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The Size Distribution Of Income And Its Relationship To Economic And Social Well-Being In The State Of California

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The Size Distribution Of Income And Its Relationship To Economic And Social Well-Being In The State Of California

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Content THE SIZE DISTRIBUTION OF INCOME AND ITS RELATIONSHIP TO ECONOMIC AND SOCIAL WELL-BEING IN THE STATE OF CALIFORNIA by Kelly Jarvis Black A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Economics) August 19 71 c - 1 iv' I I ' - - ' ■ 72-6039 BLACK, Kelly Jarvis, 1934- THE SIZE DISTRIBUTION OF INCOME AND ITS RELATIONSHIP TO ECONOMIC AND SOCIAL WELL BEING IN THE STATE OF CALIFORNIA. University of Southern California, Ph.D., 1971 Economics, general University Microfilms, A X ER O X Com pany, Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED UNIVERSITY O F SO U T H E R N CALIFORNIA T H E G R A D U A T E S C H O O L U N IV E R S IT Y PA R K LO S A N G E L E S , C A L IF O R N IA 9 0 0 0 7 This dissertation, written by KELLY JARVIS BLACK under the direction of h .is. Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Gradu ate School, in partial fulfillment of require ments of the degree of D O C T O R O F P H I L O S O P H Y f '771 Dean D ate A p ril 15, 1971, DISSERTATION COMMITTEE ........ A Chairman ..... .. PLEASE NOTE: Some Pages have i n d i s t i n c t p r i n t . Film ed as r e c e iv e d . UNIVERSITY MICROFILMS ACKNOWLEDGMENTS The author gratefully acknowledges the time given by his dissertation committee in reading the draft and final copies of this dissertation. Each member of the committee has contributed to the development of the topic, but particularly in his respective field of specialization: Dr. E. Bryant Phillips, chairman, in consumer economics; Dr. John Elliott in economic theory; and Dr. Robert Childress in statistics. In addition, the author is indebted to Dr. Paul T. Kinney, Dean of the School of Business at Chico State College, for his understanding and support, and to Drs. George D. Johnson of Chico State College and Jeffrey Nugent of the University of Southern California for valuable assistance in visualizing the methods and the statistical model. Finally, sincere gratitude is extended to Stacy, Jonathan, and Jamie for the willing sacrifice of their father's time to a cause which they may not have completely understood, and to Susan, without whom even the grandest of accomplishments would be devoid of meaning. TABLE OF CONTENTS Page ACKNOWLEDGMENTS ......................................... ii LIST OF T A B L E S .............................................vii LIST OF FIGURES.......................................... x Chapter I. INTRODUCTION ................................... 1 Income Distributions and Well-Being .... 2 The Purpose, Importance, and Methods of the Dissertation ......................... 5 Scope and Coverage......................... 8 Perspective and Context .................. 10 The Egalitarian Controversy ................ 19 Plan of the Study........................... 24 II. REVIEW OF THE LITERATURE..................... 27 Early Attempts to Construct Income Distributions .............................. 2 8 Modern Treatment of Income Distribution D a t a ....................................... 32 The Literature on Income Equality and Well-Being................................ 37 iii Chapter Page Recent Books .............................. 3 7 Journal A rticles......................... 42 Summary of Recent Literature ........... 46 III. THE FRAMEWORK FOR EMPIRICAL RESEARCH .... 47 The Empirical Data and its Sources .... 48 Population and Density .................. 5 2 Educational Attainment ................... 54 Employment................................ 5 6 Housing..................................... 5 7 Crime....................................... 5 7 Health and Public Assistance ............ 59 A g e .......................................... 6 2 M obilit y................................... 6 2 Income and Consumption .................. 6 3 Social Base Factors....................... 64 The Measurement of Income Inequality . . . 66 The Recipient U n i t ....................... 6 7 The Time H o r i z o n ......................... 69 The Income C o n c e p t ....................... 70 Distribution Shapes ....................... 70 Inequality Measurement .................. 71 Alternative Measures of Inequality . . . 75 The Gini I n d e x ............................ 79 iv Chapter Page A Factor Analytic Method of Measuring Well-Being............................... 83 An E x a m p l e ................................ 85 Application of Factor Analysis ......... 89 The Principle Components Model ......... 9 2 Derivation of Component Scores ......... 9 3 The Research Procedure and the Statistical Model.......................................... 100 IV. RESULTS OF THE STUDY: INCOME DISPERSION AND WELL-BEING IN CALIFORNIA.................104 The Distribution of Income by California Counties...................................10 4 A Comparison of Well-Being for California Counties ....................... 117 The D a t a ..................................... 117 Number of Factors......................... 12 2 Interpretation of Factors ................ 124 Communality and Explained Variance . . . 131 Factor Scores and the Index of Well-Being.................................132 Further County Comparisons .............. 136 The Effect of Income Inequality on Well-Being.............................. . 137 An Optimum Range of Inequality............160 v Chapter Page V. SUMMARY AND IMPLICATIONS....................... 16 2 Summary of the Dissertation and the Results................................ 16 3 The Literature............................16 3 The Empirical D a t a ..........................164 Measuring Income Inequality .............. 16 5 Measuring Well-Being ..................... 16 7 Income Inequality and Well-Being .... 168 Implications of the Findings.................169 Policy and the Findings ..................... 171 Limitations of the Findings.................175 APPENDIX A. BASIC DATA FOR CALIFORNIA COUNTIES . . . 178 APPENDIX B. CALCULATION OF GINI INDEX FOR 5 8 CALIFORNIA COUNTIES .................. 19 6 SELECTED BIBLIOGRAPHY ................................... 227 vi LIST OF TABLES Table Page 1. Percentage Share of Aggregate Income Received by Each Fifth of Families and Unrelated Individuals Ranked by Honey Income for Selected Years, 1947-1969 13 2. Per Cent Distribution of Families and Unrelated Individuals by Money Income in Constant 19 69 Dollars for Selected Years, 1947-1969 .............................. 14 3. The Dispersion of Income in Selected Countries..................................... 15 4. Measurement of the Distribution of Income Among States of the U.S., 19 60 .............. 17 5. Correlation Matrix for Four T e s t s ............ 86 6. Two-Factor Matrix .............................. 8 7 7. Two-Factor Matrix with h^ < 1 . 0 .............. 88 8. Rotated Factor Matrix .......................... 89 9. Curve Types and Linear Equivalents ............ 101 10. Gini Coefficients of Family Income Inequality for the Counties of California.................10 7 11. Rank of the 5 8 California Counties by Income Inequality as Measured by the Gini Index . . Ill 12. Per Cent of Families Receiving Less than $1,000, Less than $3,000, and Over $15,000 by County, 19 59 112 13. Rank of the 5 8 California Counties by Per Cent of Incomes Less than $3,000 in 1959 . . 114 vii Table Page 14. Rank of the 5 8 California Counties by Per Cent of Incomes Over $15,000 in 1959 .... 116 15. Variables Used in the Factor Analysis and the Correlation Matrix ....................... 119 16. Marginal Increment to Explained Variance with Increases in F a c t o r s ..................... 125 17. Factor Matrix before Rotation ................. 126 18. Rotated Factor Matrix .......................... 12 7 19. Factor Scores for Each County and Sums of Weighted Factor Scores ....................... 13 3 20. The Index of Well-Being for the Counties of California...................................135 21. The Education-Income Component in the 5 8 Counties of California ....................... 13 8 22. The Physical Welfare Component in the 5 8 Counties of California ....................... 139 23. The Housing Quality Component in the 5 8 Counties of California ....................... 140 24. The Mobility-Growth Component in the 5 8 Counties of California ....................... 141 25. Curve Types and Coefficients of Determination for the Gini Index and Well-Being Relationship .................................. 150 26. Rankings of the Counties of California in the Gini Index of Income Inequality and in the Index of Well-Being.................. 15 3 27. The Relationship of Individual Well-Being Components to the Gini Index of Income Dispersion........................................155 viii Table Page 28. Economic, Social, and Crime Components of Well-Being and their Relationship to Income Inequality ........................... 15 7 29. Correlation Coefficients for Variables and Well-Being and for Variables and Income Dispersion ............................. 15 8 ix LIST OF FIGURES Figure Page 1. The Lorenz Curve of Income Inequality .... 81 2. Timeshare Program for Computing the Lorenz Concentration Ratio or Gini Coefficient ................................ 84 3. Areas of Extreme Income Inequality ............ 10 8 4. Areas of Income Inequality over One Standard Deviation Less than the M e a n .............................................. 110 5. Factor Tree for Four to Eighteen Factors Showing Major Factor Loadings.......................................12 3 6. Component Scores for Santa Barbara County............................................ 142 7. Component Scores for San Francisco County............................................ 143 8. Component Scores for Los Angeles County............................................ 144 9. Component Scores for Marin County ............ 145 10. Component Scores for Madera County ............ 146 11. Component Scores for Imperial County............................................147 12. Scatter Diagram of Income Inequality and the Well-Being Index........................149 x Figure Page 13. The Line of Regression for Income Inequality and Well-Being and the 95 Per Cent Confidence Interval................152 14-. Theoretical Range of Optimum Inequality........................................161 15. Scatter Diagram of Income Inequality and the Well-Being Index Showing Clusters of Suburban, Mountainous, and Agricultural Counties.......................174- CHAPTER I INTRODUCTION Nearly every family receives an income and makes basic decisions regarding the disposition of that income. In addition, other social and economic units such as single individuals or associations receive and disburse money in accordance with their income and needs. The sum total of all incomes received in a given area of the world can be referred to as regional or national income. In this aggregate form, the study of incomes is a branch of macro economics and is commonly called income analysis. Increasing references have been made in recent years to the importance of distribution of income as opposed to the total quantity. In other words, the concept of individual and group incomes received as compared with the incomes received by others is being recognized as important in our society. This is due to some extent to the increasing availability of data concerning personal income distribution, but more important, perhaps, is an increasing realization that the manner in which the total of all incomes is distributed among the various recipients can be either beneficial or detrimental to the economic 1 2 and social well-being of society. Income Distributions and Well-Being In 1915, W. I. King, a pioneer in working with personal income distribution, stated that "income is the best single criterion of welfare."^ He further affirmed that immediate economic welfare is studied best through the 2 distribution of income. Another pioneer in this area stated his purpose as determining "whether the existing distribution of income in the United States . . . tends to 3 impede the efficient functioning of the economic system." Optimum conditions for maximizing welfare, according to Dobb, include a consumers condition and a production condition. The related Pareto optimum is well 4 known. But the state of well-being or extent of welfare in the real world may be linked to the income distribution. As Kuznets puts it: ■*"W. I. King, Wealth and Income of the People of the United States (New York: Macmillan Company, 1915), p. 217. ^W. I. King, "Desirable Additions to Statistical Data on Wealth," American Economic Review, VII, Part I (March, 1917), 157-71. 3 M. Leven, H. G. Moulton, and Clark Warburton, America’s Capacity to Consume (New York: Brookings Institution, 1934) , p. 177. i f Maurice Dobb, Welfare Economics and the Economics of Socialism (London: Cambridge University Press, 1969), p. *+8. The size distribution of income is an aspect of the economic process that links activities of enterprises with those of individuals. This linking lends a high value to the analysis of size distributions . . .5 Kuznets also found at an early stage of the development of income distribution data that a negative correlation existed between average income and income inequality. In addition, income has long been used as a proxy for an elusive quantity, the extent of economic welfare. Sturmey has noted that a unit increase in income will cause a greater increase in economic welfare if it goes to the poor than would be the case with marginal increments given to 7 the rich. All of the foregoing examples serve to emphasize the importance of the distribution of income in assessing the economic welfare of a community. Economic welfare, however, is only part of total welfare, with the balance attributable to social factors. Overall well-being, embracing both social and economic factors, must surely include such elements as education, employment, the real value of consumption, housing, health, ^Simon Kuznets, "Directions of Further Inquiry," in Studies in Income and Wealth, v. XV (New York: National Bureau of Economic Research, 1952), p. 203. 0 Simon Kuznets, "National Income," in Encyclopaedia of the Social Sciences, XI (New York: Macmillan Company, 1933), pp. 205-24-. 7 S. G. Sturmey, Income and Economic Welfare (London: Longmans, Green and Co., Inc., 19 59), p. 5. and the absence of negative factors such as overcrowding, oppressive government, crime and civil strife, and abject poverty, in addition to income. Many of these have been g treated in the literature. Indeed, economists have for 9 generations concerned themselves with wealth and welfare. Boulding says: It is impossible for us to exclude problems of welfare, of wants and their satisfactions, from the subject matter of economics.10 Accordingly, the subject matter treated here has to do with "problems of welfare," but more specifically, the relationship of well-being in general to income dispersion. How can income dispersion and welfare levels be measured? What welfare levels or conditions can be associated with high or low levels of income inequality? 8 See, for example, Enrique Roldan, Education and Income Distribution: an Empirical Study (unpublished doctoral dissertation, University of Minnesota, 1966); Jacob Mincer, "Investment in Human Capital and Personal Income Distribution," Journal of Political Economy, LXVI, No. 4 (August, 19 58), 281-93; Herman P. Miller, Income Distribution in the United States (Washington, D.C.: U.S. Government Printing Office, 1966); Gary Becker, Human Capital and the Personal Distribution of Income: an Analytical Approach (Ann Arbor: Institute of Public Administration, 1967); James Morgan, "The Anatomy of Income Distribution," Review of Economics and Statistics, XLIV, No. 3 (August, 1962) , 270-83 ; and many others too numerous to cite. 9 . See Chapter II, Review of the Literature. ■^Kenneth E. Boulding, Economic Analysis, vol. I (4th ed., New York: Harper and Row, 19 66), p. 9. These are the major questions to be investigated in this dissertation. The Purpose, Importance, and Methods of the Dissertation Greater equality with regard to income and wealth has long been held to be beneficial to society. The concentration of income among a few individuals while the majority remain impoverished is said to be an unnatural state of affairs."^ The purpose of this dissertation is to test empirically the hypothesis that there is an inverse cor relation between the dispersion of the income size distribution and the well-being of society. In other words, the assumption that levels of welfare are low when income is very unequally distributed will be subjected to empirical analysis. The major effort involved is in the collection of data regarding a) income and its distribu tion, and b) the economic and social well-being of society, and in the analysis of that data. Basic to the problem of testing the importance of income inequality in determining well-being is the 11 The "arbitrary and inequitable distribution of wealth and incomes" was viewed by Keynes as one of the outstanding faults of our economic society; the other was failure to provide full employment. John Maynard Keynes, The General Theory of Employment, Interest, and Money (New YorK: Harcourt, Brace and World, Inc., n.d.), p. 372. measurement of both well-being and inequality. In addition, the many facets of aggregate community or re gional well-being must be explored. Consumption expenditures are sometimes accepted as a measure of economic well-being (excluding the problems of home-based production for home consumption without exchange), but economic well-being cannot be considered equal to total well-being, for certain facets of well-being are sometimes beyond the direct purchasing power of money, such as health, education, criminal tendencies, overcrowding, and other environmental factors. These non-income factors are to be included in this study for analysis of possible relationship to the distribution of income. In this sense the study differs from most prior analyses of income and welfare, for the non-economic contributors to well-being have, in the past, been disregarded to a great extent. As stated, the purpose of this study is to test empirically the hypothesis of an inverse correlation between the dispersion of the income size-distribution and well-being, both economic and social. More specifically, certain dimensions of well-being, both economic and social are measured for geographic areas in the State of California. Data on the distribution of income for the same areas are also compiled. The results are then compared to one another and examined for correlation. Assuming that the measurements are valid, along with the assumptions underlying the measurements, and that all or most of the pertinent factors affecting well-being have been considered, the empirical test of the central hypothe sis will be valid. That is, if well-being is high in geographic areas displaying a high degree of income inequality and if well-being is consistently smaller wherever inequality of incomes is higher, then an assertion that decreasing inequality leads to higher levels of well being may be made. If not, then the hypothesis is rejected. The search for cause-and effect relationships takes place in all the sciences. However, it is quite difficult to prove such relationships, since the mode of inquiry involves beaming by association. Events can be observed and related, but a decision regarding causation is more of a judgment than an analytical result. Regression and correlation methods, which are used later in this study, are powerful tools providing quantitative expressions regarding the type and extent of association. They may even provide support for.a judgment concerning causation, but that judgment is reserved for possible use if high levels of association are found. It is obvious, of course, that no single variable, either economic or social, can be justified as being indicative of total well-being. A number of them are therefore included in the investigation, being chosen on 8 the basis of assumed characteristics which add to or detract from well-being. Disregarding interactions among variables for the moment, those that can be considered logically to affect well-being are (1) a measure of the central tendency of each income distribution; (2) consump tion expenditures; (3) the absence of crime; (*+) educa tional attainment; (5) personal and public health; (6) adequate housing; (7) employment; (8) lack of overcrowding; and (9) certain aggregate socio-cultural traits, such as the urban-rural mix and ethnic background. The analytical methods to be used in the analysis are statistical in nature. Correlation, regression, and factor analysis are employed. The results of the model, however, will also be examined for relevance and import, with possible policy implications to be considered. As previously indicated, three basic questions are to be treated, and they bear repeating: 1. How can income dispersion and well-being be measured? 2. What happens to certain welfare indicators as the income distribution changes? 3. Is there an optimum range of income inequality? Scope and Coverage The boundaries of economic science are perhaps wider today than at any time in the past. Samuelson’s 12 definition of economics, including the allocation of scarce resources for the satisfaction of unlimited wants, does not limit economics to the study of markets, commodities, and goods. Indeed, to the extent that income is related to our everyday activities, the definition of Marshall is more appropriate, wherein economics is known as 13 "the study of mankind in the ordinary business of life." The ordinary business of life certainly includes health, employment, income, consumption, the commission of crime, obtaining an education, our interactions with one another in overcrowded situations and housing standards. As a consequence, this dissertation has not been limited to the study of income dispersion and its relation to consumption, (which could be called a measure of economic well-being) but has been extended to include social well being as far as determinable in the available data. Nevertheless, the scope is narrow in that, theoretically, only a review of the literature is included and, empiri cally, only the relationships among the variables are hypothesized and tested, with central attention on the relationships between the income distribution variable and 12 Paul A. Samuelson, Economics, An Introductory Analysis (8th ed., New York: McGraw-Hill Book Company, 1969) , p. 5. 13 Alfred Marshall, Principles of Economics (8th ed., London: Macmillan Company, 19 30), p. TI the chosen dimensions of well-being. 10 Perspective and Context To place the present study and its very limited coverage in perspective, it is necessary first to view the study of income inequality in a larger context. The U.S. Bureau of the Census began to collect data relating to personal income in 19 4-0, despite charges of bureaucratic 14 snooping and infringement of privacy. After the 19 50 census income data were published in the form of income distributions, and this was continued in 1960. These data made it possible to study U.S. income distributions in areas for which data were not previously available and to draw conclusions regarding the overall changes in inequal- 15 lty or dispersion of incomes. Interest in the provocative problem of inequality of income did not await a complete census, however. As early as 189 6 studies of the U.S. income distribution were published, made possible by scanty data and fearless assumptions regarding their applicability. Surveys of small areas by private interests and, later, taxpayer data from the treasury department provided the 14 Herman P. Miller, Income of the American People (New York: John Wiley and Sons, Inc., 1955), p. xiii. 15 The contributions to the study of income inequality made possible by census data and prior studies done without the benefit of the same information are described hereafter in the Review of the Literature (Chapter II). 11 data. These early studies concluded that substantial differences in income size did indeed exist, and that conclusion has not been changed by later studies. In fact, a picture of the range of incomes among persons in the United States (in 1960) can be had by imagining that a building block one foot high represents an income of one thousands dollars per year. If each person were to stand on a stack of building blocks equal to his income, the majority would have been standing less than three feet from the ground, and more than nine-tenths of all persons would have been standing on blocks less than six feet high. But the highest of income brackets would have shown people 1 C standing so high they would be lost in the clouds. Those persons composing the highest five per cent of income recipients in 19 6 0 actually received over seventeen per cent of the income, with the lower twenty per cent • • . 17 receiving less than five per cent. Since it has been estimated that the top five per cent of income recipients received thirty per cent of the income in 1929, the degree 18 of inequality has been decreasing over the years. There 16 Abba P. Lerner, Everybody1s Business (Ann Arbor: Michigan University Press, 1961), p. 95. 17 U.S. Department of Commerce, Bureau of the Census Current Population Reports, Series P-60, No. 75 (Washington, D.C.: U.S. Government Printing Office, 1970), p. 26. 18 U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 19 5 7 (Washington, D.C.: U.S. Government Printing Office, 1960) , p. 166. 12 was a time period of nearly twenty years when the share of the lowest twenty per cent of the income recipients did not 19 change, but inequality has apparently resumed its decline in the years since 1960. Table 1 illustrates this point, and Table 2 shows a detailed distribution of income by size for the United States from 1947 to 1969. At this point, no value judgments are made regarding whether any distribution of incomes is good or bad. It may be worthwhile, however, to note the position of the United States among various countries of the world with reference to relative inequality (see Table 3). Note that the table is a measure of relative inequality of incomes only in the sense that the share of income going to the upper five per cent of families represents the degree of dispersion of the entire distribution. Professor Irving Kravis has summarized international income distributions among countries for which he had data in the following 20 way: More nearly equal distribution than the U.S.: 19 Herman P. Miller, m Income Distribution in the United States (Washington, D.C.1 U.S. Government Printing Office, 1966 ) , p. 3, destroys the once popular idea that the income gap between rich and poor is continually narrowing. 2 0 . Irving B. Kravis, The Structure of Income (Washington, D.C.: University of Pennsylvania Press, 1962) , p. 237. 13 Table 1.--Percentage Share of Aggregate Income Received by Each Fifth of Families and Unrelated Individuals Ranked by Money Income for Selected Years, 1947-1969 Income Rank 1947 1950 1957 1960 1963 1967 1969 Families Lowest Fifth 5.0 4.5 5.0 4.9 5.1 5.4 5.6 Second Fifth 11. 8 12.0 12. 6 12.0 12.0 12.2 12. 3 Middle Fifth 17.0 17.4 18.1 17.6 17.6 17.5 17. 6 Fourth Fifth 23.1 23.5 23.8 23.6 23.9 23.7 23.4 Highest Fifth 43.0 42.6 40 .5 42.0 41. 4 41. 2 41.0 Total 100 .0 100 .0 100 .0 100.0 100 . 0 100.0 100.0 Top 5 per cent 17.2 17.0 15.7 16. 8 16.0 15 . 3 14. 7 Unrelated Individuals Lowest Fifth 1.9 2.3 2.6 2.6 2.4 3.0 3.4 Second Fifth 5.8 7.0 7.3 7.1 7.3 7.5 7.7 Middle Fifth 11.9 13. 8 13. 7 13.6 12. 7 13. 3 13.7 Fourth Fifth 21. 4 26.5 25.4 25.7 24.6 24.4 24.3 Highest Fifth 59 .1 50.4 51.1 50.9 53.0 51. 8 50.9 Total 100 .0 100.0 100.0 100.0 100 .0 100 .0 100.0 Top 5 per cent 33.3 19 . 3 19. 8 20.0 21.2 22.0 21.0 Source: U.S. Department of Commerce, Bureau of the Census, Current Population Reports, Series P-60, No. 75 (Washington, D.C.: U.S. Government Printing Office, 1970), p. 26. 14- Table 2.— Per Cent Distribution of Families and Unrelated Individuals by Money Income in Constant 19 69 Dollars for Selected Years, 1947-1969 Money Income 1947 1950 1957 1960 1963 1967 1969 Families Under $3,00 0 24.4 24.4 17.9 16. 8 14. 8 10 .9 9 . 3 $3 ,000-$4 ,999 26.1 24.8 16. 3 15.0 14.1 11.5 10.7 $5,000-$6 ,999 22.3 23.1 21. 5 18.5 16. 8 13.7 12. 3 $7,000-$9 ,999 16.0 16.6 25.0 24.5 23.7 23.1 21.7 $10,000-$14,999 11. 3 11. 3 14.1 17.3 20. 3 24. 8 26.7 $15,000 and Over 5.2 7.9 10.1 15 .9 19 . 2 Total 100 .0 100.0 100.0 100 .0 100.0 100 .0 100 .0 Unrelated Individuals Under $1,500 47.6 00 3 - 41. 2 39.1 36. 2 30.5 26.5 $l,500-$2,999 23.1 18.9 22.0 21.1 24.9 23.5 24.3 $3,000-$4,999 19 .2 20.3 17.4 17.2 14.2 17.0 17.9 $5 ,000-$6,999 6.0 8.7 11.1 12.7 11. 6 12.4 12. 8 $7,000-$9 ,999 2.1 2.4 5.6 7.1 8.4 10 .1 10.5 $10,000 and Over 2.0 1.2 2.5 2.6 4.5 6.6 8.0 Total 100 .0 100 .0 100 .0 100.0 100.0 100.0 100 .0 Source: U.S. Department of Commerce, Bureau of the Census, Current Population Reports, Series P-60, No. 75 (Washington, D.C.: U.S. Government Printing Office, 1970), p. 24. 15 Table 3.— The Dispersion of Income in Selected Countries Per Cent of Income Year of Received by Top 5% Country Data of Families United States 1950 20% Sweden 1948 20% Denmark 1952 20% Great Britain 1951-52 21% Barbados 1951-52 22% Puerto Rico 19 5 3 23% India 1955-56 24% West Germany 1950 24% Italy 1948 24% Netherlands 1950 25% Ceylon 1952-53 31% Guatemala 1947-48 35% El Salvador 1946 36% Mexico 1957 37% Columbia 1953 42% Northern Rhodesia 1946 45% Kenya 19 49 51% Southern Rhodesia 1946 65% Source: Simon Kuznets, "Quantitative Aspects of the Economic Growth of Nations," Economic Development and Cultural Change, XI, No. 2 (January, 1963), p. 13. 16 Denmark Netherlands Israel (Jewish Population Only) About the same distribution as the U.S.: Great Britain Japan Canada More unequal distribution than the U.S.: Italy Puerto Rico Ceylon El Salvador These data are of interest, for they indicate the international differences that are somewhat correlated with economic maturity. Data collection problems, however, render a complete study of international comparative 21 inequality of incomes infeasible. For the United States, interstate comparisons of inequality have appeared in the 2 2 leading journals. Table 4 sets forth the Gini coeffi- 2 3 cient of income inequality for the states of the United 21 With due respect to Harold Lydall for his admirable effort in The Structure of Earnings (Oxford: Clarendon Press, 1968). 2 2 See, for example, Frank A. Hanna, "Analysis of Interstate Income Differentials: Theory and Practice," in Studies in income and Wealth, Vol. XXI (Princeton: Princeton University Press, 1957); Ahmad Al-Samarrie and Herman P. Miller, "State Differentials in Income Concentra tion," American Economic Review, VII, No. 1 (March, 196 7), 59-72; and David I. Verway, "A Ranking of States by Inequality Using Census and Tax Data," Review of Economics and Statistics, XLVIII, No. 3 (August, 1966), 314-21. 23 • This and other measures of inequality will be considered in detail in Chapter III. At this point it may be beneficial, however, to explain that the Gini 17 Table 4.--•Measurement of the States of the U.S. Distribution , 1960 of Income Among State Gini Coefficient Families3 CSU's^ State Gini Coefficient Families CSU’s Miss . 466 . 506 Md. . 349 .425 Ark. .437 .492 111. . 348 .429 Ky. .425 .479 Calif. .345 .436 Ala. .424 . 470 Mont. . 344 .408 Tenn. .424 .476 Colo. . 344 .424 S. Car. .421 .479 Vt. . 343 .444 La • .420 .485 Pa. .399 .417 Ga . .418 .470 Ind. . 339 .411 N. Car. .415 .466 Ida. . 338 .404 Okla. .403 .474 Wis. .336 .410 Tex. .403 .482 Mich. .334 .407 Fla. . 399 .478 N.J. .334 . 399 Va. . 398 . 461 Wyo. .334 .402 W. Va. . 397 . 452 R.I. .332 .424 Wash. D.C. . 395 .473 Nev. . 331 .416 S. Dak. . 391 .455 Conn. . 331 .412 Mo. .386 .463 Me. .330 .414 N. Mex. . 379 .437 Ore. .330 .423 N. Dak. .373 .435 Ohio .330 .406 Iowa .372 .443 Wash. .329 .410 Del. .371 .474 Mass. .327 .414 Neb. .371 .440 N.H. .319 .403 Ariz. . 369 .450 Utah . 312 . 393 Minn. . 362 .434 Kan. . 362 . 438 N.Y. . 352 . 441 Alaska n. a. .446 Hawaii n. a. .442 The data for family units are taken from Verway, "A Ranking of States by Inequality Using Census and Tax Data," Review of Economics and Statistics, XLVIII, No. 3 CAugust, 1966), 314-21. ^The data for consumer spending units (CSU's), analagous in this case to families and unrelated individ uals, are taken from Al-Samarrie and Miller, "State Differentials in Income Concentration," American Economic Review, LVII, No. 1 (March, 1967), 59-72. 18 States. Note that the southern states, which are, in general, lower in median income than the states of other regions, predominate at the top of the inequality scale, meaning that income is more unequally distributed there. While apparent progress has been made in the field of inequality comparisons among states, and while it is apparent that these data have been used (to an extent) to compare with indicators of welfare, it is felt that a significant step forward can be taken by disaggregating the state totals and averages into smaller, more intrinsically homogeneous geographic areas and by further concentration on data relationships regarding the income distribution and welfare. For this purpose, the 5 8 counties of California have been chosen and the data for income distributions and welfare-related variables have been collected. The scope of the dissertation is limited to this data base, and therefore a great deal of care must ne taken in generalizing the results. Still, such an analysis on county data has apparently not been previously coefficient has a range between zero, which would indicate that all recipients of income receive the same amount, and 1.0 which describes the situation wherein 1008 of the income goes to a single individual with none to all other individuals. The relevant range is usually from about 0.250 to 0.600. 19 24 attempted, and the field of income size distribution analysis will be enriched by the present effort. The Egalitarian Controversy In 1948 the great historian Toynbee said: . . . the unequal distribution of the world's goods between a privileged minority and an underprivileged majority has been transformed from an unavoidable evil into an intolerable injustice by the technological inventions of western m a n . 25 Bearing our the realization of this injustice, many of the advanced nations of the earth have instituted government programs to alleviate poverty and reduce income dispari ties. On the other hand, many persons who have risen to economic and perhaps political prominence in spite of their lack of inheritance have opposed redistribution of incomes, alluding to the proposition that if all wealth were evenly divided it would only be a matter of time until large disparities existed again, due to natural differences among persons. In the United States today, over half a century after the enactment of the federal income tax, there are those who despise it because of its income-equalization 24 It is quite possible that such a study has been overlooked in the literature search. However, none appeared in the Datrix file of U.S. doctoral dissertations, in dissertation abstracts since the mid-19 50's, nor in the economic journals which have been thoroughly reviewed. 9 R Arnold J. Toynbee, Civilization on Trial (New York: Oxford University Press, 1948) , p . 25"! 20 feature. In contrast, paradoxically, Nikita Krushchev was quoted in 1964 as saying, "We must fight egalitarianism, 2 6 for observing the principle of pay according to work." In comparison with the statements of some of his philosophical ancestors in socialism, Mr. Krushchev’s quotation seems unusual. Since the classical period and the beginnings of modern history, opinions have been heard in favor of economic equality. In the seventeenth century, for example, Boisguillbert argued that trade would be more active if taxation fell on the rich than if it fell on the 27 poor. Later, Malthus, Lauderdale, and Hobson joined in, along with other reformers. The latter, perhaps the most influential socialist writer of his generation, denies the connection between effort and reward, calling it the "greatest triumph of the business point of view over humanity." He goes on to say: It is not difficult to strip off the spurious ethics of the principle. You say that piece- wages or payment by result is right because it induces men to do their best. But what do we mean by ’doing their best'? A weak man may O C Reported in the Guardian, March 9, 1964 and quoted by R. W. Baldwin, Social Justice (London: Pergamon Press, 1966), p . 27. 2 7 Harry G. Johnson, "The Macroeconomics of Income Redistribution," in Alan T. Peacock, ed., Income Redistribution and Social Policy (London: Jonathan Cape, 1954) , p. 19. 21 hew one ton of coals while a strong man may hew two. Has not the former 'done his best' equally with the latter? . . . If there is merit anywhere, it is in the effort, not in the achievement or product, and piece-wages measure only the latter.2 8 A more moderate view is taken by Jay, who recognized the futility of attempting to enforce literal equality of incomes. Even the socialists of his time believed that the more skillful and diligent deserve some extra reward, but: Inequality is not justified beyond the point necessary to ensure that the productive abilities of the community are reasonably fully used . . . The skillful or diligent or responsible worker is felt to deserve more; but this perfectly valid moral judgment does not tell us how much more . . . This then emerges as the basic economic aim of the socialists; not literally "equality" but the minimum of inequality that is workable if human beings are actively to use their talents; not equal shares, but fair shares; not equality but social justice. From this it follows that equality of opportunity is not enough.29 Pigou is perhaps more analytical and dispassionate in breaking down the elements of inequality. Ultimately, therefore, it depends, first upon the influence which determines the rate of pay of various productive agents, and secondly upon those which determine the distribution 2 8 J. A. Hobson, Work and Wealth: A Human Valua tion CNew York: Macmillan Company, 191M-) , p. 193. • 2 9 Douglas Jay, Socialism in the New Society (London: Longmans, Green and Company, 1962) , pp. 8"T 16 , 326. 22 among people of the ownership of those agents . . . These cumulative processes are bound to pro mote concentration in the ownership of property. To him that hath shall be given.30 Boulding reminds us that this tendency toward monopoly "distorts the distribution of resources among various occupations away from that which is socially most 31 desirable." On the subject of social desirability, Professor Pigou says: Any cause which increases the proportion of the national dividend received by poor persons, provided that it does not lead to a contraction of the dividend and does not injuriously affect its variability, will, in general, increase economic w e l f a r e . ^ 2 Milton Friedman relates other ideas concerning the 3 3 . . distribution of income. The major factor m his model was risk and the reactions of individuals to it. A community with an aversion to risk would have built-in redistribution of incomes. He concluded that choice was the basis for inequalities, or that inequality was 30 A. C. Pigou, Income, an Introduction to Economics (London: Macmillan Company, 1948), pp. 104, 109. 31 Boulding, o£. cit., p. 562. q o A. C. Pigou, The Economics of Welfare (4th ed., London: Macmillan Company, 19 6 2!) a p . 47 . 3 3 M. Friedman, "Choice, Chance, and the Personal Distribution of Income," Journal of Political Economy, LXV, No. 4 (August, 1953), 277-290. 23 34 entirely voluntary. Abba Lerner adds, however, that: Certain inequalities of income are therefore justifiable, necessary, and socially useful. They induce people to acquire useful skills, to undertake less pleasant but necessary work and to postpone consumption whenever this would enable society to build up equipment to increase productivity. Wherever inequalities serve these functions, we may call them "functional inequalities" . . . In the Soviet Union, which started in 1917 with the idea of abolishing all inequalities, there are now inequalities as great as those in the United States.35 Perhaps Krushchev was alluding to "functional inequalities" in the statement previously quoted. In fact, it may be that the socialist and capitalist worlds, in rejecting the extremes of Hobson and Friedman may find a common ground wherein lies an optimum range of inequality of incomes. One does not need to embrace the idea of complete equality to feel that reductions in income 3 6 disparities are necessary. However utopian it may seem, the real answer may lie in the distribution of 34- Ben B. Seligman indicates that the implications of Friedman’s argument are so outlandish that it can "be rejected out of hand." See Main Currents in Modern Economics: Economic Thought Since 1870 (New York: Free Press of Glencoe, 1962) , p. 676 . 35 Abba P. Lerner, Everybody's Business (East Lansing: Michigan State University Press, 1961), p. 102. 36S. M. Miller and Pamela Roby, The Future of Inequality (New York: Basic Books, 1970), p. ITT 24 satisfactions, where satisfaction depends upon one's 37 income in relation to his needs. Plan of the Study This dissertation consists of five sections or chapters. In this introductory chapter, the reader has been introduced to the topic. The purpose of the dissertation was made explicit, and its scope was delineated. The controversial nature of the subject was summarized with a review of the background of the egalitarian discussion. Chapter II is a review of the literature on the distribution of income and the various attempts to measure it. Attempts to construct personal distributions of income prior to the availability of census data are first discussed, followed by a review of more modern treatment of income distribution data. Then the income distributions are brought into contact with well-being through a discussion of prior studies of relationship between them. The foundations for the empirical work conducted herein are presented in Chapter III. The data which have been chosen to test the hypothetical relationship of income size-distributions and well-being is presented first. Then 3 7 Such a system is developed and tested xn J. N. Morgan, M. H. David, W. J. Cohen, and H. E. Brazer, Income and Welfare in the United States (New York: McGraw-Hxll Book Company, 1962), p. 316. 25 the methods of measuring income inequality are given. The recipient unit, the time horizon, the income concept, and possible distribution functions are discussed as prelimi nary to presentation of measurement methods. The Lorenz curve and Gini index of inequality are then explained, along with a brief description of alternative measurements of inequality and reasons for the choice of the present approach. Next, the difficult process of measuring well being is assessed. A factor-analytic method is suggested, and a model of principle component-factor analysis is shown. The entire research procedure is then outlined, with the techniques of associative statistics to be used in hypothesis testing being described. Chapter IV presents the results of the analysis. First, the results of the inequality measurements for the counties of California are given. This is followed by the results of the well-being measurements, with the counties being ranked by the comparative well-being index that was constructed through factor analysis. Then the relationships that were discovered that link the distribution of income to the well-being index are presented. This forms the basic results of the study and constitutes the test of the hypothesis that well-being and distributional inequality of incomes are inversely related. In addition, the results of the investigation into the possibility of an optimum range of inequality are presented. The last chapter summarizes the entire disserta tion, including the results of the analysis which were presented in detail in Chapter IV. Chapter V also considers the implications of the findings. Possible policy alternatives, given that the dissertation results are verified, are explored. This chapter is followed by the appendices and a selected bibliography. CHAPTER II REVIEW OF THE LITERATURE The literature that could conceivably apply to the subject of this dissertation is extremely broad. That is, since in addition to the study of income and income size distributions the many sociological factors that may be correlates of well-being are also being considered, a broad approach to the literature would range from personal income through returns to education, incidence of disease, urban sociology and crime, housing, and unemployment. It is not intended, however, that all these factors be covered herein. The major thrust, it will be remembered, is in the determination of the importance of the income distribution at different levels of well-being. Therefore, the literature survey is limited to the writings on the income size distribution, its historical and conceptual development, and its relationship to well-being. First, a review of early attempts at measuring income distribution in the United States is presented, followed by considera tion of more modern treatment of the data that has become available since 19M-0. Finally, specific treatments of income dispersion as related to welfare are included. 27 28 Early Attempts to Construct Income Distributions Throughout the ages, wherever ownership of land has been coincident with receipts of income, land redistribu tion has been demanded in the name of social justice."*" As a carryover from the feudal age where landowners were the income receiving class, a good deal of the literature on income distribution concerns the distinction among receipts by landowners, receipts by capital owners, and receipts of the laboring class. This has been called the distribution 2 of income by factor shares. To an extent, the emphasis on distribution to factors has been required by the paucity of data and the logical impossibility of studying income distributions in any other way. Until the inception of the income tax, almost nothing was known about the distribution 3 of income with regard to its size. At the top of the income scale (those to whom taxes were assessed), the study of distributions by size then became popular, with the income of the top one per cent or five per cent of "*"Bertrand de Jouvenel, The Ethics of Redistribu tion (Cambridge: Cambridge University Press, 1952), p. 3. 2 For a presentation of the essential elements see George Garvey, "Functional and Size Distributions of Income and Their Meaning," American Economic Review, XLIV, (May, 1954), 236. 3 Harold Lydall, The Structure of Earnings (Oxford: Clarendon Press, 1968), p. 2. 29 recipients compared to total income, resulting in rather crude but admirable estimates of dispersion or inequality. Spahr’s pioneering effort at estimation of income size distributions was published m 189 6. His income size distribution was based on his distribution of wealth and involved assumed relationships to the distribution of income by factor shares. He was able to conclude that five-sixths of the income of the wealthiest class was received by the 125,000 richest families, while less than half of the income of the working class was received by the poorest 6,500,000 families. The next major effort at constructing an income size distribution was made by King in 1915.^ In spite of his admission that "at present it is impossible to give any accurate picture of the distribution of incomes," he proceeded to utilize data from Wisconsin income tax records, (claiming that Wisconsin was a peculiarly good sample state), along with Treasury Department figures for the wealthy and the results of private budget studies among the poor to construct an estimated distribution of incomes 4 C. B. Spahr, The Present Distribution of Wealth m the United States (New York, 1896), quoted in C. L"! Merwin, Jr., "American Studies of the Distribution of Wealth and Income by Size," in Studies in Income and Wealth, III, (New York: National Bureau of Economic Research, 1939), 31. ^W. I. King,, Wealth and Income of the People of the United States (New York: Macmillan Company, 19153. 30 for the year 1910. He used fifty class intervals with incomes from zero to $50,000,000, compared with the thirty- two class intervals used later in his 19 21 study, in which incomes were grouped by employees, farmers, and entrepreneurs . ^ Maurice Leven and F. R. Macaulay were also contributors to the early body of knowledge concerning income distributions along with their associates at the 7 National Bureau of Economic Research. R. S. Tucker, in attempting to "justify, or at least paint in favorable colors, the existing distribution of income in the United 0 States" used income tax data for the years 1914 to 1936 and applied five different measures of dispersion. The data were extended backward by extrapolation to the civil war, enabling Tucker to conclude that greater diffusion of incomes was occurring. He also found that the concentra tion of income generally increased during periods of g Maurice Leven, H. G. Moulton, and Clark Warburton, America’s Capacity to Consume (New York: Brookings Institution, 1934), pp. 177-182. 7 The contributions of this elite body are documented from time to time in a continuing series of volumes enti tled Studies in Income and Wealth, edited by the Conference on Research in Income and Wealth and published by the National Bureau of Economic Research and others. See especially volumes 3 (1939), 5, 6 (1943), 9, 10 (1947-48), 13 (1951), 15 (1952), 22 (1958), 23 (1958), 27 (1964), and 33 (1969). 0 Merwin, op. cit., p. 47. 31 9 economic boom and decreased during recessions. In 1935-36 the first significant sample survey of incomes in the United States was taken by Hildegarde Kneeland and her staff at the National Resources Committee. With a sample size of 300,000, the data were valuable and served as a basis for income distribution estimates for many years. At this point Simon Kuznets and his associates of the National Bureau of Economic Research began publishing their work in the volumes of Studies in Income and Wealth. Herbert Klarman, Horst Menderhausen, Dorothy Brady, Rose Friedman, Frank Hanna, Joseph Pechman, George Katona, Selma Goldsmith, Milton Friedman, George Garvey, Margaret Reid, and Edwin Mansfield were contribu tors to the body of knowledge through the pages of those volumes. Perhaps the most influential of the early treat ments of the income distribution is the work by Maurice Leven (through the Institute of Economics of The Brookings Institution) entitled The Income Structure of the United g Rufus S. Tucker, "The Distribution of Income Among Taxpayers in the United States, 186 3-19 3 5," Quarterly Journal of Economics, LII (August, 1938), 54-5-587 . ■^Merwin, ££. cit. , p. 59. ■^Conference on Income and Wealth, Studies in Income and Wealth (New York: National Bureau of Economic Research; and Princeton: Princeton University Press, various dates). 32 12 States. In this book Leven treats the determinants of income, income differences by occupation, industry, geographic region, age, sex, color, and social class. In doing so, he created a model which has been followed by most modern treatises on the subject. Modern Treatment of Income Distribution Data Economic theory in general has developed in advance of the required statistical data with which to test the theory. So it was with income studies. Without the dramatic innovations brought about by the development of methods of representative sampling, it is possible that income studies would have remained theoretical. Largely descriptive and evaluative at first (as, for example, the National Resources Committee work previously described) the work on distributions of income became increasingly useful. Again, the National Bureau of Economic Research was the pioneer. With the publication of Volume 5 of Studies in Income and Wealth in 19M-3, the connection between income and welfare was explored, although the data available were from income tax returns and urban area 12 Maurice Leven, The Income Structure of the United . States (Washington, D.C.: The Brookings Institution, 1938). 33 13 surveys in 1935-1936. In Volume 9, Joseph A. Pechman treated the growing emphasis on size distributions versus the traditional study of factor shares. Volume 13 served as the vehicle for the publication of several notable articles, among whose authors were Dorothy Brady, George Katona, and Selma Goldsmith, all of whom gained consider able reputations in the field of personal income distribu- 14 tion analysis. The following year (19 52) was observed by the publication of Volume 15 of the series, edited by Simon Kuznets and containing noteworthy efforts by Milton 15 Friedman, George Garvey, and others. Friedman’s "ammain" scale and Garvey's contention that no unambiguous or generally applicable "normative" distribution could be used as a basis of inequality measurements were included in the volume. 13 Joseph A. Pechman, "Patterns of Income," in Studies in Income and Wealth, IX (New York: National Bureau of Economic Research, 1948), 61-147. 14 Dorothy S. Brady, "Research on the Size Distribution of Income," pp. 2-53; George Katona and Janet A. Fisher, "Postwar Changes in the Distribution of Income of Identical Consumer Units," pp. 62-109; and Selma F. Goldsmith, "Appraisal of Basic Data Available for Constructing Income Size Distributions," pp. 266-372, Studies in Income and Wealth, XIII (New York: National Bureau of Economic Research, 1951). ■^Milton Friedman, "A Method of Comparing Incomes of Families Differing in Composition," pp. 9-21; George Garvey, "Inequality of Income: Causes and Measurement," pp. 25-36, Studies in Income and Wealth, XV (New York: National Bureau of Economic Research, 19 52). 34 During this period the data for empirical work in income size distributions was still spotty. The Survey Research Center at the University of Michigan had begun to gather its columinous data through continent-wide sampling but Treasury Department figures were still the main basis for practical observation. This method was used by Kuznets in 19 5 3 to study the shares of upper income groups in total X 6 income. The 19 5 0 census, however, offered a new and many fold more complete source of data. Herman Miller of the Census Bureau published the first of his substantial 17 contributions to the literature m 195 5. Following the Leven model, but with a vastly improved body of data, he spoke of the differences in income among families in the United States and their apparent demographic and economic correlates. The census afforded the opportunity to examine urban and rural differences, city sizes, regional factors, race, occupational groupings, age, income, family life cycle, and income changes over time and relate them all to present income. Among other results, he found over half the earners in 1950 to be earning $2,000 or less, with an enormous range of incomes about the average. His X6 Simon Kuznets, Shares of Upper Income Groups in Income and Saving (New York: National Bureau of Economic Research, 1953). 17......................................... ............ Herman P. Miller, Income of the American People (New York: John Wiley and Sons, Inc., 1955). 35 pioneering efforts included the establishment of the functional and legal basis for requiring income data to be divulged to the Bureau of the Census, thus paving the way for statistical analysis and policy decisions otherwise unattainable. In this work and a later book based on data from 18 the 19 6 0 census, Miller looked into reasons underlying income inequalities, and found that a major reason for the positive skewness in aggregate income distributions is the 19 merging of symmetrical curves for nonhomogeneous groups. However, race, region, occupation, and age impinged directly to create differences in income among those groups greater than those which could be attributed to chance or innate ability. This is now a major thesis of the equalitarian ideology; that is, large differences in income are due to structural features of our society, such as imperfect labor markets, custom and prejudice, educational opportunities being little changed between generations, and the initial distribution of wealth, with a minor portion of inequalities being due to inherent abilities and conscious family or individual decisions. 18 Herman P. Miller, ' Income Distributidn in' the United States (Washington, D.C.: U.S. Government Printing Office, 1966). 19 Herman P. Miller, Income of the American People (New York: John Wiley and Sons , Inc. , 1955) , p . 3 ~. 36 This field of inquiry sparked a renewed interest in income inequality studies. Also, the emphasis on poverty caused by urban disturbances during the 19 6 0's brought forth a veritable flood of literature on inequality 2 0 and poverty. The major economic journals accepted a number of specialized articles on the background for inequality; of special note are those having to do with 21 . 22 education and income, development of human capital, 2 3 and the distribution of abilities. During the 1960's, the University of Michigan continued publishing its Survey of Consumer Finances each year through its Survey Research Center, a unit of the 2 0 See, for example, Edward C. Budd, ed., Inequality and Poverty (New York: W. W. Norton and Company, Inc., 1967); Herman P. Miller, Rich Man, Poor Man (New York: Thomas Y. Crowell Company7 19 64); Richard M. Titmuss, Income Distribution and Social Change (Toronto, Canada: University of Toronto Press, 1962); and many others not so closely related to the topic at hand. 21 See Herman P. Miller, "Annual and Lifetime Income in Relation to Education, 19 39-1959," American Economic Review, L (December, 1960), pp. 962-986; and H. S. Houthakker, "Education and Income," Review of Economics and Statistics, XLI (February, 19 59), pp. 24-28. 2 2 See Jacob Mincer, "Investment in Human Capital and Personal Income Distribution," Journal of Political Economy, LXVI (August, 1958), pp. 2 81-30 2; and Theodore W. Schultz, "Investment in Human Capital," American Economic Review, LI (March, 1961), pp. 1-17. 2 3 Thomas Mayer, "The Distribution of Ability and Earnings," Review of Economics and Statistics, XLII (May, 1960) , pp. 189-195. 37 24 University of Michigan Institute for Social Research. This data has traditionally included sample information on incomes, and for certain years reinterviews of identical families are also available, providing a period of time in 2 5 excess of one year in which to consider inequalities. The data for the entire sample is very usable but the cell sizes for breakdowns inhibit significant inferences regarding small geographical areas. The Current Population Surveys of the Bureau of the Census were also continued year by year, as they had been since 19 44, and also 2 6 included income information from large samples. The literature on Income Equality and Well-being Recent Books One of the most useful of all the modern studies on the distribution of income is the Survey Research 24 . George Katona, William Dunkelberg, Gary Hendricks, and Jay Schmiedeskamp, Survey of Consumer Finances, 1969 (Ann Arbor: Survey Research Center, 1970). Other authors for other years. 25 Simon Kuznets has stated a major drawback of income statistics: that of grouping families by their incomes in a single year. See Herman P. Miller, Income Distribution in the' United States, op. bit. , p. 5. 20 See Bureau of the Census, Current Populat i on Survey (Washington, D.C.: U.S. Government Printing Office, various years). 2 7 Center's Income and Welfare in the United States. It offers a study of poverty and dependency within the context of a cross-sectional analysis of the United States population. Non-money incomes, necessary budget levels, personality measures, mobility, intergenerational educational levels, public and private transfers, and expectations data are combined with income analysis to set forth what is perhaps the most complete model of income determination accomplished to date. "Family income is viewed as a sequential process, with each component of income . . . combining with other factors to affect later 2 8 components." It is concluded that economic growth does not eliminate poverty, and the related policy implications are a) the rehabilitation of the disabled; b) the elimination of discrimination; c) the encouragement of capital and labor mobility; d) support to education; and e) fomenting certain attitude and personality changes. Irving Kravis published a book in 19 6 2 which dealt 29 with welfare and the distribution of income. "The strong egalitarian emphasis in our social ideals," says Kravis, 27 . . . James N. Morgan, Martin H. David, Wilbur J. Cohen, and Harvey E. Brazer, Income and Welfare in the United States (New York: McGraw-Hill Book Company, 1962). 2 8 T -K • j Ibid., p. v. 29 Irving B. Kravis, The Structure of 'Income (Washington, D.C.: University of Pennsylvania, 1962). 39 "makes us curious to know, once we are informed about the level of aggregate income and its temporal changes, how the total is distributed among consumer units and whether this distribution is becoming more or less equal." Kravis also followed the Leven line of inquiry, that is, investigation into the reasons for the differences in income from one consumer unit to another. The general tone of Kravis' approach, however, is positive, in sharp contrast to the 30 negativity which is evident m the writing of Kolko. The latter author complains that less than one-tenth of the population dominates the economic system, and within that tenth a very small slite controls the corporate structure and makes basic pricing and investment decisions for the entire nation. If it is true, as John Kenneth Galbraith 31 asserts, that poverty is an afterthought in the con temporary economic system, it is only true because social scientists ignore it, according to Kolko. Further economic equalitarianism as a reality in the United States is 3 2 strictly an "illusion." Our problems are not technologi cal, but organizational and at the bottom of this "economic 30 Gabriel Kolko, Wealth and Power in America: An Analysis of Social Class and Income Distribution (New York: Praeger Publishers, 1964). ^John Kenneth Galbraith, The Affluent Scoiety, 2nd ed., revised (Boston: Houghton Mifflin Co., 1969), pp. 93, 292. 3 2 Kolko, o£. cit., p. 132. inadequacy" is the sharply unequal distribution of income 3 3 . and wealth. Neither progressive taxation nor welfare spending has appreciably altered the income inequality nor 34 raised the standard of living of the lower classes. Kolko proceeds to argue that higher education, medical insurance and care, good housing, and good jobs are simply not as available to lower income classes as they are to others, and that the system perpetuates, and even requires poverty. Although not basically concerned with income distributions, the volume by Lampman entitled The Share of 3 5 Top Wealth-Holders m National Wealth sheds light on one of the basic sources of income inequality and compares the 3 6 two distributions of wealth and income. Among the most recent studies of income distribu- 3 7 tions and welfare are volumes by Harold Lydall, 3 8 National Bureau of Economic Research, and S. M. Miller 44 Ibid., p. 39. 3 5 Robert J. Lampman, The Share of Top Wealth- Holders in National Wealth, 19 2 2-56 (Princeton, NewJersey Princeton University Press, 1962). 36Ibid., p. 230. 3 7 Harold Lydall, The Structure of Earnings (Oxford: Clarendon Press'^ 1968). 3 8 Lee Soltow, ed., Six Papers on the Size ’ Distribution of Wealth and Income, Vol. XXXIII of Studies 4i 3 9 with Pamela Roby. Lydall's substantial contribution differs slightly in kind from those of Kravis, Miller, and Morgan, at al., in that it is more theoretical. After a review of existing theories of the income distribution (e.g., Pareto, normal and lognormal) he considers what would be a desirable distribution and then develops a 4-0 "standard" distribution. From this base proposals for a new theory are explored, followed by examination of differences in equality over time and among countries. The work is very relevant to the present dissertation, with the exception that has continually occurred; those who treat income distributions do so without measurement of resulting well-being, and treatments of welfare seldom integrate the economic and social components which emerge from or are coincident with inequality. Volume thirty-three of the Income and Wealth 41 . . . series includes searching articles by Paul Schultz on secular and cyclical behavior of income inequality, and by Melvin W. Reder on the theory of income size distributions. The Miller and Roby book explores poverty, inequality, and in Income and Wealth (New York: National Bureau of Economic Research, 1969). qq S. M. Miller and Pamela A. Roby, The Future of ' Inequality (New York: Basic Books, Inc., 19 70). 40 Lydall, 0£. cit. , p. 60. 41 Soltow, 0£. cit. 42 social policy in meaningful ways but essentially without theoretical content or empirical measurement. Journal Articles During recent years the scholarly journals in the field of economics have shown interest in income inequality by publishing an increasing number of articles. More than that, a good deal of the work has been pointed toward the results of inequality, in addition to its causes. A selected number of these more pertinent articles will be reviewed here. James Morgan and James Smith reviewed "economic well-offness" and indicated the importance of income in relation to needs, using data from the University of 42 Michigan’s Survey Research Center. Aigner and Heins, in one of many good articles for which they are co-authors, presented a measurement of inequality involving a social 43 welfare consideration as an objective utility function. The macroeconomic effect of inequality was considered by 42 James N. Morgan and James D. Smith, "Measures of Economic Well-Offness and their Correlates," American Economic Review, LIX, No. 2 (May, 1969), 450-62. D. J. Aigner and A. J. Heins, "A Social Welfare View of the Measurement of Income Inequality," Review of Income and Wealth, XIII, No. 1 (March, 1967), 12-25. 43 44 45 Metcalf and by Kuznets, while Okun found migration of persons across state lines to be connected with , . , 46 inequality. Educational welfare as related to income dispersion has been widely studies, including recent discussions by 47 48 Chiswick and Hansen. Soltow considered distributions of income to be properly related to distributions of education, age, and occupation and proceeded to test this 49 50 51 premise. Budd and Thurow treat the income size 44 Charles E. Metcalf, "The Size Distribution of Personal Income During the Business Cycle," American Economic Review, LIX, No. 4, Part I (September, 1969), 657-68. 45 Simon Kuznets, "Economic Growth and Income Inequality," American Economic Review, XLV, No. 1 (March, 1955), 1-28. 46 B. Okun, "Interstate Population Migration and State Income Inequality," Economic Development and Cultural Change, XVI, No. 2, Part I (January, 1968), 297-314. 47 Barry R. Chiswick, "Minimum Schooling Legislation and the Cross-Sectional Distribution of Income," Economic Journal, LXXIX, No. 315 (September, 1969), 495-507. 48 W. Lee Hansen, "Income Distribution Effects of Higher Education," American Economic Review, LX, No. 2 (May, 1970), 335-340. 49 Lee Soltow, "The Distribution of Income Related to Changes in the Distributions of Education, Age, and Occupation," Review of Economics and Statistics, XLII, No. 4 (November, 1960), 450-53. 50 Edward C. Budd, "Postwar Changes in the Size Distribution of Income in the U.S.," American Economic Review, LX, No. 2 (May, 1970), 247-260. 51 Lester Thurow, "Analyzing the American Income 44 distribution in general in the May, 19 70 issue of the American Economic Review, in which several articles are found on this subject. Since the present study measures and compares income distributions of various geographic areas at the same point in time (commonly called cross-section analysis), the recent studies of this nature are especially applicable. Verway used an ingenious method of combining Census and Internal Revenue data to create income distributions for each state in the United States for the 5 2 year 19 60. His methods, however, were criticized by 5 3 Schaefer, who did not offer alternative procedures. Al-Samarrie and Miller, however, did not have to utilize the Census-I.R.S. combined data for inequality among states 54 due to Miller's position in the Census Bureau. Conlisk Distribution," American Economic Review, LX, No. 2 (May, 1970), 261-269. 5 2 D. I. Verway, "A Ranking of States by Inequality using Census and Tax Data," Review of Economics and Statistics, XLVIII, No. 3 (August, 1966), 314-21. 5 3 J. Schaefer, "A Ranking of States by Inequality using Census and Tax Data: a Comment," Review of Economics and Statistics, IXL, No. 4 (November, 1967), 636-637. ^A. Al-Samarrie and H. P. Miller, "State Differentials in Income Concentration," American Economic Review, LVII, No. 1 (March, 1967), 59-72 . 5 5 also presents state cross-sectional inequalities. In spite of all the theoretical and empirical studies and expertise involved, there is nevertheless little purpose displayed in many of the published articles on income distribution. Elteto and Frigyes, two economists from Eastern Europe, are said to have developed significant new insight into income distributions. In this case, how- 5 6 ever, this insight is applied to real world problems and usage of the new procedure is recommended for planning 5 7 purposes. Such is also the case with Fry, a political 5 8 scientist, and Lampman, an economist whose name has long been associated with studies of income and wealth. Both of the latter introduce normative considerations and the application of income studies to policy making. 55 John Conlist, "Some Cross-State Evidence on Income Inequality," Review of Economics and Statistics, IXL, No. 1 (February1967) , 115-18. 5 6 0. Elteto and E. Frigyes, "New Income Inequality Measures as Efficient Tools for Causal Analysis and Planning," Econometrica, XXXVI, No. 2 (April, 1968), 383-88. 5 7 B. R. Fry and R. F. Winters, "The Politics of Redistribution," American Political Science Review, LXIV, No. 2 (June, 1970), 508-22. 5 8 Robert J. Lampman, "Transfer Appraoches to Distribution Policy," American Economic Review, LX, No. 2 (May, 1970), 270-79. 46 Summary of Recent Literature From modest beginnings in the measurement and assessment of income inequality, great strides have been taken. Kuznets, in 19 52, indicated four directions which 59 further inquiry on the subject should take. They are (1) historical changes and area differences in income distribution; (2) causal factors; (3) income size and use; and (4) normative valuations. With availability of census and survey data, the first three have been studied in depth, as Kuznets recommended. The last item, normative valuations, has been treated, but little in the way of empirical research has been done to shore up the conclu sions arrived at through analysis. The following chapters will attempt to test empirically the normative proposition that overall well-being moves upward in association with downward changes in the inequality of incomes. 5 9 Simon Kuznets, "Directions of Further Inquiry," in Studies in Income and Wealth, XV (New York: National Bureau of Economic Research, 1952), 20 3. CHAPTER III THE FRAMEWORK FOR EMPIRICAL RESEARCH There may be several different ways to apply the hypothesis developed in Chapter I to an empirical framework to test its validity. It is therefore recognized in ad vance that the methods shown in this chapter comprise only one alternative analytical formulation. Other investi gators may have chosen equally applicable data sets, methods of measuring income dispersion, well-being indices, and statistical models. However, the methods presented here have been selected by the author after considerable study of the alternatives. The data chosen as representative of overall welfare, the Lorenz method of showing income inequality and the related Gini concentration ratio, the factor analytical method pf converting the data to an index of well-being, and the regression-correlation model for analyzing relationships between income dispersion and well-being will be presented in turn in this chapter. The reader can then interpret the results presented in Chapter IV hereafter in the full light of the assumptions that were 47 48 necessary to gain those results, and will, in addition, be able to understand the inherent limitations of the find ings . The following exposition of methods is duly concerned with the strengths of the methods. Where the author is aware of weaknesses, they are also exposed; it is felt that the net resulting methodology has positive qualities for the purpose at hand. The Empirical Data and its Sources Even though total welfare is immeasurable, according to Sturmey,^ there are definite indications of ordinal rankings within the different variables that effect welfare. Thus it can be said that certain differ ences add to or detract from welfare, even though a degree of value judgment may be necessary. For example, it is apparent that if one county has a higher median income, educational attainment level, health index, or housing quality than another, then (ceterus paribus) the first is above the second in the scale of welfare for the variable involved. On the other hand, if higher levels of crime, unemployment, and overcrowding are present, then the converse must (by assumption) be true. Still other socio-economic variables are ambiguous in their effect on a prima facie basis, such as the dependency ratio, median ■^S. G. Sturmey, Income and Economic Welfare (London: Longmans, Green 8 Co., 1959 ), p. 2~. 49 age, per cent rural, level of taxation, and occupational distribution. Complicating the matter further are the possibili ties that (1) interactions among the values of different variables may render the effect of a single item void; and (2) the effect of any one variable may change over a range of the variable values from positive to negative. Rather than discourage the analysis of welfare rankings, however, these complications become a challenge to multivariate statistical methods. It is felt that a rather distinctive measure of the effect of the set of variables on total welfare can be constructed using a multivariate analysis which, by taking into account all of the variable values and their interactions, can distinguish among the levels of well-being in the counties of California and rank them. Subsequently, the effect of possible curvatures in the welfare relations must be examined. Does a given variable, as its value increases, add to, become indifferent to, and then detract from well-being? And does the total index of welfare, when plotted against the values of income distributional inequality, demonstrate such a curvature, creating an "optimal" range of the coefficient of inequality? These are the types of questions to be faced in 50 the statistical analysis. The body of data, however, must first be considered carefully. Twenty-three variables have been chosen for analysis, and their values for the year 19 59 for each of the fifty-eight counties in California have been determined. They comprise ten groups of variables of differing types. A complete listing of these variables is as follows: A. Population and Density 1. Percentage increase in population, 1950-1960 2. Persons per square mile, 1960 B. Educational Attainment 3. Percentage of 14-17 year olds in school, 1960 4. Median school years completed, 19 60 5. Percentage of persons 2 5 years and older with less than 5 years schooling, 1960 C. Employment 6. Percentage unemployed, April, 19 60 7. Percentage of employed and unemployed who are agricultural workers, 19 6 0 8. Percentage of employed classified as professional or technical, 19 6 0 9. Non-worker/worker ratio, 19 60 51 D. Housing 10. Percentage of units substandard, April, 19 60 11. Percentage of units built prior to 19 40 12. Average property tax rate per $100 assessed valuation, 1960-61 13. Percentage of units with more than 1.0 persons per room, April, 19 6 0 E. Crime 14. Adult felony arrests per 1,000 persons, 19 59 15. Major juvenile arrests per 1,000 persons, 19 59 F. Health and Welfare 16. Public Assistance payments per capita, 1959-60 17. Non-federal physicians per capita, November, 19 6 2 18. Deaths per 1,000 persons, 1959 G. Age 19. Median age, April, 19 6 0 H. Mobility 20. Percentage moving to present address with 15 months of April, 19 60 52 I. Income and Consumption 21. Taxable transactions per capita, 19 59 22. Median income, 19 59 J. Social Base Factors 23. Percentage rural, April, 19 6 0 As is apparent, there is some duplication in the variables within a group, but the types themselves are 2 rather unique. Each of these data groups will be discussed in turn. Population and Density The sheer numbers of persons in a heavily- populated county may give that county a character apart from other counties. More important than that, perhaps, is the statistic revealing the change in population over the years. An area of declining or static numbers of persons can be entirely different from an area with the same absolute numbers but whose background in time and whose outlook is one of rapid growth. Still more basic, but from another point of view, is the number of persons 2 Notice that there is no measure of psychological well-being present, and the author believes that none is available. Such things as happiness in marriage, satis faction in employment, and consumption relative to friends and neighbors ("keeping up with the Jones") defy measurement on an aggregate basis. This is not to claim that such portions of well-being do not exist. 53 per square mile, or the density of population. For example, the population of San Diego County in 19 59 exceeded that of San Francisco County by 1,0 3 3,011 to 74-0,316, but the latter houses, feeds, transports, and entertains its population in an area so small that there are 16,452 persons, on the average, per square mile, while the former has only 243 persons per square mile. Thus population alone is insufficient of description. Consider also the fact that between 1950 and 1960, San Francisco County lost 4.5 per cent of its population, while San Diego County increased in numbers at the rate of 85.5 per cent in the same period. This group of variables provides a quantity variate in county differences. The remainder of the variables chosen to go into the welfare index describe the quality, more or less, of life in these separate geographic regions. Population and the figures derived from population are taken from the United States Census of April of 1960, and the numbers proceed from a complete enumeration of all 3 persons in each county. While much has been said regarding the quality of the enumeration in the census of 1960, it is believed that no better overall source exists. 3 U.S. Department of Commerce, Bureau of the Census, I9 60 Census of Population, Vol. I, Characteristics of the Population, Part VI, California (Washington, D.C.: U.S. Government Printing Office, 1963), p. 23. 54 The best that can be done herein is to admit to a possible bias in the use of census figures, in the direction of accounting for slightly fewer persons in the central parts of the largest cities than actually was the case. Educational Attainment 4 The percentage of 14 to 17 year olds m school, 5 median school years, and the percentage of persons 25 0 years old and older with less than five years schooling were chosen as representative of educational attainment in the counties of California. The appropriateness of the assumption that higher levels of education and lower levels of illiteracy lead to higher overall well-being has not been seriously questioned in the literature. There is a possibility that this association is not direct, but indirect, through the income variate that is closely correlated with educational levels. This may be true for the economic portion of well-being, but to a lesser extent is the indirect association applicable for social well-being. The applicability of these particular data series ^Ibid., p. 227. 5Ibid. 0 California Economic Development Agency, California Statistical Abstract, 1962 (Sacramento, n.d.), p. 139 55 for the representation of educational attainment has considerable precedent. Also with precedent is the idea of utilizing not average or percentage comparisons among counties, but levels of educational inequality as measured in the distribution of educational levels within a geo- 8 graphic area, as has been done herein with income. While there is considerable merit in this approach, the statistical advisability of utilizing distributive data decreases at least proportionately with the quality and completeness of the data. For educational inequality calculations, even more assumptions and substitutive processes must be used than with income data, and for many other variables inequality estimates are impossible. For fear of excessive inaccuracies and for overall similarity in variable treatment, therefore, the data have been left 9 m their aggregative-measured form. 7 Among others, see B. R. Chiswick, "The Average Level of Schooling and the Intra-regional Inequality of Income: A Clarification," American Economic Review, LVIII, No. 3, Part I (June, 1968), 495-500. O See, for example, Lee Soltow, "The Distribution of Income Related to Changes in the Distributions of Educa tion, Age, and Occupation," Review of Economies.arid Statistics , XLII, No. 4 (November, 1960) , 450-53. 9 It must be recognized that the 2 3 variables in the 10 groups being considered are utilized for the purpose of creating a well-being index for each county, which in turn is used for comparison with the index of income inequality. 56 Employment The percentage of unemployment for a large number of workers at any one time often hides pertinent statistics regarding the percentage of employment in different occupational groups. Thus, recognizing that involuntary unemployment can be categorized as definitely harmful, the percentages of workers employed in tradi tionally high-unemployment occupations have been included as variates. The major group in this category is agricultural workers. Conversely, professional and technical workers'*'^ seem to have less unemployment and, in the aggregate, are better paid. The percentage of workers in this category are therefore included in the construction 12 of the index. Overall unemployment percentages are of 13 course considered as well. The worker to non-worker ratio indicates the number of persons in the population per employed person and is sometimes called the dependency 14 ratio. If all factors were the same m two counties "^Census of Population (see footnote 3 above), pp. 427 ff. "^California Statistical Abstract (see footnote 6 above) , p . 139. 12 . The index of well-being is constructed through factor analysis, as shown later in this chapter. 13 Census of Population, p. 228. 14Ibid. 57 with the exception of differences in this one measurement, it is believed that well-being could be said to be changed where dependency is higher, but the range of applicability of this assumption is uncertain. Housing The basic needs of human beings are manifold, but certainly one of them is adequate shelter. By 19 60 the definition of "adequate" had changed somewhat from what it had been in the dark ages and it is still changing. The U.S. Bureau of the Census uses three measures of adequacy for comparative purposes, and they are also utilized 15 herein. They are percentage substandard, percentage of units built prior to 19 4-0, and percentage of units with more than 1.0 occupants per room. In addition to these measures of housing adequacy, account is taken of another feature of ownership of real estate in our society, the property tax."^ Crime There may or may not be significant differences in well-being among counties due to the incidence of crime. 15 U.S. Department of Commerce, Bureau of the Census, 19 6 0 Census of Housing, Vol. I, Part II (Washington, D.C.: U.S. Government Printing Office, 1963), pp. 17-26, 39-48, 51-59, and 164-71. 1 C California Statistical Abstract, p. 190. 58 There are, however, differences in crime rates, and to the extent that crime occurs at a higher rate in one county than in another it is assumed that well-being decreases. Five measures of crime rates were considered, but only two were finally included in the data set. Those considered but rejected were (1) the seven major offense reports 17 regularly submitted to federal agencies; (2) juvenile 18 arrests for law violations and delinquencies; ' and 19 (3) felony defendents convicted in superior court. While there is no doubt that each of these series impinges 20 on public welfare, the arrest records for adult felonies 21 and major juvenile arrests were chosen as most appropri ate for the purposes of this study. After consultation with officials of the California Bureau of Criminal Statistics, it was determined that arrests, rather than reported crimes or convictions, constitute the best measure of public disturbance. Similarly, minor juvenile delin quencies are not considered to be of major effect on the public. The adult felony and major juvenile arrests constitute two separate series which may not be completely 17 California Department of Justice, Division of Criminal Law and Enforcement, Crime in California, 19 59 (Sacramento: Compiled in the Bureau of Criminal Statistics, n.d.), p. 109. 18Ibid. , p. 135. 19Ibid., p. 6^. 20Ibid., p. 117. 21Ibid. , p. 135. 59 independent but which vary in different ways among counties, apparently reflecting different sociological conditions in the population and environment. It is possible that "arrests" as a unit of measure understates the negative welfare effects of crime. For example, 212,797 crimes were reported in California in 19 59 , of which 9,874- reports were unfounded. Only 75, 421 crimes were cleared, however, meaning that the perpetrator had been arrested and prosecuted. Thus, only 3 7 per cent of verified crimes resulted in arrests. Nevertheless, 9 2 per cent of homicide and 76 per cent of assault cases resulted in arrests, showing that the uncleared crimes were in the lesser felonies to a large extent. It was the feeling of the officials consulted that numbers of arrests represent overall public disturbance closer than the alternatives available in collected data, which are reported crimes and convictions. This fact together with the above statistics resulted in the con clusion to use arrest records as the crime variable for the empirical study. Health and Public Assistance The health of the population, it will be agreed, is of definite import in determining and measuring well being. Although it may appear to be easily assessable on 60 prima facie grounds, it was found to be a very elusive quantity. Advice was sought from appropriate doctors and state and county officials without great success in uncovering one or more data series that determines health- related aggregate well-being. Hospital beds per capita was considered, but rejected because of possibilities of internal interdependence among counties; that is, major hospitals may be located across county lines. Incidence of various diseases was investigated for use, without positive results. Epidemics may occur, for example, and last the greater portion of a year in a single county or group of counties, thus biasing the results for the state if such a year were chosen. Only over long periods of time could differences in communicable disease incidence be trusted to represent health well-being. However, the offices of physicians are fairly well dispersed within and among counties, and their presence or absence could dictate "well-offness" in the face of an epidemic or with normal conditions and chronic disorders among the population. The non-federal physician series (excluding physicians in government employ, such as military and federal agency doctors) was chosen as repre sentative of cross-sectional welfare of the health dimension.^ 22 California Medical Association, Bureau of Research and Planning, Characteristics of Physicians in 61 In addition, the mortality records from the various states are kept and life tables, presenting average life expectancy, have been derived from them for the states of the United States. After considerable effort was expended, however, it was determined that life tables are not available on a county basis for California. It is believed that this would have been a valuable addition to the body of data. In its place, however, deaths per 1,00 0 persons 2 3 was included. At the risk of having a major local incidence of mortal disease in the year 19 59 adversely influence the calculations (none was found in a rather superficial investigation), the death series was put into the data as an overall indication of local health conditions. There are dimensions of welfare, however, not measurable by these health statistics. Disability, blindness, old age, and needy children may also have an effect on public well-being. For this reason, public assistance payments are included in this group of data, assuming that such payments account for real conditions existing within counties and that differences in these California:, Spring 19 61, Part I, Series 2 (n.p., November, 1962) , table 6a. 2 3 U.S. Department of Health, Education, and Welfare, Vital Statistics of the United States, 1959, Vol. II (Washington, D.C.: U.S. Government Printing Office, n.d.), pp. 414--20. 62 21± payments measure differences between counties. The payments series chosen represents federal, state, and county funds expended for old age security payments, aid to the blind, aid to needy children, and general relief; these data were summed and expressed as tital public assistance payments per capita. Age The median age of the population was also 25 included. This is indicative of the assumption that the age of the population, in general, will be important in its effect on well-being. Occupational interactions are obviously present, but the factor analytical construct (to be described later in this chapter) permits unlimited interactions among the variables. Mobility Economic growth and optimum resource allocation are aided to a great degree by mobility of the labor force. On this assumption, the number of persons moving to their present dwelling (as of April, 1960) within the last 24 California Department of Social Welfare, Public Welfare in California, Annual Summary of Statistical and Fiscal Data, 1959-60, Statistical Series AR-1-2 (Sacramento: n.d.). 2 5 Census of Population, pp. 179-94. 63 fifteen months was considered to be important informa- 2 6 tion. This was expressed as a percentage of all households and included in the data set as a comparative measure among counties. Income and Consumption The economic dimension of well-being is expressed in this group of data. Consumption is measured by self-assessed taxable transactions under sales and use 27 . tax laws. While it is well known that certain items of consumption are not included in the California sales tax (food purchased for consumption off-premises is the major item), the taxable transactions were nevertheless deemed to be the most reliable data series for this purpose. Expressed as per capita expenditures, the data is assumed to be representative of well-being as derived from purchasable consumption and is also assumed representative of differences in consumption-derived well-being among counties. Data were taken from the census for the proportion of families with incomes less than $3,000 and over 2 8 $10,000. These were initially considered important, 2 6 Census of Population, p. >+9. ^ California 'Statistical Abstract, p. 19 2. n o Census of 'Population, p. 22 8 64 giving a measure of predominance of either end of the spectrum within the area, but were later deleted, due to the fact that no apparent additional information was being gained over and above the median income figures. Per 29 capita personal income was also deleted from the data set. Initial correlation results from the computer indicated that very little value was gained by this 30 variable, and that family median income was sufficient for the purpose of measuring income levels. Social Base Factors The percentage of residents living in a rural 31 environment is the first variable in this group. In a sense, it partially belongs in the first group of quantity variates, since it is closely related to population density. Yet there is another side to it. The overall feeling in rural areas and the certain differences from the hustle, bustle, and noise of the city is unique. Differences in educational and income levels in the rural-urban dichotomy are already accounted for, yet differences remain. The value judgment regarding these differences, prima facie, is difficult to make, and will be 29 Derived from total personal income in 'California Statistical Abstract, p. 164. 3 Q Census' of Population, p. 22 8 . 31Ibid., p. 227. 65 left for the factor analysis program in the next chapter. The same is true of ethnic groups. Ethnicity does not imply, to the impartial, any value judgments. Yet a distinct variable seemed at first to be present, only to be deleted later for no distinct advantage from retention was 32 apparent. The percentage non-white and the percentage of foreign stock with ancestral roots in Latin America were 3 3 the two ethnic groups considered. Non-whites included Negro, Indian, Japanese, Chinese, Filipino, and "other" according to the census. Mexican-Americans are not classified as non-white, nor are they identifiable as a separate group in the census. This ethnic culture, however, is very important in California and an effort was made to calculate their numbers by county. "Foreign stock" is defined in the census as persons who have been born in a foreign country, or whose parents were born in a foreign country. Since there are many Californians of latin ances- 3i + try whose families have been here for generations, this two-generation concept does not describe the ethnic 32Ibid., p. 439ff. 33Ibid. , pp. 447-48 . 34- In all fairness it must be noted that the original Californians (aborigenes excluded) were Mexicans. 66 3 5 group, but it was used as indicative of the relative presence of members from that group in each county in the absence of complete descriptors. Deletion of these two ethnic groups from the data base eliminates the possibility of implied value judgments concerning them. The complete data set is shown in Appendix A. The Measurement of Income Inequality In the nineteenth century the problem of the income distribution was handled by economic theoreticians in a very approximate fashion. Allowing for the scarcity of good data, it is well not to criticize, but Smith, Ricardo, and Malthus took it for granted that landlords were rich, laborers were poor, and capitalists were somewhere in the 3 6 middle. Thus the distribution concept became one of factor shares. Inequality discussions followed the same lines, with the laborers lamenting their small share and the others inventing theories to rationalize the status quo. But this view entirely overlooks the great dispersion among individual workers and among persons belonging to the 35 Despite their long history as Californians, the latin-americans have not been assimilated to a great extent either culturally or socially, but have chosen to retain their separate identity; thus they may still be spoken of as an ethnic minority. 3 6 Harold Lydall, The Structure of Earnings (Oxford: Clarendon Press, 1968), p. 2. 67 37 other categories. If we are really interested in the distribution of income as to persons, then the dispersion within factors must be accounted for. This is accomplished with the size-distribution of income. Nevertheless, there remain significant problems to be solved, even with the data made available by detailed census reports and surveys. They include the definition of the recipient unit, the time interval (for income is a flow variable definable only over a set time period), the income concept, assumed distribution shapes, and comparability of two or more distributions. These must be discussed in turn before measurability of inequality can have meaning. The Recipient Unit Families, all adults, individuals, and consumer spending units have all been hailed as the appropriate 3 8 recipient unit for studies of income distributions. 3 7 See George Garvey, "Functional and Size Distributions of Income and their Meaning," American Economic Review, XLI, No. 2 (May, 195*+), 236-53 . 3 8 Nearly every treatise on the size distribution of income recognizes the importance of the definition of the recipient unit. See especially T. Paul Schultz, "Secular Trends and Cyclical Behavior of Income Distribution in the United States: 1944-1965," in Lee Soltow, ed., Six Papers on the Size Distribution of Wealth and Income. Studies m Income and Wealth, Vol. XXXIII (New York: National Bureau of Economic Research, 19 69), p. 79. 68 The first is used by the Census Bureau to mean a group of two or more persons related by blood, marriage, or adop tion, and living together. Another Census Bureau concept is that of families and unrelated individuals, with families, under the prior definition, being the same but also included are those persons (other than inmates of 39 institutions) who are not living with relatives. Consumer spending units are modified families with account being taken of those in the family having separate incomes and spending patterns. The importance of the concept can be understood after contemplation of the structural changes 40 m family units that take place over time. Since the mid-forties, the paternal family has been decreasing in size, and today it is the exception to have relatives permanently living within the household of a family unit. In addition, social security payments and increased pensions make it possible for older persons to live alone, and the new independence of young adults is well known. Table 4 shown previously indicates how the addition of 3 9 Ben B. Seligman, in his monumental volume on economic though, favors individual income as the base for income studies. See Main Currents in Modern Economics: ' Economic Thought Since 18 70 (New York: Free Press of Glencoe, 1962) , p"] 866 . 40 James N. Morgan, Martin H. David, Wilbur J. Cohen, and Harvey E. Brazer, Income and Welfare in the United States (New York: McGraw-Hill Book Company, T96 2), p. 312. these unrelated individuals can increase a measure of inequality over one which is computed on families alone. Unfortunately, the data available for the counties compiled by the Census Bureau include only the family as recipient of income. This situation can be much less unfortunate if it is recognized that absolute inequality of incomes is being severly understated, but that comparative measures of inequality are nonetheless valid. The Time Horizon The time interval, however, has a net effect of increasing the actual inequalities of income. All data considered here are for income of one year duration, the year 19 59. It is well known that temporary aberrations in income due to unfortunate employment markets or any other cause, or due to fortunate windfalls or business condi tions , cause variations in income that would be smoothed out over a longer period. Dorothy S. Brady has this to say on the subject: The customary interval for income studies, 12 months, is obviously too short for studying the inequality of the income distribution. Individuals experience a substantial variation in receipts from year to year and a given years income may deviate considerably from the norm. The income distribution for a 70 single year taken as a measure of the norm will thus tend to exaggerate the inequality of incomes. Again, however, the choice is to recognize the impurities of the data in an absolute sense and allow for their value in comparative analyses. The Income Concept The choice of the income concept affects the measure of inequality. No attempt is made herein to account for multiple earners in a family or for non-money income in the form of home production, imputed rent, or fringe benefits. In the parlance of the national income analyst, this is gross factor income less imputed rent and 42 home production, plus money transfers. In actuality, it is simply the income category reported to the census taker. Distribution Shapes The distribution of income has been historically assumed to have a skewed shape, with the right tail being longer than the left and with the mode considerably to the left, or toward the smaller incomes, from the mean. There are those who feel that this characteristic shape is 41 Dorothy S. Brady, "Research on the Size ...... Distribution of Income," in Vol. XIII of Studies in' Income and Wealth (New York: National Bureau of Economic Research, 1951), pp. 20-21. 42 ......... Morgan, op. cit. , p. 315. 71 due to the differences in ability among individuals, and others who claim it to be only the result of the combina tion of many rather symmetrical distributions representing i|3 the different cohort groups in our society. In general, this characteristic shape of the income distribution comes from studies by Vilfredo Pareto. While he assumed that the form of the income curve was universal and has since been discredited, his analysis is still applied to the upper tail of distributions in the absence of exact data. Another method of approximating the income distribution in the absence of data is to assume log- normality. That is, the distribution is normal in the logarithms of the data, which implies, again, a skewed 44 distribution with a right tail. Wage and salary income has been shown to fit this model quite well. The concern of the present study, however, is not the fitting of the curve of income, but the measurement and comparison of inequalities in two or more distinct areas. Inequality Measurement It cannot be said, however, that complete data were 43 For a complete review of the theory involved, see Lydall, 0£. cit., pp. 12ff. 4 4 However, a displaced log-normal distribution is said to fit the data without skewness. See Charles Metcalf, "The Size Distribution of Personal Income during the Business Cycle," American Economic Review, LIX, No. 4, Part I (September, 1969), 657-68 . 72 available and that no assumptions regarding the distribu tions for the counties in California were necessary. In actuality, the Census Bureau publishes the number of per sons in each of their income groups; in the case of counties it is the numbers of families in each income category. It is therefore possible to construct a histogram of income for each county, and with some heroic assumptions regarding the midpoints of the classes, the data can be converted to a density function. An idea from 4-5 Verway makes this unnecessary, fortunately. For the comparison of interstate inequalities of income, and in order to construct the Gini coefficient of inequality, he overcame the inadequacies of densus data (which includes numbers of persons in income categories, but not the amount of income received by those persons) by supple menting it with figures from the Internal Revenue Service. Verway calculated the mean of the incomes in each class from the tax data, and by multiplying this mean by the respective class frequencies was able to determine the total income for the income classes, and proceed to the construction of the Lorenz curve and the related Gini h 5 D. I. Verway, "A Ranking.of States by Inequality using Census and Tax Data,"' Review of Economics and Statistics, XLVIII, No. 3 (August, 1966), 314-21. 73 LlK coefficient. Correspondingly, data on income taxes paid to the State of California has been utilized to estimate the means of each of the 13 income distribution categories from the census. This leads to the ability to calculate cumulative percentages of both income and income receiving units, which is necessary for the Lorenz curve approach 47 and the resulting Gini coefficient of inequality. Considerable work on the data from the Franchise Tax Board of the State of California was necessary, how- 48 ever, before it became usable. The annual report was 46 Jeffrey Schaefer cautions that Verway*s method is "fraught with many dangers and tends to bias the result towards greater income inequality." The basic problem is that the "adjusted gross income" used by the Internal Revenue Service (and by the California Franchise Tax Board) is not the same as the census definition of income. Adjusted gross income includes realized taxable net gains on sales of capital assets, while the census income excludes it. Furthermore, adjusted gross income for tax purposes excludes transfer payments and wage supplements, but census income includes them. Since gains from sale of capital assets occur mainly in high income groups, and since transfer payments are received by lower income groups, the use of adjusted gross income to estimate the means of income classes tends to overstate inequality. See "A Ranking of States by Inequality Using Census and Tax Data: A Comment," Review of Economics and Statistics, IXL, No. 4 (November, 1967), 636-37. 47 This approach has been taken m spite of Schaefer's caveat regarding bias, for the comparative value is still present. Nevertheless, one "should realize fully the limitations of such operations." See Jeffrey Schaefer, op. bit., p. 637. 48 California Franchise Tax Board, Annual Report of the Franchise Tax Board for' the Year 19 6 0 (Sacramento: n.d.). 74 not in sufficient detail, and a trip to Sacramento was necessary to obtain raw data from the files. After combination of the detailed tax data on number of taxpayers and on adjusted gross income for non-taxable, taxable short form, and taxable long form returns, for each of the income categories (a conversion program was necessary to make the categories comparable), it was then possible to divide the adjusted gross income by the number of taxpayers and obtain a mean for each income category. It should be pointed out that the tax data was taken from a sample of taxpayers 1 returns, in the following percentages: Strata Sampling Ratio Form 540A 2.5% Form 540 Small incomes 5.0% Medium incomes 20.0% Large incomes 100.0% This sample size provided for maximum percentage error at the two sigma (95.4%) confidence level of 20.8% for form 540A, 5.8% for small returns, 6.5% for medium sized returns, and 0.0% for large returns using the long form. This sample was considered adequate, and except for some of the smaller counties, more than sufficient. Note that the errors quoted are maximum, and in the majority of the 75 49 counties would be far less. It is notable that the mean incomes of most of the counties were very near the midpoints of all the income classes except for the first two ($0-$l,000 and $1,000- $2 ,000) and the last two ($15 ,000-$25 ,000 and over $25,000). Those midpoints tended to be in the neighborhood of $300, $1,500, $18,000, and $40,000, respectively, and were rather consistent among the counties with a few exceptions. Differences were tested for significance, however, among all the midpoints of several of the counties and were found to be important. The detail and extra labor of calculations rather than assuming aritmetic midpoints or distributional methods such as Pareto or log-normal assumptions was therefore deemed advisable and beneficial toward higher confidence in the resulting measurements of comparative inequality. Alternative Measures of Inequality An explanation of the derivation of the chosen measure of inequality is now in order. But first, the alternative methods of measuring inequality which were considered will be described. Kuznets, in a monumental work, used the share of the upper income groups as his 4Q Ibid., p. 13. 76 50 measure of relative inequality. On the other hand, Miller and Roby use the bottom fifth of the population when 51 ranked as to income and their share of total income. The coefficient of variation of income as well as that of the 52 logarithms of income were used by Kravis. Inequality based on a welfare function was employed by Aigner and 5 3 Heins, But the vast majority of income inequality studies which were surveyed employed the Lorenz curve and concentration ratio approach. Some of the reasons given are that it is a ratio and therefore comparable among distributions and that it possesses the same qualities for measurement of dispersion as do the mean difference and the standard deviation with the additional advantage that it can be presented graphically. No commitment to a theory of income is implied in its use as is the case with Pareto or log-normal assumptions. Also, no goodness-of-fit tests 50 Simon Kuznets, Shares of Upper Income Groups' in Income and Savings (New York: National Bureau of Economic Research, 1953). 51S. M. Miller and Pamela Roby, The Future of Inequality (New York: Basic Books, 1970TT 5 2 Irving B. Kravis, The Structure of Income: Some Quantitative Essays (Washington, D.C.: University of Pennsylvania Press, 1962). 5 3 D. J. Aigner and A. J. Heins, "A Social Welfare View of the Measurement of Income Inequality," Review of Income and Wealth, XIII, No. 1 (March, 19 67), 12-25. 77 54- are necessary. The simple fact that they are well-known and understood is also important, and their ability to summarize the entire distribution is not shared by the shares of upper or lower income methods. But the strength of a single coefficient— that of summarizing an entire distribution in a single figure--is also its major weakness. The Gini coefficient says nothing about the shape of the distribution, or whether the inequalities are due to inordinate numbers of rich or the masses in poverty. This, in part, can be corrected by the calculation of percentiles of the distribution and the graphical presentation of the accompanying Lorenz curve. It is not possible to determine which method is absolutely superior to all others, if any. When Yntema calculated four different measures of inequality for four 5 5 countries, he found little agreement among them. The choice seems, at this point, rather arbitrary, but governed by the necessity to have comparative results and to have them understood. Thus the Gini-Lorenz method is chosen. 5 4 Fuat M. Andie, Distribution of Family Tricornes in Puerto Rico (Rio Piedras: University of Puerto Rico, 1964). 5 5 D. B. Yntema, "Measures of the Inequality of the Personal Distribution of Wealth or Income," Journal of the American Statistical Association, XXVIII, No. 184 (December, 19 33), 42 3-43 3. 78 This choice is made with full realization, once again, of a major drawback in fulfilling the present purposes. Edward C. Budd has shown in a penetrating 5 6 article recently that Lorenz curves are rather insensi tive to all but major changes in distribution, and that the Gini concentration ratio, while being the most useful of inequality measures, produces an ambiguous measure of comparison of two relevant Lorenz curves if the two curves intersect. Such an intersection is implied if both the rich and the poor are worse off relative to the middle section of a distribution, when compared with the distribu tion of another area. He recommends use of the derivative of the Lorenz curve, or the "slope of the chord connecting the lower and upper points on the Lorenz curve for the quantile" involved. In addition, he shows that the method of approximating the concentration ratio used here tends to understate inequality, due to discrete geometry as opposed to continuity as used in calculus. Knowledge about the ambiguity involved in intersecting Lorenz curves is not new. Nevertheless, the advantages in using the Lorenz-Gini method overcome these disadvantages. 5 6 "Postwar Changes in the Size Distribution of Income in the U.S.," American Economic Review, XL, No. 2 (May, 1970), 249-260. 79 The Gini Index The calculation of the Gini coefficient of income 57 inequality is demonstrated by many authors. It will be summarized here. First, though, a note about the various names that are used for this measure is in order. The phrases, "Gini coefficient," "Gini index," "concentration ratio," "Lorenz coefficient," and "Lorenz concentration ratio" seem to be used interchangeably in the literature to describe the measure of inequality used here. Actually, they all refer to Gini's mean difference divided by twice the arithmetic mean of a distribution. Lorenz approached it graphically, with the percentage of total income on a vertical axis and the percentage of recipients on a horizontal axis. A diagonal line midway between the axes represents complete income equality, for at that line ten per cent of the recipients would have ten per cent of the income; twenty per cent of recipients would have twenty per cent of the income; and so forth. However, if twenty per cent of the people had only five per cent of the income, then the curve of inequality or Lorenz curve would 57 See especially Herman P. Miller, Income Distribution in the United States (Washington, D.C.: U.S. Government Printing Office, 1966), p. 221; James N. Morgan, "The Anatomy of Income Distribution," Review of Economics and Statistics, XLIV, No. 3 (August, 1962), 270-83; and Lee Soltow, Toward Income Equality in Norway (Madison, Wisconsin: University of Wisconsin Press, 1965), p. 8ff. 80 sag below the diagonal, as seen in Figure 1. The area between the diagonal and the income curve is called the area of concentration and is denoted by M in the figure. The balance of the area below the diagonal is denoted N. The inequality measure L may be calculated as follows: . . M area between curve and diagonal L = = ----------------------------------------------- M + N total area below diagonal Kendall shows that this quantity, with an upper limit of 1.0 and a lower limit of zero, is equal to twice the area of concentration.^ Determination of that area and calculation of the actual Gini coefficient is acomplished by assuming that any two points such as A and B on the horizontal axis can delineate a segment of the axis, however small, and that C and D are indicators of the income values for A and B Thus (C + D) Area ABDC = (B - A) -------- . 2 It follows that when all segments of the curve are con sidered, the area under the curve (area N in the figure) is C O M. G. Kendall, The Advanced Theory of Statistics (4-th ed. , London: Griffin and Company, 194-8), pT. 44. 81 % of Income 80 60 40 20 0 20 A 60 B % of families Figure 1.— The Lorenz Curve of Income Inequality where and represent height of the curve at all points and respectively, i = 1,2, . . .,n. Since the area under the diagonal is one half of a square whose dimensions are l x l (or 100% x 100%), then that area is equal to 0.5 and since the area of concentration is 1/2 L, then n (C. + D.) 1/2 L = 0.5 - I (B. - A.) — ------ — i=l 1 1 2 and n L = 1 - I (B.-A.)CC.-D.). i = l 1 1 1 1 Thus we have the over-all measurement of relative inequal ity , and at the same time, the calculations are available 59 with which to graph the Lorenz curves. This process was accomplished for the 58 counties of California with the use of a General Electric 265 computer accessed through a time-shared network. The basic computer program developed to accomplish this purpose 59 The entire calculation procedure is adapted from Morgan, "The Anatomy of Income Distribution," o£. cit. 83 is shown in Figure 2, and the calculations for each of the counties are placed hereafter as Appendix B. A Factor Analytic Method of Measuring Well-Being The degree of well-being or the extent of welfare has historically been difficult to measure. An attempt is made here to utilize the tenets of factor analysis to arrive at a measure of well-being. There is little in the way of precedent for doing 60 61 so. Roberts and McBee and Adelman and Morris have employed factor analysis to discern independent forces at work in the process of economic development, and psychologists and educational testing specialists have used it to develop measures of intelligence, inquisitiveness, numbers skills, and other intellectual traits through a battery of tests. But specific instances of prior attempts to measure welfare through factor analysis, if any, have 6 2 escaped the author's attention. 6 0 Robert E. Roberts and George W. McBee, "Modernization and Economic Development in Mexico: a Factor Analytic Approach," Economic Development and Cultural Change, XVI, No. 4 (July, 1968) , 603-12. 61 Irma Adelman and Cynthia Taft Morris, Society, Politics, and Economic Development: a Quantitative Approach (Baltimore: Johns Hopkins Press, 1967). 6 2 George D. Johnson has utilized factor analysis to categorize small communities into viable and non-viable groups. The approach to measuring well-being taken here is 84 1 PRINT i t LORENZ CONCENTRATION' RATIO CALCULATIONS" 3 PRINT i t X(I) Y(I) Z(I)" 5 PRINT i i INCOME CUM PERCENT CUM PERCENT " 7 PRINT i i CLASS OF FAMILIES OF INCOME (B-A)(C+D)" 8 PRINT 9 PRINT 10 DIM F(15),M(15),K(15),G(15),h(15),H(15),X(15),Y(15), C(15),Z(15) 11 DIM P(15) 15 FOR J = 1 TO 10 20 LET S=K(I)=T=X=Y=C=P=Z=Q=0 21 LET L=0 30 READ A$ 40 FOR 1= 0T012 50 READ F(I) 60 LET S=S+F(I) 70 NEXT I 80 FOR I = 0 TO 12 9 0 READ M(I) 100 LET K(I)=F(I)*M(I) 110 LET T=T+K(I) 12 0 NEXT I 130 PRINT " ";A$ ; "COUNTY" 135 PRINT 180 PRINT 190 FOR I=0T012 200 LET 6(I)=F(I)/S 210 LET H(I)=K(I)/T 220 LET X=X+G(I) 2 30 LET Y=Y+H(I) 240 LET C=Y-H(I) 250 LET P=C+Y 260 LET Z=P*G(I) 270 LET Q=Q+Z 280 PRINT I,X,Y ,Z 290 NEXT I 300 LET L=l-Q 309 PRINT 310 PRINT " SUM OF (B-A)(C+D)=",Q 3 20 PRINT 330 PRINT 340 PRINT " LORENZ = 1 - SUM((B-A)(C+D) = "; L 341 PRINT 342 PRINT 345 NEXT J Figure 2.— Timeshare Program for Computing the Lorenz Concentration Ratio or Gini Coefficient 85 An Example Perhaps an exemplary model of factor analysis from the field of testing (for which it was originally developed) will aid in the understanding of the concept. Assume that a battery of tests is given to a group of individuals, and that the simple correlation coefficients between the test scores indicate high intercorrelation. Each test is apparently measuring some abilities that are also measured by the other tests. But since the correla tions are incomplete, there may be some unique elements of intellect or ability measured by the tests. A particular test score on a given test might be represented as a,C, + a0C0 + . . . + a C + bU 1 1 2 2 n n where S = the test score C. = the common factors contained in the set of tests a. = the factor coefficients (loadings) or the extent to which a test reveals a common factor quite similar. See Short Run Determinants of Small Community Growth: a Multivariate Analysis of Factors Affecting the Movement of Short Run Mobile Resources. (Unpublished Ph.D. dissertation, Kansas State University, 1970), especially Chapter III, Methodology, pp. ^5-54. 86 U = the factor unique to a given test b = a scalar weight for U. In terms of intercorrelation among test scores, and disregarding, for the moment, the unique factor, the correlation matrix for a series of four tests might be represented by Table 5. Table 5.— Correlation Matrix for Four Tests 1 2 3 1 (1.00) . 80 .96 .60 2 . 80 (1.00) .60 .00 3 .96 .60 (1.00) . 80 i f .60 .00 .80 (1.00) It can be seen that the four variables can be more parsimoniously described in two vectors of unit length which are at right angles (orthogonal) to each other; that is < H II CO < N> + V2 = 1.0V2 + .ov4 II CO > .6V2 + .8V4 < -p II • ov2 + i.ov4 . 87 This is the equivalent of a very simple factor analysis, and can be put in the form of a factor matrix as 2 shown m Table 6. Notice that the h (known as communality) is the sum of the squares of the factor "loadings" for each variable. In this case the communality is 1.0, meaning that the two factors included have explained all the differences in test scores; the tests involved were assumed to have no unique elements. Table 6.--Two-Factor Matrix Test I Factor II h2 1 . 8 .6 1.0 2 1.0 .0 1.0 3 .6 . 8 1.0 4 .0 1.0 1.0 Imagine now four different tests which, when given to a number of recipients, resulted in a correlation matrix leading to the following factor matrix: 88 Table 7.— Two-Factor Matrix with h2 < 1.0 Test I Factor II h2 1 . 6 .4 .52 2 . 6 .6 .72 3 .7 -.3 .58 4 . 4 -.5 .41 2 This factor matrix shows h (less than 1.0, owing to the presence of unique factors or insufficient numbers of common factors) as determined by a specific position of the factor axes I and II in the two dimensional factor space. In reality, however, the points on a graph can be located with reference to X and Y axes in any position, and thus the position of axes I and II and the resulting factor loadings above are rather arbitrary. To optimize the factor loadings, or in other words, to maximize the descriptive power of the two factors involved, it is permissible to rotate the axes until an optimum position is found. Note that the interpretation and identification of the factors would also change. For example, a 50 degree rotation of the system in Table 7 results in the rotated factor matrix in Table 8. 89 Table 8.--Rotated Factor Matrix Test I Factor II h2 1 .08 .72 .52 2 -.07 . 85 .73 3 .68 . 34 .58 4 .64 CM O I .41 It is now apparent that Factor I is highly correlated with tests 3 and 4 and that Factor II is more closely related to tests 1 and 2.^ Application of Factor Analysis The factor analysis model used in this dissertation is called "principle components." It differs from classical factor analysis in that it does not provide for any unique factors in the variable. Instead, the correla tions among the variables are analyzed so as to isolate the 64- principle components present in the data. In a complete 6 3 This example is due to Benjamin Fruchter, Introduction to Factor Analysis (New York: D. Van Nostrand Company, 1954) , pp. 33-41. 64 According to R. J. Rummel, "It should be clear that component analysis simply defines the basic dimensions of the data. There is no assumption about common factors. Indeed, the factor dimensions emerging from a component 90 system of principle components, the number of components is equal to the number of variables. However, it is often the case that the first few components are able to account for such a large portion of the variance among observations on the variables that further extraction of components is unnecessary. Note that a given factor or component does not have an a priori identity. It is only a system of cor relations among variables that is completely independent of other such systems, and it must be given meaning by interpretation. In the rotated factor matrix of Table 8, for example, if tests 1 and 2 are intelligence related, then Factor II is the intelligence factor, while Factor I must be interpreted by examining the nature of tests 3 and 4 with which it is correlated. In terms of the data for the counties of California (see Appendix A), the process of factor analysis is given the task of determining the principle components which are present in the variables. After determination of a given number p of these completely independent 2 components, a certain percentage h of the differences among counties will be accounted for. As p increases, 2 h will increase, but after a time the rate of increase in analysis mix up common, specific, and random error variances." Applied Factor Analysis (Evanston: Northwestern University Press, 19 70), p. 112. 91 2 h will begin to decline, and the efficiency in selecting more factors will decrease. The objective is to select p 2 2 such that h will be large and increases in h with additional increments to p will be small. In other words, the data set of 2 3 variables in 5 8 counties is described as completely and efficiently as possible in terms of p independent components. This gives a com ponent matrix similar to the factor matrix in Table 7. Once that point is reached, then the factor matrix is rotated for maximum interpretability and identification of factors, that is, with the goal of achieving either very high or rather low rotated factor loadings. This was accomplished for the California data with an I.B.M. 360 series computer at the University of Southern California, 6 5 using the Biomed software package BMDX72. The Varimax method of orthogonal rotation was chosen, due to the requirement of independence of components for summing county well-being scores, and due to the ease of interpre tation and general acceptability of the process. This choice was made free of any computer program constraint, for several alternative processes of rotation were available in software form. 6 5 W. J. Dixon, ed. , Biomed Computer Programs (Berkeley: University of California Press, 19 68). 92 The Principle Components Model As a linear system representing one case or set of observations, the model described above can be shown as where X. allFl + a12F2 + a21Fl + a22F2 + ‘ . + a. F lp p . + a0 F 2p P • • • X_ m amlFl + am2F2 + • . + a F mp p X. l *th the value of the i variable for a given case, i = l,2,...,m Fj a. . 19 principle component, j = 1,2,...,p the loading of component Fj with respect to variable X^, i = l,2,...,m; j = 1,2,...,p. In the notation of factor matrices, this becomes 66 where z1 = Af’ 66, For a complete exposition of the methods of factor analysis, as well as a chapter on essential matrix methods, see Harry H. Harman, Modern Factor Analysis (2nd ed., revised, Chicago: University of Chicago Press, 1967). 93 X. X, X m = the column vector of m variables for a given case A = 11 21 12 * 22 lp 2p cL i H m • • • 3. ml m2 mp component loading matrix E 2 • • • ] = the principle components Derivation of Component Scores The rotated factor matrix is not suitable for the purpose being pursued, but is only an intermediate step. It is used, however, to identify and interpret the components. Essentially, it shows component loadings with respect to the variables of the system, while the values being sought for the purpose of measuring well-being must have reference to the cases involved (in this application, 94 the counties). The measurements of components with respect to cases or sets of observations are termed "component scores. The emphasis of the analysis changes, then, from the prior explanation of variables with the case given, 1 6 7 an explanation of cases, with variables given. Thus xli F11 X2i F21 # = ail • Xni F n nl — where + a i2 12 22 ' n2 + . . . + a . ip IP 2p np X. . ki kD A. . 19 the value of the k^*1 case in the i" * " * 1 variable, k = l,2,...,n; i = l,2,...,m "fch the component score for the j principle component for the k ^ case, j = l,2,...,p; k = 1,2 ,. . . ,n the component loading on the j component in the i ^ variable, j = l,2,...,p; i = 1,2 ,. . . ,m. This will perhaps be made simpler by the use of matrix notation, in the expanded form which depicts the 6 7 Rummel, 0£. cit., p. 108. 95 entire system of cases, variables, principle components, and loadings: Z = $A' where X11 x12 * • * xim X21 X22 ‘ ‘ X2m X , X _ . . . X nl n2 nm the data matrix of n cases and m variables $ = F F 11 12 IP F F F 21 22 2p • • • F , F „ . . . F nl n2 np the component scores for n cases and p principle components A = lll 12 21 22 . . . a IP • • • 3. 2p cL - i 3. n • • • 3 ml m2 mp the matrix of loadings for m variables and p components Since this equation represents the data set in terms of the set of components, then the components themselves in 96 terms of the data may be shown by $ = A '-1 Z but since A 1 is not square, then Z A = $ A* A and $ = Z A (A* A )-1 . In this form the component scores can be estimated, and it produces a matrix of n cases, or counties, with a quantitative measurement of the score for 6 8 that county on each of the p independent components. Since the scores are listed in a standardized form and are comparable among counties for each component, then the counties can be ranked with respect to their relative performance in each component. Furthermore, the scores can be weighted and summed and the counties ranked according to their overall performance. This is inter preted as the comparative well-being index. In addition, an absolute index representing a county's well-being is available through the use of the 6 8 The author is indebted to George D. Johnson for aid in understanding and using this model. For a complete and efficient explanation of this and other factor analysis methods, see his Short Run Determinants, op. cit. score itself, which is expressed in terms of the number of standard deviations from the mean for each component. The sum of the scores (weighted according to factor importance) can also be used as a measure of overall well-being. Returning to the rotated factor loading matrix, the standardized form of the loadings can be explained. Since each of the cells of that matrix is expressed in standard deviation units, the square of the cell value will be the variance in the variable being considered which can be explained by the factor at hand. Adding the squares (variances) across each row determines the total variance in a variable explained by the p chosen factors. This 2 2 value is known as h , where 0 < h < 1.0. Summing the squared loadings down each column will therefore give the portion of total variance explained by 2 each factor, and the sum of the h column is the total variance explained by all factors among all m variables. Expressed as a percentage of m, this shows the percentage of total variance for which explanatory factors have been included. Thus 98 all al2 ’ * alp ! ai-2 j=i ^ a21 • a22 • • ' ’ a2p • • • ? 2 . “ ■ , a2j D 1 J • aml am2 . . a mp ? 2 ) a. . 5=i 13 m 0 I a.-,2 5=i 11 m „ I a. 2 . i=l 12 m 0 . • I a..2 i = l ^ I a..2 i=l j=l ^ where = the component loadings n £ 'i a..^ = the total variance explained i=l j=l X3 and since each variable has unit variance and the total variance in the data is equal to the number of variables, then I ? a±j* i=l j=l 3 m the percentage of total variance explained by the chosen components . The component scores are also expressed in standard deviation units, with each component having zero 99 mean and unit variance. Thus the component score matrix appears F11 F12 IP ? F, .2 9 = 1 13 F21 F22 ’ . . p 2p f F 2 • n 2j D = 1 J Fnl Fn2 * . . F np • ^ rkj2 9 = 1 J n 9 y f 2 L kl k=l =n n , I Fk22=n . k=l n 9 . . T F. =n k=i kp n E 9 I Z •=Pn k=l j=l showing the relationship among the n counties, p components, the standardized scores, and explained variance. After applying weights according to each factor's importance to each of the factor scores, the sum of the scores for a county becomes its well-being index. The sum of the indices for all counties is zero, with any single county's expected value also zero. Thus the deviations from the zero mean for individual counties represent a valid measure of differences and are used as the well being index in the analysis. 100 The Research Procedure and the Statistical' Model The hypothesis stated in Chapter I is that aggregate levels of well-being in California counties depend upon and are inversely related to income inequality. The general model can thus be shown as WI = f (L) where WI = the well-being index developed through factor analytic methods L = the income distributional inequality or Gini index f = a function which relates values of WI to values of L. Since WI and L are expressed as absolute numbers, the relationship between them (given a set of empirical data) can be determined by statistical methods. In addition, the rank of each county as compared to the other counties in WI and L can be used as a comparative evaluation and rank correlation methods will determine whether a relationship exists. Both linear and non-linear forms of relationship are tested. The functions which are used can be shown as follows: 101 Table 9.— Curve Types and Linear Equivalents• Curve Type Linear Equivalent WI = a + b(L) linear WI a e ML) In (WI) = ln(a) + b(L) WI = a (L) In (WI) = ln(a) + b ln(L) WI = a + TlT WI = a + b Tl T wi = a + b(L) WI a + b (L) WI (L) a + b (L) _1_ WI = b + a i n Each of these forms are fit to the data in turn, using least squares as the criterion for goodness of fit. The 2 coefficient of determination p is then applied as the criterion for choice of the best form from among the above equations. Since the data includes observations on all the counties, rather than being a sample of counties, and since no further inferences are intended, no test of significance of the regression hypothesis is necessary. Additional analysis of the relationship of the well-being data to income inequality is conducted through regression of single component scores upon the Gini index 10 2 of income dispersion, as opposed to their sum, as is the case in the model above. This operation takes the form F. = f(L) where the Fj represent the component scores. Linear estimation of the regression coefficients is accomplished by the form Fj = a + b(L) and the related beta coefficients are calculated F., - F. Ok j — s = B F rJ . ( ¥ ) where I (Lk - L)2 n These beta coefficients allow expression of the weightings of all components in similar units, and enable the 103 comparison of factors for analysis of relative importance 6 9 in association with L, the index of income inequality. The question of whether a single variable or a simple set of variables can predict levels of welfare as well as the well-being index is also of interest. If so, then the factor analysis is unnecessary. In other words, is the time used in constructing the index of well-being used efficiently, or could income alone (for example) account for a large portion of the variance in the index? A search for a proxy variable for the well-being index serves to answer this question. The candidate proxy variables are correlated with the sum of the component scores in this analysis, as well as with the Gini index of inequality. g Q General Electric, Information Service Department, Regression Analysis: Program Library User's Guide (n.p.; General Electric, 1968), p. 15. CHAPTER IV RESULTS OF THE STUDY: INCOME DISPERSION AND WELL-BEING IN CALIFORNIA The previous chapter set forth the framework for the empirical study of income distributions, well-being, and their relationships in the counties of California. The present chapter outlines the application of the data base to the framework and gives details of the results of the analysis. Briefly, the chapter is divided into three sections, which are (a) the details of the study of income dispersion and the resulting inequality measurement for each county; (b) an explanation of the well-being index and the comparative well-being ratings for the fifty-eight counties; and (c) the exercising of the regression- correlation model and the resulting relationships, together with the testing of the hypothesis that well-being is inversely related to inequality of incomes. The Distribution of Income by California Counties The basis source of data for the distribution of income of families in the counties of California is the 104 105 United States Census.^ Because of the lack of dollar figures for the income associated with the persons in each income classification, however, it was necessary to determine the mean income of each classification from state 2 . . income tax returns. The process of combining the information and of computing the Gini coefficient of inequality was explained in Chapter III. Basically, the Gini index describes the tendency of a distribution to be dispersed horizontally over a range of incomes. It is derived from Gini's mean difference, and thus has the attraction of being dependent on the disper sion of variate values among themselves, rather than on deviations from central point. The mean difference must be stated in standardized terms to be comparable among different distributions, and the coefficient of concentra tion or Gini index accomplishes this. It can be expressed as follows: U.S. Department of Commerce, Bureau of the Census, I9 60 Census of Population, Vol. I, Characteristics of the Population, Part VI, California (Washington, D.C.: U.S. Government Printing Office, 1963), p. 23ff. 2 California Franchise Tax Board, Annual Report of the Franchise Tax Board for the Year 19 60 (Sacramento: n.d. ). 3 M. G. Kendall, The Advanced Theory of Statistics (4-th ed. , London: Griffin and Company, 19 48), p. 42. 106 where: L = the Gini index = the mean difference u j j = the distribution mean. The use of the Gini index has certain complications and limitations. These were accounted for in Chapter III. There is considerable precedent for the use of this measure of inequality in income studies, beginning early in the 5 twentieth century and continuing into the 19 70's. The results of the measurement of inequality of family incomes in the 5 8 California counties are shown in Table 10. The average of the Gini coefficients is .35055 and the standard deviation is .03153. Figure 3 shows the counties of California and emphasizes those counties whose inequality indices exceed the mean of all counties by more than one standard deviation. It is notable that all of the counties in this high comparative inequality group are agriculturally oriented. In addition, other 4Ibld. , p. 43. ^See Chapter II, Review of the Literature, and the section entitled The Measurement of Income Inequality in Chapter III. 107 Table 10.— Gini Coefficients of Family Income Inequality for the counties of California County Gini County Gini County Gini Madera .m3 Modoc . 362 Mono .331 Mariposa .407 Sutter . 362 Del Norte . 328 Lake .402 Mendocino . 361 Siskiyou . 326 Tulare . 399 San Joaquin . 358 San Bernar Colusa . 399 Kern . 355 dino . 325 Merced . 398 San Diego . 354 Napa . 324 Santa Cruz . 394 Butte . 354 Placer . 323 Kings . 390 Nevada . 354 Santa Clara . 323 Glenn . 386 Marin . 353 Conta Costa . 318 Imperial . 384 San Mateo . 351 Solano . 317 Stanislaus . 383 Yuba . 349 Sacramento . 316 Santa Barbara . 382 Alameda . 346 Calaveras . 316 San Francisco . 381 Tehama . 344 Yolo . 314 San Benito . 380 Humboldt . 343 Inyo . 314 Fresno .380 Ventura . 342 Tuolumne . 312 Monterey . 378 El Dorado . 342 Amador . 306 Riverside . 370 Shasta . 337 Plumas . 306 Sonoma . 369 Orange . 332 Lassen . 300 San Luis Obispo . 365 Alpine .3 31 Sierra . 291 Los Angeles . 364 Trinity .288 U = .35055 O - .03153 State Total— .361 10 8 Figure 3.— Areas of Extreme Income Inequality aThe shaded areas are counties where the Gini coefficient of inequality exceeds the mean by more than one standard deviation. 109 counties with heavy agricultural bases were above the mean, including Fresno, San Benito, Monterey, San Joaquin, Kern, and Butte counties. By contrast, those counties with income inequality ratings more than one standard deviation below the mean were largely mountainous and sparsely populated, with the exception of Sacramento, Contra Costa, Yolo, and Solano counties. Figure 4 bears out this relationship. The counties are ranked by inequality of incomes (according to the Gini index) in Table 11. There is another aspect to the comparison of income distributions. It concerns the extent of the extremes of the distribution. For example, what per cent of the income recipients receive less than $3,000 annually? What per cent receive over $15,000 annually? The Gini index has been attacked for the accomplishment of its purpose; that is, expression of the dispersion of income in a single figure, deemphasizing the relative position of the extremes. The counties of California have been studied as to the extremes of their income distributions, and Table 12 gives the per cent of families in each county receiving less than $3,000, and over $15,000. Table 13 shows the ranked set of counties by per cent of families with 19 59 incomes less than $3,000. The Spearman formula for rank correlation was used to determine the consistency between the under $3,0 00 percentage and the Gini index. The 110 Figure --Areas of Income Inequality over One Standard Deviation Less Than the Mean Ill Table 11.— Rank of the 5 8 California Counties by Income Inequality as Measured by the Gini Index County Rank County Rank Madera 1 Mariposa 2 Lake 3 Tulare 4 Colusa 5 Merced 6 Santa Cruz 7 Kings 8 Glenn 9 Imperial 10 Stanislaus 11 Santa Barbara 12 San Francisco 13 San Benito 14 Fresno 15 Monterey 16 Riverside 17 Sonoma 18 San Luis Obispo 19 Los Angeles 20 Modoc 21 Sutter 22 Mendocino 23 San Joaquin 24 Kern 25 San Diego 26 Butte 27 Nevada 28 Marin 29 San Mateo 30 Yuba 31 Alameda 32 Tehama 33 Humboldt 34 Ventura 35 El Dorado 36 Shasta 37 Orange 38 Alpine 39 Mono 40 Del Norte 41 Siskiyou 42 San Bernardino 43 Napa 44 Placer 45 Santa Clara 46 Contra Costa 47 Solano 48 Sacramento 49 Calaveras 50 Yolo 51 Inyo 52 Tuolumne 53 Amador 54 Plumas 55 Lassen 56 Sierra 57 Trinity 58 112 Table 12.— Per Cent of Families Receiving Less Then $1,000, Less Than $3,000, and Over $15,000 by County, 1959 ................................. r . Less Than Less Than More Than counry $1,0 00 $3,0 00 $15,000 Alameda 8.1 20.1 6.1 Alpine 17.1 39.0 2.9 Amador 10.0 26.2 2.2 Butte 11.4 33.0 3.0 Calaveras 12. 3 27.0 2.4 Colusa 10 .9 30.1 5.2 Contra Costa 6.0 15.0 7.1 Del Norte 5.9 21. 3 4.3 El Dorado 8.2 21. 8 5 . 3 Fresno 12.2 31.6 4.6 Glenn 11.9 34. 7 3.0 Humboldt 7.6 21.2 4.9 Imperial 12.6 31. 7 5.1 Inyo 10 .9 27.5 2.0 Kern 10.5 28.1 4.3 Kings 14. 7 37.3 3.6 Lake 17.7 45.2 3.2 Lassen 8.8 22.1 1.3 Los Angeles 7.2 19 .1 7.8 Madera 16.2 42.6 3.9 Marin 4.7 14.2 12.2: Mariposa 20.9 40 .6 2.4 Mendocino 10.8 26.8 3.8 Merced 14. 5 40 .1 3.6 Modoc 11.1 28.6 4.6 Mono 3.9 16. 3 7.0 Monterey 9.0 28.8 5 . 3 Napa 7.9 22.3 4.1 Nevada 12.0 32.1 3.0 Orange 6.4 11.0 6 . 8 Placer 8.9 24.1 3.6 Plumas 8.0 23.6 2.8 Riverside 11.1 30 . 3 4.4 Sacramento 5.6 16.6 5.9 San Benito 12.1 32.3 4.5 San Bernardino 9.1 25.7 3.5 San Diego 8.6 23.0 5.6 113 Table 12— Continued County Less Than Less Than More Than . . . . $1 , . 0. 0.0.... . . $.3, 0 0.0 . . . . $15., 000 . San Francisco 7.8 21. 0 7.2 San Joaquin 10.5 28.0 4.5 San Luis Obispo 12.4 31.4 4.0 San Mateo 4.1 11. 3 10 . 8 Santa Barbara 6.7 20.7 7.4 Santa Clara 6.0 15 .5 7.6 Santa Cruz 14.4 36. 3 4.8 Shasta 9 . 5 25.0 3.5 Sierra 9. 8 23.4 1.6 Siskiyou 9.2 26. 2 3.1 Solano 8.0 25.9 3.0 Sonoma 12.5 30 .9 3.9 Stanislaus 14. 2 35.2 3.7 Sutter 9.4 29 .9 4.7 Tehama 12.1 30.0 2.6 Trinity 7.5 20.6 2 . 3 Tulare 13.7 40.5 4.1 Tuolumne 8.1 27.2 2.3 Ventura 7.9 22.8 4.9 Yolo 7.1 23.1 3.8 Yuba 11.4 34. 7 2.5 State Total 8.0 21.4 114 Table 13.— Rank of the 5 8 California Counties by Per Cent ■ of Incomes Less Than $3,000 in 1959 ......... County.............. Rank .County . ....... Rank Orange 1 Calaveras 30 San Mateo 2 Tuolumne 31 Marin 3 Inyo 32 Contra Costa 4 San Joaquin 33 Santa Clara 5 Kern 34 Mono 6 Modoc 35 Sacramento 7 Monterey 36 Los Angeles 8 Sutter 37 Alameda 9 Tehama 38 Trinity 10 Colusa 39 Santa Barbara 11 Riverside 40 San Francisco 12 Sonoma 41 Humboldt 13 San Luis Obispo 42 Del Norte 14 Fresno 43 El Dorado 15 Imperial 44 Lassen 16 Nevada 45 Napa 17 San Benito 46 Ventura 18 Butte 47 San Diego 19 Glenn 48 Yolo 20 Yuba 49 Sierra 21 Stanislaus 50 Plumas 22 Santa Cruz 51 Placer 23 Kings 52 Shasta 24 Alpine 53 San Bernardino 25 Merced 54 Solano 26 Tulare 55 Siskiyou 27 Mariposa 56 Amador 28 Madera 57 Mendocino 29 Lake 58 115 Spearman "rho" coefficient for this data is: 6 d2 p = 1 -------5------ = .611 n(n - 1) indicating that the Gini index represents a good portion of the differences among counties in the $3,000 and under group. Table 14 ranks the counties by percentage of families with incomes over $15,000. Again, the correlation between these ranks and those of the Gini index was com puted, resulting in a Spearman "rho" of -.305. This indicates little correlation or consistency between the two series, possibly reflecting the fact that most serious inequalities of income come from the low-income levels, in terms of per cent of families affected. Low correlation was also found between the per cent of families with less than $3,00 0 income and per cent with over $15,000. That is, it is not indicated in the data that high and low incomes are substitutes for one another; the middle income group absorbs a good deal of the differences. As was pointed out in Chapter III, families are being used as the recipient unit in the inequality calculations. County data were not available for "families and unrelated individuals," which would be more in touch with reality. In justification of the comparative value 116 Table 14.— Rank of the 5 8 California Counties by Per Cent of Incomes over $15,000 in 1959 County Rank County Rank Marin 1 San Luis Obispo 30 San Mateo 2 Sonoma 31 Los Angeles 3 Madera 32 Santa Clara 4 Mendocino 33 Santa Barbara 5 Yolo 34 San Francisco 6 Stanislaus 35 Contra Costa 7 Placer 36 Mono 8 Merced 37 Orange 9 Kings 38 Alameda 10 Shasta 39 Sacramento 11 San Bernardino 40 San Diego 12 Lake 41 El Dorado 13 Siskiyou 42 Monterey 14 Glenn .43 Colusa 15 Butte 44 Imperial 16 Nevada 45 Humboldt 17 Solano 46 Ventura 18 Alpine 47 Santa Cruz 19 Plumas 48 Sutter 20 Tehama 49 Fresno 21 Yuba 50 Modoc 22 Calaveras 51 San Benito 23 Mariposa 52 San Joaquin 24 Trinity 53 Riverside 25 Tuolumne 54 Kern 26 Amador 55 Del Norte 27 Inyo 56 Napa 28 Sierra 57 Tulare 29 Lassen 58 117 of the family base, however, a Spearman test for rank correlation was done on the Verway and Al-Samarrie and 6 Miller series of estimates of the Gini index for states. Verway uses "families and unrelated individuals" while Al-Samarrie and Miller use families only. The rank correlation coefficient of .918 indicates high association; thus one is acceptable as an estimate of the rank of the other and each is valuable in rank comparisons. It is interesting to note that the State of California's Gini index for families calculated by Al-Samarrie and Miller is .34-5, compared to .361 by the method used here. The "family and unrelated individual" Gini coefficient for California was calculated as .436 by 7 Verway, .440 by Conlisk, and .42 8 by the methods of this dissertation. All are from 19 60 census data. A Comparison of Well-Being for California Counties The Data In measuring the socio-economic well-being for the 5 8 counties of California, it was assumed that the data g See David I. Verway, "A Ranking of States by Inequality using Census and Tax Data," Review of Economics and Statistics, XLVIII, No. 3 (August, 1966), 314-321 and Ahmad Al-Samarrie and Herman P. Miller, "State Differentials in Income Concentration," American Economic Review, LVII, No. 1 (March, 1967), 59-72. 7 John Conlisk, "Some Cross-State Evidence on Income Inequality," Review of Economics and Statistics, IXL, No. 1 (February, 1967), 115-18. 118 set in Appendix A appropriately includes the necessary and sufficient information for that purpose. For a discussion of the data, see Chapter III. The criteria for inclusion of variables were rather broad; such concepts as availability in a primary source and general applicability as socio-economic phenomena influencing aggregate welfare (taken rather subjectively) were considered. Certain variables originally included were later deleted, within dual objectives of simplicity (non-duplication) and absence of implicit value judgments. As a result, twenty- three sets of observations constitute the chosen data bank, all taken as cross-sections of the 5 8 California counties g for the year 1960, or as close to 1960 as possible. The list of these variables, together with the correlations among them, is given in Table 15. It will be noted that the correlations between variables are generally quite small, with the exception of the education and income intersection. Also notable is the fact that the diagonal elements have correlations of 1.0. This is not surprising, but in the factor analysis model these coefficients are called "communalities" (see the discussion of the model in Chapter III), and the fact that they are retained at 1.0 in the g Income data were reported in 1960, but reflect income for the year 19 59. 119 Table 15.— Variables Used in the Factor Analysis and the Correlation Matrix Variable 1 2 3 1. Per Cent Increase in Population 1.00 2. Per Cent of 14— 17 Year Olds in School .09 1.00 3. Median School Years Completed .28 .14 1.00 4. Per Cent Over 25 Years with Less than 5 Years Schooling -.15 -.22 -.83 5. Per Cent Unemployed -.25 .41 -.15 6. Per Cent Agricultural Workers -.32 -.09 -.70 7. Per Cent Professional and Technical Workers .46 -.04 .50 8. Non-Worker/Worker Ratio -.02 .56 -.04 9. Per Cent of Housing Units Substandard -.41 - .23 -.47 10. Per Cent of Units Built Prior to 1940 -.74 -.07 -.20 11. Average Property Tax Rate . 39 . 38 .21 12. Per Cent of Units with > 1.0 Persons Per Room .07 -.27 -.69 13. Persons per Square Mile -.08 .04 .16 14. Adult Felony Arrests per 1,00 0 Persons -.12 .15 -.12 15. Major Juvenile Arrests per 1,000 Persons .07 . 39 -.05 16. Public Assistance Payments per Capita -.45 -.16 -.47 17. Physicians per Capita .13 . 31 . 31 18. Deaths per 1,000 Persons -.31 -.23 -.28 19. Median Age -.42 -.06 .14 20. Per Cent Moving to Present Address within 15 Months .46 -.22 .04 21. Per Cent Rural -.42 -.36 -.32 22. Taxable Transactions per Capita -.02 .16 . 31 23. Median Income . 33 .41 .70 120 Table 15— Continued 4 5 6 7 8 9 10 11 12 13 00 20 1.00 72 -.09 1.00 22 -.37 -.56 1.00 29 .42 .02 -.29 1.00 21 . 35 .40 -.63 .02 17 .08 .29 -.42 -.11 12 -.05 -.33 . 26 . 27 70 .04 .49 -.27 -.34 01 -.08 -.19 .08 -.26 13 .17 .09 -.33 .11 14 .15 .08 -.12 .17 31 .22 . 38 -.21 -.01 21 .03 -.36 . 30 .09 21 .05 .17 -.09 -.36 30 .09 -.25 .07 .01 06 -.12 -.12 .15 -.28 03 .19 .22 -.35 -.03 15 -.02 -.25 .05 -.14 65 -.04 -.58 .28 .33 1.00 .28 1.00 -.51 -.27 1.00 .52 -.12 -.25 1.00 -.24 . 39 .27 -.22 1.00 .15 .20 .17 .02 .22 -.23 .01 .46 -.03 .08 .27 .20 -.37 .22 -.08 -.48 .15 .51 -.46 .53 .22 .28 -.27 .18 .13 .01 . 36 -.22 -.46 . 20 .03 -.53 -.14 .41 -.17 .69 .21 -.74 . 30 -.31 -.28 .11 .29 -.25 .57 -.40 -.22 .53 -.66 .16 121 Table 15.— Continued 14 15 16 17 18 19 20 21 22 23 1.00 .39 1.00 05 z t O 1 1.00 15 .27 -.25 1.00 01 -.12 .68 -.04 1.00 05 -.15 .48 .18 .59 1.00 01 -.09 -.21 - .12 -.19 -.43 1.00 20 -.48 .52 -.56 .41 .44 .02 1.00 41 . 32 -.10 .51 .02 .07 -.04 -.42 12 .13 -.76 .42 -.61 -.11 -.09 -.55 12 2 factor extraction process is important. The direct Principle Component technique of extracting a given number of factors through the criterion of maximum variance was used, with 1.0 as the a priori estimate of communality. Number of Factors The decision process for selection of the appropriate number of factors involved observation of the explained variance increment as additional factors were chosen. As this increment decreased, consideration was given to whether another factor should be called for. Limitation of the factors to those with eigenvalues greater than unity proved unsatisfactory, leaving factor loadings in the rotated factor matrix that were rather ambiguous. Therefore, ease of interpretation of factors is also admitted as a criterion of selection of quantity of g factors. The literature also indicates that, m general, overfactoring is preferable to underfactoring.^ Fourteen factors, or components, were chosen based on this decision process. A "factor tree" diagram is presented as Figure 5, indicating that successful division of factors occurred up to the fourteenth factor, resulting in ability to better g For an explanation of the "rules of thumb" which can be used in determining the desired number of factors, see R. J. Rummel, Applied Factor Analusis (Evanston: Northwestern University Press , 19 70), pp. 359-6 5 . 10Ibid., p. 365. 123 bJ 5S = 1 0 c *8 « o "S S3 s 2 2 m S 5 f t . M a : u M S 5 f t . M o 0 H I S it O " s S* Ik <M O *5 S 3 ; i 33 «sl f- s l 1 sa? 1sisl 124 relate a specific factor to the data it encompasses. With 16 and 18 factors, however, new factors appeared which were impossible to interpret, having no high loadings. This fact, together with the decrease in the marginal increment to explained variance (shown in Table 16), settled the number of factors at 14. The resulting factor matrix before rotation is seen as Table 17. Interpretation of Factors As explained in Chapter III, the varimax technique of orthogonal rotation of the factor matrix was applied, resulting in a rather successful (in terms of interpret- ability) rotated factor matrix. It is presented as Table 18. Twenty-seven iterations of the varimax process were required to rotate the matrix. The interpretation of the factors proceeded on the basis of the high loadings of the rotated factor matrix.^ Component 1 (or factor 1) is seen to have high loadings on the education, per cent agricultural workers, overcrowding, and income variables. The factor increases its scores as per cent agricultural workers, overcrowded housing, and per cent of persons over age twenty-five with less than five years schooling increase, while the scores decrease as income and median education increase. Thus ■'"'''Interpretation of factors is described by Rummel in his Chapter 21. Ibid., pp. 472ff. 125 Table 16.--Marginal Increment to Explained Variance with Increases in Factors Factor Cumulative Marginal Cumulative Marginal Number Proportion Increment Proportion Increment of Variance of Variance (Unrotated Factors) (After Rotation) 1 . 2789 . 2789 .1731 .1731 2 .4298 .1509 .2904 .1173 3 .5571 .1273 .3614 .0710 4 . 6667 .1096 .4200 .0586 5 . 7325 .0658 .4721 .0521 6 . 7912 .0587 .5805 .1084 7 . 8255 .0343 .6304 .0499 8 . 8525 .0270 .6798 .0494 9 . 8766 .0241 . 7337 .0539 10 . 8972 .0206 . 7853 .0516 11 .9166 .0194 . 8324 .0471 12 .9343 .0177 .8678 .0354 13 .9486 .0143 .9191 .0513 14 .9619 .0133 .9619 .0428 15 .9724 .0105 16 .9810 .0086 17 .9878 .0068 18 .9913 .0035 X 2 3 4 5 6 7 8 9 10 IX 12 13 14 15 16 17 18 19 20 21 22 23 Table 17.— ' Pactor Matrix before Rotation F 1 P2 F3 P4 P5 P6 P 7 .5 1 .6 5 - . 0 1 .0 6 - . 1 9 .22 .0 4 .4 1 - . 2 7 - .4 4 - . 4 0 - .2 8 .0 8 .1 7 .7 6 - .0 8 .4 7 - . 0 9 .2 0 .0 4 - .1 7 -.5 9 .2 4 - . 4 9 .4 7 - .1 6 - . 1 9 .0 7 *.13 - .3 5 - . 2 4 - .5 4 - .0 5 .5 0 .32 *.69 .0 6 - . 4 6 .07 - .0 7 - .3 5 - .1 1 .5 4 .2 7 .4 7 .32 - .3 3 .0 1 .0 5 .1 9 - . 2 3 - .3 3 - .7 5 - .2 5 - .0 8 - . 0 1 -.7 2 - .0 5 - . 0 8 - .3 2 - . 4 0 .1 8 .1 1 -.3 4 - . 7 0 - .0 7 .1 8 .3 1 - .3 4 .1 3 .6 8 - .0 2 - . 4 1 .12 - .2 8 - . 0 1 .08 -.6 4 .52 - .3 2 .1 9 .0 4 .2 4 .2 0 .2 8 - . 4 7 - .0 6 .58 .2 3 .05 .35 .0 4 - . 3 0 - .5 5 .1 1 .3 5 .3 1 - .3 8 .2 5 - .1 6 - .6 6 .1 1 - . 2 1 .1 5 - .3 5 -.6 6 - . 3 4 .1 1 .1 0 - .4 8 .2 3 - . 1 4 .6 1 - . 4 0 - .1 3 .32 - .0 9 .0 8 .2 9 * .51 - .3 8 .2 7 .3 8 - . 3 1 .3 1 - . 0 3 *.11 - . 7 0 .5 5 .0 3 - .2 3 .12 - .1 3 .0 3 .6 9 .0 5 .1 0 .2 4 .4 9 - . 0 1 -.7 5 - . 0 9 .4 5 - .3 1 .0 9 .1 5 .0 0 .42 - . 3 9 - . 2 0 .4 4 .2 6 .32 - : i 3 .8 7 - .0 6 - .0 2 - .2 8 .26 - .1 2 - . 0 2 . 6 .4 1 3 .4 7 2 .9 2 2 .5 2 1 .5 1 1 .3 5 .7 9 2 7 .8 9 1 5 .0 8 1 2 .7 3 1 0 .9 7 6 .5 8 5 .8 7 3 .4 3 > 8 P9 P10 P11 P 12 P13 P 14 .21 - .0 5 .0 9 - .1 5 .2 1 - . 0 4 - .0 8 .23 - .1 5 .1 4 - .4 1 - .0 5 - .0 9 .0 9 .19 .0 5 .1 0 - .0 6 .0 6 .0 6 - .0 7 .03 - .0 2 - . 0 9 - .0 3 - .1 4 - .0 4 .09 .18 .1 8 - .0 3 .1 0 - . 1 4 .0 8 - . 1 6 .08 - . 2 4 .08 - .0 9 .12 .1 0 - .0 5 .05 .0 8 - . 1 3 - . 1 0 - . 3 0 - . 0 3 .1 6 .21 - .2 7 - .0 7 .1 4 .02 - .0 5 .0 3 .17 .1 4 .0 3 - .0 5 .1 1 .0 6 .2 1 .11 .1 1 - .1 6 - .0 8 .0 5 .0 0 - .0 5 .33 .2 3 .0 9 .1 6 .0 6 .0 1 .02 .00 .1 3 .0 8 - .0 5 - . 0 1 - .0 2 .1 3 .09 - . 1 1 .15 .0 4 .0 3 - .3 2 - . 1 4 .30 - . 0 3 - .1 2 - . 1 9 - .2 6 .0 1 - .1 2 .26 .2 9 - .1 5 .0 4 .2 3 - .1 8 .0 6 .05 - .1 4 .0 8 .1 9 - .0 8 - .0 2 - .0 4 .03 - .1 6 - .3 5 .0 0 .1 5 .22 .0 8 .13 .0 9 .12 - . 2 3 .1 5 .1 9 - .0 8 .15 - .0 2 - .1 2 - .0 7 .0 5 - . 1 4 .1 0 .12 - .2 5 - .2 6 .02 .0 9 - .0 7 - .0 6 .07 - .0 5 - .0 4 - .0 2 .0 8 - .1 7 .1 4 .14 - .2 1 .2 6 .1 8 - .0 3 .1 0 .2 5 .11 .0 4 - .0 4 - .0 7 .0 1 .0 0 .1 1 .6 3 .5 5 .4 7 .4 5 .4 1 .3 3 .3 1 2 .7 0 2 .4 1 2 .0 5 1 .9 5 1 .7 7 1 .4 2 1 .3 3 ia t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Table 18.--'Rotated Factor Matrix3 F1 P2 P 3 F4 P5 P6 P 7 P8 P 9 P10 P 11 P 12 P 13 .1 4 .2 1 .1 5 .0 6 .0 6 .82 - .0 2 - .2 5 .1 9 .0 8 .1 1 .02 - . 0 3 .12 .12 .12 - . 2 7 - .0 5 - . 0 1 - .0 2 - .0 8 - .2 4 .1 1 .8 6 .0 0 - . 2 0 .9 0 .1 5 .2 0 .1 6 .0 7 .0 9 - . 0 1 .02 .1 1 .0 5 .0 5 .05 .0 0 - .9 5 - . 0 1 .0 4 .1 3 - .0 8 - .0 7 - .0 2 .0 0 .1 6 - . 0 1 - .0 5 .0 3 - . 0 7 .0 5 - . 1 0 - .1 8 - .1 7 - .0 7 - . 0 9 .0 4 .0 1 - .9 1 - . 0 1 .2 0 - .0 5 - .0 7 - .7 4 - . 0 4 - .0 3 - .0 8 - .0 2 - .2 3 .1 7 * .1 4 .1 9 - . 1 3 .0 9 - .4 6 - .0 2 .2 8 - . 0 1 .42 .2 4 .2 1 .2 9 .0 3 - .0 8 .22 .15 .02 .6 5 .1 0 .1 3 .1 0 - . 0 3 - .8 6 - .0 6 - .0 4 .16 - .1 2 - .2 2 .0 4 .2 9 - .1 2 - .0 5 - .2 8 - .0 7 - . 8 0 .02 - .1 2 - .1 6 .1 4 .1 0 - .2 3 - .1 7 - .0 9 - .1 8 .1 6 - . 1 0 - . 1 1 - .1 5 .1 4 - . 1 0 - . 8 4 - .2 7 .1 4 - . 0 1 .18 - . 0 3 - .1 8 - . 0 3 .12 .2 3 .2 7 - . 1 9 - .0 8 .1 9 - .1 8 - . 7 0 .0 0 .2 5 .0 8 .1 1 - .3 1 - . 7 7 .0 4 - .3 5 .3 0 .02 .3 1 .0 5 .0 3 - .1 3 - .1 8 - .0 7 - .0 2 .0 0 .0 7 - . 0 4 .12 .1 4 - . 1 1 - .1 8 - .8 8 - . 1 0 .0 4 .22 .0 1 .0 1 .0 1 - .0 7 .0 3 - .0 5 - . 0 4 - .9 5 - .0 7 - .0 9 - .0 3 - .0 7 .0 4 .0 4 - .0 7 - .1 7 - . 0 9 .0 7 .1 3 - .0 4 - . 1 9 - . 0 1 .0 1 - . 1 3 - .0 7 .0 9 .16 - . 0 4 - .9 2 - .3 7 - . 8 0 .05 - .1 6 .0 8 - .1 5 .07 .1 4 - . 1 9 - .1 9 - . 1 0 - .0 2 .0 0 .2 2 .0 1 .2 3 - .0 5 - .0 5 - .0 5 - .2 6 - .1 3 - .0 2 .8 4 .1 1 .0 9 - .1 2 - . 1 7 - .8 7 - . 1 0 .3 3 - .0 4 - . 1 0 - . 0 4 - .0 8 - .0 1 .0 8 - . 0 1 - . 1 0 .0 8 .3 7 - .7 6 - . 1 3 - . 1 3 .0 0 - .3 5 - . 1 4 .1 0 .07 .1 0 - .0 2 .22 .0 3 - . 0 9 .22 - . 0 9 .1 7 - .0 6 .76 .0 1 .4 6 - . 0 4 .07 - .2 1 .02 .0 0 - . 0 9 - .4 5 - .5 9 - . 0 9 .1 3 - .1 3 .0 9 .3 8 - .0 8 - . 2 9 - .1 5 .0 1 .25 .1 9 - . 0 1 .1 0 .0 9 - . 2 3 - .0 3 - .2 9 - .0 5 .0 1 .2 0 .0 4 - . 0 1 - .1 6 .6 8 .52 .0 5 - .1 7 - . 1 3 .0 4 -.0 5 * - .2 5 .1 1 .1 6 .22 .1 0 - .0 3 3 .9 8 2 .7 0 1 .6 4 1 .3 5 1 .2 0 2 .5 0 1 .1 5 1 .1 4 1 .2 4 1 .1 9 1 .0 9 .8 1 1 .1 8 1 7 .3 2 1 1 .7 4 7 .1 1 5 .8 7 5 .2 2 1 0 .8 5 4 .9 9 4 .9 4 5 .3 9 5 .1 6 4 .7 1 3 .5 4 5 .1 3 1 0 , 1 2 , an d 13 a r e r e f l e c t e d . 128 larger values of the scores would have a negative effect on well-being, were it not for the ability to "reflect" the factor. This means that each of the coefficients in the factor vector can be multiplied by minus one without affecting the factor’s ability in explaining variance, and without affecting any other factors. Accordingly, 12 component 1 is reflected, so that its scores increase with increasing education and income and decrease with increasing overcrowding, per cent employed in agriculture, and per cent over twenty-five with less than five years schooling. Since the educational loadings are highest but income is also important, this is called the Education- Income Component. Interestingly enough, it retains the close association between educational levels, income, and overcrowded housing in spite of efforts to separate them by additional factor extractions. Factor 2 is interpreted as the Physical Welfare Component of well-being. It contains negative loadings on the age variable, on deaths per 1,0 00 persons, and on public assistance payments per capita. Thus, it has a positive effect on overall welfare, for its scores will increase with lower levels in these variables. The Housing Quality Component is the interpretation 12 Ibid., p. 4-7 8. Also see Harry H. Harman, Modern Factor Analysis (2nd ed., revised, Chicage: University of Chicago Press, 1967), p. 174. 129 given to the third factor extracted, since it has a high value for substandard housing. This value is negative, however, so that the factor will give higher factor scores where lower levels of substandard housing exists. Factor 4 - is called the Dependency Component, for its only high loading is on the non-worker-to-worker ratio. Again, the loading is negative and an increase in the factor score is beneficial. Factor 5 is the Adult Crime Component, with all loadings insignificant except for the adult felony arrest variable, with a high negative loading there. Factor 6 is called the Mobility-Growth Component. The loadings in the rotated factor matrix for this component are definitive, with high loading on the per cent of persons moving to present address within 15 months (mobility), change in population from 1950 to 1960 (growth), and negatively on the per cent of housing units built prior to 1940. The Population Density Component of well-being is interpreted from Factor 7. Its only high loading is on persons per square mile. The effect of increasing population density is negative. The Property Tax Component (Factor 8) represents the decrease in economic well-being brought about by increasing taxation (ceteris paribus). The only high 130 loading here (negative) is on the property tax rate per $100 assessed valuation variable. Since state law sets assessed valuation at 25 per cent of market value, this component is assumed to perceive differences in well-being among counties. The factor’s scores will increase as the tax rate decreases over the cross-section of counties. Factor 9 is interpreted as the Unemployment Component. Its only high loading is negative, on the unemployment rate variable. Factor 10 is called the Medical Services Component, although it only represents differences in numbers of physicians per capita. It is reasonable to believe, however, that the presence of other medical services is coordinated with the presence of physicians. The loading is negative but increases in physicians per capita is believed beneficial. The factor was therefore reflected; that is, all the loadings were multiplied by minus one. Factor 11 is the Youth Education Component of well-being. Only variable two, per cent of 14 to 17 year olds in school, had a significant loading. Factor 12 represents the Professional-Technical Employment Component, where the highest of the variable factor-coefficients was on the per cent of employed persons classified as professional and technical. The loading was negative; hence the factor was reflected. 131 The Juvenile Crime Component is shown as Factor 13. It is easily interpreted with the loading on major juvenile arrests per 1,00 0 persons being 0.9 2 and all other loadings near zero. Since crime is assumed to be a detriment to well-being, the entire factor was reflected, producing a detraction from well-being as juvenile crime loadings increase. The last factor is the Consumption Component of well-being. Its only high loading is on self-assessed taxable transactions per capita. As transactions increase, the factor score will increase. As is noted in Chapter III, the transactions exclude food purchases, but are perhaps representative of differences in consumption among the counties when standardized. Communality and Explained Variance Returning to Table 17, it will be noted that the 2 factor matrix contains a column entitled h . This is the communality, or the per cent of the variance in a variable explained by the extracted factors. Each variable has a 2 high h , the lowest being variable one at 9 0.59 per cent. The component model used here allows for all of the variance to be explained when the number of factors is equal to the number of variables, which is twenty-three. Fourteen factors, however, have explained 96.19 per cent of total variance. 132 The rotated factor matrix (Table 18) has changed the loadings and thus the per cent of variance explained by- individual factors. (However, the explained variance within fourteen factors is the same for both the rotated matrix and .the factor matrix before rotation.) The explained variance and the explained variance as a per cent of total variance are given across the bottom of the table. Factor Scores and the Index of Well-Being Each of the coefficients in the factor matrix was used in the procedure of transforming the standardized variable values to derive the factor scores by county. The matrix manipulation for this process was shown in Chapter III. The factor scores for the 14 factors and 5 8 counties are shown in Table 19. Also shown are the totals of the weighted factor scores, weighted according to their relative contribution to the explanation of total variance for each county. This is the well-being index. Table 2 0 presents the counties by their ranking in the well-being index. The process used for weighting the factors for the well-being index is as follows. First, each standard ized factor score (shown in standard deviation units) was multiplied by the weighting for the rotated factor vector to which it belongs. Each factor vector’s weighting is Table 19.— Factor Scores for Each County and Sums of Weighted Factor Scores C o u n ty F i F2 F 3 F 4 P5 F6 P 7 f b F 9 F 10 F 11 F 12 F13 F , . £ F , .W. 14 k } 3 A lam eda .5 0 .3 9 1 .0 0 .88 .02 - 1 .1 6 .4 1 - 1 .4 7 - .2 6 .9 8 - .5 7 .6 3 - .4 8 .8 3 .1 2 6 A lp in e - 3 .7 8 - 2 .4 4 .6 1 4 .1 5 1 .5 1 1 .2 0 - .1 7 .0 1 1 .3 5 - .8 6 - 1 .9 6 1 .3 2 1 .0 5 - .9 2 - .4 7 3 Amador - .0 3 1 .6 5 - .1 4 - 1 .7 8 1 .7 8 - 1 .1 6 - 1 .1 4 3 .4 4 .3 7 - 1 .6 1 .2 8 2 .5 5 .3 1 - .0 5 .217 B u tte .2 4 - 1 .2 5 1 .0 4 - .5 7 - . 5 1 .1 1 .5 3 - .3 5 -1". 78 .1 4 - .2 8 .4 4 .6 0 .3 6 - .1 4 7 C a la v e r a s .45 - 1 .1 0 - . 6 1 - .8 1 - 2 .6 9 .2 9 - . 7 0 1 .1 4 .9 7 - .9 4 .82 .56 1 .7 4 - 2 .3 0 - .1 8 4 C o lu s a .2 7 - . 7 9 - .8 6 .4 0 - . 1 0 - 1 .3 7 .7 4 - - .0 9 1 .9 5 - 1 .1 6 1 .2 9 - 2 .1 9 - . 8 0 .7 4 - .1 9 3 C o n tra c o s t a .75 .9 8 1 .4 3 - .1 1 .7 4 - . 4 4 - .4 8 - 1 .9 7 - . 2 0 - 3 .6 4 .1 3 1 .4 9 - .5 6 - . 5 0 .0 2 0 D e l N o rte .1 9 .3 0 - 2 .5 7 .16 - .1 2 2 .1 0 - . 9 1 - 2 .0 4 - . 3 0 - 1 .3 9 .2 4 - .9 7 - .6 6 - .0 6 - .1 8 3 E l D orado .8 6 - .1 2 - 1 .0 5 - .4 6 - .3 5 1 .8 0 - .7 7 1 .2 9 .0 9 - .8 1 .42 - .1 5 - .1 7 .2 6 .222 F re s n o - 1 .0 2 .4 5 .66 - .5 5 - .5 1 - .2 2 .5 0 - .0 5 - .5 2 - .1 4 - . 0 3 - .2 1 .57 1 .2 6 - .1 0 2 G len n - .0 7 .1 3 .1 6 .5 3 .55 - 1 .1 4 .4 0 .3 9 1 .0 2 - . 1 1 1 .2 5 - 2 .3 9 1 .2 9 .22 .092 H um boldt .0 3 .6 8 - 1 .1 1 - .2 5 .2 9 .4 6 - . 1 3 - 1 .4 2 - .5 2 .0 6 - .3 2 - .4 5 .63 1 .1 4 .0 0 4 I m p e r ia l - 2 .7 2 1 .2 4 - 1 .4 9 .1 9 - 2 .6 3 - .3 2 .3 4 - .2 3 1 .0 6 .3 0 .32 .4 5 - 1 .1 3 .3 4 - .5 4 8 In y o .6 4 - . 6 4 - 2 .0 7 .8 1 - . 2 0 - .3 1 .8 0 .8 0 .7 1 - . 0 1 .7 8 1 .6 0 - 1 .6 7 1 .5 3 .086 K ern - .8 2 .72 .5 1 - .5 1 - .3 3 .3 0 .4 5 - .3 1 - . 6 0 - . 3 0 - .1 3 .2 3 .9 8 1 .3 9 .037 K in g s - 1 .9 6 .5 3 - .5 4 - . 8 0 - .6 7 - . 7 0 .3 9 - .5 8 - . 2 3 .25 .4 3 - .3 2 .98 .4 0 - .4 2 3 L ake .1 7 - 3 .5 0 .0 0 - 2 .4 3 1 .1 3 .4 8 - .2 5 .3 4 .3 1 .02 - .1 5 .0 0 - 1 .0 6 - . 1 1 - .4 7 6 L a s s e n .3 3 .9 0 - .3 6 1 .0 4 1 .3 0 - 2 .2 1 .1 8 - . 0 4 - 2 .2 6 - .3 3 - . 0 1 .5 6 - .8 3 - .7 8 - .1 6 7 Los A n g e le s .82 .0 3 1 .4 7 .8 9 - 3 .1 8 - . 4 0 1 .0 2 - .5 5 .35 .1 1 - .0 1 1 .0 4 - . 2 0 .6 0 .199 M adera - 2 .1 5 - . 0 4 .12 - 1 .8 9 - 1 .4 3 - .0 4 .1 8 .1 9 - . 1 9 - .8 9 - .2 1 .1 9 - .6 7 .6 9 - .6 2 8 M arin .9 3 .92 .3 0 .3 0 .5 7 - .2 5 1 .0 1 - .6 5 1 .6 5 2 .2 3 .6 6 1 .6 3 .6 0 - . 6 1 .6 5 1 M a rip o s a .5 0 - 2 .5 7 .72 .4 0 .8 0 - .0 7 .6 4 .92 - . 5 1 - .6 1 .6 4 1 .1 7 .95 1 .2 4 .0 8 9 M endocino - .2 5 .0 9 - 1 .0 5 - .8 5 .39 - .1 7 - . 0 3 - . 6 5 - .4 3 .42 - .2 3 .95 - .3 9 - .3 3 - .2 1 0 M erced - 1 .5 1 .9 3 .1 1 - 1 .1 5 .3 3 .1 3 - .4 4 - .1 3 .0 5 - .5 6 - .0 9 - .9 4 .97 - . 1 0 - .2 3 6 Modoc .82 - . 2 0 - .7 7 1 .5 4 .6 5 - 1 .7 8 .7 1 - .0 9 .48 - . 9 0 .9 9 - 2 .1 6 - .7 1 .06 - .0 5 9 Mono 1 .8 3 .2 9 - 1 .7 4 .5 9 - .3 3 - . 0 4 .5 1 1 .2 4 1 .5 9 - 1 .8 5 - 3 .6 5 - . 2 9 1 .0 7 2 .5 6 .312 M o n tere y .1 8 1 .3 5 .5 0 1 .0 8 .1 4 .84 - .1 7 2 .0 3 - .1 7 .6 3 - 1 .0 5 - .8 5 - 2 .3 5 - 1 .2 1 .2 6 1 N apa .3 1 - . 3 3 - . 4 0 - 1 .4 9 .4 7 - .4 3 .12 - . 8 3 1 .5 4 .9 5 .42 1 .3 5 1 .1 9 - .7 7 .0 7 3 N evada .87 - 1 .8 1 .4 0 .6 3 - 2 .3 1 - .6 7 .42 .4 4 - 1 .5 8 - . 2 9 .5 3 1 .1 1 - . 3 4 - 1 .1 1 - .2 5 8 133 Table 19. -continued C o u n ty p i P2 F3 F4 FS F6 F7 FS P9 F10 F 11 P X2 PX3 14 ^ k j 3 O ran g e 1 .0 3 .4 3 .9 4 - . 0 3 - . 7 0 2 .7 0 - . 9 1 - .7 2 1 .2 6 - .1 6 .67 - 1 .1 3 - .1 9 - 1 .4 5 .467 P l a c e r .12 - . 0 4 .82 - . 5 0 .52 .2 1 .02 .0 1 .3 3 .1 4 .32 1 .0 4 - 1 .3 5 - . 1 3 - .0 6 9 P lum as .6 3 .3 5 - . 4 1 1 .2 5 - .6 9 - 1 .1 6 .4 0 1 .5 0 - 2 .0 6 .9 1 .4 9 .1 3 1 .2 8 - .7 6 .1 2 9 R iv e r s i d e .2 3 - . 1 9 .66 .0 4 .2 1 1 .2 6 .02 .4 3 .1 8 - .0 2 .12 - . 7 3 - 1 .0 3 - .2 5 .1 6 9 S a c ra m e n to .5 9 .4 7 .82 .4 0 .1 4 .6 5 .2 7 - . 9 4 .1 3 - . 3 0 .2 1 .3 1 .4 5 1 .1 1 .382 San B e n ito - 1 .3 7 .5 3 - .6 5 .4 4 .6 3 - 1 .5 6 .0 7 - .6 0 1 .0 2 1 .1 0 1 .2 2 - 1 .1 3 .3 3 - 1 .2 4 - .2 1 4 S an B e rn a rd in o .4 6 .1 6 .9 6 - . 0 1 - .1 6 .58 - .2 2 - . 2 9 - .1 6 - . 7 0 - .2 9 - .2 2 - 1 .7 5 - 1 .0 3 - .0 0 4 San D ieg o .6 9 .9 0 1 .2 2 .75 .25 1 .2 1 .0 3 .4 0 - .4 6 .3 1 - .7 5 - .0 2 - .7 6 - . 3 0 .4 4 1 S an F r a n c i s c o .3 1 - . 5 0 .5 4 .9 9 - . 8 0 - 1 .4 4 - 6 .6 4 - .3 2 .12 1 .5 6 .0 8 - .0 6 .1 4 1 .8 4 - .2 8 9 S an J o a q u in - .8 3 .2 0 .12 - . 4 4 .6 4 - . 7 0 .02 - 1 .1 4 - . 3 3 .12 - .7 2 .3 0 - 1 .8 2 - . 0 1 - .3 8 0 S an L u is O b isp o - . 0 1 - . 4 0 .3 0 - .9 7 .5 3 1 .0 3 .0 9 .4 1 .3 9 1 .0 8 - .0 5 - .4 8 .72 .1 9 .1 9 1 San M ateo 1 .0 3 .72 .67 .0 3 1 .0 9 .0 9 .1 9 - 1 .8 0 1 .5 4 .15 .5 0 .57 .2 1 .5 8 .4 9 1 S a n ta B a rb a ra .3 1 .7 0 .1 3 .2 1 .6 4 .9 5 .5 3 1 .6 4 1 .2 5 2 .2 2 .2 4 .18 .2 6 .9 0 .6 7 7 S a n ta C la r a .2 8 .8 3 .9 6 .0 9 .6 0 .8 9 .6 0 - .5 1 .62 1 .0 6 .4 9 1 .2 7 .1 6 .5 7 .5 6 3 S a n ta C ru z .3 4 - 1 .8 6 .2 7 - . 8 1 .3 0 - .3 5 .2 7 - . 1 0 .5 8 1 .4 3 - .2 6 - .4 5 - 1 .7 3 - .6 1 - .2 4 9 S h a s ta .2 6 .1 0 - .2 7 - . 0 1 - . 0 1 .8 1 .58 - . 1 0 - 1 .5 6 .2 5 .32 - . 2 1 1 .4 3 1 .8 4 .246 S i e r r a 1 .1 2 .1 9 - .7 7 - 1 .2 1 - . 6 0 - 1 .5 7 .0 7 - .6 2 .3 8 .8 8 - 4 .8 1 - .7 5 1 .1 4 - 2 .3 4 - .3 7 6 S is k iy o u .3 6 - .0 8 - . 6 1 .7 6 - .2 3 - 1 .1 9 - .0 8 - . 1 0 - .1 8 - . 4 0 .3 4 - .0 2 - 1 .0 9 - . 9 0 - .2 1 5 S o la n o .4 5 1 .0 7 1 .1 2 .5 4 .58 .0 7 .0 1 - . 0 9 - .7 8 - .1 2 - . 1 3 - .8 6 .8 6 - .8 2 .286 Sonoma .0 4 - .6 2 .1 3 - . 4 9 .1 4 - . 0 9 .4 4 - .8 4 .2 9 1 .3 0 .1 0 - . 3 3 .6 7 - .2 2 - .0 3 2 S t a n i s l a u s - . 8 3 - . 4 1 .6 4 - 1 .2 1 .3 3 - . 2 9 .1 3 - . 8 0 - 1 .0 9 .22 - .6 8 - .1 4 - .3 3 .3 3 - .3 5 1 S u t t e r - .2 6 .2 6 1 .7 3 - . 5 0 1 .1 2 - .1 5 - .3 2 1 .0 8 - .2 5 - 1 .3 3 .6 6 - 1 .5 1 1 .3 6 - . 7 0 .0 9 7 Tehama .3 3 - . 4 1 .0 5 - . 0 9 .2 1 .1 0 .12 .12 - .4 2 - .0 7 .2 5 - 1 .4 0 .4 5 - .1 2 - .0 0 4 T r i n i t y .0 7 .4 1 - 3 .4 0 .8 3 .9 8 1 .7 3 - .4 6 - .7 7 - 2 .1 6 .6 9 .8 3 .9 4 1 .3 6 - 1 .6 1 .0 3 9 T u la r e - 1 .9 1 .3 3 .22 - 1 .0 3 .3 1 - .4 3 - .0 7 .0 0 - .4 2 - . 1 1 - .3 3 - .3 6 - . 7 1 - .1 5 - .4 9 0 T uolum ne .7 8 - 1 .5 1 - . 5 1 .0 9 .7 7 - . 2 9 .1 5 - . 6 0 - .9 8 - .3 7 .5 5 - . 0 3 .22 .2 0 - .1 1 8 V e n tu ra - .1 2 .9 7 .3 3 - .0 4 - . 0 1 .8 5 - .1 8 .6 8 .7 0 - .1 7 .1 8 .5 3 - .7 8 - .6 2 , .2 2 9 Y o lo - .0 2 .6 6 1 .0 4 .72 - 1 .9 1 .3 4 .32 .3 6 .0 8 - .7 2 .65 .2 3 .8 8 - . 4 9 .2 0 0 Yuba - . 4 4 .1 3 .0 9 .1 9 - . 2 0 1 .3 2 .4 1 1 .7 5 - 1 .9 4 1 .3 3 - .7 7 - 1 .1 4 - 1 .3 0 1 .4 2 .0 8 0 tiST 135 Table 20.— The Index of Well-Being for the Counties of California Rank County Index Rank County Index 1 Santa Barbara .678 30 Humboldt -.927 2 Marin .651 31 Tehama -.859 3 Santa Clara . 563 32 San Bernardino -.004 4 San Mateo . 491 33 Sonoma -.032 5 Orange .467 34 Modoc -.059 6 San Diego .441 35 Placer -.069 7 Sacrament . 382 36 Fresno -.102 8 Mono . 312 37 Tuolumne -.118 9 Solano . 286 38 Butte -.147 10 Monterey . 261 39 Lassen -.167 11 Shasta . 246 40 Del Norte -.183 12 Ventura .229 41 Calaveras -.184 13 El Dorado . 222 42 Colusa -.19 3 14 Amador . 217 43 Mendocino -.210 15 Yolo . 200 44 San Benito -.214 16 Los Angeles .199 45 Siskiyou -.215 17 San Luis Obispo . 191 46 Merced -.236 18 Riverside .169 47 Santa Cruz -.249 19 Plumas .129 48 Nevada -.258 20 Alameda .126 49 San Francisco -.289 21 Sutter .097 50 Stanislaus -.351 22 Glenn .092 51 Sierra -.376 23 Mariposa .089 52 San Joaquin -.380 24 Inyo .086 53 Kings -.423 25 Yuba .081 54 Alpine -.473 26 Napa .073 55 Lake -.476 27 Trinity .039 56 Tulare -.490 28 Kern .037 57 Imperial -.548 29 Contra Costa .020 58 Madera -.628 U = 0.0 a = .300 8 136 derived from its importance relative to other factors in explaining variances in the data; that is, the per cent of total variance explained by the factor was divided by the explained variance percentage for all factors with the resulting quotient being the factor's weight. For example, factor 1 explains 17.32 per cent of total variance; explained variance due to all fourteen factors is 96.19 per cent; therefore, the weight of factor 1 is i7.32 _ i«m 96.19 " *1801- Similarly, factor 2 has a weighting of 11.74- 96 .19 .1221 and so forth. Next the weighted scores were summed. In considering n counties, n = 1, 2, ..., k and p factors, p = 1, 2, ..., j, and allowing Wp to represent the weights spoken of, the weighted factor score totals can be shown as WIk = £ Fkj ^ which is the comparative well-being index for each of the 58 counties. Further County Comparisons In addition to examining the differences in the overall well-being index, the factor analysis makes 137 possible the comparison of the counties with respect to each of the 14- independent components individually. Accordingly, the counties have been ranked with respect to 13 their scores in each of the components. The Education- Income, Physical Welfare, Housing Quality, and Mobility- Growth Components are of special interest, and the ranked counties are shown in Tables 21 through 24, respectively. These four factors account for 47 per cent of the variance in the data set. Another method of making comparisons among the counties is to assess the affect of each of the components on the well-being index. That is, it may be interesting to note that certain counties would have been higher in the well-being rankings, except for a poor performance on one particular factor. San Francisco, for example, received a heavy negative score in population density, and except for that component, would have had a much higher rank in the well-being index. Figures 6 through 11 illustrate some of the most interesting of these comparisons. The Effect of Income Inequality on Well-Being The first section of this chapter presented the 13 Note, however, that the rank of a county m a variable does not necessarily carry over to a factor which has high loadings in that variable. The factors have become mutually independent; this is not the case among variables. 138 Table 21.--The Education-Income Component in the 5 8 Counties of California Rank County Score Rank County Score 1 Mono 1. 834 30 Shasta . 260 2 Sierra 1.120 31 Butte .236 3 San Mateo 1.036 32 Riverside .232 4 Orange 1. 031 33 Del Norte .189 5 Marin .931 34 Monterey .182 6 Nevada . 868 35 Lake .170 7 El Dorado . 856 36 Placer .121 8 Modoc . 822 37 Trinity .066 9 Los Angeles . 817 38 Sonoma .043 10 Tuolumne .780 39 Humboldt .031 11 Contra Costa .747 40 San Luis Obispo .005 12 San Diego .686 41 Yolo -.017 13 Inyo .637 42 Amador -.028 14 Plumas .631 43 Glenn -.072 15 Sacramento .587 44 Ventura -.120 16 Alameda .499 45 Mendocino -.254 17 Mariposa .496 46 Sutter -.264 18 San Bernardino .461 47 Yuba -.445 19 Calaveras .454 48 Kern -.820 20 Solano .453 49 Stanislaus -.826 21 Siskiyou . 365 50 San Joaquin -.832 22 Santa Cruz .335 51 Fresno -1.024 23 Tehama . 332 52 San Benito -1.369 24 Lassen . 328 53 Merced -1.514 25 San Francisco . 315 54 Tulare -1.919 26 Napa . 308 55 Kings -1.958 27 Santa Barbara . 307 56 Madera -2.151 28 Santa Clara . 277 57 Imperial -2.717 29 Colusa .271 58 Alpine -3.781 y = 0.0 a = 1.0 139 Table 22.— The Physical Welfare Component in the 58 Counties of California Rank County Score Rank County Score 1 Amador 1. 651 30 Sierra .188 2 Monterey 1. 346 31 San Bernardino .158 3 Imperial 1.237 32 Glenn .129 4 Solano 1.073 33 Yuba .127 5 Contra Costa .981 34 Shasta .096 6 Ventura .974 35 Mendocino .090 7 Merced .935 36 Los Angeles .027 8 Marin .920 37 Madera -.036 9 San Diego .905 38 Placer -.037 10 Lassen .901 39 Siskiyou -.084 11 Santa Clara . 832 40 El Dorado -.124 12 San Mateo . 722 41 Riverside -.189 13 Kern .721 42 Modoc -.201 14 Santa Barbara . 704 43 Napa -.332 15 Humboldt .679 44 San Luis Obispo -.400 16 Yolo .657 45 Stanislaus -.411 17 Kings .531 46 Tehama -.413 18 San Benito .528 47 San Francisco -.504 19 Sacramento .474 48 Inyo -.640 20 Fresno .454 49 Colusa -.786 21 Orange .433 50 Sonoma -.824 22 Trinity . 414 51 Calaveras -1.101 23 Alameda . 394 52 Butte -1.247 24 Plumas . 352 53 Tuolumne -1.508 25 Tulare . 335 54 Nevada -1.813 26 Del Norte . 303 55 Santa Cruz -1.861 27 Mono . 286 56 Alpine -2.439 28 Sutter .258 57 Mariposa -2.565 29 San Joaquin .19 8 58 Lake -3.503 ] i = 0.0 a = 1.0 m o Table 23.— The Housing Quality Component in the 5 8 Counties in California Rank County Score Rank County Score 1 Sutter 1.729 30 Sonoma .133 2 Los Angeles 1.466 31 Madera .121 3 Contra Costa 1.433 32 San Joaquin .119 4 San Diego 1. 220 33 Merced .115 5 Solano 1.121 34 Yuba .096 6 Yolo 1.042 35 Tehama .053 7 Butte 1.041 36 Lake .000 8 Alameda 1.003 37 Amador -.143 9 San Bernardino .965 38 Shasta -.267 10 Santa Clara .963 39 Lassen -.358 11 Orange .936 40 Napa -.396 12 Stanislaus . 837 41 Plumas -.408 13 Sacramento . 824 42 Tuolumne -.514 14 Mariposa . 722 43 Kings -.548 15 San Mateo .673 44 Siskiyou -.612 16 Riverside .660 45 Calaveras -.615 17 Fresno .658 46 San Benito -.651 18 Alpine .607 47 Sierra -.770 19 San Francisco .545 48 Modoc -.774 20 Kern .514 49 Placer -.824 21 Monterey . 504 50 Colusa -.864 22 Nevada .402 51 Mendocino -1.050 23 Ventura . 333 52 El Dorado -1.050 24 San Luis Obispo . 304 53 Humboldt -1.113 25 Marin . 299 54 Imperial -1.492 26 Santa Cruz . 269 55 Mono -1.738 27 • Tulare . 222 56 Inyo -2.069 28 Glenn .162 57 Del Norte -2.566 29 Santa Barbara .134 58 Trinity -3.405 y = 0.0 a = 1.0 •141 Table 24.--The Mobility-Growth Component in the 5 8 Counties of California Rank County Growth Rank. County Growth 1 Orange 2.698 30 Sonoma -.099 2 Del Norte 2.099 31 Sutter -.151 3 El Dorado 1.796 32 Mendocino -.166 4 Trinity 1. 732 33 Placer -.214 5 Yuba 1. 323 34 Fresno -.219 6 Riverside 1.262 35 Marin -.246 7 San Diego 1.208 36 Stanislaus -.289 8 Alpine 1.203 37 Tuolumne -.289 9 San Luis Obispo 1.033 38 Inyo -.307 10 Santa Barbara .940 39 Imperial -.316 11 Santa Clara . 89 3 40 Santa Cruz -.346 12 Ventura . 845 41 Los Angeles -.401 13 Monterey . 841 42 Napa -.426 14 Shasta . 814 43 Tulare -.432 15 Sacramento .647 44 Contra Costa -.438 16 San Bernardino .583 45 Nevada -.667 17 Lake .480 46 Kings -.704 18 Humboldt .457 47 San Joaquin -.705 19 Yolo . 341 48 Glenn -1.138 20 Kern . 298 49 Alameda -1.157 21 Calaveras .286 50 Plumas -1.157 22 Merced .127 51 Amador -1.159 23 Butte .114 52 Siskiyou -1.193 24 Tehama .105 53 Colusa -1.368 25 San Mateo .094 54 San Francisco -1.438 26 Solano .073 55 San Benito -1.562 27 Mono -.038 56 Sierra -1.566 28 Madera -.042 57 Modoc -1.775 29 Mariposa -.069 58 Lassen -2.209 y = 0.0 a = 1.0 Standard Deviations from the Mean 142 2.0 1.0 0.0 1 I I I i I 1 2 3 4 5 6 7 8 9 10 II 12 13 14 - 1.0 - 2.0 County Figure 6.— Component Scores for Santa Barbara Standard Deviations from the Mean 143 10 11 -1 -2 -6 Figure 7.— Component Scores for San Francisco County Figure 8.— Component Scores for Los Angeles County Standard Deviations from the Mean i i i CO K> H O I — > 1 1 1 H 1 ro ] CO -P Cn ■<! 00 CO H o 3 I H N3 H H 3 H CO H -P tltll Standard Deviations from the Mean 145 14 10 11 12 13 -1 -2 -3 Figure 9.— Component Scores for Marin County Standard Deviations from the Mean 3 146 Figure 10.— Component Scores for Madera County Standard Deviations from the Mean 147 13 10 11 12 14 -1 -2 -3 Figure 11.— Component Scores for Imperial County 14 8 results of the income inequality measurements which have been made for the counties of California. Then the outcome of the factor analytic method of measuring well-being was shown, and the counties were ranked on the well-being scale which was taken as the sum of the weighted factor scores. The next step in the analysis is to determine the degree and type of relationship that exists between income inequality and well-being. It will be recalled that the hypothesis developed in Chapter I is that an inverse relationship exists between income inequality and well-being. This disserta tion lends little support to that hypothesis. Although a negative linear correlation does in fact seem to exist, the strength of the relationship is such that one must qualify any judgments made on the basis of it. A scatter diagram of the relationship is shown in Figure 12. The coeffi cients of determination for the curve types fitted to the data are shown in Table 25. Thus the linear form most closely approximated the data, but only ten per cent of the variations in the well being index were associated with changes in income inequality. The hyperbolic forms were less efficient and the exponential forms were not able to be fit to the data at all. The linear equation which minimizes the squares of the deviations is Index of Well-Being 149 O.81- 0 n 5a.n+«. 8 * rb * rd u ' ' “ /v ja lr in • 0 . 6 — S a n i* . C{*-r-o. O r Al cTe o • 5xr> Die-g<j 0.4 0.0 5a.cy-AMi<n - f ’ o M ovlo ° ‘ 3 I" , * ( . ? . „ '’ "'‘ S'- /.I. L., 0 . I — • Dorvudo • 3ftn Luis Obl5f>«» A tm e-d n ^.vers'iie- 0.1- p/a.pa. * 9 ff(ey\>i Mariposa. T r m 'i +y • v • 5«rTer • • C o n ^ o s t * ^ ■Sa-w # X nyo • K<*-n • Fresno -.l|- ## ^(»cer • L a » e * ’■•'"‘“ "‘’“ -6.iw.rt,. « 714 C o l US* - . 2 |- C . U ^ « ; ^ " ' ^ t r e e d S 4 H . v . u M e n i o t m o • ^ • Sanh. Cruz O | /vCV«-d«. • “ • O p“ ^ F r o . r % t lito S,. er r a ' *ar, J o j v ' * S t a n IS I*US -.4|— A l p ' i . a-Ke. -.5 -.6 -.7 -.8 X m pena.1 T u I« .y e Mo.de r«. J I I I I I I I I I I L Gini Index of Inequality Figure 12.— Scatter Diagram of Income Inequality and the Well-Being Index 150 Table 25.— Curve Types and Coefficients of Determination for the Gini Index and Well-Being Relationship Curve Type Curve of Determination WI WI = a e a + b(L) b (L) -0.097 no fit WI = a (L) no fit WI = a + Try 0.076 WI a + b(L) 0 .0001 WI (L) a + b(L) 0.00005 151 WI = 1.04 - 2.97 (L) . The standard error of estimate of the regression line is .291. Figure 13 shows the regression line along with perimeter lines drawn at the regression line level plus and minus two standard errors of the estimate, thus encompassing 95 per cent of the observations. This wide interval resulted in uniformly bad prediction capability for the model, with calculated levels of the well-being index showing values far from the actual values. In addition to testing the relationship of the absolute values of the well-being index (WI) and the Gini index (L), the ranks of the counties in these two dimen sions were also examined. Table 2 6 shows the paired rankings, and the Spearman coefficient of rank correlation between the two series is r a2 P = 1 ----------- = - .329 n(n - 1) where d = the difference in rank of a given county in WI and L. Again the general lack of association (and certainly the lack of causation) is demonstrated, since only 3 3% of the WI rankings are explained by the Gini rankings. Empirically, there is little justification found in the data for the counties of California to support the Index of Well-Being 152 . 8 .7 . 6 .5 .4 .3 2 .1 .0 .1 . 2 . 3 .5 .6 . 7 8 00 C M rH 00 LO 00 CO CD CSI O CO CD CO CD O ' CO CO H CM 00 • = t " r j - J- 00 CO O J- c r > oo Gini Index of Inequality Figure 13.— The Line. of. Regression for Income' Inequality and Well-Being and the 9 5 Per Cent Confidence Interval 153 Table 26.--Rankings of the Counties of California in the Gini Index of Income Inequality and in the Index of Well-Being „ . Gini WI „ Gini WI oun ^ Rank Rank oun ^ Rank Rank Madera 1 58 Mariposa 2 23 Lake 3 55 Tulare 4 56 Colusa 5 42 Merced 6 46 Santa Cruz 7 47 Kings 8 53 Glenn 9 22 Imperial 10 57 Stanislaus 11 50 Santa Barbara 12 1 San Francisco 13 49 San Benito 14 44 Fresno 15 36 Monterey 16 10 Riverside 17 18 Sonoma 18 33 San Luis Obispo 19 17 Los Angeles 20 16 Modoc 21 34 Sutter 22 21 Mendocino 23 43 San Joaquin 24 52 Kern 25 28 San Diego 26 6 Butte 27 38 Nevada 28 48 Marin 29 2 San Mateo 30 4 Yuba 31 25 Alameda 32 20 Tehama 33 31 Humboldt 34 30 Ventura 35 12 El Dorado 36 13 Shasta 37 11 Orange 38 5 Alpine 39 54 Mono 40 8 Del Norte 41 40 Siskiyou 42 45 San Bernardino 43 32 Napa 44 26 Placer 45 35 Santa Clara 46 3 Contra Costa 47 29 Solano 48 9 Sacramento 49 7 Calaveras 50 41 Yolo 51 15 Inyo 52 24 Tuolumne 53 37 Amador 54 14 Plumas 55 19 Lassen 56 39 Sierra 57 51 Trinity 58 27 154 hypothesis that well-being varies in close inverse association with income inequality. Additional investigations were conducted into the relative importance of each of the elements in the well being index as it relates to income inequality. This model was of the form Fj = f (L) , j = 1, 2, ..., 14 where F. = the components of well-being individually L = the Gini index . As can be seen in Table 27, few of the components of well being were significantly related to income inequality. The Education-Income Component was most closely related, but the square of the correlation coefficient was only 0.16 7. Other significant components, in the order of the absolute value of their beta coefficient, are Professional-Technical Employment, Consumption, and Dependency. The value of t for significance at the five per cent level is 2.00 using n - 2 = 56 degrees of freedom. This means that more trust can be placed on those relationships for which t is equal to or greater than 2.00. The beta coeffients rank the relationships by their relative degree of correlation. On close inspection, it will be noted the beta coefficient for two-variable regressions is equal to 155 Table 27.--The Relationship of Individual Well-Being Components to the Gini Index of Income Dispersion Component R2 t 3 1. Education-Income .167 CO • 00 1 -.408 2. Physical Welfare .060 -1. 88 -.244 3. Housing Quality .054 1.79 .233 4. Dependency .066 -2.00 -.258 5 . Adult Crime .005 - .52 -.069 6 . Mobility-Growth .008 - .67 -.089 7. Population Density .000 .06 .008 8. Property Tax .004 .45 .059 9 . Unemployment .039 1.52 .19 8 10. Medical Services .029 1. 29 .170 11. Youth Education .022 1.12 .148 12. Professional-Technical Employment .119 -2.76 -.346 13. Juvenile Crime .038 -1.49 -.196 14. Consumption .09 7 2.46 .312 2 the correlation coefficient, the square root of R . It should be noted at this point that economic well-being is more closely related to income inequality than social well-being, assuming that the data for the components of well-being can be subdivided into such groups. Table 2 8 shows the relationships between a) the sum of the weighted economic components and the Gini index b) the sum of the weighted components which are related to social factors and the Gini index; and c) the sum of the weighted values for the two crime components and income dispersion. It is possible that among the original variables there is a good substitute for the well-being index. If this is the case, then the factor analysis, which is quite involved, is not really necessary. A search for this proxy variable was conducted, involving the correlation of each variable with the well-being index. Furthermore, it may be possible to identify a single variable which can serve as a suitable proxy for the Gini index. Correlation between the variables and the Gini index was also accomplished. The results are shown in Table 29. While no suitable proxy was found for either well being or income dispersion, it is noted that education, income, and public assistance are rather well correlated with well-being, the latter being a negative correlation. All well-being tests of this type were exceptionally 157 Table 28.— Economic, Social, and Crime Components of Well-Being and Their Relationship to Income Inequality 2 Component Group R Sum of Weighted Economic Components .122 -2.78 -.349 Sum of Weighted Social Components .001 .18 .0 25 Sum of Weighted Crime Components .035 -1.42 -.186 158 Table 29.— Correlation Coefficients for Variables and Well-Being and for Variables and Income Dispersion Variable Correlation with Well-Being Correlation with Gini Index 1. Per Cent Increase in Population, 1950-1960 .54 -.18 2. Per Cent of 14-17 Year Olds in School .15 .16 3. Median School Years Completed .78 -.34 4. Per Cent Over 2 5 Years with < 5 Years Schooling -.5 7 .39 5. Per Cent Unemployed -.2 8 -.0 8 6. Per Cent Agricultural Workers -.56 .59 7. Per Cent Employed as Professional-Technical .61 -.2 8 8. Non-Worker/Worker Ratio -.10 .16 9. Per Cent of Housing Units Substandard -.5 2 -.11 10. Per Cent of Units Built Prior to 1940 -.48 .13 11. Average Property Tax Rate .12 .08 12. Per Cent of Units with > 1.0 Persons per Room -.40 .05 .12 13. Persons per Square Mile -.08 159 Table 29--Continued Variable Correlation Correlation with with Well-Being Gini Index 14. Adult Felony Arrests per 1,000 Persons 15. Major Juvenile Arrests per 1,000 Persons 16. Public Assistance Payments Per Capita 17. Non-Federal Physicians Per Capita 18. Deaths per 1,000 Persons 19. Median Age 20. Per Cent Moving to Present Address within 15 Months 21. Per Cent Rural 22. Taxable Transactions Per Capita 23. Median Income -.28 -.18 -.64 . 27 -.46 -.23 . 38 -.41 .18 .64 .20 . 33 . 34 .18 .22 .02 -.13 -.13 .27 -.26 160 significant; this fact probably derives from using these same variables (through the factor analysis) in construct ing the well-being index. No high correlations and almost no significance were found in the variable-Gini index tests. An Optimum Range of Inequality Due to the possibility of diminishing incentives for industry and thrift under complete equality, it may be that the optimum level of the Gini index falls short of zero, where all persons would be receiving like amounts of income. In addition, welfare may be maximized under conditions of sufficient income relative to given needs, rather than arbitrary equality. A theoretical system in which well-being increases with diminishing inequalities of income, reaches a plateau or optimum range, and then decreases as further equality is forced upon society is shown in Figure 14. It was originally thought that perhaps such a plateau or optimum range would be demonstrated by the data for California counties. This, however, was not the case. Reference to Figure 12, the scatter diagram of counties on inequality and well-being axes, shows no strong relationship of this type. It is noted, however, that those counties with high well-being ratings are not located at extreme positions of either income equality or inequality. Increasing Values of the Well-Being Index 161 Range of Optimum Inequality Increasing Values of the Gini Index. Figure 14.— Theoretical Range of Optimum Inequality CHAPTER V SUMMARY AND IMPLICATIONS There have been very few attempts to measure the effect of economic phenomena on the general well-being of man. Perhaps this is due to an air of futility which is usually attached to the measurement of well-being. Boulding indicates that if economics is restricted to the study of quantities which are numerically measureable, then well-being is not a part of economics at all.1 Neverthe less, economists have always been interested in wealth and welfare. Indeed, it may be said that the central thrust of economic inquiry is toward the problem of creating a maximum level of welfare by properly allocating resources under certain scarcity constraints. But both the quantity of welfare extant and the increment to welfare deriving from specific actions or policies are measurements which generally are avoided. There has been a current of thought since the early decades of the industrial revolution concerning the inequities of the capitalist system. Fortunately, this 1Kenneth E. Boulding, Economic Analysis, Vol. I (M-th ed. , New York: Harper and Row, 19 66), p. 8. 16 2 163 current has caught up many of the policy makers of the twentieth century, and resulted in a moderation of those inequities, possibly realizing the salvation of our economic construct of enterprise and democracy. The basic or central idea behind this egalitarian line of reasoning is that the society as a whole is better off without such extreme inequality in the distributions of wealth and income as would exist under unchecked capitalistic operations. The reasoning has stopped short, however, of testing its tenets through quantitative analysis, apparently because of the supposed futility of measurement. Summary of the Dissertation and the Results The purpose of this dissertation has been to subject the hypothesis that society's well-being increases with decreases in income inequality to empirical testing. Measurement of levels of well-being and of levels of income inequality were important and concomitant goals. A review and summary of the dissertation and of the results of the analysis will now be shown. The Literature An extensive review of the literature concerning the size distribution of income was undertaken. Attempts to construct income distributions in the early part of the twentieth century were first considered, followed by 164 the more modern treatments of income inequality and dis persion which have utilized vastly improved data, especially since the advent of the income inquiries within the forms for the decennial census. Recent books on the subject of the income inequality and well-being nexus were considered, and the work entitled Income and Welfare in 2 the United States seemed to be most valuable. Artxcles in scholarly periodicals concerning the current status and measurement of income size distribution have been appearing with increasing regularity over the past few years, due in part to the socio-economic conditions of 3 poverty to which attention has been drawn. Specific instances of cross-sectional measurement were found, and the methods utilized were carefully noted in Chapter II. The Empirical Data The dissertation was placed in context by reviewing current income inequality among the nations of the world and the states of the United States. It was found that no prior measurement of income inequality at a 2 James N. Morgan, Martin H. David, Wilbur J. Cohen, and Harvey E. Brazer, Income and Welfare in the United States (New York: McGraw-Hill Book Company, 1962). 3 See, for example, several articles xn Papers and Proceedings of the Eighty-Second Annual Meeting of the American Economic Association, American Economic Review, LX, No. 2 (May, 1970), 247-299. 165 level of disaggregation as small as the county had taken place. Since a great deal of heterogeneity in income distributions is hidden in data aggregation by states, it was decided to test the hypothesized relationship between income inequality and well-being by using county data. The 5 8 counties in the State of California were chosen as the frame of the empirical analysis. Availability of various economic and social data series, external heterogeneity coupled with internal homogeneity, and personal interests of the author prompted the choice. The census year 19 6 0 was picked as the time period in which to place the analysis, and a cross-sectional data bank was prepared. Data were collected for each of the 5 8 counties concerning the many facets of well-being, along with the necessary statistics for constructing the income size distribution. Twenty-three variables were chosen, representing the broad categories of population change and density, educational attainment, employment, housing, crime, health, age, mobility, income and consumption. In addition, incomes of families by county for thirteen income size classifications were determined. Measuring Income Inequality Utilizing the data on family income by county from the 19 6 0 census and combining with it information taken from the files of California income tax returns, it was 166 possible to compute a measure of income dispersion. The Gini index of income inequality and the Lorenz method of computing that index were chosen, based on their general acceptability and capacity to be understood. The Gini index was found to have been used far more than any other dispersion index for income, even in the face of certain rather severe disadvantages. Calculation of the Gini index for each of the 5 8 counties was aided by a computer program especially pre pared for that purpose along with access to a General Electric 265 computer via a time-shared network. The results of the calculations show that while differences in income distributions among California counties are not severe, a definite pattern does exist. All the counties which are oriented toward commercial agriculture have rather unequal income distributions, while the majority of the counties with high equality of incomes were sparsely populated and oriented toward lumber operations. Extremes of inequality were not found to exist in urban, suburban, or commercial centers. Reference is made to Table 10 of Chapter IV for further details. The major drawback to the use of the Gini index is its failure to account for particular portions of the distribution. That is, it is monadic in its descriptive capability, while the interactions between compared distributions may be complex. Measuring Well-Being A factor analytic construct was utilized for the measurement of aggregate well-being in each of the 5 8 counties. The particular factor analysis model chosen was the direct Principle Component method of isolating independent dimensions or factors within a data set. Since the size of the problem (twenty-three variables and 5 8 counties) made matrix manipulation unweildy, a prepared analysis software package and an IBM 360 series computer were utilized. Varimax rotation of fourteen extracted components was performed by the computer, resulting in highly interpretable factors representing non-redundant elements of well-being. This independence provided the quality of additivity, and the scores for all elements of well-being were therefore weighted according to explained variance and summed, with the sum for each county being taken as the county's index of well-being. Conceptually, the well-being indices contain positive elements for income, education, health, and consumption and negative elements for substandard housing, crime, population density, and unemployment. The results are quite plausible, showing the counties where new developments and quality environments have caused residency by persons with high education and income levels to be in the lead. These include Santa Barbara, Marin, Orange, and 168 San Mateo counties. On the other hand, areas where economic and social conditions of life are generally thought to be less acceptable have shown up in lower positions on the well-being scale, including Madera, Imperial, Kings, and Tulare counties. The extremes of the well-being index do not include highly urbanized or industrial counties, with the exception of San Francisco which received a low total score primarily because of a very negative element for population density. The com parative results among counties are presented in Table 20 of Chapter IV. Income Inequality and Well-Being A test of the hypothesis of the dissertation was made by setting up an associative model for the analysis of the relationship between income inequality and well being. The model took the form WI = f (L) where WI = the well-being index L = the Gini index of income inequality. Several equations, including linear, exponential, and hyperbolic types were tested, utilizing a stepwise regression program with linear transformations to non linear forms. The program was run on a Control Data 169 Corporation Model 3150 computer. The linear form was most closely in conformity with the data. Even in the linear case, however, only ten per cent of the variations in well-being were found to be associated with variations in income inequality. The next step in the analysis was to determine if other economic or social elements from the factor analysis construct were correlated with income inequality. It was concluded that although economic well-being is apparently more closely associated with income inequality than is total well-being, the relationships are such that the absence of causation is apparent, and the associative relationships are minor. Thus the hypothesis of an inverse correlation between income inequality and well being in California is rejected, or at least subject to serious doubt. Implications of the Findings The concern about income distribution that has come to the fore in recent years is based on humanitarian, 5 economic, political, and social considerations. In the humanitarian realm, mankind has been made increasingly aware of the plight of his fellow man in poverty and of the c Joseph W. McGuire and Joseph A. Pichler, Inequality: The Poor and the Rich in America (Belmont, California: Wadsworth, 1969 ) , p. 2 ~ . affluence of the rich through increased mobility and communications. Our willingness to concern ourselves about those in poverty may be due to a lessening need, as standards of living in the middle classes increase, to be concerned about our own day to day sustenance. Economi cally, the idea of the diminishing marginal utility of money indicates that a dollar taken from a rich man and given to a poor man will increase the satisfaction of the poor man to a greater amount than the decrease in satisfaction of the rich man; and since the public welfare is simply the sum of all individual satisfactions, aggregate well-being will increase. Economic efficiency is also a criterion for concern about large numbers of persons in poverty. Total product, given a set of resources, increases with the better utilization of those resources and it is inefficient to have in our midst a potentially productive resource being wasted in poverty, unemployment, and underemployment. The social considera tion derives from the weakened social fabric which results when either riches or poverty create social values alien to our society, such as idleness, disrespect for authority, and nonconformance for its own sake. Politi cally, extremes of the income distribution are seen as threatening to existing power structures, for revolutions have occurred repeatedly where wide class and income gaps 171 g exist. Whatever the considerations, however, it is apparent that the concept of mixed capitalism, including government as a participant in the economy with a measure of egalitarian concern, is winning out over the forces of social Darwinism and other rationalizations for income inequities. Policy and the Findings Regarding policy alternatives and the distribution of income, the National Bureau of Economic Research indicates: Usually treated under the heading "size distribution of income" are the structure of the income distribution; the factors accounting for changes in this structure, including change in the position of families within the distribution; and the influence of the income distribution and its changes on economic behavior, especially savings and consumption. That these topics bear on many problems of policy and are therefore important is obvious.^ Instruments of policy which are available for use g in combating poverty and bringing about a more equitable distribution of income include taxation, transfers, and 6Ibid., p. 4. n National Bureau of Economic Research, Studies in Income and Wealth, V, XIII (New York: National Bureau of Economic Research, 19 51), xiii. g Opponents of redistribution have defined "equity" as receiving what is due, as opposed to "equality" which is receiving, whether due or not. R. W. Baldwin, Social Justice (Oxford: Pergamon Press, 1966), p. 2. 172 methods of modifying the underlying distributions of factor ownership, prices, or employment. The results of this dissertation, however, cast some doubt on the propriety of altering the overall distribution of income with the purpose of increasing the general welfare. It is especially illogical, if these results are to be trusted, to pretend that income inequality adjustments will alter the social dimensions of well-being. If a single policy is implied, it would be that education, being foremost in its effect on the well-being index and capable of explaining more of the variations in the county data than any other variable or factor, should be fostered. It will be remembered that the mechanics of factor analysis were unable to separate income variance from educational level variance, thus lending credence to the already well-accepted (in most quarters) tenet of income-education correlation. In addition, since the variable with highest negative correlation with well-being is public assistance payments, it would seem that fomenting education of all types among current and potential welfare recipients would reduce the welfare burden and increase g both aggregate and individual well-being. g The inadequacy of present educational institutions of California in the fostering of equal educational opportunities is pointed out by W. Lee Hansen in "Income 173 Another implication is the close relationship found between poverty and the Gini index of inequality; apparently the majority of inequality is due to the low end of the distribution. Again, this implies the wisdom of policy concentration in the area of the lower income groups rather than the deliberate breaking up of high income receiving groups. A major consideration for the policy-maker in the State of California is the problem of the agricultural worker. Figure 15 shows the scatter diagram of income inequality and well-being with three distinct clusters emphasized. They are a) the high well-being counties of a suburban nature which are grouped at the top; b) the sparsely populated mountainous counties grouped at the left; and c) the commercial farming counties which have the dual characteristics of low well-being and high income inequality. The agriculturally oriented counties, especially Madera, Imperial, Tulare, Kings, and Stanislaus, appeared grouped at or near the bottom of the Education-Income, Housing Quality, Dependency, Youth Distribution Effects of Higher Education," American Economic Review, XL, No. 2 (May, 1970), 335-340. Public subsidies for education, by and large, are shown to be flowing to those with the least need and who originate in the middle class, while those who are from lower income groups receive no educational subsidy at all. Low and even zero tuition has not been sufficient to encourage low income students to take advantage of the redistribution effects of higher education. Index of Well-Being 174 0.8 0.7 0.6 0.5 0.1+ 0.3 0.2 0.1 0.0 -.1 -.2 -.3 -.4 -.5 -.6 -.7 -.8 Sa.n'ta-^Bo-r I f f a . YX o So.„+* Cj*ro- <>«.*<)«■ *+o Sa . r \ Wo-fe® gI».er«-,y'*','TO S a n Di « 3 ° V » / f i n , t P \ Y o l ° \ £1 Ooyo-Oo pltimaS iviontevev Los eiw«»€(cs • .y ^ w Li/i's O b i s p o Rinersi « < « • \ • - , • V W iu m .o * V*"* Sa.-n 8«r>i4.yiJi»io T"*oX>* «r /KCrn "fe. Frer^T IfSe*, To a |* m w* p ^ l \ l a y t« ( • ColwisX S<n0evnt* • \ V • • ’ i ^MoirfotiTio 9 M ey ceil , W f i y « . d « . I CVw,L St'anisla.os Saw JoolOui> Lake Tu |dye. InTpeyuil l ^ l a - d eya J I I I I I I I I J I 1 CD C M O H C M O O - l f L O CD C * * - CO CD CO CO CO CO CO CO - CO CO CO CO o St H C M s t s t Gini Index of Inequality Figure 15.--Scatter Diagram of Income Inequality and the Well-Being Index showing Clusters of Suburban, Mountainous, and Agricultural Counties 175 Education, and Adult Crime Components. This non-random difference between these areas and other counties is largely due to the agricultural worker's characteristics, including low incomes, overcrowded and substandard housing, large families, young people who do not attend school, and the resulting crime rates. While these findings emphasize the need for action, the recommendation of specific policies to correct the situation is beyond the purview of this paper. Limitations of the Findings In spite of the care taken in organizing and carrying out this research project, there are certain caveats that must be expressed concerning its applica bility. First, the results do not necessarily apply to areas not included in the study, and extension of the implications into other states is neither provided for in the sample design nor possible through statistical inference. Second, the range of the data may not have been sufficient to fully evaluate the hypothesis. As was previously pointed out, the counties of California were not found to possess a distribution on the Gini index with wide variations; the range extended from .288 to .413, as opposed to the range of the states of the United States 176 of from .312 to .466.^ The hypothesis may have been supported if all counties in the United States had been included. Third, the calculation of the Gini index was approximate, using geometric techniques rather than the calculus. It was based on family income alone in a single year, the first of which artificially decreases inequality and the second creating overstatement of it. Thus this index must be used with full knowledge of its usefulness and of its origin. Lastly, the index of well-being is constructed with the data that was fed into the factor analysis routine. Different sets of data, or omission of relevant data series, would result in a different index. The sensitivity of the index to data changes has not been tested. Note, however, that the weighting system is free from bias or value judgment once the data are determined. It is hoped that these limitations are few by comparison with the contributions of this dissertation. In review, the major contributions are a) the measurement of income inequality on a level of disaggregation previously unattempted, including the calculation of Gini ■^Ahmad Al-Samarrie and Herman P. Miller, "State Differentials in Income Concentration," American Economic Review, LVII, No. 1 (March, 1967), 63. 177 coefficients of income inequality via an ingenious and time-consuming method of combining census and income tax data; b) the application of factor analytic techniques to the problem of measurement of well-being, with resulting efficiency in weighting the components or elements of well-being, and ability to sum those elements because of the independent nature of the factor structure; and c) the application of these advances in measurement to the timely but difficult problem of determining the impact of differences in income inequality on general social and economic well-being. APPENDIX A BASIC DATA FOR CALIFORNIA COUNTIES 178 BASIC DATA FOR CALIFORNIA COUNTIES 1 2 3 Per Cent Increase Persons Per Cent of County in Population, per 14-17 Yr. Olds 1950-1960 Square Mile in School 1. Alameda 22. 7 1239 .0 89 .9 2. Alpine 64.7 0.5 na 3. Amador 9.2 16. 8 91.7 Butte 26. 3 49.3 92.9 5. Calaveras 3.9 10.0 95.9 6. Colusa 3.6 10.5 95.1 7. Contra Costa 36.8 557 .3 94.0 8. Del Norte 120.0 17.7 90.3 9 . El Dorado 81.3 17.1 92.9 10. Fresno 32. 3 61.4 87.7 11. Glenn 11.6 13.1 92.8 12. Humboldt 51.5 29.4 90.3 13. Imperial 14.5 16.8 86. 8 14. Inyo 0.2 1.2 97.0 15. Kern 27.9 35.8 89 .4 16. Kings 6.8 35.8 90.1 17. Lake 20.1 11.0 88.6 18. Lassen -26.4 3.0 92.5 19. Los Angeles 45.5 1487.4 90.3 20. Madera 9.5 18.9 86. 3 21. Marin 71.5 282. 3 95.0 22. Mariposa -1.6 3.5 85.0 23. Menocino 25.0 14.6 87.9 24. Merced 29 .6 45.6 87.8 10 25. Modoc -14.2 2.0 91.0 1 Per Cent Increase County in Population 1950-1960 26. Mono 4.6 27. Monterey 52.0 28. Napa 41.4 29. Nevada 5.1 30. Orange 225 .6 31. Placer 36.9 32. Plumas -14.0 33. Riverside 80.1 34. Sacramento 81.4 35. San Benito 7.1 36. San Bernardino 78. 8 37. San Diego 85.5 38. San Francisco -4.5 39. San Joaquin 24.5 40. San Luis Obispo 57.6 41. San Mateo 88.6 42. Santa Barbara 72.0 43. Santa Clara 121.1 44. Santa Cruz 26.6 45. Shasta 63.3 46. Sierra -6.8 47. Siskiyou 7.0 48. Solano 28.4 49 . Sonoma 42.5 50 . Stanislaus 23.6 2 3 Persons Per Cent of per 14— 17 Yr. Olds Square Mile in School 0.2 na 59 .7 74.6 86.9 90 .3 21.4 95.5 900 .2 90.4 40.0 94.1 4.5 93.6 42.7 91. 3 511.5 93.1 11.0 91.3 25.0 91.4 242. 8 81.8 16451.5 90.3 177.4 85.6 24.4 90.8 978.8 95.0 61. 7 89 .0 493.3 91.6 191. 8 90.2 15 .7 92.9 2.3 na 5.2 94.8 162. 8 92.1 93.3 88.4 104.9 88.5 H 00 O 1 2 3 County Per Cent Increase in Population, 1950-1960 Persons per Square Mile Per Cent of 14-17 Yr. Olds in School 51. Sutter 27.2 55.0 91.5 52. Tehama 31. 3 8.5 94.2 53. Trinity 90.8 3.0 90.2 54. Tulare 12. 8 34. 8 85.3 55. Tuolumne 14. 5 6.3 96.0 56. Ventura 73.7 107.6 89 .0 57. Yolo 61.7 63.6 91.3 58. Yuba 38.7 53.2 87.2 H oo H 4 Median County School Years 1. Alameda 12.1 2. Alpine 8.6 3. Amador 11.4 it. Butte 11.4 5. Calaveras 10.6 6. Colusa 11.7 7. Contra Costa 12.2 8. Del Norte 10.3 9 . El Dorado 11. 8 10 . Fresno 10.5 11. Glenn 11. 3 12. Humboldt 11.0 13. Imperial 9.0 14. Inyo 12.1 15. Kern 10.9 16. Kings 9.5 17. Lake 10.6 18. Lassen 11.0 19 . Los Angeles 12.1 20. Madera 9.0 21. Marin 12.6 22. Mariposa 11.7 23. Mendocino 10.8 24. Merced 10.2 25. Modoc 12.0 26. Mono 12.4 27. Monterey 11.9 28. Napa 11.2 29 . Nevada 11.5 5 6 Per Cent of Persons Per Cent 25 Yrs. and Older with Unemployed Less Than 5 Yrs. School 5.7 6.4 26.9 na 5.8 6.0 4.5 11.1 5.7 5.4 7.2 4.3 4.8 6.4 4.1 8.1 3.1 7.9 12.2 8.1 6.5 5.7 4.7 7.5 23.3 6.2 4.4 6.0 9.0 7.5 14.9 8.3 5.3 8.4 5.1 12.4 4.7 5.8 14.6 8.1 2.3 2.9 4.4 8.8 6.9 8.2 12.5 6.3 3.8 7.1 1.4 2.8 8.2 6.5 5.6 4.4 3.9 12.1 4 Median County School Years 30. Orange 12.2 31. Placer 11.1 32. Plumas 11. 3 33. Riverside 11.9 34. Sacramento 12. 2 35. San Benito 9.4 36. San Bernardino 11. 8 37. San Diego 12.1 38. San Francisco 12.0 39. San Joaquin 10.0 40. San Luis Obispo 11.4 41. San Mateo 12.4 42. Santa Barbara 12.2 43. Santa Clara 12.2 44. Santa Cruz 11.0 45. Shasta 11.6 46. Sierra 11.6 47. Siskiyou 11.2 48. Solano 11.9 49. Sonoma 11.1 50. Stanislaus 10 .0 51. Sutter 11.2 52. Tehama 11.5 53. Trinity 11.0 54. Tulare 9.4 55. Tuolumne 11.5 56. Ventura 11.6 57. Yolo 11.5 58. Yuba 10.8 5 6 Per Cent of Persons Per Cent 2 5 Yrs. and Older with Unemployed Less Than 5 Yrs. School 3.2 4.8 7.1 7.4 4. 3 12.0 7.1 6 . 5 4.8 6.0 15.2 5.9 5.5 6.6 3.3 6.5 7.4 6.2 12.8 8.0 4.8 5.3 3.2 3.3 6.1 3.6 6.2 5.4 6.9 6.6 3.9 10.7 2.8 5.3 5.8 7.8 4.7 6.8 7.4 6.8 9.2 9.6 6.9 7.3 3.8 7.7 3.8 13.1 14.0 8.3 3.7 10 .0 8.4 5.3 7.8 6.6 6.5 10 .7 7 Per Cent County Agricultural Workers 1. Alameda 1.3 2. Alpine 28.7 3. Amador 6.4 4. Butte 11.5 5. Calaveras 8.1 6. Colusa 33.7 7. Contra Costa 1.9 8. Del Norte 3.7 9 . El Dorado 5.2 10. Fresno 17. 8 11. Glenn 32.6 12. Humboldt 3.6 13. Imperial 37.5 14. Inyo 4.2 15. Kern 15.9 16. Kings 31.4 17. Lake 16.6 18. Lassen 8.1 19. Los Angeles 1.1 20. Madera 32.0 21. Marin 2.4 22. Mariposa 8.6 23. Mendocino 6.7 24. Merced 28.7 25. Modoc 26.7 26. Mono 4.0 27. Monterey 14.5 28. Napa 6.0 29. Nevada 4.5 8 9 Per Cent Non-Worker/ Professional 8 Worker Technical Ratio 14. 3 1.40 17.0 na 13.7 1. 74 11.5 1.74 10.8 1.66 7.7 1.53 15.4 1.66 7.7 1.63 10.3 1.56 9 . 8 1. 71 8.1 1.51 9.2 1.66 6.8 1.37 13.0 1. 38 11.5 1.66 8.9 1. 89 11.0 1.91 10 .4 1.46 14.1 1.37 8.8 2.01 19 .2 1.52 15.1 1.33 11.6 1. 88 8.5 1.76 8.4 1.42 10.8 0.99 11. 3 1.24 14.4 1. 88 13.3 1.66 7 Per Cent County Agricultural Workers 30 . Orange 3.3 31. Placer 7.8 32. Plumas 3.8 33. Riverside 12.1 34. Sacramento 3.1 35. San Benito 29. 3 36. San Bernardino 4.8 37. San Diego 2.6 38. San Francisco 0.4 39. San Joaquin 13.4 40. San Luis Obispo 10.5 41. San Mateo 1.4 42. Santa Barbara 7.5 43. Santa Clara 3.4 44. Santa Cruz 10 .5 45. Shasta 4.4 46. Sierra 9 . 3 47. Siskiyou 10.2 48. Solano 5.4 49 . Sonoma 10.4 50. Stanislaus 16.9 51. Sutter 26.5 52. Tehama 15.2 53. Trinity 3.8 54. Tulare 33.2 55. Tuolumne 2.8 56. Ventura 13.5 57. Yolo 13.6 58. Yuba 13.1 8 9 Per Cent Non-Worker/ Professional 8 Worker Technical Ratio 14.7 1.64 12.1 1. 70 9.7 1. 39 12.0 1.56 14.7 1.44 7.6 1.55 12.3 1.66 14.9 1. 35 12.2 1.01 9.8 1.58 12. 7 1.79 15.4 1.43 15.0 1.44 18.6 1.60 10 .9 1.76 10.9 1.64 9.4 1.62 9.9 1.48 11.2 1.53 12.1 1.77 10.0 1.74 10.7 1.70 9 . 7 1.64 12. 8 1.55 9.1 1.71 10.8 1.66 13.9 1.53 13.2 1.45 9.2 1.55 10 Per Cent of County Housing Substandard 1. Alameda 9 . 3 2. Alpine 24.5 3. Amador 20.0 4. Butte 23.6 5. Calaveras 29 .5 6. Colusa 33.5 7. Contra Costa 9 . 3 8. Del Norte 32.9 9. El Dorado 20.2 10. Fresno 21. 8 11. Glenn 21.4 12. Humboldt 23.2 13. Imperial 36.2 14. Inyo 32. 3 15. Kern 21.5 16. Kings 34.1 17. Lake 18. 8 18. Lassen 28.1 19. Los Angeles 7.4 20. Madera 29.9 21. Marin 10.1 22. Mariposa 14.3 23. Mendocino 25.1 24. Merced 25.4 25. Modoc 31.7 26. Mono 35.1 27. Monterey 13.9 28. Napa 15.5 29. Nevada 22.0 11 12 Per Cent of Average Units Built Property Prior to 19 40 Tax Rate 56. 7 9 .11 40.5 3.55 53.7 3.42 39 .9 6.85 43.4 5.11 59.3 5.26 25.6 8.52 26.7 7.78 28.4 5.84 40.8 5.93 55.9 4.87 42.5 8.10 46. 8 7.10 45.3 5.73 32.9 7.04 52.1 6 . 35 34.5 6.17 60.9 5.59 40.8 7.40 39.7 6.02 36.0 7.96 33.9 4.52 43.8 7.11 40.8 6.95 6 3.3 5.07 38.4 3.19 36.6 6.29 39.2 7.12 19 .6 7.30 10 Per Cent of County Housing Substandard 30. Orange 6.1 31. Placer 19.1 32. Plumas 30.0 33. Riverside 14.4 34. Sacramento 11.4 35. San Benito 26.1 36. San Bernardino 11.3 37. San Diego 8.7 38. San Francisco 9.0 39. San Joaquin 18.5 40. San Luis Obispo 17.9 41. San Mateo 3.9 42. Santa Barbara 11.1 43. Santa Clara 8.0 44. Santa Cruz 15.4 45. Shasta 25.2 46. Sierra 32.4 47. Siskiyou 23.9 48. Solano 15.6 49. Sonoma 17.4 50. Stanislaus 17.1 51. Sutter 14.9 52. Tehama 25.9 5 3 . ' : Trinity 50.4 54. Tulare 26.2 55. Tuolumne 22.9 56. Ventura 14.1 57. Yolo 17.6 58. Yuba 2 3.9 11 12 Per Cent of Average Units Built Property Prior to 1940 Tax Rate 19 .6 7.30 41.0 6.65 56 .1 3.78 26.9 6. 76 30.6 8.00 65.7 4.21 26.5 7.49 28.2 7.51 80.4 8.41 44.9 7.86 36.7 6.89 24. 3 8.50 39 .0 6. 35 26.4 7.53 50 .0 6.94 28.6 5.61 62.3 5.68 61. 8 6.45 34.6 6.75 44.2 7.11 39 .8 7.52 40.3 4.83 45 .5 6.18 26.4 5.96 46.6 6.72 43.9 6.04 30 .9 6.93 35.6 5.97 36.3 5.78 13 Per Cent of Units County with More Than 1.0 Persons per Room 1. Alameda 8.2 2. Alpine 31.2 3. Amador 10.5 4. Butte 9.2 5. Calaveras 8.7 6. Colusa 10 .1 7. Contra Costa 9.1 8. Del Norte 20.1 9. El Dorado 13.7 10. Fresno 13.7 11. Glenn 12.0 12. Humboldt 15.0 13. Imperial 21.6 14. Inyo 13.7 15. Kern 15.1 16. Kings 16.9 17. Lake 7.9 18. Lassen 11.0 19 . Los Angeles 8.6 20. Madera 17.4 21. Marin 6.1 22. Mariposa 10.3 23. Mendocino 14.5 24. Merced 16.1 25. Modoc 10.7 26. Mono 9.1 27. Monterey 13. 3 28. Napa 7.3 29. Nevada 9.4 15 Adult Felony Arrests Major Juvenile Arrests 3.55 0.0 0.70 4.08 5, 4, 83 14 1.77 4. 3. 4. 2 . 3, 7. 4, 00 78 38 55 34 93 36 3.99 4.68 1.74 1.69 8.03 6.20 1. 89 1.77 3.02 3.08 2.76 3.16 3.33 1.98 6.41 1.73 0.0 0.50 1.17 - 0- 1.90 1.64 1.63 1.12 1. 38 0.52 0.88 2.45 2.23 0.99 1.14 1. 1. 2. 2. 67 69 00 30 1.04 0.59 1.51 0.72 1.69 - 0- 2.56 0.46 1.72 H CO CO 13 Per Cent of Units County with More Than 1.0 Persons per Room 30. Orange 9.3 31. Placer 11. 8 32. Plumas 10.7 33. Riverside 12.0 34. Sacramento 9.5 35. San Benito 14.0 36. San Bernardino 11.4 37. San Diego 10.5 38. San Francisco 6.3 39 . San Joaquin 11.6 40. San Luis Obispo 11.4 41. San Mateo 6.2 42. Santa Barbara 10.5 43. Santa Clara 9.0 44. Santa Cruz 7.2 45. Shasta 13.8 46. Sierra 8.1 47. Siskiyou 12.0 48. Solano 10.6 49. Sonoma 8.9 50. Stanislaus 11.1 51. Sutter 11.4 52. Tehama 11. 3 53. Trinity 20.0 54. Tulare 16.8 55. Tuolumne 10 .4 56. Ventura 13.0 57. Yolo 12.2 58. Yuba 16.0 14 15 Adult Maj or Felony Juvenile Arrests Arrests 3.91 1.67 2.88 2.07 3.96 0.52 3.05 1.96 2.96 1.18 2.14 1.17 3.75 2.43 2.70 1.75 6.04 1.64 2.82 2.52 2.28 0.79 1.50 1.26 2.12 1.05 2.24 1.56 2.96 2.32 3.65 0.72 3.56 -0- 3.95 1. 82 1. 87 0.71 2.87 1.01 3.32 1. 74 1.08 0.42 3.04 0 .99 1.44 0 .21 3.51 1.94 2.08 1.04 3.21 1.77 5 .64 1.10 4.46 2. 36 189 16 Public Assistance County Payments Per Capita 1. Alameda 29.10 2. Alpine 72. 30 3. Amador 37.17 4. Butte 39.37 5. Calaveras 39.65 6. Colusa 49.63 7. Contra Costa 26.82 8. Del Norte 27.99 9. El Dorado 30.29 10. Fresno 41.08 11. Glenn 28.25 12. Humboldt 25.85 13. Imperial 26.90 14. Inyo 41. 88 15. Kern 37.04 16. Kings 38.77 17. Lake 76. 74 18. Lassen 31. 30 19. Los Angeles 26.64 20. Madera 53.37 21. Marin 12. 80 22. Mariposa 62.58 23. Mendocino 33.70 24. Merced 34.63 25. Modoc 35.36 26. Mono 26.86 27. Monterey 15.25 28. Napa 26.04 29. Nevada 49.42 17 18 Non-Federal Deaths Physicians Per 1,000 Per Capita Persons 1. 35 90 0.0 201 0.40 -0- 0.99 111 0 .29 122 0.50 115 0.90 58 0.34 90 0.58 79 0.85 79 0.70 98 0.84 82 0.72 74 0.94 106 0.79 71 0.70 94 0.94 147 0 .74 75 1.25 85 0.54 84 1.68 65 0 .79 152 0.94 89 0 .54 64 0.48 117 -0- 90 0.97 61 1.15 90 0.77 142 16 Public Assistance County Payments Per Capita 30 . Orange 12.15 31. Placer 29.25 32. Plumas 29 .59 33. Riverside 32. 81 34-. Sacramento 27.40 35. San Benito 27.84 36. San Bernardino 33.22 37. San Diego 19.39 38. San Francisco 31.08 39. San Joaquin 37.81 40. San Luis Obispo 40 .08 41. San Mateo 14.47 42. Santa Barbara 20.91 43. Santa Clara 20.89 44. Santa Cruz 49.74 45. Shasta 35.71 46. Sierra 35 .16 47. Siskiyou 34. 39 48. Solano 20.24 49. Sonoma 35 .68 50. Stanislaus 48.70 51. Sutter 42.76 52. Tehama 45.35 53. Trinity 25.65 54. Tulare 48.72 55. Tuolumne 47.86 56. Ventura 21.40 57. Yolo 24.88 58. Yuba 40.70 17 18 Non-Federal Deaths Physicians Per 1,000 Per Capita Persons 0.98 57 0.95 84 1.03 96 0.91 87 0.93 76 0.84 109 0.80 75 1.00 65 2.33 129 0.92 87 1.09 96 1. 26 61 1.45 75 1. 37 62 1. 31 132 1.06 82 0.89 80 0.70 99 0.79 74 1.20 122 1.04 90 0.36 81 0 .79 101 0 .72 94 0.73 78 0.76 136 0.80 59 0.65 76 1.21 92 191 19 Median County Age 1. Alameda 30 .7 2. Alpine 29.6 3. Amador 31.6 4. Butte 33.0 5. Calaveras 36.4 6. Colusa 31.4 7. Contra Costa 27.7 8. Del Norte 25.9 9. El Dorado 31.8 10. Fresno 26.9 11. Glenn 30.8 12. Humboldt 26.7 13. Imperial 26.4 14. Inyo 34.2 15. Kern 26.2 16. Kings 26.1 17. Lake 43.6 18. Lassen 31.4 IS. Los Angeles 31.5 20. Madera 26.8 21. Marin 30.6 22. Mariposa 39.4 23. Mendocino 31.2 24. Merced 24. 8 25. Modoc 31. 3 26. Mono 33.3 27. Monterey 24.8 28. Napa 36.0 29. Nevada 38.0 20 21 Per Cent Moving to Taxable Present Address Transactions within 15 Months Per Capita 31.2 $1555 43.3 705 36.1 1004 34.8 1226 29.7 714 26.3 1272 27.8 955 38.9 1205 44.9 1304 33.5 1406 29.2 1189 36.4 1450 38.3 129 3 36.2 1511 37.6 1356 52.2 1167 31.2 1082 27.4 998 31.7 1596 34. 8 1229 33.5 1053 32.4 1354 33.3 680 36.5 991 27.2 1173 42.9 1674 47.6 1032 29.0 991 32.0 1189 19 2 19 Median County Age 30. Orange 26.5 31. Placer 33.3 32. Plumas 32.5 33. Riverside 29. 3 34. Sacramento 27.9 35. San Benito 29 .6 36. San Bernardino 28.0 37. San Diego 26.4 38. San Francisco 37.3 39. San Joaquin 30.4 40. San Luis Obispo 30.4 41. San Mateo 30.6 42. Santa Barbara 28.8 43. Santa Clara 26.7 44. Santa Cruz 38.6 45. Shasta 28.9 46. Sierra 34.9 47. Siskiyou 32.4 48. Solano 26.4 49. Sonoma 32.5 50 . Stanislaus . Sutter 30.5 51. 28.1 52. Tehama 29.9 53. Trinity 29.3 54. Tulare 27.0 55. Tuolumne 36.0 56. Ventura 27.1 57. Yolo 27.2 58. Yuba 25.9 Per Cent Moving to Taxable Present Address Transactions within 15 Months Per Capita 38.7 $1144 32.8 1210 34.8 1073 40.2 1155 36.7 1466 30.1 908 35.6 1061 44.2 1216 28.9 2330 31.0 1220 41.2 116 8 29.3 1326 46.0 1436 36.4 1354 31.5 119 3 35.9 1529 30.4 619 30 .7 1107 37.9 928 31.8 1189 30.8 1230 35.2 834 35.7 1087 42.5 631 34.0 1018 30.2 1216 41.4 1061 37.5 1143 47.5 1558 22 Median County Income 1. Alameda $6766 2. Alpine -0- 3. Amador 5636 4. Butte 5408 5. Calaveras 5824 6. Colusa 5604 7. Contra Costa 7327 8. Del Norte 6277 9. El Dorado 6603 10. Fresno 5634 11. Glenn 5290 12. Humboldt 6282 13. Imperial 5507 14. Inyo 5837 15. Kern 5933 16. Kings 4957 17. Lake 4438 18. Lassen 5861 19 . Los Angeles 7046 20. Madera 4596 21. Marin 8110 22. Mariposa 4704 23. Mendocino 5808 24. Merced 4806 25. Modoc 5709 26. Mono 6321 27. Monterey 5770 28. Napa 6524 29. Nevada 5419 23 Per Cent Rural 1. M - 100.0 100 .0 47.0 100.0 70.9 18.9 66.0 84.9 32.7 61. 3 55.4 36.5 75.4 31.8 58.3 100.0 58.9 1.2 53.2 12.1 100.0 65.3 63.9 66.1 100.0 41.5 62.3 76.7 22 Median County Income 30. Orange $7219 31. Placer 6069 32. Plumas 5854 33. Riverside 5693 34. Sacramento 7100 35 . San Benito 5538 36. San Bernardino 5998 37. San Diego 6545 38. San Francisco 6717 39 . San Joaquin 5889 40. San Luis Obispo 5659 41. San Mateo 8103 42. Santa Barbara 6823 43. Santa Clara 7417 44. Santa Cruz 5325 45. Shasta 5989 46. Sierra 5863 47. Siskiyou 5558 48. Solano 6140 49. Sonoma 5725 50. Stanislaus 5260 51. Sutter 5670 52. Tehama 5589 53. Trinity 6210 54. Tulare 4815 55. Tuolumne 5602 56. Ventura 6466 57. Yolo 6240 58. Yuba 5031 23 Per Cent Rural 4.2 60.4 76.5 32.4 15.2 60.6 25.6 11.1 0.0 26.7 44.1 2.5 32.0 4.5 40.1 50.0 100.0 67.0 20.9 55.1 47. 3 56.0 59 .7 100.0 56.0 81.1 38.1 31.0 h on i , tD APPENDIX B CALCULATION OF GINI INDEX FOR 5 8 CALIFORNIA COUNTIES 196 197 LORENZ CONCENTRATION RATIO CALCULATIONS :x(i) Yd) z(i) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Alameda County 0 3.38791E-02 2. 010 32E-0 3 6.81079E-05 1 8.0 5151E-02 1.17048E-0 2 6 . 39 619E-04 2 .136103 2.96575E-02 2. 299 22E-0 3 3 .201189 5.9 0 611E-0 2 5.77435E-03 4 .286031 .108209 1.41915E-02 5 .403899 .191231 3.529 43E-0 2 6 .529438 .295489 6.11025E-02 7 .636036 .397609 7.38827E-02 8 .720886 .489944 7.53096E-02 9 .787809 .571595 7.10404E-02 10 .939349 .799155 .207724 11 .983455 .904199 7.51284E-02 12 1. 1 . 3 .15054E-02 Sum of (B-A)(C+D) = .65396 Lorenz = 1 - Sum((B-A)(C+D) = .34604 Alpine County 0 .047619 2.01498E-03 9 .59 515E-05 1 .171429 4.15 2 54E-0 2 5 . 39072E-03 2 .390476 .151079 4.2189 5E-0 2 3 .390476 .151079 0 4 .390476 .151079 0 5 .647619 .42557 .148281 6 .761905 .569328 .113703 7 .87619 .737422 .149343 8 .971429 .894796 .155449 9 .971429 .894796 0 10 .971429 .894796 o ■ 11 1. 1. .054137 12 1. 1. 0 Sum of (B-A)(C+D) = . 668589 Lorenz = 1 - Sum( (B-A) (C+D) = .3314-11 198 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Amador County 0 2 . 56714E-02 9 . 06533E-04 2.32720E-05 1 .100316 2.07858E-02 1.619 21E-03 2 .187599 5.72158E-02 6.80819E-03 3 . 2622113 .100245 1.17536E-02 4 . 392575 .196043 3.86157E-02 5 .561611 .346626 9 .17308E-02 6 .68128 .472247 9.79932E-02 7 .771722 .583261 9.54626E-02 8 .830174 .663866 7.28968E-02 9 .875197 .733204 6. 29 013E-0 2 10 .977883 .932037 .170996 11 1. 1. 4. 27307E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .306468 Butte County 0 .693532 0 3.62881E-0 2 1.22744E-03 4.45415E-05 1 .114235 2.21919E-02 1.82547E-03 2 .222017 6.5 83 3 8E-0 2 9 .48751E-0 3 3 .329978 .127506 2.0 87 34E-0 2 4 .443311 .211954 .038472 5 .582325 . 33672 7 . 62736E-02 6 .695387 .456462 8.96787E-02 7 .785792 .567274 9 . 25502E-02 8 .843112 .64672 6.9 5872E-02 9 .884952 .71147 5. 6826 3E-0 2 10 .96976 .875204 .134562 11 .991605 .943524 3 . 9 730 3E-02 12 1. 1. Sum of (B-A)(C+D) = 1.6 3159E-0 2 .646227 Lorenz = 1 - Sum((B-A)(C+D) = .353773 199 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Calaveras County 0 3 . 30669E-02 1.16872E-03 3.86460E-05 1 .12282 2. 50928E-02 2.35705E-03 2 .203488 5 . 87789E-02 6.7658IE-0 3 3 .270349 9.73549E-02 1.04392E-02 4 .382994 .180226 3.12682E-02 5 .525073 .306907 6.9 2112E-02 6 .672965 .462294 .113759 7 .78234 .596665 .115824 8 .849564 .689449 8.64576E-02 9 .884084 .742649 4.9 436 9E-0 2 10 .975654 .920126 .152261 11 .998547 .990534 4. 37 39 7E-02 12 1. 1. 2 . 89 322E-03 Sum of (B-A)(C+D) = .684451 Lorenz = 1 - Sum((B-A)(C+D) = .315549 Colusa County 0 4.80832E-02 1.79132E-03 8.61325E-05 1 .109162 1. 55588E-02 1.0597 2E-0 3 2 .18616 4.39 884E-0 2 4 . 5 8502E-0 3 3 .30052 .100481 1.65215E-02 4 .416829 .177166 3 .2292 8E-02 5 .554581 .286229 6.38334E-02 6 .661468 .38578 7.18294E-02 7 .737492 .467069 6.48365E-02 8 .807667 .552705 7.156 31E-02 9 .862898 .628772 6 . 52538E-02 10 .947693 .776316 .119145 11 .980182 .864897 5 . 33208E-02 12 1. 1. 3 .69586E-02 Sum of (B-A)(C+D) = .601286 Lorenz = 1 - Sum((B-A)(C+D) = .398714 200 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Contra Costa County 0 2. 67595E-02 1.130 46E-0 3 3.02505E-05 1 6 . 04352E-02 7.55654E-0 3 2.92540E-04 2 .101541 2.01316E-02 1.13815E-03 3 .15024 4.07044E-02 2.96263E-03 4 .217267 7.69679E-02 7. 88727E-03 5 .328326 .150861 2.53023E-02 6 .461809 .254783 5.41467E-02 7 .578497 .359212 .071646 8 .673103 .455438 .077071 9 .749724 .542667 7.6475 3E-02 10 .929162 .796459 .240291 11 .982414 .913428 9.10 5 54E-0 2 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .318053 Del Norte County 3.36489E-02 .681947 0 2.42136E-02 5.9 209 IE-04 1.43367E-05 1 5.88368E-02 8.40266E-03 3.11427E-04 2 .13442 3.52818E-02 3 . 30179E-0 3 3 .212944 7.41176E-02 8.59 05 4E-0 3 4 .341254 .155693 2.94869E-02 5 .467979 .253583 5.18658E-02 6 .58339 .358279 7.06154E-02 7 .722562 .503492 .119934 8 .796108 .591302 8.05178E-02 9 . 853134 .667853 7.18052E-02 10 .957004 .841726 .156799 11 .982802 .907226 4.51189E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .328837 3.28014E-02 .671163 201 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) El Dorado County 0 3.35687E-02 1.63790E-03 5.49 821E-05 1 8.22495E-02 .011113 6 . 20726E-04 2 .143069 3.1489 7E-02 2. 59U0E-03 3 .218382 6. 65045E-02 7.38022E-03 4 .308188 .121188 1. 68558E-02 5 .436269 .21687 4. 329 89E-02 6 .5419 3 .308207 5.54802E-02 7 .652298 .41927 8.02902E-02 8 .731698 .509431 7. 3739 3E-02 9 .807878 .60499 8.489 64E-0 2 10 .947355 .822282 .199072 11 .986127 .919539 6.75325E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .341557 Fresno County 2. 66305E-02 .658443 0 4.66589E-02 1.9 80 31E-0 3 9 . 2399 OE-O 5 1 .122084 2.14154E-02 1.76462E-03 2 .214671 5.63343E-02 7.19 861E-0 3 3 .31575 .109876 1. 6 8004E-02 4 .425389 .184478 3. 227 25E-02 5 .543099 .282386 5.49547E-02 6 .650855 . 387868 .072224 7 .735858 .483388 7.40589E-02 8 .805503 .572402 7.35306E-02 9 .852073 .638894 5.64104E-02 10 .954172 .821878 .149142 11 .98606 .911392 5.52712E-02 12 1. Sum of 1. (B-A)(C+D) = .026645 .620366 Lorenz = Sum((B-A)(C+D) = .379634 202 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) ZCI) Income Class Cum Per Cent of Families Cum Per Cent of Income (B-A)(C+D) Glenn County 0 4. 880 32E-02 2 . 016 80E-0 3 9.84260E-05 1 .119452 1.96812E-02 1.53293E-03 2 .23565 6 . 72721E-02 1.01038E-02 3 .346735 .128142 2.17077E-02 4 .461771 .212275 3 .9160 2E-02 5 .593772 .328203 7.13436E-02 6 .701604 .439607 8.2 79 43E-02 7 .785266 .538839 8 .1859 3E-02 8 .850569 .627236 7.61485E-02 9 .891471 .689723 5.38659E-02 10 .969556 .840436 .119483 11 .985127 .887528 2.69053E-02 12 1. 1. 2. 80738E-02 Sum of (B-A)(C+D) = .613076 Lorenz = 1 - Sum((B-A)(C+D) = .386924 Humboldt County 0 3.55012E-02 1. 72836E-03 6. 135 89E-05 1 7.56183E-02 1.0180 7E-0 2 4. 77757E-04 2 .13615 3.12841E-02 2.50995E-03 3 .212444 6.74097E-02 7.52972E-03 4 .320036 .133966 2.16664E-02 5 .465118 .243666 5 . 47 875E-0 2 6 .588659 .353321 7.37524E-02 7 .69096 .458389 8. 30 383E-02 8 .773708 .554472 8.38127E-02 9 .831538 .629455 6.84666E-02 10 .951364 .821389 .173849 11 .985289 .907787 5 . 86623E-02 12 1. 1. 2.80652E-02 Sum of (B-A)(C+D) = .656679 Lorenz = 1 - Sum((B-A)(C+D) = .343321 203 LORENZ CONCENTRATION RATIO CALCULATIONS x(i) y (i) zci) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Imperial County 0 5 .40222E-02 2.9 7965E-03 1. 609 67E-04 1 .125746 2.01332E-02 1.65773E-03 2 .210385 5 . 28502E-02 6.17725E-03 3 .31679 .110407 1.73715E-02 4 .437816 .193196 3.67437E-02 5 .560414 .294962 5 .9 8475E-02 6 .670229 .403202 7.66685E-02 7 .745427 .48868 6.70681E-02 8 .802137 .561337 5.95467E-02 9 .846391 .624927 5.24965E-02 10 .949256 .810078 .147612 11 .987085 .91869 6.53969E-02 12 1. 1. 2.47808E-02 Sum of (B-A)(C+D) = .615528 Lorenz = 1 - Sum((B-A)(C+D) = . 384472 Inyo County 0 3 . 87748E-02 1.35146E-0 3 5 .2402 8E-05 1 .10883 1.9 766IE-02 1.47940E-0 3 2 .182796 5.02247E-02 5.17690E-03 3 .275334 .102875 1.41676E-02 4 . 35712 .162209 2.16801E-02 5 .518084 .303739 7.50012E-02 6 .672206 .463425 .118237 7 .775823 .588958 .109045 8 .839687 .675883 8.0778 3E-0 2 9 .900293 .768006 8.7 50 84E-0 2 10 .979798 .919952 .134201 11 .994461 .964424 2.76302E-02 12 1. 1. 1. 0 8815E-02 Sum of (B-A)(C+D) = .685838 Lorenz = 1 - Sum((B-A)(C+D) = .314162 LORENZ CONCENTRATION RATIO CALCULATIONS Income Class X(I) Cum Per Cent of Families Y( I) Cum Per Cent of Income Z(I) (B-A)(C+D) 0 3.80412E-02 Kern County 1.9 469 5E-0 3 7.40644E-05 1 .10537 .018104 1. 35001E-03 2 .1861116 4.79719E-02 5 . 33733E-03 3 .281827 9 . 76048E-02 1.39289E-02 4 .383757 .165408 2.68087E-02 5 .508354 . 266556 5.38215E-02 6 .625313 . 378202 7 . 54101E-02 7 .718737 .481519 8 . 0 3185E-0 2 8 .78897 .569269 7.38002E-02 9 .841779 .643366 6. 40 381E-02 10 .957266 .844376 .171814 11 .989279 .93279 5. 68924E-02 12 1. 1. 2. 0 722 3E-0 2 Lorenz = 1 - Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .355684 .644316 Kings County 0 5 . 712 3 8E-02 3 . 39 2 20E-0 3 1.9 3776E-04 1 .147486 2.7909 7E-02 2. 82 851E-0 3 2 . 2538 7 .1266 7E-0 2 1.0 5438E-0 2 3 . 372975 .142137 2.54323E-02 4 .505679 .242651 5.10629E-02 5 .621597 .348057 6.84736E-02 6 .723067 .458182 8.18089E-02 7 .791298 .543304 6.83325E-02 8 .843661 .617924 6.08059E-02 9 .881577 .677796 4.912 7 8E-0 2 10 .964256 .843317 .125764 11 .989811 .925142 4.519 36E-02 12 1. 1. 1.9 614 8E-0 2 Sum of (B-A)(C+D) = .609183 Lorenz = 1 - Sum((B-A)(C+D) = .390817 205 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Lake County 0 5.01672E-02 1. 58207E-03 7. 9 36 81E-0 5 1 .177258 3. 85568E-02 5.10126E-0 3 2 .31677 .102543 1.9 6 85 2E-0 2 3 .4-51505 .18848 .039211 4 .562351 .279367 5 .185 88E-0 2 5 .665074 .381701 6.79071E-02 6 .751792 .483154 7.499 81E-0 2 7 .817248 .571236 6.90164E-02 8 .858576 .634873 4.9 846 3E-0 2 9 .901577 . 709315 5 .7 800 7E-0 2 10 .96775 .852172 .103328 11 .988533 .920227 3.68368E-02 12 1. 1. 2.20188E-02 Sum of (B-A)(C+D) = .597688 Lorenz = 1 - Sum( (B-A) (C+D) = .<+02312 Lassen County 0 2.9 3542E-02 1. 26752E-03 3.72070E-05 1 8.83422E-02 1.59157E-02 1.01360E-0 3 2 .145373 3 . 83014E-02 3.09 206E-0 3 3 .220855 7 .99 7 85E-0 2 8.92803E-03 4 .355046 .174257 3.41161E-02 5 .523344 .316215 8.25452E-02 6 .654739 .447938 .100406 7 .739446 .546511 8.42376E-02 8 .816606 .647558 9.21339E-02 9 .876433 .735792 8.27613E-0 2 10^ .98686 .940276 .185085 11 .994129 .960897 .013819 12 1. 1. 1.15121E-02 Sum of (B-A)(C+D) = .699687 Lorenz = 1 - Sum((B-A)(C+D) = .300313 206 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Los Angeles County 0 2. 9 86 3 3E-0 2 1.39105E-03 4.15412E-05 1 7 .19 0 84E-0 2 9.51476E-03 4 . 5 85 36E-04 2 .12576 2.56468E-02 1. 89 350E-0 3 3 .191196 5.30637E-02 5.15051E-03 4 .274259 9 . 7637 3E-0 2 1.25176E-02 5 .381775 .167867 .028546 6 .495251 .255378 4. 80281E-02 7 .598015 .346682 6.18703E-02 8 .684465 .433804 6.74728E-02 9 .754332 .512492 6.61149E-0 2 10 .9 2-2 38 8 .748435 .211907 11 .977644 .870528 8.9 4564E-0 2 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .364725 Madera County .041818 .635275 0 6.91969E-02 3 . 5 76 32E-0 3 2.47470E-04 1 .162427 3.0 2406E-02 3.15277E-03 2 .297617 8.75058E-02 .015918 3 .425696 .166471 3. 2529 IE-02 4 .550471 .262941 5 . 3579 7E-02 5 .656619 .366898 6.68565E-02 6 .746745 .468682 7.5307 7E-0 2 7 .802023 .540626 5.57919E-02 8 . 85559 8 .619793 6.21695E-02 9 .888744 .675417 4.29 316E-02 10 .961246 .824403 .108739 11 .98538 .903746 4.17068E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .413236 2.78337E-02 .586764 LORENZ CONCENTRATION RATIO CALCULATIONS Income Class X(I) Cum Per Cent of Families YCI) Cum Per Cent of Income Z(I) (B-A)(C+D) 0 2.21763E-02 Marin County 1. 09393E-03 2. 42 59 2E-0 5 1 .01+6742 5 . 26169E-0 3 1.56130E-04 2 8. 80 876E-0 2 1.58006E-02 8 . 70 835E-04 3 .142159 3.53 811E-0 2 2 . 76747E-03 1 + .20211 6.30795E-02 5 .90283E-03 5 .287433 .111437 1.48902E-02 6 .387602 .178433 .029036 7 .489731 .256973 4.44676E-02 8 .585577 .341533 5 . 73648E-02 9 .666148 .420531 6.1399 7E-02 10 .877681 .67976 .232749 11 .965903 .848044 .134786 12 1. 1. 6.30122E-02 Lorenz = 1 - Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .352573 .647427 0 .102305 Mariposa County 4.12716E-0 3 4.22 231E-04 1 . 208934 .036568 4. 339 25E-03 2 .289625 7.50278E-02 9 .0 0 485E-0 3 3 .40562 .151414 .026266 4 .539625 .263939 5.56598E-02 5 .673631 .400315 8.90139E-02 6 .784582 .533371 .103593 7 .855187 .632376 8. 2307 8E-0 2 8 .897695 .699341 5 . 66076E-02 9 .926513 .750042 .041769 10 .976225 .860008 8. 00 385E-02 11 .985591 .892887 1.64176E-02 12 1. 1. .027275 Sum of (B-A)(C+D) = .592715 Lorenz = 1 - Sum((B-A)(C+D) = .1+07285 208 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Mendocino County 0 4. 30464E-02 1.14101E-03 4.91163E-05 1 .107931 1.55219E-02 1.0 8117E-0 3 2 .176049 4.17075E-02 3 . 898 31E-0 3 3 .267502 .090505 1.20913E-02 4 .386471 .171087 3.11213E-02 5 .527909 .286164 6.46727E-02 6 .657127 .41061 9 . 00 356E-02 7 .742668 .506429 7.84443E-02 8 .815831 .599571 8.09183-02 9 .864711 .669375 6.20267E-02 10 .961605 .837984 .146054 11 .989593 .91754 4.91336E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .360518 Merced County 1.9 9 555E-02 .639482 0 6.0 87 87E-0 2 2.71877E-03 1.65515E-04 1 .144928 .025154 2.34267E-03 2 .264322 7.60729E-02 .012086 3 .400845 .157265 3.18558E-02 4 .523829 .251158 5 . 0 2294E-02 5 .636682 .356957 6.86274E-02 6 .726955 .455913 7.33802E-02 7 .793785 .541394 6 . 66 50 3E-02 8 .845668 .61615 .060057 9 .882241 .675852 4.72519E-02 10 .963745 .840468 .123587 11 .988188 .918011 4.29 813E-02 12 1. 1. Sum of (B-A)(C+D) = 2.26 561E-0 2 .601871 Lorenz = 1 - Sum((B-A)(C+D) = .398129 209 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Modoc County 0 3.47349E-02 1.452 31E-0 3 5.04457E-05 1 .110603 .019695 1.60441E-03 2 . 20064 5.39155E-02 6.62763E-03 3 .285649 9 .9 3647E-02 1. 30 30 2E-0 2 4 .406307 .181448 3.38824E-02 5 .538391 .289328 6.2182IE-0 2 6 .653108 .400685 7.91559E-02 7 .734004 .491837 7.22013E-02 8 .792505 .56602 6.18856E-02 9 . 850091 .648258 6.99265E-02 10 .953839 .834283 .15381 11 .989488 .932205 6.29735E-02 12 1. 1. 2.0 3111E-0 2 Sum of (B-A)(C+D) = .637641 Lorenz = 1 - Sum((B-A)(C+D) = .362359 Mono County 0 4.89396E-03 1.36979E-04 6.70371E-07 1 3.91517E-0 2 7 . 36833E-03 2.57115E-04 2 .096248 2. 62495E-02 1.919 45E-0 3 3 .163132 5 .6 80 89E-0 2 5.55529E-03 4 .313214 .144246 3.01746E-02 5 .464927 .251368 6.0 019 6E-02 6 .574225 .342308 6.48879E-02 7 .649266 .415314 5 . 6 8526E-02 8 .77814 .556176 .1252 9 .805873 .590027 .031787 10 .929853 .780306 .169895 11 .982055 .90745 8.81047E-02 12 1. 1. 3.42283E-02 Sum of (B-A)(C+D) = .668882 Lorenz = 1 - Sum((B-A)(C+D) = .33118 210 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Monterey County 0 .038961 1.5 35 34E-0 3 5 .9 8185E-05 1 .08967 1. 3170 3E-02 7.45711E-04 2 .169588 4. 215 35E-0 2 4.42139E-0 3 3 .288032 .101275 1.69882E-02 4 .406383 .177249 3.296 39E-0 2 5 .52797 .27273 5.47116E-02 6 .635377 .372441 6. 9295 7E-0 2 7 .723647 .466663 .074068 8 .790097 .54708 6.73626E-02 9 .841701 .616825 .060062 10 .947547 .794172 .149349 11 .983663 .891028 6.0 8624E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .378216 Napa County 3.0893 8E-0 2 .621784 0 2.82828E-02 1.38665E-03 3.9 218 3E-0 5 1 7.9229 8E-0 2 1.30265E-02 7.34306E-04 2 .148485 3.74542E-02 3.49 60 4E-0 3 3 .222601 7.449 77E-02 8.29 745E-0 3 4 .317992 .134415 1.99285E-02 5 .43346 .222291 4.11878E-02 6 .560354 .336551 7.09137E-02 7 .674937 .457542 9 .09 89 7E-0 2 8 .76774 . 56804 9.51771E-02 9 .833018 .654817 7.9 8254E-02 10 .959028 .857385 .190553 11 .990215 .942281 .056126 12 1. Sum 1. of (B-A)(C+D) = 1. 90059E-02 .676274 Lorenz = 1 - Sum((B-A)(C+D) = .323726 211 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Nevada County 0 3.36035E-02 1. 516 8 3E-0 3 5.09 707E-0 5 1 .120061 2.3960 2E-0 2 2.20268E-03 2 . 225599 6 . 72 75 3E-0 2 9 .627 82E-0 3 3 . 3205 .122041 1.79652E-02 4 .437521 .207987 3.86202E-02 5 .586626 .339461 8. 1627 2E-0 2 6 .689463 .447231 8.09009E-02 7 .766971 .541517 7.66355E-02 8 .82945 .62705 7 . 3010 7E-0 2 9 . 879433 .70411 6.6 5 35 5E-0 2 10 .970111 .879643 .143613 11 .992063 .944741 4.00489E-02 12 1. 1. 1.54345E-02 Sum of (B-A)(C+D) = .646273 Lorenz = 1 - Sum((B-A)(C+D) = .353727 Orange County 0 2.87942E-02 1.12 804E-0 3 3.24809E-0 5 1 6. 3596 3E-02 7.7 3 821E-0 3 3.0 8564E-04 2 .110308 2.20549E-02 1.39168E-03 3 .168014 4.6866 5E-0 2 3.9 7719E-0 3 4 .244529 8.87765E-02 1. 0 37 88E-0 2 5 . 353653 .16169 2.73319E-02 6 .475147 .257516 5.09 30 7E-0 2 7 .588607 .360657 .070138 8 .684963 .459726 7.9 049 2E-0 2 9 .758152 .543781 7.34454E-02 10 .932499 .792036 .232896 11 .982694 .904457 8.51554E-02 12 1. 1. .032958 Sum of (B-A)(C+D) = . 667993 Lorenz = 1 - Sum((B-A)(C+D) = .332007 212 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B.-A).(C+D) Placer County 0 3.72322E-02 7.9 229 3E-04 2.9498 8E-0 5 1 8.85391E-02 1.31942E-02 7.17605E-04 2 .164044 4.19 79 3E-0 2 4.16 5 85E-0 3 3 .240657 8. 20 715E-0 2 .009504 4 .353255 .157547 2. 69 806E-02 5 .49116 .269805 .058934 6 .618595 .395025 8.47229E-02 7 .719337 .508554 9.1028 3E-0 2 8 .792276 .600633 .080903 9 .853221 .686702 7.84557E-02 10 . 9636 .881887 .17314 11 .994384 .966674 5 .69064E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .323467 Plumas County 1.10449E-02 .676533 0 2.48307E-02 1. 06556E-03 2.64585E-05 1 7.9 6 517E-0 2 1.459 47E-0 2 8. 5 8513E-0 4 2 .140922 3.84957E-02 3 . 2 52 88E-0 3 3 .236053 9.06965E-02 1.22901E-02 4 .378265 .189993 3.9 9174E-0 2 5 .5208 .309476 7.11915E-0 2 6 .651725 .439916 9.81144E-02 7 .746533 .549559 9 . 3 810 3E-0 2 8 .821025 .64651 8. 9 09 77E-0 2 9 .870042 .718353 6.69007E-02 10 .971622 .905291 .16493 11 .99613 .974385 4.60675E-02 12 1. 1. Sum of (B-A)(C+D) = 7.64032E-03 .694098 Lorenz = 1 - Sum((B-A)(C+D) = .305902 213 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class. . of. Families of Income (B-A)(C+D) 0 3.9392 3E-0 2 Riverside County 1. 59 836E-0 3 6 . 296 32E-05 1 .110823 1.85804E-02 1.4413 8E-0 3 2 . 206034 5.41364E-02 6.92343E-03 3 .303229 .105917 1. 55565E-02 4 .416915 .182661 3. 2 80 71E-0 2 5 .53686 .281746 5 .570 35E-0 2 6 .644108 .386282 7.16442E-02 7 .731443 .484782 7. 60743E-02 8 .795633 .566826 6.75034E-02 9 .846388 .639019 6.12021E-02 10 .956396 .836593 .16233 11 .988549 .927119 5 .67079E-02 12 1. 1. 2. 20679E-02 0 Lorenz = 1 - 2. 200 34E-02 Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .369976 Sacramento County 1. 0 300 8E-0 3 .630024 2.26651E-05 1 5 . 59 325E-02 7.99 774E-0 3 3.06306E-04 2 .103138 2.26891E-02 1.4485 8E-0 3 3 .165704 . 0503 4.56669E-03 4 .248047 9.67123E-02 1.21054E-02 5 . 366665 .178171 .032606 6 .489129 .276964 5.57376E-02 7 .598063 .378659 7.14202E-02 8 .690855 .476938 7.9 39 22E-02 9 .765782 .565312 7. 809 24E-02 10 .941193 .822592 .243453 11 .98674 .927857 7.9 7274E-02 12 1. 1. 2.55643E-02 Sum of (B-A)(C+D) = .684443 Lorenz = 1 - Sum((B-A)(C+D) = .315557 214 Income Class LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y (I) Z(I) Cum Per Cent Cum Per Cent of Families of Income (B.-A).(.C+D) 0 4.9 329 8E-0 2 San Benito County 1.96111E-0 3 9.67410E-05 1 .120643 1.91144E-02 1.50298E-03 2 .201877 5.11209E-02 5.7 0 545E-0 3 3 . 32252 .114717 2. 000 72E-02 4 .439678 .197146 3 .6537 3E-0 2 5 .551743 .291826 5.479 6 4E-0 2 6 .67185 .411198 8.4438 3E-0 2 7 .760858 .512759 8.22396E-02 8 . 829759 .602483 7.68411E-02 9 .868901 .66001 4.94166E-02 10 .95496 .819802 .127351 11 .98874 .918086 5 . 87062E-02 12 1. 1. 2. 159 7 8E-0 2 Lorenz = 1 - Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .380763 .619237 San Bernardino County 0 3.37071E-02 1.71674E-03 5.78664E-05 1 9.11094E-02 1.54931E-02 9.87884E-04 2 .171149 4.57464E-02 4.90157E.03 3 .256581 9 . 07429E-02 1.16606E-02 4 .36499 .164913 2.77154E-02 5 .5003 .277386 5.9 8474E-0 2 6 .625282 .399747 8.46296E-02 7 .720142 .506839 8 .599 86E-02 8 .79351 .600689 8.12566E-02 9 . 850296 .681645 7.28191E-02 10 .965511 .883405 .180317 11 .993368 .959929 5.13485E-02 12 1. 1. 1. 29991E-02 Sum of (B-A)(C+D) = .67454 Lorenz = 1 - Sum((B-A)(C+D) = .32546 LORENZ CONCENTRATION RATIO CALCULATIONS Income Class. . X(I) Cum Per Cent . of Families Y( I) Cum Per Cent of Income.... Z(I) (B-A).(C+D) 0 3.97216E-02 San Diego County 1. 8 8 75 3E-0 3 7.4975 8E-0 5 1 8.61553E-02 1.18384E-02 6 . 37345E-04 2 .150606 .033337 2.9116 OE-O 3 3 .229927 7.04911E-02 8 . 23576E-0 3 4 .322819 .126279 1.82782E-02 5 .436221 .209224 3.80467E-02 6 .553235 .310152 6.0 7 743E-02 7 .653425 .409932 7.21454E-02 8 .736921 .504145 7.63222E-02 9 .798548 .581777 6.69219E-02 10 .944057 .809374 .202425 11 .984752 .909653 .069955 12 1. 1. 2.91187E-02 Sum of (B-A)(C+D) = .645847 Lorenz = 1 - Sum((B-A)(C+D) = .354153 San Francisco County 0 3.18 359E-0 2 1.62165E-03 5.16268E-05 1 7.79994E-02 1. 07974E-02 5.7 3307E-04 2 .134656 2.81613E-02 2.20726E-03 3 .210469 6 . 06958E-02 6.73652E-03 4 .305784 .113013 1.6 55 72E-02 5 .419267 .188506 3.42174E-02 6 .531844 .277054 5.24112E-0 2 7 .62889 .365314 6.23392E-02 8 .707587 .446367 6.38769E-02 9 .773814 .522539 6.41672E-02 10 .928318 .743203 .195563 11 .978498 .857175 8 .0 3059E-02 12 1. 1. 3.99 3 35E-0 2 Sum of (B-A)(C+D) = .61894 Lorenz = 1 - Sum((B-A)(C+D) = .38106 216 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) San Joaquin County 0 4.19 315E-02 2.43770E-03 1.02216E-04 1 . 104-771 1.74131E-02 1.24742E-03 2 . 18821+ 4.81084E-02 .005469 3 . 279905 9 . 59 333E-02 1.32035E-02 4 .387616 .168287 2.84595E-02 5 .514051 .270836 5 . 55206E-02 6 .628628 .380462 7 .46236E-02 7 .721787 .483349 .080472 8 .796485 .576853 7.919 52E-0 2 9 .850719 .652209 6.66562E-02 10 .95526 .837922 .15578 11 .98755 .927145 5.69 9 47E-0 2 12 1. 1. 2.39924E-02 Sum of (B-A)(C+D) = .641717 Lorenz = 1 - Sum((B-A)(C+D) = .358283 0 4.83235E- San Luis Obispo County 02 1.71880E-0 3 8. 305 84E-0 5 1 .124337 2.069 21E-0 2 1.70353E-03 2 .211543 5 .50023E-02 6 . 60102E-0 3 3 .313835 .110759 1.69561E-02 4 .426833 .19012 3. 399 88E-02 5 .537934 .284683 5.27508E-02 6 .647525 .396033 7.46 0 09E-0 2 7 .737992 .501853 8.12288E-02 8 .813081 .600719 8.27908E-02 9 .866028 .679121 6.77632E-02 10 .959901 .850066 .14355 11 .989537 .934595 5 . 289HE - 02 12 1. 1. 2.02413E-02 Lorenz = Sum of (B-A)(C+D) = 1 - Sum((B-A)(C+D) = .364841 .635159 217 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) San Mateo County 0 1.8466 3E-02 7 .9 3064E-04 1.46450E-05 1 4.12662E-02 4.53851E-03 1.21559E-04 2 7.24691E-02 1. 20 891E-02 5.18829E-04 3 .112739 2 . 56804E-02 1.52098E-03 4 .170335 .050754 4.40228E-03 5 .257992 9. 73 80 8E-02 1.29851E-02 6 .371676 .168415 3.02168E-02 7 .489669 .253367 4.9 76 71E-0 2 8 .589892 .335148 5 . 89 833E-02 9 .676435 .414057 .064838 10 .892514 .726138 .246372 11 .967265 .859905 .118558 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .350816 Santa Barbara County 6.0 8847E-02 .649184 0 2.84555E-02 2.21025E-03 6. 289 36E-05 1 6.6 7 701E-0 2 9.60486E-0 3 4.5269IE-04 2 .127596 .027593 2.26259E-03 3 . 2074 6 .1060 3E-02 7.0 7491E-0 3 4 .296276 .108634 1.50817E-02 5 .401886 .177207 3.01876E-02 6 .521127 .268849 .053188 7 .619002 .355822 6.11399E-02 8 .698806 .434415 6.30643E-02 9 . 76763 .511667 6.5112 3E-0 2 10 .926092 .735627 .19765 11 .977489 .848018 8.139 39E-02 12 1. 1 . Sum of (B-A)(C+D) = 4.16014E-02 .618272 Lorenz = 1 - Sum((B-A)(C+D) = .381728 218 LORENZ CONCENTRATION RATIO CALCULATIONS xu) y (i ) zd) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Santa Clara County 0 2. 57 374E-0 2 1.09 25IE-0 3 2.81182E-05 1 5 .95 831E-0 2 7 . 5 7 36 7E-0 3 2.9 3 313E-04 2 .101525 2.00858E-02 1.16008E-03 3 .155357 4.2 5411E-02 3.37139E-03 4 .226769 8.06862E-02 8. 799 85E-0 3 5 .332335 .149705 2.43215E-02 6 .453254 .24297 4.74819E-02 7 . 565403 .342622 6.56 7 3 3E-0 2 8 .663151 .440893 7.65869E-02 9 .73786 .524817 7.21472E-02 10 .924282 .786972 .244547 11 .982604 .913743 9 .9189 3E-02 12 1. Lorenz = 1 - 1 . Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .323109 Santa Cruz County .033291 .676891 0 5.35491E-02 4. 77751E-0 3 2.5 5 832E-04 1 .143515 2.81468E-02 2.9 6207E-0 3 2 . 258534 7 . 35 887E-02 1.17015E-02 3 .363006 .130734 2.13461E-0 2 4 .461022 .200413 3.24575E-02 5 .580948 .304434 6.05443E-02 6 .683182 .409674 7.30062E-02 7 . 757608 .49797 6.75526E-02 8 .813525 .57318 5 .9 89 51E-0 2 9 .855452 .635512 5.06765E-02 10 .95209 .814113 .140089 11 .986096 .914926 5 . 879 82E-02 12 1. 1. Sum of (B-A)(C+D) = 2.66248E-02 .60591 Lorenz = 1 - Sum((B-A)(C+D) = .39409 LORENZ CONCENTRATION RATIO CALCULATIONS Income Class X(I) Cum Per Cent of Families Y( I) Cum Per Cent of Income Z(I) (B-A)(C+D) 0 3.42427E-02 Shasta County 1.4850 3E-0 3 5.0 8513E-05 1 9.53225E-02 1.53736E=-2 1.029 72E-0 3 2 .170264 .044123 4.45876E-0 3 3 .250142 8.55504E-02 1.0 35 81E-0 2 4 .359959 .159418 2.69018E-02 5 .501487 .273219 6 .12 30 2E-0 2 6 .620862 .388389 7.89792E-02 7 .719603 .498391 .087561 8 .800494 .598659 8.87417E-02 9 .85594 .676199 7 .06865E-02 10 .965061 .867809 .168483 11 .990696 .937797 4 . 6 2 859E-0 2 12 1. 1. .01803 Lorenz = 1 - Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .337203 .662797 Sierra County 0 4.6 5116E-0 2 2.13154E-0 3 9.91414E-0 5 1 9.76744E-02 1.56156E-02 9.07995E-04 2 .16124 4.20965E-02 3.66852E-0 3 3 .234109 8 .479 76E-0 2 9.24654E-0 3 4 .378295 .192311 3.99552E-02 5 .51938 .318613 7.20839E-02 6 .710078 .52151 .16021 7 .790698 .62108 9.2115 8E-02 8 .855814 .711585 8.67782E-02 9 .883721 .755267 4.09 354E-02 10 .984496 .953322 .172183 11 1. 1. 3.0 2841E-02 12 1. 1. 0 Sum of (B-AXC+D) = .708468 Lorenz = 1 - Sum((B-A)CC+D) = .291532 220 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Siskiyou County 0 3.38888E-02 5 . 9 0 510E-04 2.00117E-05 1 9.17123E-02 1.53343E-02 9.20829E-04 2 .167655 4.5 320 7E-0 2 4. 60628E-03 3 .262163 9 .9680 3E-0 2 1. 370 38E-02 4 .414271 .208739 4.69131E-02 5 .567834 .341719 8.45296E-02 6 .684935 .463081 9.42429E-02 7 .772285 .568355 9 .00963E-02 8 .836819 .655777 7;899 84E-0 2 9 .883458 . 726608 6.44732E-02 10 .969355 .881623 .138141 11 .993513 .956488 4.4405 8E-0 2 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .326257 Solano County 1.26917E-02 .673743 0 3.0149 8E-02 1. 38560E-0 3 4.17757E-05 1 8.0 309 3E-02 1.21959E-02 6.81241E-04 2 .16122 4.28184E-02 4.45127E-0 3 3 .25853 9.39553E-02 1. 3309 4E-02 4 .360564 .163573 2.6 2 76 7E-0 2 5 .481796 .26466 5.1915 3E-02 6 .611813 .391664 8. 5 3336E-02 7 .70807 .499264 8.57578E-02 8 . 787507 .599479 8.72805E-02 9 .848619 .687122 7.86269E-02 10 .970061 . 89 8092 .192511 11 .993621 .963373 4.38565E-02 12 1. Sum 1. of (B-A)(C+D) = 1. 25244E-02 .682567 Lorenz = 1 - Sum((B-A)(C+D) = .317433 221 Income Class LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Cum Per Cent Cum Per Cent of Families of Income (B-A)(C+D) Sonoma County 0 4.70698E-02 2.25527E-03 1.06155E-04 1 .124-776 2.119 34E-02 1. 82212E-0 3 2 .219331 5.76 691E-0 2 7.45679E-03 3 .30852 .105813 1.45808E-02 4 .415619 .180302 3 .06427E-02 5 .532075 .278735 5. 345 77E-02 6 .649335 . 394757 7 .89 7 36E-02 7 .741375 .500271 8.23785E-02 8 .809181 .588384 7.38167E-02 9 .857028 . 658049 5 .96386E-02 10 .960887 .848327 .156451 11 .988906 .929496 4.9 812 8E-0 2 12 1. 1. 2.14049E-02 Sum of (B-A)(C+D) = .630543 Lorenz = 1 - Sum((B-A)(C+D) = .369457 0 . 5.96867E-02 Stanislaus County 3. 36164E-0 3 2.00645E-04 1 .142127 2.31424E-02 2.18499E-03 2 .245393 6.61679E-02 9.222 71E-0 3 3 .351697 .128246 2.06671E-02 4 .467587 .214663 3 . 9 739 8E-02 5 .59205 .326965 6.74125E-02 6 .701591 .443554 8.44035E-02 7 .78203 .542283 7. 9 299 5E-0 2 8 .841346 .624992 6 . 92 383E-02 9 .882603 .689558 5 .42 343E-02 10 .962795 .846038 .123142 11 .989253 .928678 4.69569E-02 12 1. 1. 2.0 726 7E-0 2 Sum of (B-A)(C+D) = .617429 Lorenz = 1 - Siam((B-A) (C+D) = .382571 222 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) ZCI) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Sutter County 0 .04-2 72 7. 85944E-04 3. 35756E-05 1 9.43352E-02 1.33875E-02 7.31565E-04 2 .184691 4.76287E-02 5.51317E-03 3 .299274 .108538 1.78941E-02 4 .420295 .191502 3.63109E-02 5 .539209 .290344 5.72981E-02 6 .652037 .40075 7.79745E-02 7 .741105 .501204 8.03355E-02 8 .79986 .576702 .063332 9 .849251 .647795 6.04796E-02 10 .953301 .831736 .153945 11 .98853 .929578 .06205 12 1. 1. 2.2132 3E-0 2 Sum of (B-A)(C+D) = .63803 Lorenz = 1 - Sum((B-A)(C+D) = .36197 Tehama County 0 4.25 816E-02 1. 78620E-03 7.60592E-05 1 .121217 2.17437E-02 1.85028E-03 2 .204599 .056409 6.51660E-03 3 .299555 .109225 1.57278E-02 4 .404896 .187427 3.12497E-02 5 .56632 .331332 8.37404E-02 6 .690653 .461718 9.86018E-02 7 .779822 .569075 9.19149E-02 8 .84822 .663055 8.42747E-02 9 .895549 .736452 6.62378E-02 10 .974036 .890221 .127672 11 .993472 .94989 3.57648E-02 12 1. 1. 1.27293E-02 Siam of (B-A) (C+D) = . 656356 JX Lorenz = 1 - Sum((B-A)(C+D) = .343644 223 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income .(B-A)(.C+D) Trinity County 0 .024787 6.41947E-04 1.59119E-0 5 1 7 .47483E-02 .012579 6.60533E-04 2 .132843 3.44604E-0 2 2 . 732 7 3E-0 3 3 .206042 7.28027E-02 7 . 85156E-03 4 .320294 .149736 2.54256E-02 5 .475213 .276479 6 .60 2 86E-0 2 6 .593339 .389973 7 . 87249E-02 7 .69907 .506818 9 .4 819 4E-0 2 8 .783501 .613584 9.45962E-02 9 .850116 .708292 8.80568E-02 10 .976762 .932826 .207841 11 .998451 .991149 4.17 2 84E-0 2 12 1. 1. 3.0 846 6E-0 3 Sum of (B-A)(C+D) = .711566 Lorenz = 1 - Sum( (B-A) (C+D) = . 2881+34 Tulare County 0 4.77878E-02 2.01140E-03 9 . 6120 3E-05 1 .136854 2.59137E-02 2.48717E-03 2 . 269946 8.11482E-02 1.42491E-02 3 .405449 .161292 3.28514E-02 4 .521423 .248375 4.75105E-02 5 .633466 .35188 6.72546E-02 6 .725811 .452238 7.42 561E-0 2 7 . 79296 .536688 6.64052E-02 8 .845184 .611283 5 .9 9 519E-02 9 .882508 .671049 4.78614E-0 2 10 .95906 .82366 .114423 11 .987486 .91378 4.9 3898E-02 12 1. 1. 2.39482E-02 Sum of (B-A)(C+D) = .600685 Lorenz = 1 - Sum((B-A)(C+D) = .399315 224 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y CI) Z(15 Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Tuolumne County 0 2.72473E-02 9 .51831E-04 2. 59 348E-05 1 8.12 325E-0 2 1.51744E-02 8. 705 81E-04 2 .174943 5.38513E-02 6.46 841E-0 3 3 .271709 .109032 1.5 7616E-0 2 4 .4082 .208278 .04331 5 .560733 .342699 8.40426E-02 6 .677617 .464076 9.429 84E-0 2 7 .768271 .574153 9.41201E-02 8 .842373 .675242 9.25831E-02 9 .885918 .741581 6.16951E-02 10 .976827 .915717 .150663 11 .995926 .973773 3.60 86 5E-0 2 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .312032 Ventura County 8.0 4186E-0 3 .687968 0 3.48275E-02 1.66567E-03 5.80112E-05 1 .078543 1.11454E-02 5.60041E-04 2 .144724 3 . 39 851E-02 2.9 86 76E-0 3 3 .228062 7.45111E-02 9.0419 2E-0 3 4 . 326214 .13487 2.05512E-02 5 .440309 .219884 4.04756E-02 6 . 568408 .33265 7.07787E-02 7 .670461 .436658 7.85098E-02 8 .751881 .530325 7.87321E-02 9 .812797 .60878 6 .9 389 8E-02 10 .951105 .830376 .199047 11 .986743 .920932 6.24121E-02 12 1. 1. Sum of (B-A)(C+D) = 2.54667E-02 .65801 Lorenz = 1 - Sum((B-A)(C+D) = .34199 225 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) Yolo County 0 2.78087E-02 1.18099E-03 3 .28417E-05 1 7.05722E-02 .011571 5.45322E-04 2 .13997 3.62114E-02 3.31601E-03 3 .230627 8.32629E-02 1.08311E-02 4 .33871 .15327 2 . 55652E-02 5 .471759 .259435 .05491 6 .589482 .370343 7.4139 6E-02 7 .690829 .478676 8.60457E-02 8 .77784 .585698 9.26114E-02 9 .837227 .667099 7 . 439 9 8E-0 2 10 .961933 .876906 .192547 11 .992399 .957133 5 . 58758E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .314304 Yuba County 1.48762E-02 .685696 0 4.31914E-02 9.41509E-04 4.0 6651E-0 5 1 .113977 2. 10 373E-02 1.55579E-03 2 .212478 6.37778E-02 8.35431E-03 3 .347451 .143843 2.80232E-02 4 .496221 .259109 5 . 99473E-02 5 .617756 .373259 7.68553E-02 6 .721896 .486155 8.9 49 87E-0 2 7 .79808 .583811 8.15151E-02 8 .85039 .6595 .065037 9 .886503 .718298 4.9 75 61E-02 10 .975525 . 89793 .14388 11 .993761 .957559 3. 38373E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .349486 1.22127E-02 .650514 226 LORENZ CONCENTRATION RATIO CALCULATIONS X(I) Y(I) Z(I) Income Cum Per Cent Cum Per Cent Class of Families of Income (B-A)(C+D) CAL.FAM.ONLY 0 3. 269 72E-02 1.517 79E-0 3 4.9627 5E-05 1 7.96525E-02 1.10916E-0 2 5.9207 6E-0 4 2 .140977 3.0599 3E-02 2.55667E-03 3 .213846 6. 307 89E-02 6.82620E-03 4 .303031 .113999 1.57927E-02 5 .415862 .19242 3.45736E-02 6 .531829 .287527 5.56 581E-02 7 .632854 .383093 6. 7749 IE-0 2 8 .716066 .472313 7.11804E-02 9 .7816 .550827 6.70505E-02 10 .934285 .778651 .20299 11 .981755 .890119 7.92171E-02 12 1. Lorenz = 1 - 1. Sum of (B-A)(C+D) = Sum((B-A)(C+D) = .361279 CAL.FAM+UNREL. 3.4485 3E-02 .638721 0 9.45526E-02 5 . 29760E-03 5 . 00902E-04 1 .196962 3.0 50 01E-0 2 3 . 66602E-0 3 2 .275045 6.0 480 3E-0 2 .007104 3 . 356763 .104444 1. 347 74E-0 2 4 .446945 .166591 2.44423E-02 5 .547559 .250996 4.2015 3E-0 2 6 .642927 .345399 5 .68769E-02 7 .722359 .436093 6. 20 75 7E-02 8 .786323 .518871 6.10828E-02 9 .835754 .590351 5. 48 304E-0 2 10 .950105 . 796296 .158564 11 .985955 .897903 6.07367E-02 12 1. 1. Sum of (B-A)(C+D) 2.66566E-02 = .572029 Lorenz = Sum((B-A)(C+D) = .427971 SELECTED BIBLIOGRAPHY 227 SELECTED BIBLIOGRAPHY Books Adams, Frances Gerard. Some Aspects of the Income Size Distribution; A Statistical Study. Unpublished Ph.D. dissertation, University of Michigan, 195 7. Adelman, Irma and Morris, Cynthia Taft. Society, Politics, and Economic Development: A Quantitative Approach. Baltimore: Johns Hopkins Press, 1967. Ames, Edward. Income and Wealth. New York: Holt, Rinehart and Winston, 196 9. Andie, Fuat M. Distribution of Family Incomes in Puerto Rico: A Case Study of the Impact of Economic Development on Income Distribution. Rio Piedras, P.R.: Institute of Caribbean Studies, University of Puerto Rico, 19 6*1. Baldwin, R. W. Social Justice. Oxford: Pergamon Press, 1966 . Becker, Gary Stanley. Human Capital and the Personal Distribution of~Tnocme: an Analytidal Approach, Ann Arbor: Institute of Public Administration, 1967 . Boulding, Kenneth E. Economic Analysis. Revised ed. New York: Harper and Brothers, 19*41. Brady, Dorothy S. "Measurement and Interpretation of the Income Distribution in the United States." International Association for Research in Income and Wealth. Income and Wealth. Series VI. London: Bowes and Bowes, 1957. ___________ . "Research on the Size Distribution of Income." Studies in Income and Wealth. Vol. XIII. New York: National Bureau of Economic Research, 1951. Budd, Edward C., ed. Inequality and Poverty. New York: W. W. Norton S Company, Inc., 1967. 228 229 Carter, Allen Murray. The Redistribution of Income in Postwar BritainT A Study of the Effects of the Central Government. New Haven: Yale University Press, 19 5 5 . Cole, Charles Leland. Income Distribution and the Social Welfare Junction: A Study of Theories of Distributive Justice. Unpublished Ph.D. Dissertation. University of Southern California, 1964. Cole, Dorothy and Utting, J. E. G. "The Distribution of Household and Individual Income." International Association for Research in Income and Wealth. Income and Wealth. Series VI. London: Bowes and Bowes, 1957. Conference on Research in Income and Wealth. Income Size Distributions in the United States: Part I. Vol. V of Studies in Income and Wealth. New York: National Bureau of Economic Research, 1943. Studies in Income and Wealth. Vol. III. New York: National Bureau of Economic Research, 1939 . ' ______. An Appraisal of the 1950 Census Income Data. Vol. XXII of Studies in Income and Wealth. 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Wealth and Power in America: An Analysis of Social Class and Income Distribution! New York: Praeger Publishers, Inc., 1962. Kravis, Irving B. The Structure of Income: Some Quantitative Essays! Washington, D.C.: University of Pennsylvania Press, 1962. Kuznets, Simon. Shares of Upper Income Groups in Income and Savings. New York: National Bureau of Economic Research, 195 3. _________. "Directions of Further Inquiry." Studies in Income and Wealth. Vol. XV. New York! National Bureau of Economic Research, 19 52. Lerner, Abba P. Everybody*s Business. East Lansing: Michigan State University Press, 1961. Leven, Maurice. The Income Structure of the United States. Washington^ D.C.: The Brookings Institution, 1938. ___________Moulton, H. G.; and Warburton, Clark. America* s Capacity to Consume. New York: Brookings Institution, 1934. Liebenberg, Maurice and Kaitz, Hyman. "An Income Size Distribution from Income Tax and Survey Data, 1944." Studies in Income and Wealth. Vol. XIII. 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Creator Black, Kelly Jarvis (author)

Core Title The Size Distribution Of Income And Its Relationship To Economic And Social Well-Being In The State Of California

Degree Doctor of Philosophy

Degree Program Economics

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

Tag Economics, General,OAI-PMH Harvest

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Advisor Phillips, E. Bryant (committee chair), Childress, Robert L. (committee member), Elliott, John E. (committee member)

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