50 is transform ed into: z ( u j ) = (5.2) 7*1 ( c j - 7T)r2 + 7-3 { u - 7T) S trictly speaking, param eter r4 is red u n d an t to r* i and 7 -3; however, having it will greatly sim plify model calibration. Figure 14 illustrates equation (5.1) indicating effects that each of the param eters has on it. It is w orth noticing th a t a m ortality function is inversely proportional to th e function relating income and life expectancy, or w hat is called the health production fu n c tio n , which is com m on in the microeconomic analysis fR avallion 1997). The function is somewhat sim ilar to the Cobb-Douglas production function (Preston) as life expectancy increases w ith income, but experiences dim inishing returns. Improvem ents in h ealth technology' shift th e health production function up, ju s t like im provements in th e technology para m eter shift up the Cobb-Douglas production function. HortAli^y D Iinprovemenls in health technology Rairiom epidemics d Figure 14: A m ortality function for incomes above 7 r. Some potential maximum life expectancy in the absence of negative effects from crowd ing, low income, epidemics and low h ealth technology translates into th e m inim um mor tality level d. A similar variable can be found in Jones (1999). However, unlike in Jones, in G E M Europe, d is not affected by h ealth technology due to an assum ption th a t only Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H IS T O R Y OF M O R T A L IT Y 51 genetic modifications are capable of extending the average life expectancy of the hum an population beyond som e num ber between 85 and 100 years of age(see sections 5.1 and 5.3 for m ore discussion of th e topic). T he shape of the h ealth technology im pact function. /i(.), which determ ines ht, m ust be such th a t at th e lowest levels of the health technology h(.) is unity, that is there is no contribution from th e health technology to lowering m ortality. As the stock of health and m edical knowledge, H , increases, the value of th e function drops below unity, thus reducing m ortality. However, assum ing th a t there are dim inishing m arginal improvements due to senescence diseases th a t we cannot fight effectively, th e lowest value th at h (H ) can take is h. Then 0 < h < h t = h (H t) < 1 (5.3) T he functional form th a t satisfies the above requirem ents is: h (H t) — -rfr , (5.4) where 0 < v < 1 (Figure 15). h ( H , & H Figure 15: A health technology benefit function. H ealth knowledge is a dynam ic variable that develops according to a modified learning by doing rule of section 3.7: H t+l = H t + v H t (5.5) P aram eter u measures th e ra te of the health knowledge grow th. I assume th a t the stock Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A PTE R 5. A H IS T O R Y OF M O R T A L IT Y 52 of health knowledge is passed on from one epoch to the next, even though the ra te of learning varies for epochs. As Jones, I m odel epidem ics as random shocks, k t > 1, to th e m ortality function. Jones acknowledges th a t m ortality shocks required by his model to m im ic historic population trends are very large. It possibly happens because the random elem ent in his m odel is additive unlike in this m odel. P aram eter ct = c(xt) is th e crowding dam age function. T he crow ding dam age function has th e following form: T he functional form is sim ilar to the one of the environm ent dam age function (3.10), except th a t the power is a negative num ber. Param eter G is a scaling factor th at indi cates th e potential dam age from crowding. T he relationship is shown in Figure 16. As population approaches th e environm ental capacity for the regim e, x . the dam aging effect goes to infinity. 5.8 Mortality parameters Figure 17 shows sensitivity analysis for m o rtality function (5.1) w ith respect to changes in various param eters. G raphs of Figure 17 were plotted for param eters in Table 11. T hese are th e param eter values adopted for th e m odel. Param eters r i , ro, r%, and r4 form th e (5.6) C ( X ) Figure 16: A crow ding dam age function. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H IST O R Y OF M O R TA L ITY 53 basis for the intergenerational m ortality pattern. T h e m inimum m ortality level, d, is 10 persons per 1000 for all of the epochs; it approxim ately corresponds to the life expectancy of 100 years. According to condition (5.3), the lowest value of health technology, H q, must satisfy th e equation h(H 0) = 1, (5.7) th a t is a t its lowest level the health knowledge does not contribute to the m ortality decline. Using equation (5.4) and condition (5.7), we get H q = (1 — h ) ~ . T hen, given param eter values in Table 11, the initial value of health technology-' is H q = 1.8937. 5.9 Epidemic shocks A ccording to Livi-Bacci, epidem ic outbreaks were com ing as waves, rolling over wast regions. D uring an outbreak m ortality rose by some factor. He gives estim ates of the m agnitudes of the outbreaks, which I approxim ate by three levels: 3, 4, 5. and 7. T he tim es and the m agnitudes of th e sim ulated outbreaks are given in Table 12. D uring regular years, when there are no epidemic outbreaks, the shock param eter, A rt, of equation (5.1) is set to 1. D uring the period of an outbreak the p aram eter is set to a corresponding factor from the table. All the shocks, as has been reviewed in section 5.2, occurred between 80 AD and 1670 AD. Following the classification adopted in the model they are all w ithin the Industrial regime (regime 4). Therefore, I use a formulation th a t produces a series of shocks w ith delays after the sta rt of period four: IF (t = T4 + A i) TH EN (A r£ = fa cto ry) ELSE (A rt = 1) (5.8) In this equation t is the current period of the model an d T4 is the first period of regime Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H IST O R Y OF M O R T A L IT Y 54 four, A i is the delay of the shock after th e start of regime 4. an d f a c t is the corre sponding shock m agnitude. M o r t a l i t y M o r t a l i t y 5 01 40 30 20 10 Incom e 2 2 4 8 1 5 6 7 40 30 20 1 2 3 4 S 6 7 8 a)solid line: rq = 0.8, dashed line: r \ = 2 b) solid line: r 2= 0.1,dashed line: r2=0.3 M o r t a l i t y M o r t a l i t y 50, i 20 10 50, 4 0 \ 30 20 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 c) solid line:r3=0.0007, dashed line: r3=0.1 d) solid line: r4= 20 , dashed line: r4=10 Figure 17: Sensitivity analysis o f the m ortality equation Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 5. A H IS T O R Y OF M O R T A L IT Y T a b le 11: M ortality P aram eter Values 55 P aram eter System 1 H unting S ystem 2 V illage System 3 C ity-state System 4 T rading System 5 Industrial System 6 Inform. economy 7* 1 0.8 0.8 0.8 0.8 0.8 0.8 7*2 0.1 0.1 0.1 0.1 0.1 0.1 r 3 0.0007 0.0007 0.0007 0.0007 0.0007 0.0007 20.0 20.0 20.0 20.0 20.0 20.0 7 T 0.15 0.15 0.15 0.15 0.15 0.15 d 10.0 10.0 10.0 10.0 10.0 10.0 V 0.8 O.S 0.8 0.8 0.8 0.8 h 0.4 0.4 0.4 0.4 0.4 0.4 G 1.01 1.18 1.2 1.22 1.3 1.0 ip 0.0115 0.02 0.2 0.015 0.015 0.02 V 1.13213e-5 1.13213e-5 1.13213e-5 0.01 1.3 1.13213 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A PTE R 5. A H IST O R Y OF M O R T A L IT Y T a b le 12: Sim ulated epidem ic shocks shock index, i historical tim e delay a fter start o f system / in 500 BC, years/generations m ortality increase during each wave, fa cto r 1 76-100 AD 600/24 7 2 151-17-5 675/27 7 3 526-550 1050/42 7 4 1326-1350 1850/74 7 5 1351-1375 1875/75 7 6 1376-1400 1900/76 7 7 1401-1425 1925/77 5 8 1426-1450 1950/78 5 9 1451-1475 1975/79 4 10 1626-1650 2150/86 3 11 1651-1675 2175/87 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 6 A Simulation of World Development 6.1 The dynamic structure of GEM Europe S tructures discovered in previous chapters form th e com plete G eneral E volutionary Model for E urope, G E M Europe. The dynam ic stru ctu re of th e m odel is expressed in the fol lowing equations: K{x) % =“ £ ,S ) {(x “ *)*' “xK - [* •> ■ (1 " - ~ lM r Y r (2'_ I - x ) ‘ 0r] } • B i+1 = (1 + p‘)B i - B* Hl+\ = j j 7- i- f(u) = m in (ir’ , n(ui)) ° , u<ri n(cj ) = < ; -# + r—? ---------------- rsr----- rrr + a*d , othenvise a i( c * ;—77)a 3 a r/) 1 7 cf(cut ) = < D , W t < 7 T k tCthtz{uJt) + d , oJt > t t H t+\ — Ht + uHt %t+1 = x £ + ~ ^dd(ojt) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 6. A SIM U L A TIO N OF W O RLD D EV E LO P M EN T 58 w here Af and A < * are scaling param eters th a t account for the discrepancy in m easurem ent units between population, x t , and births, /( - ) , and deaths, cf(.). P opulation is m easured in persons. B irths and d eath s are m easured in persons per 1000 persons. Therefore, the scaling param eters m ust take values A ' = A ' = lS o - T he rest of the param eters is set to the values in Tables 3, 5, and 11. 6.2 A numerical simulation A sim ulation was sta rte d w ith an initial population of 100 families (2:0 = 100) and was continued for 4,082 generations, which is about 102,050 years. F igure 18 illustrates pop ulation time series for th a t run. In this graph, as in all Stella’s6 tim e series graphs, tim e is shown on the horizontal axis and th e variables th a t the graph is for are shown at the very top of the graph. T his particular g raph is for only one variable, nam ely "Popula tion” . To assist in th e reading of the graph, Stella assigns a num ber to each variable; thus ’ ’Population” is assigned a num ber 1 (it is som ew hat unnecessary in this graph, but will come handy in other, more com plicated graphs). Vertical axis shows the scale for the variable — population scale starts w ith zero families and th e m axim um num ber of families that could be displayed is 5.18 x 10s . For the longest tim e, population numbers were insignificant com pared to the relatively recent past. However, soon after agricul tu re was adopted in system 2 around period 3678, population grow th accelerated. T he sim ulation com pares well to th e population estim ates for Europe, as F igure 19 shows. It plots sim ulated population as a sm ooth line, while the dots represent th e estim ates of population taken from Livi-Bacci for the period from 500 B.C. to the present. Figure 20 gives a more detailed p ictu re of the sim ulated Industrial regime. F igure 21 was plotted 0 Stella is one of the program s used for com puter sim ulations by System D ynam ics. T h e model in this stu d y was developed in Stella. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P TE R 6. A SIM U LATIO N OF WORLD D E V E LO P M E N T 3Q61.5C 4082.00 1020.50 2041.00 Figure 18: A sim ulated population history. 5 x l 0 8 1 4 x l 0 8 | 3x 1 0 * 2x 10" i I x l O 3 f A J - ¥ • 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0 Figure 19: Sim ulated (sm ooth line) and estim ated (dots) population dynam ics. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 6. A SIM U LATIO N O F WORLD D E V E LO P M E N T 0 1: Population 1: 5.18e+008-r 2: 6.00 2: system 100.00 -1 1.0 0 - — 4082.00 3979.00 4004.75 F igure 20: Populatoin dynamics after the sw itch to regime 4. .a 9 .a 1 0 4 0 8 0 4 0 2 0 4 0 6 0 4 0 C 0 4 0 4 0 3 9 8 0 Figure 21: Real d ata for regim e 4. Source: Livi-Bacci 1996. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 6. A SIM U LATIO N OF W ORLD D EV E LO P M EN T 61 using real d ata. In both graphs the tem porary declines in population were due to the epidemics. As has been discussed in earlier chapters, there have been two dem ographic transitions in hum an history during which the rate of population grow th accelerated. The dram atic increase in population in Figure 38 cleaxly indicates the second, m ost recent, demographic boorn. However, th a t linear graph hides the first transition. To uncover it, transform ing population num bers into logaritm s may help (Figure 22). A logarithm ic scale exaggerates sm all populations, thus m aking early hum an population patterns m ore prom inent. In the logarithm ic presentation, we see how sim ulated population grew faster after the adoption of agriculture around period 3680, or about 8700 B .C. £ 1: log population I: 30.00-.--• 15.50- 1.00 0.00 1020.50 2041.00 3081.50 4032.00 Figure 22: Logarithm of sim ulated population (to the base e). By explicitly m odeling causality of fertility and m ortality this w ork allows us to have a closer look at th e mechanism s behind the two dem ographic transitions. Time series of the vital rates for th e period around the first dem ographic transition are illustrated in Figure 23. G raph 1 is for fertility rates, graph 2 is for m ortality, and graph 3 shows the dom inant system . Having the system graph 3 in th e sam e figure w ith th e rates allows Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 6. A SIM U LATIO N O F W O RLD D EVELO PM EN T 62 us to trace exactly how a regime change affected dem ographics dynam ics. T h e first a t tem pts to sw itch to agriculture (regim e 2) resulted in higher m o rtality (graph 2). Even though fertility rates positively ad ju st to higher death rates, the econom ic conditions of early shifts to agriculture were so poor th a t fertility did not raise to the level sufficient to com pensate losses in population. Consequently, the population of the agricultural society declined and people found it more beneficial to go on w ith th e hunting and g ath ering production. T hus the agricultural society was replaced w ith hunter-gatherer groups (regime 1). A fter the switch, the population started growing again. A fter a sho rt while th e diseconomy due to th e lim ited environm ental space becam e felt and population again chose agriculture. Such transitions back and forth repeated a num ber of tim es until the society perm anently locked into system 2 around period 3680. T he eventual lock occurred because due to the m echanism of learning by doing the society' eventually learned how to achieve high yields in agricultural production, which ensured th a t from th a t m om ent on agriculture was preferred to hunting-gathering. As people becam e more skilled in agriculture, yields im proved leading to b e tte r living standards. B e tte r nutrition reduced m ortality; however, th e negative effects of crowding did not allow the m ortality rates to fall below the preagricultural levels. D ue to the changing a ttitu d es tow ard children (an agricultural family needed ex tra hands — see chapters 4 and 5 for a review of th e m echa nism of fertility and m ortality) an d b e tte r nutrition fertility increased after a perm anent adoption of agriculture. T he fertility rate (graph 1) also grew in th e postagricultural regime. Notice the flat intervals in th e fertility graph; these were th e tim es w hen fertility reached the ceiling im posed by th e fecundity, or the m axim um possible fertility. Exam ination of Figure 24 for th e vital rates explains the second dem ographic transi tion. Again, as in the previous graph, following graph 3 for the dom inant system , ailows us to m atch changes in rates to stru c tu ra l evolution. M ortality (graph 2) began to decline rapidly after the shift to system 5 around period 4067 due to higher incomes (leading to b e tte r nutrition) and due to im provem ents in health technology. Fertility responded by increasing at first due to the incom e effect. B ut eventually births declined because falling m ortality and changing family preferences outweighed the incom e effect (notice, th a t income continued a steady climb up). T he shift in the response of fertility to higher Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 6. A SIM U LA TIO N OF W O RLD D EVELO P M EN T & 1: fertility 1: 70 H O 2: 40 H O 3: 6.00 3: system 35 H O 30.00 3.50 O H O 20 H O 1.0 0 ' 3725.00 3602.50 3847.50 Figure 23: Increase in vital rates after the shift to agriculture. £ 1: fertility 2: mortality 3: system 4: income 240.00 50.00 6.00 163.09 120.00 32.63, 3.50 81.96 0.00 15.25 1.00 0.84' 4082.00 4056.00 F igure 24: Second demographic transition. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 6. A SIM U LATIO N OF W O RLD D E V E L O P M E N T 64 incomes d uring th e Industrial regim e is illustrated in a sc a tte r plot of Figure 25 th a t has fertility on the vertical axis and incom e on its horizontal axis. T he changing m odality of th e incom e-fertility relationship is clearly visible: a t lower levels of incom e th e income effect is positive, while a t higher levels o f income th e incom e effect to negative. Figure 24 also gives a p attern th a t has been well docum ented in history: rig h t after the epidemics of the 14th century there were surges in fertility, as people were com pensating for th e hum an losses. In the tim es others th a n the two dem ographic transitions, m ortality and fertility were more stable. R ates for the hunting and gathering regime in Figure 26 give an exam ple. T h e sim ulation explains why so often in the surveys of th e developing countries women respond th a t the ideal num ber of children is as m any as come. For practically all the regimes of the sim ulation fertility was lim ited by fecundity. In other words, women of this sim ulation had less children th an they m ight have preferred to have. Incom e-fertility graphs in Figure 27 show fertility lim ited by fecundity. N otice th a t the graphs do not align perfectly well along the theoretical sh ap e predicted in Figure 3. T he theoretical fertility g raph was built for a constant levels o f m ortality. In the sim ulation fertility adjusted to m ortality, an d therefore variations em erged. The greatest variation from Figure 3 is observed for period 4 (graph d), which is not surprising. We m ay recall th a t it is during th a t period th a t all th e m ortality shocks due to epidemics occurred. A nd as fertility adjusts to m ortality directly (see fertility causal chain in Figure 9 and equation (4.2)) it is higher for individual tim e periods as com pared to w h at it could have been w ithout the epidemic shocks. T h e theoretical shape of m ortality w ith relation to income has been given in Figure 14. However, an interplay of effects due to epidem ic shocks, crowding and h ealth tech nology erodes the theoretical shape into the one of Figure 28. T he scatter p lot was built for the entire duration of th e sim ulation run, as the m ortality equation does not change intertem poraly through the phases. In th e graph, incom e is on the horizontal axis and m ortality rate is on the vertical axis. W e can see th a t even at very low incom e levels mor tality rates can vary dram atically. T hus, even a very poor country can reduce m ortality by, for exam ple, improving available h ealth technology (confirm from the m o rtality Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 6. A SIM U LA TIO N OF W ORLD D E V E L O P M E N T t : income v . f ertiltty5 300.00' 150.00- 0 .00- 1 99.32 1.30 50.31 Figure 25: Incom e vs. fertility relationship during th e In d u stria l regime. 1: fertility 70 .C 60.00 6.00 2: mortality 3: system 35.00 35.00' 3.50 0.00 10.00 1D 0' ! ! I ! - ---------r i I 1 K > ro ------2------ 0.00 925.00 1850.00 2775.00 3700.00 Figure 26: F ertility and m ortality rates before the sh ift to agriculture. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 6. A SIM U LATIO N OF W ORLD D EV ELO PM EN T 66 1: income v . fertility! 20.00 1 : incom e v . fertility2 1.00 5.50 10.00 1.10 15.55 a) Income vs. fertility of regime 1 1: income v. fertility 3 50.001 25.00' 0 .00 ' ♦ f i . 4..................i......................... t ! i i t i b) Incom e vs. fertility of regim e 2 1 : incom e v. fertility4 1.00 20.50 40.00 0.00 8.05 1.10 c) Income vs. fertility of regime 3 d) Incom e vs. fertility of regim e 4 Figure 27: S catter plots for income and fertility causal chain in F igure 9 th a t health technology has a negative effect on m ortality). Most of the data points in the graph are concentrated in th e low income area, as most of th e European h istory occurred in that area. D ata points for higher incomes and lower m ortality were generated in the last few periods of the sim ulation while th e system was in Industrial and G lobal Inform ation Economies regimes. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 6. A SIM U LATIO N OF W ORLD D E V E LO P M E N T 67 t : income v. mortality 60.00-1 35.00- 10.00 1.10 29.38 57.62 Figure 28: Incom e-m ortality relationship. Figure 29 displays a tim e series for the dom inant production. T he series is sim ilar to the one observed for population. T here was a very long m oderate growth w ith some intertem poral fluctuations and an extrem ely fast grow th in th e last few periods of the sim ulation, after the system locks into regimes 5 (Industrial Economies) and 6 (G lobal Inform ation Economies). T he next Figure 30 shows production in a logarithm ic scale. In section 3.5, Figure 2 suggested w hat a shape o f a production function for one regim e should look like in the absence of technological progress. W hen technology level can be improved, a typical shape of the production function as it unfolds dynam ically is illu strated in Figure 31. T he num ber of people is shown on th e horizontal axis, while vertical axis displays values for production. T he graph traces the system for regime 1. C om pared to the graph in Figure 2 this graph is stretched upw ards for higher levels of population. The stretching is due to th e fact th a t technology level increases as the system stays in a particular regim e. Of course, from th e above analysis we know th at population was also continuously growing. Thus, for each population level the sim ulated production was greater than th e production predicted in Figure 2. T h e epoch transitions th a t the m odel passes through are sum m arized in Table 13. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P TE R 6. A SIM U LATIO N OF W ORLD D E V E LO P M E N T 0 1: dominant production 1: 1.25e-t011-r-—-— - 1 : S.26e+O10' 206.84-F1= 0.00 1020.50 :1s 2041 no 3081.50 4082.00 Figure 29: A production tim e series. £ 1: log production 35.00 5.00 3061.50 4082.00 2041 H O 0.00 1020.50 Figure 30: A production tim e series in logs (base e). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 6. A SIM U LA TIO N OF WORLD D E V E LO P M E N T 69 1: Population v. chosen produc... 2000103.42- 206.84' 800050.00 100.00 Figure 31: A sim ulated dynam ic production function for regime 1. T a b le 13: T he tim es o f transitions in the experim ent System 1 H unting System 2 Village System 3 C ity-state System 4 T rading System 5 Industrial System 6 Inform. economy P eriod of locking 1 3678 3856 3979 4067 4080 D uration in experim ent (since locked) 3678 178 123 88 13 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 Chapter 7 Conditional Scenarios 7.1 A history without epidemic shocks An interesting question arises: Would E uropean dem ographic history have been different if the devastation caused by the Black D eath had never happened? To answer this question, let us run a sim ulation w ithout any epidem ic shocks. T he results of the run are shown in Figures 32 and 33; they are counterparts of Figures 18 and 22 for the run w ith the shocks. T here are no visible differences between these two sets of graphs. Just as in the sim ulation w ith the shocks, the m odel passes six epochs as sum m arized in Table 14. A com parison of this table to Table 13 reveals th a t epoch 4 is shorter by 12 periods in the absence of m ortality shocks. This is not surprising as without the m ortality epidemics (due to the plague) the population grows faster and reaches the environm ental capacity of regime 4 sooner. T his experim ent confirms an observation by M althus that epidemics act as positive checks to the population growth. B ut it also suggests th at the stru ctu re of this model, however simple com pared to the real world, is sufficient to produce dem oeconom ic dynam ics mimicking the real world w ithout any need for shocks. In ocher words, th e adapting nature of the reproductive behavior, population driven phase switching an d the variable m ortality w orking together are capable of producing complex dem oeconom ic dynamics. This is a great im provem ent over m any m odern economic models th a t rely on shocks to generate realistic paths. For exam ple, the model by Jones, from which I adopted the basic form of th e m ortality function, required excessive m ortality shocks to mimic the population p attern s, which suggested th a t the overall structure of th a t m odel was not realistic. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 7. CONDITIONAL SC E N A R IO S 1: Population 1: 5.18e I: 2.59e+008' 1 f 1 f . Bi — h j i - 1 O D D 1020.50 2041.00 3081.50 4082.00 Figure 32: A sim ulated population and system history w ithout shocks. 0 1: log population 15.50 0.00 2041.00 3081.50 1020.50 Figure 33: Population in logarthm w ithout shocks. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 7. C O ND ITIO N AL SC E N A R IO S 72 T a b le 14: T he tim es of transitions in th e experim ent w ith no shocks System 1 Hunting System 2 Village System 3 City-state System 4 Trading System 5 Industrial System 6 Inform. economy Period of locking 1 367S 3856 3979 4055 406S Duration in experiment (since locked) 3678 178 123 76 13 14 7.2 Possible future scenarios Let us have a peek into the virtual future of our model. G iven the above param eters, population continues to grow for an o th er 25 generations up until generation 4107. or year 2625. T hen it reaches the level of environm ental capacity for system 6 (Inform ation econom y). A t th a t m om ent, as there is no b etter technology available to replace th e obsolete one, p roductivity rapidly (w ithin one generation) falls below th e subsistence incom e level, 7 r, and th e model population drops to zero. T h is is the end of our v irtual w orld (Figure 34). A few words are in order to explain this strong result. O ne might doubt a possibility of such a collapse. A nd th e doubt is well justified — after all, we are only looking at a sim ulation of a com puter model. However, there are very prom inent examples from hum an history th at show th a t a socioeconomic system can indeed self destruct. One m ight think of the tragedy of the Polynesian E aster Island. T he island being separated by about 1.200 miles of w ater from th e nearest land is com pletely isolated. F irst settlers arrived to the island about 2,500 years ago, bringing w ith them dogs, food rats and some plants. T hey w ere not only able to survive on the island, b u t created a sublim e civilization. T h e m ost fam iliar signs of it are th e massive ritu alistic stone heads placed around the perim eter of th e island. T he econom y was based on local palm trees. U ncontrolled production led to all trees being eventually cut down. W hen precious trees becam e in short supply, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 7. C O ND ITIO N AL SCENARIO S 73 previously peaceful culture turned to welfare an d even cannibalism (M iller 1996). By the tim e outsiders arrived to th e island in 1722, the population sh ru n k from about 10,000 at its peak to about 2,000 people living in prim itive conditions on a barren island. In term s of G EM Europe, the system exhausted its fixed environm ental space and collapsed. O ne possible explanation w hy a sim ilar collapse has never happened in Europe is th a t tech nological advances were always expanding its environm ental space. O ne must rem em ber though th at rath er th a n being a crystal ball, this sim ulation tells us w hat m ay happen to a world th a t has lim ited technological and n atu ra l resources. 0 1: Population 1: m0e-tC09- | 1: 5.00e+003- I: 0.00- =1------------------------- -- - - - - - - - - -h ----------------------------------- 1 1 1L — 4 0.00 1070.50 2141.00 3211.50 4282.00 Figure 34: Future population dynamics. 7 .2 .1 I m p a c t o f f a m ily p la n n in g p r o g r a m s T here is a num ber of strategies that will allow a society eith er to postpone or even avoid the doomsday. For one thing, the population can do w h at it has done before, nam ely increase its environm ental sp a c e ,^ , by inventing and adopting a new more advanced technological system . For another thing, curbing population grow th m ay allow the society to never exhaust its environm ental space. This could be done by controlling fertility. Indeed, the fertility structure uncovered in this model predicts th at reproductive Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 7. C O ND ITIO N AL SC EN AR IO S 74 behavior can ad a p t to changes in a num ber of param eters. One of th e variables that families respond to is the cost of childrearing, q. In this m odel the variable is exogenous to the system. Its affected by th e cost of child education, existing economic opportunities for parents, costs o f health care, and governm ent fam ily planning program s. W hat follows is a num ber of sim ulations in which population grow th was restrained through m anipulations of the cost of childrearing. Rising the cost of children in regime 6, q§, to 0.2 lowers fertility, and therefore lowers population grow th ra te over the age of th e inform ation economy. Lower rates allow more tim e before the environm ental slack is com pletely exhausted. Nevertheless, th e level of xq is still reached by generation 4234 and population takes a sudden plunge. However, th e end is not as nigh: to reach this point takes additional 127 generations, o r around 3175 years, th a n w ith the original cost of childrearing. T he scenario is shown in Figure 35 which is very sim ilar in shape to Figure 34. 0 1: Population 1: 1.00e+009 1: 5.00e+008 1: O D D 0.00 1070.50 2141.00 3211.50 4282.00 Figure 35: P opulation dynam ics for qe = 0.2. Figure 36 shows a situation at qe = 1.0. T he graph indicates th a t at this level of child-rearing costs fertility reached a point a t which birth s com pensate for d eath s ju s t to keep the population level about constant. In other words, fertility and m ortality reached Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 7. C O N D ITIO N AL SCENAJU O S an equilibrium (C arey 1995 reviews th is phenom enon as observed in h isto ry ). This seems to be the path th a t E u ro p e follows now as the average fertility is a t th e replacem ent level. £ 1: Population 1: IDOt 1 : 1 : 5.00e-tC08- r 1 ------------------- I L _ 0.00 1095.50 2191.00 3280.50 F igure 36: Population at equilibrium for qe = 1.0. 4382.00 As the cost of children goes up even further, to qe = 1.5, p aren ts choose lower fertility, which results in a population decline. A t som e point the society finds th a t its population is not at the sufficient level to m aintain the socioeconomic sy stem 6. As this model does not allow im m igration of labor from o utside of the system, the lab o r shortage results in th e society sw itching back to the previous, sim pler regime (F igure 37). Assuming th a t th e conditions of th a t sim pler regime are m ore congenial to higher fertility, population grows again. E ventually th e society has enough people to m eet th e dem ands of the more advanced regime, so it finds more beneficial to switch once m ore to regime 6. However, as family param eters of the advanced regim e are such th a t people opt for fewer children th a n in regime 5, the p a tte rn of a p opulation decline followed by a sw itch to regime 5 repeats itself. T hus, population is tra p p e d in a two period cycle. These three sim ulations tell us th a t fam ily planning program s m ight have a strong effect on the dem ographics. A finely tu n e d fam ily planning program m ay not only prolong th e tim e before a crash, b u t can actually achieve a zero p o p u latio n grow th m aintaining Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H A P T E R 7. CONDITIONAL SC EN ARIO S 76 the sta tu s quo into perpetuity (Figure 36). However, an overzealous b irth control program m ay cause an excessive population decline, which m ay result in dem ographic fluctuations (Figure 37). 4 9 1: Population 1: 1.00e+009 1: 5.00e-t008 1: 0.00 0.00 1095.50 2191.00 3286.50 4382.00 Figure 37: Periodic fluctuations of population for qe = 1-5. A ttem pts to control reproduction through direct and opportunity costs of childrearing have been m ade in a num ber of countries w ith th e result of lowering population growth. For exam ple, Comm unist C hina has had a series of family planning cam paigns since the first one was prom ulgated in 1956. T he most effective of those cam paigns was the 1979 "one child” policy. In addition to putting out propaganda and m aking a wide array of contraceptives available, the authorities have been offering financial or other material incentives to the couples th a t agreed to stop a t one child. The program proved to be very effective as by the mid-1980s b irth rates fell to th e replacement level (Gillis 1996). 7 .2 .2 T h e B la c k D e a t h in 2 0 7 5 W h at would happen to population dem ographics if there were an epidem ic of the magni tude of the Black D eath in ano th er 75 years, or 100 years after the Inform ation economy is adopted? As has been m entioned in the chapter on m ortality, viral evolution is next to I 1 I .........i . •=1 — r1 .............- - f 1 ............ jL — i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 7. CONDITIONAL SC EN ARIO S 77 im possible to predict, and therefore we cannot rule ou t a possibility of such an epidemic. R esults of such a sim ulation are presented in Figure 38. G raph 3 of th a t figure shows an enorm ous increase in the m ortality level due to an epidem ic. T h a t causes population to drop by the factor of about 2 (Figure 39). Such a su b stan tial drop in population imme diately puts th e system in a situ a tio n in which it can no longer support th e Inform ation economy regime and it slips into a m ore prim itive m ode of production, nam ely regime 5 (see G raph I in Figure 38). As the causal graph of Figure 9 would suggest, an increase in m ortality induces a baby boom. G raph 2 of Figure 38 captures th a t tem porary increase in fertility as a spike. The system stays in regime 5 for 5 generations, or 125 years. D uring th a t tim e population recovers to th e level th at can su p p o rt regime 6, which is prom ptly adopted again. Such a speedy recovery from th e devastating epidem ic was made possible by the som ew hat unrealistic assum ption th a t no loss of the knowledge stock occurs during the 125 years of the recession. However, even if this assum ption were relaxed, th e n the only change from th e current dynam ics would have been a slower recovery. 0 1: system 2: fertility ;: rr.;C3.'ffy 6 .00-1 460.00 600.00 3.50 225.00- 305.00 1.00 0.00 10.00 4150.00 4131.75 4077.00 Figure 38: System , fertility an d m ortality tim e series w ith an epidemic in 2075. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 7. C O ND ITIO NAL SC E N A R IO S 78 £ I: Population t 1 0.00 4091.00 4136.50 4182.00 Figure 39: A population drop after an epidem ic. 7 .2 .3 E n v ir o n m e n t a l c o n c e r n s Recently, environm ental concerns becam e of prim ary interest. W hat does this model predict will happen if production becom es more environm entally friendly? In the for m ulation of this m odel, this implies reducing param eter 6 in th e environm ent dam age elem ent of production function (3.11). A population dynam ics of a sim ulation conducted for 8 = 0.01, instead of the original 0.1, resembles the graph in Figure 34. However, the collapse comes a t a later stage, in period 4114, which is 7 periods, or 175 years, later, th a n originally. W orsening environm ental pollution by raising 8 to 0.4 shortens the period before the collapse by 13 periods, to 4094. 7 .2 .4 I m p a c t o f lo w e r e d m o r t a lit y A n interesting experim ent can be staged to find out the effect of lowering th e im pact of crowding on m ortality. This is controlled by param eter G in equation (5.6). Lowering the potential dam age from crowding, (?, lowers m ortality at any given population size, which, following the causality in Figure 9, leads to lower fertility (Figure 40). However, th e drop in m ortality outw eighs the drop in fertility resulting in higher n et population increase. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H APTER 7. C O N D ITIO N AL SC E N AR IO S 79 H igher population grow th leads to a faster exhaustion of the environm ental space. W ith G = 0.1 the system collapses in 4107. or 1 generation sooner th a n w ith G = 1. This experim ent suggests th a t attacking m ortality only can produce counterintuitive results: unless backed by developm ent th a t im proves economic opportunities for parents, lowering m ortality does not induce proportional fertility decline and m ay lead to even higher population growth. 4 1 0 0 4 0 9 0 Figure 40: As crow ding dam age lowered, fertility declines (G soud < Gdashed)- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 Chapter 8 Conclusion T his m odel expanded the General Evolutionary Model in order to explain th e dynamics of fertility and m ortality rates over E urope's history, including during the two demographic transitions. This study confirms th a t the model is capable of doing so. Not only the sim ulation mimics real data, b u t it also suggests w hat can be done to avoid difficulties linked to overpopulation and lim ited environm ental resources. A series of experiments showed th a t a finely tuned family planning cam paign can reduce population grow th, thus postponing a severe economic difficulties due to overpopulation. A nother experim ent that targ eted m ortality only showed th a t lowering m ortality m ay not be sufficient to induce a drop in population growth. It suggested th at m ortality decline m ust be accom panied by economic development in order for population grow th to decline. This stu d y also dem onstrated how tools of System D ynam ics can be used to develop a sophisticated economic model. It was shown th at a step by step model creation procedure th a t uncovers intrinsic behavioral mechanisms at a m icro level results in a credible macro model. Additionally, a newly introduced causal sign rule proved to be very effective in the process of model sim plification. T he m odel may benefit from th e use of a yearly ra th e r th a n generational tim e interval. In its present form ulation, the m odel does not cap tu re the changing age stru ctu re of the population, which is of pivotal relevance to the policy analysis of health care and age- based entitlem ent program s. M oreover, a yearly tim e scale would allow to differentiate betw een infant, child and adult m ortalities th a t will lead to a more accurate fertility sector — as we know, it is prim arily infant and child deaths, rath er than th e general level of m ortality, th a t affect fertility. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bibliography 81 1. Bach, Nguyen an d K halid Saeed, Sum m er 1992. Food Self-Sufficiency in V ietnam : A Search for a V iable Solution. 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A nnual Review of A nthropology, v. 21, 143-170. 45. Strauss, John an d D uncan Thom as, June 1998. H ealth, N utrition, and Econom ic Developm ent. JE L , 36, 766-817. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. B IB LIO G R A P H Y 85 46. Van de Walle, E tienne, N ovem ber 1992. F ertility Transition, Conscious Choice, and Numeracy. D em ography, v. 29, no. 4, 487-502. 47. Voland, Eckart, 1998. Evolutionary Ecology of H um an R eproduction. Annual Review of A nthropology, v. 27, 347-74. 48. Wells, Colin, 1984, T h e R om an Em pire (S tanford, CA: Stanford University Press). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 Appendix A Glossary of Mathematical Notation Sym bol Definition D m axim um d eath rate L size of th e labor force S the am ount of social slack X population as m easured in households M size of th e social infrastructure B production technology E environm ental slack X environm ental capacity P technology' acquisition rate H stock of health knowledge k im pact on m ortality from epidemic shocks c im pact on m ortality from crowding d lowest d e a th rate h best contribution by health technology to the m ortality function 7 T subsistence income level h im pact on m ortality from health technology F highest fertility level or fecundity- n{ui) desired fertility / M fertility g (x - x) environm ental dam age function K{x) production function d{ui) m ortality rate function Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 7 Appendix B Computer implementation B .l System Dynamics: Introduction T he m ost startling feature of system dynam ics th a t makes it w orth going through the m aze of new term inology is the well developed sim ulation base. In fact, the whole field of System Dynamics is built around sim ulation. This stands in great contrast to the sim ulations in Economics, which are m ere extensions of simple pap er and pencil models. Indeed, com puter sim ulations are rarely used in Economics as a way to understand prob lems, though com puter models are able to form alize even the m ost sophisticated net of relationships (K rugm an 1993). To this effect, K rugm an writes: I suddenly realized the remarkable ex ten t to which the m ethodology of eco nomics creates blind spots. We ju st d o n ’t see what we c a n ’t formalize. ... Trade theorists had failed to address the role of increasing retu rn s, not out of empirical conviction, but because they thought it was too h ard to model. Since the tim e w hen M acintosh com puters introduced the easy to use Graphical User Interface (GUI), System Dynamics was relying on potent sim ulation software th at is ’’childishly simple” to use. T he graphics based sim ulation environm ent has been a stan d ard in many engineering fields for years. B u t this is a novelty for econom ists. A good system dynamics m odel can be created w ith rudim entary knowledge of com puter pro gram m ing either from scratch or from blocks built by other people. Thus many new' researchers potentially could enter th e field of com puter sim ulation, who were previously deterred by the high tim e and effort costs required to conduct sim ulation studies. T here is no longer a need to learn com puter languages and algorithm s o r hire professional pro gram m ers to develop a model. Just click, d rag and drop. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. COM PUTER IM P LE M E N TA TIO N 88 A nother benefit of using System Dynamics softw are is the ease of sharin g the model or its com ponents among researchers. Combined w ith the ease of creating a n d modifying models, such portability of models m ay result in g reater cooperation betw een researchers in disparate disciplines. This will lead to better m odels th a t take into account facts that researches in separate disciplines are not aware of. For exam ple fertility research could only benefit from an active interdisciplinary cooperation (Voland 1998). T he clarity of complex models can be achieved through meticulous d etail accounting and inform ation layering, which is already available in th e current versions of system dynam ics program s (though the la tte r needs further developm ent). B.2 System Dynamics: the Language Possibly one of the reasons th a t system dynamics has been ignored by econom ists is the specific lingua franca that system dynam ics developed. Such neglect is n o t unusual in Econom ics. K rugm an (1993) w rites th a t until recently econom ists alm ost completely ignored geography also prim arily because of the unfam iliar language. Therefore, before plunging into th e com puter im plem entation of th e model, let us review the basics of th e system dynam ics language based on the form alism of Stella — a system dynamics program used in this study.. T he prim ary building block of a system dynam ics model is the stock, w hich represents anything th a t accumulates. Exam ples of stocks in G EM Europe are population and technology. T he stock is represented by a rectangle as in Figure 41. Stock F igure 41: A stock. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. C O M PU TER IM PLEM EN TATIO N 89 A nother im p o rtan t building element is th e flow, w hich is used to represent changes in th e stock. Exam ples of flows are births and deaths. T h e icon for a flow looks like a m etaphoric pipe (Figure 42). The object allows its content to flow in the direction of th e arrow either into or out of the stock. T he circle w ith a " T ” a t the top holds the algebraic expression th a t regulates the flow. Figure 43 shows a stock w ith an inflow and outflow attach e d to it. Clouds a t th e ends of flow pipes indicate sources and sinks. 0 — 5 > F lo u > Figure 42: A flow. Stock ° 6 ^ Inflow Figure 43: An exam ple of a stock w ith two flows. A nother elem ent is the converter. It is designed to hold a constant or an equation th a t generates an o u tp u t value each tim e interval. T h a t is th e m ain difference between a converter and a stock is th a t a converter does not accum ulate any value. For example, in this m odel desired fertility will be set in a converter as th a t variable m ust be determ ined in each period. All constant param eters th a t are used in th e equation for desired fertility (4.2) will also be held in a converter. G raphically, in Stella, a sim ple circle designates a converter (Figure 44). o Converter Figure 44: A converter. i ' Outflow Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. CO M PU TER IM PLE M EN TA TIO N 90 Inform ation is transferred to and from various blocks in the model through connectors th a t look like wires. Figure 45 shows two connected converters. o ------------------o Converter 1 Converter 2 Figure 45: Two connected converters. A model of any com plexity may be built using th e objects given above. However, very soon the m odel might rem ind a "p late of spaghetti with meatballs" (Day 1974). the logic of which w ould be practically im possible to understand. This difficulty is resolved by introducing three handy objects. T he first of them is the Space Compression Object (SCO). SCO m anages com plexity by hiding p a rt of the model. Figure 46 shows a closed SCO. Clicking on th e object opens it so we can deposit other building blocks into it. Figure 47 shows an exam ple of an opened SCO w ith two connected converters hidden in it. A nother object adds clarity to the m odel not by' hiding but rather grouping other elementary' objects. The Sector Frame surrounds stocks, converters and the connectors between them ; having related blocks visually organized together helps trem endously to grasp the logic of the model. Figure 48 shows a typical Sector Fram e w ith a stock, two flows and a converter connected to one of the Hows. SCO /■ -------- ' ) Figure 46: A space compression object. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. AP P E N D IX B. C O M PU TER IM P LE M E N TA TIO N 91 SCO a : : Converter 1 ;- o Converter 2w Figure 47: A SCO with two connected converters. 0 5 )0 Sector Stock Inflow Outflow o Converter Figure 48: A typical sector object. To cut on the num ber of ”spaghetti” (th a t is connectors) th a t clu tter the model, one can utilize ghost objects. A ghost object does n o t add any real structure to th e model as it is only a replica or an alias of an individual stock, flow or converter. Figure 49 gives an exam ple of how one m ight w ant to use a ghost. Instead of having a connector cross Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. C O M PU TER IM P LE M E N TA TIO N 92 from some O utside C onverter to th e stru ctu re inside of th e Sector, as in F igure 49 a), a ghost object (a dashed circle) was placed into the Sector an d connected to Outflow, as in Figure 49 b). T here is no longer a need to have a connector crossing the sector boundary. O f course, in such a sim ple exam ple it is not yet quite clear why someone m ight want to create a ghost for O utside Converter: however, review ing sectors of G E M Europe will make a clear case in favor of using ghost objects. rtsi Stock inflow Outflow Converter Outside Converter a) T his m odel does not have a ghost object. d s )(g ) Sector C O < 1 Stock 0 — t C X ,'° / Inflow Outflow 6 ✓ -- o Converter Outside Converter Outside Converter b) A ghost object was created for O utside C onverter. Figure 49: A n example of using a ghost object. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. C O M PU TER IM PLEM EN TATIO N 93 B.3 Diagrams A fter th e introduction to the system dynam ics language, we are ready to look ac the Stella im plem entation of the model. A good place to start explaining th e model is the graph of Figure 50 th a t was generated by S tella after each sector h a d been implem ented. T he graph does not show all th e details of each individual sector, b u t th e internetworking of th e m odel is clear. T h e model has seven sectors, each logically organizes a part of the model. T h e Production sector contains a stru ctu re th at generates dom inant production and th e dom inant sector. M ortality sector finds the death rate. T h e birth rate is the o u tp u t of the Fertility sector. T he arrows of th e graph say th a t H ealth technology and Epidem ics affect M ortality. Production influences Mortality, Fertility, and Production Technology. At the sam e tim e the output of the Production Technology sector is used in P roduction. B oth M ortality and Fertility determ ine the P o p u latio n . To learn the specifics of the interaction between the sectors and how each of th e sectors is built we need to look at the detailed graphs of the sectors themselves th a t a re given below. Production F igure 50: T he schem atic im plem entation of the m odel. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. CO M PU TER IM PLEM EN TATIO N 94 We s ta rt by looking at th e Fertility sector (Figure 51). T he basis of th e sector is the fertility causal chain of F igure 9. Two additional blocks th a t are not in Figure 9. but are present in Figure 51 are ” a” and "system ". C onverter ” a” holds param eters a j. ao. and < 23. A ghost converter "system ” holds the value of the dom inant socioeconom ic sector, w hich is then used to choose th e correct set of param eters for desired fertility. Notice that because a ghost is used for th e "system ", there is no need to have a connector extending from th e Production sector, w here "sector” is determ ined, into th e F ertility sector. costs stem family pref param income fertility threshold previous mortality Figure 51: T he Fertility block. T he m ortality causal g rap h of Figure 13 is translated into M ortality sector as in Figure 52. T h a t sector makes an extensive use of ghost converters — it has four of them . T he rates for m ortality an d fertility are used in the Population sector (Figure 53) to find the inflow and outflow from the stock of population. Two connectors from the stock to th e flows inform the flows of the current level of the stock "P o p u latio n ” . T he inflow "b irth s” and th e outflow "d e a th s” are measured in num ber of people, while the fertility and m ortality rates, denoted in the graph of Figure 53 as "fertility” an d ’ ’m ortality” , are in people per 1000 people; therefore, we use the following conversion equations to go from th e rates to ’ ’births” and ’ ’d eath s” : , . , Population births = -----——----- * fertility Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPEN D IX B. C O M PU TER IM PLE M EN TATIO N cO previous mortality income k ( ) , mortality epidemics Figure 52: T he M ortality block. i~P Population Population birtfls fertility Figure 53: T he Population block. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. C O M PU TER IM PLEM EN TA TIO N 96 Population deaths = ---------------- * m ortality 1000 * These equations are held in th e circular p a rt o f th e flow icon (th e one which has a ” T" on top). Given these ’’births" and ’ ’deaths” , the stock ’ ’P opulation” , which corresponds to x . is: P opulation = Population 4- births — deaths . T his form ulation, which is com mon in com puter sciences, implies th a t the variable ("P op u lation” ) is equal its previous value plus ’ ’b irth s” less ’ ’deaths” . It is equivalent to a difference equation x t+i = x t 4- B t — D t , w here x t and are population levels of this and the next periods respectively, B t is th e num ber of births a n d D t is the num ber of deaths. T he Epidemics sector (Figure 54) generates epidem ic shocks, kt, of equation (5.1). To following is the Stella im plem entation of equation (5.8): IF ( TIM E = s ta rt _ o f_ reg im e_ 4 4 -delay) TH EN (1 4- m agnitude) ELSE (1) In this equation T IM E is the current period of th e model and ” sta rt_ o f_ re g im e _ 4 ” is th e first period of regim e four th a t is stored in th e converter ’’s ta rt of regime 4” . It is placed in the ’ ’epidem ics” converter. E quation (3.11) is im plem ented as the production sector (Figure 55). In each period, a potential m axim um production value is determ ined for each of th e com peting regimes in the corresponding Space Compression O bjects. Figure 56 gives an example of such a SCO; this one is for the hunting and gathering space compression object. The arrayed con verter ’’P aram sl” contains production param eters for th e hunting and gathering regime: p, (3, M , N , 6, and x . C onverter ’ ’Possible P roductions 1” generates productions th a t Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. C O M PU TER IM PLEM EN TATIO N 97 can be achieved w ithin the hunting and gathering regime for various num bers of bands. T he highest of them is selected in ”chosen production 1” . N otice th a t ” Possible Pro ductions 1” takes inputs from "Technology” and "Population” ghost stocks. T he former stock provides current value of technology B , and la tte r stock keeps track of population, x. epidemics start or regime 4 F igure 54: The epidemics block. T he chosen productions o u t of the six SCOs are com pared in the SCO called "system and production preferences". T h a t object has only one function: to choose the regime th a t gives the highest production, th a t is it im plem ents equation (3.12). T he system that allows the highest production for a given population is chosen as th e dom inant system and th a t production technology becomes the dom inant production technology. Converter "incom e” is ’ ’dom inant production” over ’ ’Population” . T he learning by doing sector for the production knowledge is show n in Figure 57. C onverter ’ ’rate of learning” holds values for param eter p of equation (3.14) for six regimes of the model. Stella indicates th a t a block has m ore than one value by draw ing it as a stack of pancakes. Such blocks are called arrayed blocks (thus an arrayed converter or an arrayed stock). Figure 58 shows the com puter im plem entation of equations (3.6) and (5.4) that are grouped into the H ealth technology sector. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. COM PUTER IM PLE M EN TA TIO N 98 C S r - Figure 55: T he production sector im plem entation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX B. C O M PU TE R IM PLE M EN TA TIO N 99 Technology Population Technology Technology hunter gatherers production' city stSte production f system and. production’ preference; : I j .4 — • O r — i rchosen production 1 :Params1 iPossible Productions 1 Figure 56: An open Space Com pression O bject for the hunting-gathering production. Production Technology Technology learning max technology level system rate of learning Figure 57: The P ro d u ctio n technology sector. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P PE N D IX B. C O M PU TE R IM PLEM EN TA TIO N 3 Health technology health technology improvements rate p3ram s for h Figure 58: The H ealth technology sector. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Creator Pavlov, Oleg V. (author)

Core Title Demoeconomic dynamics: Evidence from historic Europe

School Graduate School

Degree Doctor of Philosophy

Degree Program Economics

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

Tag Economics, General,history, European,OAI-PMH Harvest,sociology, demography

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Day, Richard H. (committee chair), [illegible] (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-65652

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