THESIS LIBRARY Mi~ higan State University This is to certify that the thesis entitled An Econometric Analysis of the Demand for Basic Living Materials in Japan presented by Feng-Yao Lee has been accepted towards fulfillment of the requirements for .M— degree in- Economics /'.¢¢n¢II§zEE:;.rc///’ /41'M%¢’m Date July 28, 1965 0-169 Iv-il... l... .lvvl l l :- ABSTRACT AN ECONOMETRIC ANALYSIS OF THE DEMAND FOR BASIC LIVING MATERIALS IN JAPAN by Feng—Yao Lee In this study, information from both cross—section and time-series data was utilized to derive the statistical consumer‘demand functions for basic living materials in Japan during the period of 1951-1962. Basic living materials were classified into four groups: food, housing, fuel and light, and clothing. Food was further subdivided into four- teen items, housing into three, and clothing into two. In the cross—section analysis, the elasticities of income and family size were estimated by both the method of instrumental variables and least-squares regressions. Dummy variables were employed to investigate the stability of de— mand over time as well as the differences in consumption patterns among occupations, regions, city sizes, number of earners, and types of dwelling house. The expenditure elasticities obtained from cross— Section data were combined with the time—series data to estimate the elasticities with reSpect to own—price, "all Other prices," and related goods' prices. Also the income Feng-Yao Lee elasticities and other demand elasticities were estimated by the original least—squares regressions. The expenditure elasticities estimated by the instrumental variables method are very little different from those obtained by the least-squares regressions using total expenditure as an explanatory variable, but they are considerably larger than the corresponding income elasti- cities estimated by least-squares regressions. Since the expenditure elasticity obtained from the instrumental variables method has been shown to be the consistent estimate of the "true” parameter, and since it can be interpreted as the permanent income elasticity, the least— squares regression bias in estimating expenditure elasticity may be negligible with a sufficiently large sample size, and the income elasticity obtained by the least—squares regressions tends to be underestimated. Income elasticities estimated from the pure time— series equations are, in the majority of cases, considerably different from their corresponding cross-section estimates. 'Despite the divergence between the income elasticities from cross section and time series, the order of magnitudes of the income and expenditure elasticities resulting from both analyses contains few surprises. The own-price elasticities for a few items have im- plausible signs, but for most commodities the elasticities have the "right“ signs. Many of the cross—elasticities with reSpect to the prices of related goods have the expected Feng—Yao Lee signs and their magnitudes seem reasonable, but surprising relationships were found in quite a few cases. The results obtained by using the conditional regression and the pure time—series equation differ considerably in many cases and the latter approach appears to be superior to the former in terms of goodness of fit and the standard error of estimates. A cross-section test of the permanent income hypo— thesis indicates that Friedman's method of testing the per— manent income hypothesis with respect to individual goods is inadequate although the hypothesis cannot be rejected on the basis of this test. In time—series analysis, permanent income is found to be a better variable than disposable income in determining expenditures on basic living materials for farm households, but the opposite is true for urban households. Whenever transitory income was introduced along with perma— nent income in the equation, the results always appear to be better than those estimated by using disposable income alone as an independent variable. It is also found that expenditures on non—durable goods are determined almost solely by permanent income, and that the transitory income seems more important than permanent income in explaining the consumption of consumer durable goods. Although this study of the demand for basic living Inaterials has been based on somewhat imperfect data and has Litilized relatively simple methods, the analyses show that the puattern of consumer's behavior in quantitative terms can be slcetched out. In the great majority of cases, the results obtuained are those expected. AN ECONOMETRIC ANALYSIS OF THE DEMAND FOR BASIC LIVING MATERIALS IN JAPAN by Feng—Yao Lee A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1965 ACKNOWLEDGEMENTS The author wishes to express his deepest appreciation to Professor Thomas R. Saving, chairman of the thesis guidance committee, for his continual guidance, valuable suggestions and criticisms. Many of his ideas appear throughout this thesis. Special gratitude is expressed to Professors Paul E. Smith and Victor E. Smith, both members of the guidance com— mitee, for their advice and criticisms, which helped improve a great deal the contents and style of this thesis. Appreciation is also due to Professor Anthony Y. C. Koo for his comments on the proposal of this study, and to Professor Robert L. Gustafson for his suggestions in the Econometrics Workshop at Michigan State. Phillip Caruso and David R. Kamerschen deserve the author's appreciation for their comments on the early draft. Sincere thanks are due to Chin—Ching Liu, of Tokyo University, Japan, who patiently collected the data used in this study and questioned the staffs in the Japan's Bureau of Statistics concerning the data. Gratitude is also expressed to William IQuble for his generous help in the computer programs, and to Ddichigan State University for allowing many free hours on the CIDC 3600computer. Grateful acknowledgement is made to the Asian Studies Center of Michigan State University which supported this study through funds granted to Professor Thomas R. Saving. The author owes a great debt to his wife for her in- valuable assistance in many ways and her constant encouragement. TABLE OF CONTENTS ACKNOWLEDGEMENTS LIST OF TABLES LIST OF APPENDICES Chapter I. INTRODUCTION Purposes of the Study . Sources and Nature of the Data Used II. THEORETICAL CONSIDERATIONS AND STATISTICAL FORMULATIONS A Brief Survey of the Empirical Studies of Consumer Demand Theoretical Considerations of the Relevant Variables in Demand Relation Statistical Formulations III. ANALYSIS OF CROSS—SECTION DATA National Survey of Family Income and Expenditure Annual Report on Family Income and Expenditure Surveys . Farm Households Economy Survey Summary . . . . . . . IV. THE ANALYSIS BASED ON TIME SERIES General Report on Family Income and Expenditure Surveys Farm Households Economy Survey Summary . . . . . . 'V. REVIEW AND CONCLUSIONS BIBILIOGRAPHY . . . . . . .. APPENDICES Page ii viii Jl‘UU 11 22 U8 51 93 100 108 118 124 1A0 1A5 1A9 167 Table 10. LIST OF TABLES A comparison of the parameters estimated by least— squares and limited information methods . . . . . . . A comparison of elasticities estimated using price and quantity as the dependent variables in the least—squares equation Estimates of Engel Curves using least—squares and instrumental Variables Methods by Prais and Houthakker, and by Liviatan A comparison of the elasticities estimated from the tables classified by income groups and by total expenditure classes, all households . . . . . . . . . . A comparison of the elasticities computed from the resultant tables of different classifications, all Japan, worker house— holds . . . . . . . . Demand elasticities estimated for typical worker households Results of the estimation of coefficients, all Japan, all households . . . . Monthly expenditure on rent by type of tenure of dwelling houses, worker households, all Japan . . . . . . . . . . . . Income elasticities estimated for five types of tenure of dwelling houses using dummy variables, all Japan . . . . . . . Income elasticities estimated for the number of earners using dummy variables, worker households, all Japan . . . . V Page 31 M6 53 SH 57 59 61 63 65 67 Table 11. 12. 13. 1A. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. Page Average monthly receipts and disbursements per household by number of earners, worker households . . . . . . . . . . . . . . . . 69 A comparison of the estimates of income elasticities among four occupational groups 72 Monthly average income and the consumption of basic living materials per household in different occupations . . . . . . . . . . 75 Results of the test using dummy variables in differences of income elasticity among ten occupations, all Japan . . . . . . . . 78 Distribution of the number of households among the five types of tenure of dwelling houses, all Japan . . . . . . . . . . . . . . . . . 82 Income elasticities estimated for the eight regions using dummy variables . . . . . . . . 86 Income elasticities estimated for four city sizes using dummy variables, worker households 89 Income elasticities estimated for urban-rural using dummy variables, all Japan . . . . . . 92 Estimates of ARFIES (worker households), 1951, 1957, and 19 2 . . . 95 Income elasticities estimated for urban house— holds from 1951 to 1962, using dummy variables 97 Income elasticities estimated for urban house- holds from 1953 to 1962, using dummy variables 97 Demand relationships for basic living materials for farm households, 1962 . . . . 101 Income elasticities estimated for farm house- holds from 1959 to 1962 using dummy variables 103 A comparison of income elasticities of farm households with worker households (in the cities with population of 50,000 or more), 1959 . . . . . . . . . . . . . . 106 Summary of the B1 estimated for basic living materials . . . . . . . . . . . . . . . . . . lll Table 26. 27. 28. 29. Summary of the family size elasticities for basic living materials . . . Demand analysis for basic living materials based on time series, 1951—1962 and 1953—1962, urban worker households (Family Income and Expenditure Survey) Demand analyses for basic living materials based on time series, 1951—1962 (Far Households Economy Survey) . . . . . . Summary of demand elasticities based on time—series data . . . . . . . . Page 113 126 1A1 147 Appendix A. LIST OF APPENDICES 0n the practical application of the dummy variables . A comparison of the elasticities estimated from the tables classified by income groups and by total expenditure classes, worker households . . . . . . A comparison of the elasticities estimated from the tables classified by income groups and by total expenditure classes, general households . . . . . . . . Occupation classification table The Bi of basic living materials in ten occupations . . . . . . . . . . . Tests of the equality of coefficients among ten occupations . . . . . . . . . Computed values of F— statistic of the variances homogeneity of the regressions of ten occupations . . . . . . Test of the equality of the regression coefficients for ten occupations Page 168 171 172 173 1711 176 178 CHAPTER I INTRODUCTION Although the econometric study of demand relation— ships can be traced back to a little more than a century ago when Engel studied the pattern of consumer expenditure and proposed a law of consumption in 1857, there had not been much progress in this area before the 1930's. Compared with Mflier fields of economics, the empirical study of demand is stiLll in its infancy. The reason for this is not that this area.was unimportant or neglected, but rather that its re— search involved many difficulties. As recently as three decades ago data were seldom available, and statistical tech— niques of estimation and testing hypotheses were not well developed.1 Over the past few decades, a considerable number of empirical demand analyses have been made. These studies, however, have almost exclusively been based on data of the United States and some European countries because of the lack of suitable observations in the rest of the world. To be sure, Japan is a noteworthy exception to this generalization. In fact, Japan seems to have the greatest wealth of data in the WOI‘ld. It is,perhaps, the only country that has had both urban \ 1The difficulties and problems of empirical demand analVsis have been fully discussed by Richard Stone, The ~§$§g§ement of Consumers' Expenditure and Behavior in the gEieg Kingdom, 1920-1938, Vol I (Cambridge University I’e'fis, 195A), and Herman Wold and Lars Jureen, Demand Analy— EEE: (New York: John Wiley and Sons, Inc., 1953 . l .L 2 :family budget survey and farmer's budget survey every year cover a long period of time. And Japan's national income and expenditure survey in 1959 covered as many as 42,000 house— holds. This sample is probably the largest available any— where. Yet, in spite of the rich data available, no one has attempted a rigorous and systematic study of demand conditions. It is hoped that the present study will add to the knowledge of consumer demand, which is now limited to the United States and Europe, by presenting a picture of the demand conditions in Japan. The main line of approach in this study is to utilize information from both cross section and time series so as to obtain a clear demand structure in Japan. In cross-section analysis, the method of instrumental variables is used to estimate the demand elasticities and that of dummy variables is employed to investigate the differences of consumer be— havior among different group samples. Both the original least—squares regression method and the combined techniques are to be used in the time—series analysis. Although the family budget data from 1926 to 1941 in Japan are available, they should not be combined with post— war data since the prewar and postwar data have different Coverages. As the differences in coverage preclude any meaningful comparison between the estimates obtained from the prewar and postwar periods, we shall exclude the prewar data from our present discussion. Furthermore, because 3 .Iapan‘s economy from 1946 to 1950 had not recovered from VJorld War II and the data in these years were published in a way that severely limits their usefulness for our pur— poses, the period dealt with in this study is 1951— 1962. The study is divided into five chapters: The first chapter presents a statement of the purposes of the study and a brief description of the sources and nature of the data used. Empirical consumer demand studies are briefly surveyed in Chapter II; the bulk of our theoretical frame- work is developed in detail and our statistical models are also formulated. Our empirical results from cross—section data and time—series data are analyzed in Chapters III and IV respectively. Finally, our analyses are reviewed and some conclusions drawn in the last chapter. PURPOSES OF THE STUDY In this study we are to derive statistical demand functions for basic living materials in Japan. For the pur— poses of this study, basic living materials are classified into four groups: food, housing, fuel and light, and clothing. Food is further subdivided into 14 items; these are rice, barley, bread, fish, meat, milk and eggs, vegetables, pro— cessed food, condiments, cakes and candies, fruits, alcoholic beverages, non-alcoholic beverages, and food prepared outside the household. Housing includes rent, repairs and improve— ments, and furniture and utensils. Clothing is subdivided into clothes and personal effects. The primary purpose of tliis study is to obtain reliable estimates of the effect of ijicome on demand for basic living materials. Another ob— jective is to investigate how consumer demand for basic living materials is affected by family size, type of tenure of dwelling houses, number of earners in household, prices (own price and other prices), occupation of the head of the household, social class, and regional variations such as geographical location, city size, and urban—rural effects. Information of this kind is not only extremely valu- able in such areas as economic development and planning, interregional and international trade, and population and consumer economics,but is also very useful for a number of sociological purposes. The present study, though primarily empirical in nature, attempts to narrow the gap between the existing economic theory of consumer behavior and empirical investigations by stressing how they support each other. In the process of our analysis, an attempt will be made to test the permanent income theory of consumption with respect to the individual category of consumption. This study, although primarily concerned with basic living materials only, has significant implications for the analysis of the savings and consumption pattern in general. SOURCES AND NATURE OF THE DATA USED The specific data used in the present study were taken from: (1) National Survey of Familyglncome and Expen— diture of 1959, conducted by the statistics Bureau of the PI'ime Minister’s Office, Japan; (2) Kakei Ch6sa (Family Budget Survey) from 1951 to 1962, conducted by the same bureau; and (3) Noka Keizai Ch5sa (Farm Household Economy Survey) from 1951 to 1962, conducted by NBrinsho (Depart— ment of Agriculture and Forestry). These sources can be briefly described as follows: (1) National Survey of Family Income and Expenditure 20f l959.——This national survey covered 42,841 non—farmers' and non—fishers' households in 544 cities and 253 towns and villages, and was published in six volumes in 1961 by the Bureau of Statistics, Office of the Prime Minister, Japan. It was conducted continuously for three months from Septem— ber to November of 1959 and surveyed detailed income and ex— penditures as well as quantities of durable goods possessed by' these households.2 Average monthly income and total exgaenditure were classified into sixteen groups. These data enalnle us to investigate the differences in consumption pattesrn due to household size, number of earners in house— hold, regional variation, city size, age and occupation of houseliold heads, social class, and type of tenure of dwel— ling liouses. Since not all the information was classified in the same manner, this survey also enables us to analyze the classification bias. (2) Kakei Ch5sa (Family Budget Survey) l951-l962.—- This Source covered about four thousand urban households eVery Inonth in the 28 cities with population of more than \ _ 2However, one person households (732) were surveyed in OCtOber and November only. fifty thousand. The survey was published monthly in Monthly Report on Family Income and Expenditure Survey and yearly in Annual Report on Family Income and Expenditure Survey. The results were also published in General Report on Family Income and Expenditure Survey (1946—1962) for the convenience of researchers who wished to do time—series analysis. The method of selection was stratified, multistage random samp- ling. Average monthly income and total expenditure were classified into fifteen classes in 1951, eleven in 1952, sixteen in 1953 and in 1959-1962, and twenty—one in 1954— 1958. Both receipts and disbursements were published in every detail. This study was based on the monthly average for the eleven months from January to November. This was done because the Statistics Bureau of the Prime Minister's Office excluded December from the yearly average on the grcnlnd that bonuses were mostly awarded in this month and henc:e both income and expenditures were very different from thosee of the rest of the year. Income and total expenditure in Deacember were almost twice as much as the average of the rest of the year. Because of the large expenditures in Decennaer, the expenditures in January and February reduced considerably as compared with those of the other months. This survey can be utilized for both cross—section and time— Series analyses. This kind of repeated survey produces the mOSt Valuable data for time—series analysis, in spite of the llmitations on their scale and classifications. 7 (3) Noka Keizai Ctha (Farm Household Economy Survey) l951—l962.—-This survey covered almost six thousand house— holds each year. It has been conducted on the fiscal year basis, from April 1 to March 31. Although this survey pro- vides data for time—series analysis for the period from 1951 to 1962, it enables us to do cross-section estimations only from 1959 to 1962, because the resultant tables of the sur- vey before 1959 were either unpublished or without income information. Income in this survey was classified into only eight classes, but these classes had cross-classifications of family size and income groups, which enabled us to inves— tigate the effects of family size. Owing to the differences in demand structure between farm and non—farm households, this survey could not be conducted and classified in the sauna way as the urban family income and expenditure survey. CHAPTER II THEORETICAL CONSIDERATIONS AND STATISTICAL FORMULATIONS The purpose of econometrics, which is nothing but a combination of economic theory and facts by means of mathe- Inatical and statistical techniques, is to explain economic phonomena and to make predictions. The critical problem of econometric demand analysis is how to relate the data avail- able to the theoretical formulation of demand relationships. Since theories provide guides for empirical studies, it is necessary to formulate a pure theory of demand relationship basecl on the theory of consumers‘ choice, and to develop the statxistical models of estimation. In this chapter, the earlier related empirical studixes will be briefly surveyed before discussing the rele— vant \Iariables in demand relation in Section 2. In the final section, the statistical model of estimation will be developed and formulated. The main topics in this final sectiorl are: (l) the combination of information from time series and cross section; (2) least—squares vs. simultaneous eQuations; (3) the method of instrumental variables; (4) the forms of demand equation; and (5) time—series equations. A BRIEF SURVEY OF THE EMPIRICAL STUDIES OF CONSUMER DEMAND The empirical work in consumer demand goes back to a little more than a century ago when Ernest Engel (1857) studied the pattern of consumer expenditure based on the Belgian family budget data and formulated a famous law: "The poorer a family, the greater the proportion of its expenditure that must be devoted to the provision of food." He later extended his law by saying, ”the wealthier a nation, the smaller the proportion of food to total expen— diture."l About a decade later (1868) Hermann Schwabe studied Berlin budget data and proposed a law now referred to as the Schwabe Law: ”The poorer anyone is, the greater the amount relative to his income that he must spend for housing."2 Since then, Engel's law has been verified by a ginsat number of other budget surveys and similar laws have: also been formulated for other expenditure patterns.3 Although econometric study of demand started early, it 113 still, compared with other fields of economics, in its idifancy owing to the fact that it was not undertaken 1For an excellent survey of the empirical studies of ccnisumer behavior up to World War I, see George J. Stigler, "The Early History of Empirical Studies of Con— sumer‘ Behavior," Journal of Political Econom , XLIII, (August, 1935), 433—E81f 2Ibid., p. 100. 3For the bibliography of recent studies, see James Morgan, "A Review of Recent Research on Consumer Behavior,” in Lincoln H. Clark (ed.), Consumer Behavior: Research on 92nsunuer Reactions (New York: Harper, 1958), pp. 93—219. 10 on a sound theoretical and statistical basis until the turn of this century. Fortunately, for the past two decades, a number of empirical researches on demand conditions have been done. Although Moore, in the 1910's} became the first significant economist to do statistical demand analysis, the stage of "take—off” in this area began probably in 1935 when Allen and Bowley published their excellent econometric study 5 Since that time, the major contribu— of family budgets. tions have been made by Schultz,6 using the U. S. agricul— tural data; Wold and Jureen,7 using Swedish budget and market data; and Stone,8 and Prais and Houthakker,9 working with British data. For a comparison of their works, the reader is referred to an excellent survey article by Hood.lO “Henry Moore, The Laws of Wages (New York: The Mac— millan Company, 1911); Economic Cycles: Their Law and Cause (New York: The Macmillan Company, 1914); and Forecasting the Yield and the Price of Cotton (New York: The Macmillan Company, 1917). 5Ray G. D. Allen and Arthur L. Bowley, Family Expen— diture (London: Staples, 1935)- 6Henry Schultz, The Theory and Measurement of Demand (Chicago: The University of Chicago Press, 1938). 7H. Wold and L. Jureen, op. cit. 8 R. Stone, 0 . cit. E9s.J.Prais and Hendrik s. Houthakker, The Analysis of Family Budget (England: Cambridge University Press, 1955). lOWm. C. Hood, "Empirical Studies of Demand: Canadian Journal of Economic and Political Science, XXI (August, 1955), 309—327. For other good survey article, see Robert Ferber, "Research on Household Behavior,” American Economic Review, LII (March, 1962), 19—63. 11 THEORETICAL CONSIDERATIONS OF THE RELEVANT VARIABLES IN DEMAND RELATION It is well known that according to the theory of con— sumer demand, individual expenditure depends on income and the prevailing prices under a given set of preferences. How— ever, a number of variables in addition to income and prices play a role in determining demand for basic living materials. These variables, regarded as preferences or tastes and habit in the economic theory, include type of family (family size and composition, age of head), region, rural—urban, city size, nutmer of earners in the family, occupation of the head of the household, amount of wealth, debt, family liquid assets holdings, home tenure, consumer credit terms, education, stocks of durable goods, new products, income change and in— come expectations, past consumption patterns, supply condi— tions, etc. Assume X1, X2, X3, ..... ,Xh denote income, prices, family size, and other variables, respectively, then the household demand for commodity i can be expressed implicitly as: ci = f(Xi) i = l, 2, 3, ...... n (1) Although there are many factors that determine the pattern of demand for a commodity, no one has attempted to include explicitly a large number of the variables into an flmirical study of demand. The fact is that some of the factors are extremely difficult to handle statistically. Shme most of the factors are closely associated with the level of income, in order to avoid the bias in the demand 12 relationship, all the previous demand studies have made a considerable effort to keep ”other variables constant" by using an ”equivalent adults" or "consumer units" scale to deal with the variations in family size and composition, and by classifying family into relatively homogenous groups to overcome the factors affected by place of residence, occupation, and so forth. Because of the nature of cross—section and time- series data, some factors are more suitable for analysis from corss—section data while others are better analyzed from time—series data.ll Of course, not all of the vari— ables listed above will enter the present study. Some of the relevant variables of demand for basic living materials are discussed below. Income Income is the most important factor in explaining consumer behavior. However, owing to the unavailability of information on income, many early budget studies used total expenditure as a proxy for income in investigating variations in food, clothing, housing, and other items of consumption.12 11For discussion of this point and the listing of the relevant variables with reference to house furnishings and equipment in cross-section and time-series analyses, see: Vernon G. Lippitt, Determinants of Consumer Demand for House Furnishings and Equipment (Harvard University Press, 1959), pp. 6—8. 12 . . For example, Rlchard Stone, op. olt.; R. G. D. Allen and A. L. Bowley, op. cit., and S. J. Prais and H. S. Houth— akker, op. cit., all used total expenditure as the determin- ing variable in the Engel Curve. Stone derived income elas- ticities by discounting 10 percent of the estimated expenditure elasticities. 13 Even if income data were available, a number of demand analysts argued that total expenditure should be used as an explanatory variable because it was too difficult to obtain accurate and reliable income data. Thus Prais and Houth— akker used total expenditure in examining the household con— sumption behavior on the grounds that it was too difficult toascertain the information on income, and that savings could be ignored when total expenditure was used as an ex— planatory variable. Nevertheless, for the purposes of com- parison with expenditure elasticity, they did estimate some income elasticities of the middle—class household. A further argument in favor of using total expendi- ture as an explanatory variable is that it is a better measurement of a household's permanent economic status than measured income if Friedman's permanent income hypothesis13 is accepted. Friedman argues that measured income consists of two parts: the systematic part called the permanent in- come and the non-systematic part called the transitory income, 13Milton Friedman, A Theory of Consumption Function (Princeton: Princeton University Press, 1957). The perma— nent income theory has been vigorously discussed intensively and extensively by many economists, in particular see Franco Modigliani and Richard Brumberg, "Utility Analysis and the Consumption Function," in Post Keynesian Economics, Kenneth K. Kurihara (Editor), (Rutgers University Press, 1954), pp. 388—436; Margaret G. Reid and Marilyn Dunsing, ”The Effect of Variability of Income on Level of Income—Expendi- ture Curves of Farm Families," Review of Economics and Statistics, XXXVIII (February, 1956), 90—95; Irwin Friend and Irving B. Kravis, "Consumption Patterns and Permanent Income," Proceedings of the American Economic Review, XLVII (May, 1957), 548—555; H. S. Houthakker, "The Permanent In— come Hypothesis,” American Economic Review,XLVIE (June, 1958), 396—404; and Robert Eisner, "Permanent Income Hypothesis: Comment,” American Economic Review, XLVIII (December, 1958), 972—990. 14 and that mean transitory components of income and consumption tend to be zero. His hypothesis postulates that consumption is a function of the permanent component of income, wealth possessed, the interest rate, and tastes such as the size and composition of households, and other variables. The perma- nent component of income determines people's consumption, but the transitory income does not affect the consumption deci- sion. However, permanent income cannot be observed directly because measured income consists partially of transitory income. It is argued that total consumption is closer to the permanent component of income than is recorded income.lu Reid used measured income as an explanatory variable in in- vestigating the housing-income relations for 1950 and 1960 in the United Stated and found the elasticity of housing was less than l.O——about 0.35 for 1950. This result is consis— tent with Schwabe's law of rent-—as income increases the proportion of income spent for housing decreases. But when Reid used permanent income instead of the measured income, she obtained the income elasticities of housing of between 1.5 and 2.0. From this she concluded that housing was a luxury item according to the American standard of living. She then used total consumption as the explanatory variable in the regressions and found that expenditure elasticity of housing was on the average 39 percent greater than the elas— ticity obtained by using measured income as an independent 14 . One of the bas1c hypotheses of the permanent in— come theory is that total consumption tends to be a constant proportion of permanent income. 15 variable. Because of the fact that the expenditure elasti- city is much closer than the measured income elasticity to the permanent income elasticity, she argued that total con- sumption was more suitable than measured income to stand as proxy for permanent component of income.15 However, family budget surveys usually show that total expenditure is approximately proportional to income in each income class and that the higher the income of these income classes, the relatively smaller prOportion of income is spent. So, if we assume that total expenditure is a function of income, C = c(Y), it is readily shown that nciY = ”sic - ”CY where r‘ciY is the elasticity of expenditure on item 1 with respect to income, nciC the elasticity of expenditure on item 1 with respect to total consumption, and nCY elasticity of total expenditure with respect to income. The formula clearly shows that income elasticity has the tendency to be smaller than expenditure elasticity, although they are ap— proximately equal.l6 Since they are almost the same, do we have any reason for prefering one to the other as an explanatory variable? With regard to this question, Wold and Jureen state: 15Margaret G. Reid, Housing and Income (The Univer- sity of Chicago Press, 1962). 16If we are dealing with the economic concept of hmome and consumption, and accept the hypothesis that per— Hmnent consumption is a constant fraction of permanent in- come, then income elasticity is the same as expenditure elasticity. In the case of measured income and consumption, CY is usually slightly less than one, hencerb.C is slightly greater than nC y' 1 i 16 Since they are nearly equal, there is not a great deal to choose between two elasticity variants in prac— tice. If nonetheless we wish to pursue the distinction between the two elasticities, they should not be re— garded as competitive but rather as complementary. They answer different questions, and which variant should be employed depends upon whether we are concerned with the effect of changes in income or in total expenditure. Both elasticities have a place in demand analysis. It would seem, however, that from the viewpoint of the ap- plications it is the income elasticity that is of primary relevance, problems referring to total expenditure enter- ing secondarily via assumptions concerning the propensity to consume. Crockett and Friend give one of their reasons for using income rather than total expenditure as an explanatory variable as follows: A further decision to relate all expenditure cate- gories directly to income, rather than relating only total consumption to income and individual consumption items to total consumption, was based in part on a belief that certain types of expenditure-—for example, purchase of durables, educational expenses, and abnormal medical expenses—-may be largely competitive with saving rather than with other areas of consumption only. The danger of least squares bias may be substantially increased 18 when total consumption is used as an explanatory variable. Prices As with such variables as interest rates and wage rates, prices are held constant in cross—section analysis. they are, however, the important variables in the time—series studies of the demand relationships.19 However,the fact 17H. Wold and L. Jureen, op. cit., p. 221. l8Jean Crockett and Irving Friend, "A Complete Set of Consumer Demand Relationships,” in Irving Friend and Robert Jones (eds.), Consumption and Savingp (University of Pennsyl— Vania Press, 1960), Vol I, p. 7. 19Because of inter—regional price differentials, at- tempts have been made to estimate price elasticities in cross- section analysis; however, no satisfactory results have been obtained yet. Although 46 regional income and expenditures cross—section data of Japan are available, price elasticities cannot be estimated owing to the lack of an inter-regional price index. It is possible to construct such an index from the data available, but the work involved is too heavy to be included in this study. 17 that prices are not treated as variables in the cross—section data does not imply that the same prices are paid by every household. It is only assumed that over a given period of time all the households in the survey faced the same market possibilities. Indeed, differences in prices frequently occur under many circumstances--for example, imperfect mar— ket conditions, quality and product differentiations (which include the location, services, and environment of the shop), economies of scale of purchase in large quantity, and so on. Family Size and Composition The size and the age and sex composition of a family, which are the most important forms of variation in preferen— ces, greatly affect the demand for basic living materials. In fact, since income and expenditures of a family are highly correlated to its size and composition, income elasticities estimated from cross—section data will be biased if income and expenditures are not adjusted to family size and composi— tion. The reason for the strong correlation between family Size and income in household surveys is that larger families tend to have more earners so that their family income is higher, and that in families with more children, the heads 0f the families are usually older so that their earning powers increase. The larger the family size, the more the expenditure on food, clothing, and housing would have to be. But the relationship between family size and expenditures is not proportional. The coefficient of family size estimated 18 by Houthakker2O is only 0.24, which suggests great economies of scale. The economies of scale result from many factors: the reduction of per unit price if purchases are in large quantity, the indivisibility of goods, the chances of giving outgrown clothes to other members of the family, and families of all sizes tend to use kitchens and bathrooms of the same size. The low family size coefficient can also be explained by the fact that the larger family usually con- sists of more children and living expenses of children are lower. Allen21 and Nicholson22 have studied the effect of children on household concumption pattern and noted that the net effect of an additional child will be smaller the more children there are already. To appraise the effect of the age and sex composition in estimating the income effect on family budget study, dif— ferences in age and sex have been usually adjusted by means of an equivalent adult male or "unit consumer” scale. Un— fortunately, the budget data available would not permit the application of such a scale in this study. However, this 2OHendrik S. Houthakker, ”An International Compari— son of Household Expenditure Patterns Commemorating the Centenary of Engel's Law," Econometrica, XXV (October, 1957), 532-551. 21R. G. D. Allen, "Expenditure Patterns of Families of Different Types,” in Oscar Lange, Francis McIntyre, and Theodore O. Yntema (eds.), Studies in Mathematical Economics and Econometrics (The University of Chicago Press, 1942), pp. 190—207. 22 J. L. Nicholson, ”Variations in Working—class Family Expenditure,“ Journal of Royal Statistical Society, Series A, CXII (1949). ' 19 would probably not cause bias in the parameters, since the surveys covered a large number of households where composi— tion and size do not vary widely; also, the average family size in each income group is approximately equal. We expect that the age and sex composition in each income group is nearly the same. Even if the data are available, the use of the equivalent adult male scale is not without problems-- the economic significance of the application of this scale was seriously questioned by Allen.23 With respect to the use of this scale, Houthakker warns: . a more correct treatment of family size is quite complicated, whereas blind application of an equivalent—adult scale intended for nutritional pur- poses to all commodities is probably worse than useless not to speak of the difficulty of choosing between the many scales that have been proposed from Engel's days to our own.2 Oc1c2upations of and Number of Eailrners in the Household Occupation of the household head certainly does afoWect the demand for basic living materials. Laborers pur- <flia15e larger quantities of food but spend less on clothing that) office workers with the same level of income. Strictly SFHealcing, the differences in consumption pattern among dif— ferenqt occupations arise from the necessity of the work in— VOlVrsd, not from variations in preferences. 23R. G. D. Allen, Op. Cit. . 2Ll"An International Comparison of Household Expen— dltuPe Patterns," op. cit., p. 543 20 It can be seen from family budget data that income and the number of earners in the household are usually inter— correlated; the larger the number of earners in the house— hold, the larger the family income. Hence, the demand for basic living materials may be affected by the number of earners. Even though income and expenditure data are ad— justed by using an equal number of earners in each income or total expenditure class, some difficulties still appear. For example, when many members of the family are at work, they may have lunch at restaurants and hence cause the ex— penditure on food to increase. Also they are likely to spend more on clothing, and probably need babysitters or other domestic help. In spite of these considerations, the biases in the demand elasticities estimated are probably small, if any, if the number of earners is disregarded since the principal effect of the number of earners on the expen— diture on basic living materials is very likely due to the fact that the number of earners in the household and the family size are highly positively correlated. Home Tenure The type of tenure of dwelling——owned house, rented, and issued house——p1ay821part in determining the consumption of basic living materials chiefly through an income effect 21 and specific effect.25 The difference in consumption pattern of different types of dwelling arises because the owned house and issued house rents are seldom estimated, hence income and 26 expenditure on rent are incorrectly measured. Regional Variations Regional differences such as rural—urban, size of city, and geographical location undoubtedly make differences in the demand for basic living materials. As a general rule, living expenses are higher in urban areas than in rural areas and in big cities than in small ones. Supply Price and income elasticities from time—series data may also be influenced by supply conditions. A priori, the more elastic the supply is, the lower the income elasticity tends to be. Failure to include supply of basic living materials might bias the estimates of parameters in the de- mand equation. However, because of lack of data, the in— fluences of prices on supply will not be included in the 25Specific effect and income effect are equivalent to the Slutsky—Hicks' substitution effect and income effect. For the discussion of the effects, see H. S. Houthakker, "The Econometrics of Family Budgets," Journal of the pral Statistical Sociepy, Series A, CXV (Part I, 1952), 1-28, The effect has been interpreted in terms of changes in pref- erence by S. Ichimura, "A Critical Note on the Definition of Related Goods,” Review <3f Economic Studies, XVIII (1950-51), 179—183; and J. R. Hicks, ”A Comment on Mr.Ichi- mura's Definition,” Review of Economic Studies, XVIII (1950— 1951), 184—187. 26Although people were asked to estimate their owned and issued house rents in the Japanese surveys, it is ap- parent from the data that they did not do it well. 22 present study, and it is believed that this will not bias the estimates of the demand parameters, as shown by Tobin.27 Other factors, such as the initial stocks of con- sumer goods, especially durable goods, are sometimes taken into account in a few demand studies. Nevertheless, the inventory of consumer goods is not included in this study, since the stocks data are not available. But it is believed that our study of the demand for nondurable living materials such as most food, fuel, and light would be little affected. STATISTICAL FORMULATIONS On the Combination of Time—Series and Cross—Section Analysis In demand analysis, three types of data are generally 28 used: (1) cross—section surveys for a single period; (2) continuous cross—section surveys through time; and (3) ag— gregate or macroeconomic time series. While the first and second surveys have the same coverage, cross section and aggregate time series are usually different in their coverage and in population involved, and macro time-series data have the statistical problem of aggregation. Although we have 27James Tobin, "Statistical Demand Function for Food in the U.S.A.,” pral Statistical Society Journal, Series A, CXIII (Part II, 1950), 113-140. He investigates the possibility of bias due to a relationship between supply and prices and concludes that the relationship between supply and prices with respect to food is not significant. 28For the nature and problems of the three types of data, see Marguerite C. Burk, "Some Analyses of Income—Food Relationships,” Journal of American Statistical Association, LIII (December, 1958), 905—927. J 23 abundant data of all the three types, the aggregate time— series data will not be utilized in this study.29 The re— peated surveys data can be used not only for investigating the stability of cross—section function over time but also to obtain a closer combination of cross—section with time— series data. Cross—section data reflect a particular period of time and hence provide a static picture, i.e., variables such as prices, tastes, technological changes, and changes in market structures of the economy are assumed constant. Time-series data generally cover a much longer period of time and relfect dynamic changes in the sense that the vari— ables held constant in the cross—section analysis are no longer assumed to be unchanged. Income elasticities estimated from time—series data are usually lower than that from cross section in various studies of the demand for food. For example, using U. S. 30 data, Tobin obtains .56 for the year 1941 from cross—section data, and .27 from time-series data for the period 1913-1941. . 29Expenditures on broad categories of commodities such as food, housing, fuel and light, and clothing for the _ whole country were estimated for a long period of time by l the Bureau of Economic Planning, Japan, and were published - in its National Income White Paper. But these data differ , considerably from the expenditures estimated by Miyohei I Shinohara, "An Estimate of Food Expenditure in Japan, 1909— ; 1940," Keizai Kenkyu, XII (January, 1961), 31—41, and . Kazushi Okawa, Miyohei Shinohara, and Tsutomu Noda, ”An Estimate of Investment and.Consumption in the Postwar Period," Keizai Kenkyu, X (January, 1959), 29—47. The main reason for not doing aggregate time—series analysis is that no re- liable price index covering the country as a whole is avail— able. 3OJ. Tobin, op.cit. 24 31 Wold and Jureen get .51 for Sweden for 1938 from cross— section data and .28 from time-series data for the period 1921—1939. But working with U. S. cross—section data, Burk32 obtains .30 and .25 for 1942 and 1955, respectively, and using time—series data she obtains .68 for 1929—1941 and .38 for 1948—1957. Although others have attempted to explain the rea— sons the estimates differ in the two different approaches, Kuh and Meyer have probably done the most comprehensive work in this area.33 Their main arguments are summarized as follows: (1) The basic reasons that cross—section estimates of income elasticity are generally larger than those esti- mated by time series are: (a) cross—section data tend to measure long-run adjustments but time—series data typically 34 tend to reflect shorter—run reaction; (b) owing to the 31H. Wold and L. Jureen, op. cit. 32M. C. Burk, op. cit., p. 919. 33Edwin Kuh and John R. Meyer, "How Extraneous Are Extraneous Estimates?" Review of Economics and Statistics, XXXIX (November, 1957), 386L393. Also see Edwin Kuh, "The Validity of Cross—Sectionally Estimated Behavior Equations in Time Series Applications," Econometrica, XXVII (April, 1959), 197—214; Richard Stone, "The Demand for Food in the U. K. Before the War,” Metroeconomica,III (1951—1952), 8—28; and Trygve Haavelmo, "Family Expenditures and the Marginal Propefisity to Consume,” Econometrica, XI (January, 1947), 335-3 1. 3LlThis is only a tendency. It is not always true that cross—section data cannot show short—run changes and that time-series data cannot measure long—run adjustments. In fact, both cross-section and time—series data can be designed to estimate both short— and long—run parameters. For this, see Lawrence R. Klein, An Introduction to Econo- metrics (Englewood Cliffs, N.J.: Prentice—Hall, 1962), p. 73- 25 availability of data, cross—section data usually measure outlay elasticity whereas time—series data tend to estimate quantity elasticity, and outlay elasticity is greater than quantity elasticity because of quality differences.35 (2) The estimates of parameters are different because of using different estimating equations. (3) The length of time to which the cross section pertains also plays a role in the quality differential and hence causes the discrepancy between the two approaches. (4) The differences in estimate between the two data are partly due to the differences in coverage in the two types of data. The time-series, but not the cross-section, relationships are affected by the changes in the distribu- tion of families by income group. The results obtained by cross—section or time-series data alone are always unsatisfactory. Although estimation of parameters from cross section encounter much less statis— 36 it is difficult to tical pitfalls than from time series, use cross section as a basis for prediction because it is static in nature. In order to overcome some of the statisti— cal difficulties in time series and to get consistent 35For the comparison of quantity and outlay elasti— cities from cross-section data, see H. Wold and L. Jureen, op. cit., and S. J. Prais and H. S. Houthakker, op. cit. 36For the statistical pitfalls in time series, see R. Stone, ”The Analysis of Market Demand: An Outline of Methods and Results," Review of the International Statistics Institute, III (1948), 23—35. 26 parameters from both cross-section and time—series data, the method of combining the two types of data has been widely 37 employed by research workers since Marschak suggested it in 1939. Briefly speaking, the method is to insert the in— come elasticity estimated from cross—section analysis into 38 the equation used in analyzing the time series. 39 The prob— lem of multicollinearity encountered in time series is believed to be overcome by this conditional regression analysis. With regard to this method, Hood notes that ”we do not yet have an adequate theoretical economic framework to guide us in attempts to combine these two kinds of information."L10 37J. Marschak, ”On Combining Market and Budget in Demand Studies: A Suggestion,” Econometrica, VII (October, 1939), 332—335. This method has been developed and commented upon by many writers, in particular, Hans Staehle, ”Relative Prices and Post—War Markets for Animal Food Products,” Quarterly Journal of Economics, LIX (February, 1945), 237—279; J. Tobin, op. cit., J. Durbin, ”A Note on Regression When There Is Extraneous Information About One of the Coefficients,” Journal of American Statistical Association, XLIX (1953), 23— 32; H. Wold and L. Jureen, op. cit. R. Stone, The Measurement of. , p. cit. ,and Irving Hoch, ”Estimation of Production Function Parameters Combining Time Series and Cross Section Data," Econometrica, XXX (January, 1962), 34- 53. 38It is to note that this combining technique is in— consistent with Friedman's permanent income hypothesis. For this, see M. Friedman, op. cit., pp. 136-137. The method of instrumental variables to be discussed later in this chapter is in fact a way suggested by Friedman to combine cross—sec— tion and time-series data. 39This term refers to the situation where independent variables in the equation(s) are related to each other. For example, income elasticities estimated from time series are subject to bias due to intercorrelation of income and the price series. Multicollinearity is first discussed by Ragnar Frisch, Statistical Confluence Analysis By Means of Complete Regression Systems (Publication No. 5, 1934, University In— stitute of Economics, Oslo). “Owns Hood, op. cit., p. 323. r, 27 Because the cross-section and time—series data are influenced by the many different factors mentioned above, Kuh and Meyer question the validity of the combined techni- 41 que. The income elasticity estimated from cross—section data is usually larger than the equivalent time-series estimate, and this usually tends to overestimate the price elasticities when the conditional regression technique is used. For example, using time series alone, Tobin obtains a price elasticity of .27, but he gets an estimate of .53 when he uses the combined cross—section, time-series tech— nique.”2 Why are the price elasticities from the combined technique usually larger than the price elasticities from "pure" time series? Let us assume the simplest conditional regression model: log q = log a + n log Y + b log P (2) where q denotes the original time—series values of the de— pendent variable such as quantity of consumption, P the "own" price level, Y income, b the price elasticity and n the income elasticity estimated from cross section. As "own" price elasticity is expected to be negative and it is conventionally reported as a positive number, the above equation is multiplied by minus one, then the relationship between price elasticity and income elasticity is 41 E. Kuh and J. R. Meyer, op. cit. 42 . Op. Cit. 28 -d log q + n d log Y P d q PdY d log P q d P YdP Because of the various reasons mentioned earlier, income elasticities estimated from cross—section data are usually larger than those from time—series estimations. Since a majority of the empirical evidence shows that price and income elasticities are positively correlated, the rela— tionship of equation (3) indicates that the larger estimate of the income elasticity tends to overestimate the price elasticity by conditional regression.“3 Despite the fact that we cannot accept this com- bined method without reservation, we use this technique because so far no better technique of dealing with both cross—section and time—series data is available. In con— cluding the discussion of this combination of cross section and time series, let us borrow Kuh and Meyer's words: In sum, great care should be exercised in utilizing cross section parameters estimates jointly with time series. In particular, careful thought must be given to the possibility that a cross—section estimate is likely to measure very different influence from those represented by time series movements. Clearly, there is such a thing as being too extraneous. Since this method is not without problems, the original least—squares (without this restriction) will also be applied iri time—series analysis. uBFor the similar argument, see E.Kuh and J. R. Meyer, Op. cit., p. 391 44 . Ibld., p. 393. 29 Some Considerations Concerning Least-Squaresvs. Simultaneous Equations Since the appearance of Haavelmo's article“5 in 1943, the problem of estimating economic parameters by single equation or equation system method has caused vigorous dis— cussion. The main argument against the classical least- squares is that it could lead to biased estimates even for large samples. But no definite conclusion has been reached in favor of the alternative method. In discussing the choice of the two methods, Christ concludes: Thus the question of which method to use for any finite sample size is still open, for we do not know how to tell whether the bias of the limited—informa— tion method at a given sample size is smaller than that of the least—square method by enough to compen— sate for its bigger variance. In order to determine the relative merits of equa- tions fitted by least—squares and limited information for use in forecasting, the Agriculture Marketing Service of the Department of Agriculture designed a Monte Carlo experiment and found that coefficients estimated by both methods are almost the same, unless a high degree of correlation exists among the unexplained residuals in the simultaneous equations. Truls they recommend that, if the above correlations are not arusicipated to be high, the structural coefficients could be €81:imated by least-squares method because of its computational u5”The Statistical Implications of A System of Simul— taxieous Equations," Econometrica, XI (January, 1943), l-l2. M6Carl F. Christ, "Aggregate Economic Models: A Re‘View Article,” American Economic Review, XLVI (June, 1956), 3O simplicity. “7 It should also be noted that the parameters obtained in a few empirical researches are not much different whether fitted by least—squares or by limited information (Table l). The reason that the results of the two approaches are in certain instances so close has been explained by Wold and Faxeyu8 Wold and Jureen state in the section, "Least— squares regression under debate": ”The final conclusion must be, no doubt, that the regression analysis as traditionally applied is essentially sound. In demand analysis, at least, it can still be safely recommended."u9 ”A Symposium of Simultaneous Equation Estimation" presented by four econometricians in October, 1960 issue of Econometrica is probably the most complete discussion of the controversy on single equation versus equation system method.50 Christ concludes his arguments there as follows: In summary, it is not yet clear that the least squares method for structural estimation is dead and should be discarded....The important task ahead is to u7Richard J. Foote, Analytical Tools for Studying Demand and Price Structures (Agriculture Handbook, No. 146, USDA, Washington, D. C.), p. 69. u8Herman Wold and P. Faxey, "On the Specification Error in Regression Analysis," Annals of Mathematical Sta— tistics, XXVIII (1957), 265—267. 49 H. Wold and L. Jureen, op. cit., p. 59. 50"A Symposium on Simultaneous Equation Estimation," {Econometrica, XXVIII (October, 1960), 835-871: Carl Christ, 'Simultaneous Equation Estimation: Any Verdict Yet?" pp. 835-845; Clifford Hildreth, "Simultaneous Equations: Any Verdict Yet?" pp. 846—854; Ta—chung Liu, "Underidentifica— tion, Structural Estimation and Forecasting," pp. 855—865; LaWrence R. Klein, "Single Equation vs. Equation System Methods of Estimation in Econometrics,” pp. 866—871. 31 TABLE 1.-—A comparison of the parameters estimated by least—squares and limited information methods* Current Lagged Price Income Income Elasti— Elasti— Elasti- Authors Commodity cities cities cities Girshick & Haavelmo a) food (LS) —.37 .28 .06 (LI) —.25 .24 .05 Judge b) eggs (LS) —.53 .31 .22 (L1) —.58 .44 .29 Nordin, Judge & Wahby c) pork (LS) —.78 .43 .22 (L1) —.79 .76 .29 French d) eggs (LS) —.81 .18 ——— (L1) —.43 .17 ——- *(LS) denotes least—squares estimated (by linear logarithmic form, and consumption per capita was used as the dependent variable); (LI), limited information maximum like— lihood estimates. The estimates were from time-series data. a) M. Girshick and T. Haavelmo, “Statistical Analysis of the Demand for Food: Examples of Simultaneous Equations of Structural Equation,” Econometrica, XV (April, 1947), 79— 110. b) G. Judge, ”Econometric Analysis of the Demand and Supply Relationships for Eggs," Storrs Agricultural Experiment Station (Storrs, Connecticut, Bulletin 456, 1954). c) J. Nordin, G. Judge and O. Wahby, "Application of Econometric Procedures to the Demands for Agricultural Pro— Chicts,” Iowa Agricultural Experiment Station (Research Buljetin 410, 1954). d) Burton L. French, ”The Statistical Determination Of' the Demand for Meat," Econometrica, XX (January, 1952),96. 32 learn more about how to decide which estimation method is likely to be best for any given actual econometric problem. For this present, the situation appears to be as follows: For structural parameters, least squares sometimes is preferable ‘to simultaneous equations method and sometimes is not.5l Klein stated there: A strong case can be made for the use of least squares methods in the estimation of Engel curves and other cross—sectional relationships. The fields of ap- plication of single equation methods is indeed broad, but each situation must be separately analyzed in terms of the most appropriate statistical technique. Since the simultaneous equation method has not yet been proved to be superior to the least—squares approach, and the latter is believed to be suitable for estimating the parameters in the demand analysis, no attempts are made to use the system equations in this study. Method of Instrumental Variables Least-squares, perhaps, is still the most common method used in estimating the demand parameters, despite the availability of other alternative methods. However, the bias obtained from direct application of the least-squares method in family budget study should be pointed out here. In spite of an effort to adjust the size and composition of fanuly by a consumer unit scale and of sub—grouping family illto social class, geographical location and so on, the es— tiJnated bias in the traditional analysis of household be— haArior still could not be eliminated. The reason has been 511bid., p. 845. 520p. cit., p. 871. 33 53 clearly pointed out by Summers. His main argument is that the various expenditures and income are interdependent, and hence the biases will result from estimating regression co— efficients by least—squares regression of individual items expenditures on total expenditure or income, which are not actually independent. In other words, his main objection to the least—squares method in household expenditure analysis is that total expenditure or income and expenditures on in— dividual items are endogenous to the household and are determined simultaneously. On the basis of Summers‘ analysis, 54 Liviatan has shown that the bias from the relation between the systematic parts of total expenditure C, and its compo— nents can be eliminated in a large sample by using measured income, Y, as an instrumental variable.55 The main purpose of using an instrumental variable is to eliminate or to mini— mize the random error of the independent variable. Let us 53Robert Summers, ”A Note on Least-Squares Bias in Household Expenditure Analysis,” E nometr'ca, XXVII (January, 1959), 121—126. 5uNissan Liviatan, ”Errors in Variables and Engel Curve Analysis," Econometrica, XXIX (June, 1961), 336—362. 55Letfz=ax'+b and x: x' + x", then 2 is called instru— Inental variable if it is a variable correlated with X' but not Witfli X" or b, which is the disturbance term. Valavanis des— Crijaes an instrumental variable as ”exogeneous to the economy, --- not entering the particular equation, or equations, we Wamrt to estimate, nevertheless used by us in estimating these equiition.” See Stefan Valavanis, Econometrics (New York: MeG-I‘aw—Hill Book Co., 1959), p. 107. For further discussion Of'Zinstrumental variables, see Albert Madansky, "The Fitting Strwiight Lines When Both Variables Are Subject to Errors," Journdal of American Statistical Association, LIV (March, 1959), 173—205. A number of writers have shown that instrumental Variables can be used to obtain consistent estimators in cer- tain cases, in particular, see H. Wold, op. cit; Olav Reiersol, 34 state briefly Liviatan's method. Suppose the estimate equa— tions in cross section (Engel curve) are: (4) where Ci denotes expenditure on the ith commodity, Yp the permanent income, uncorrelated with the error term V's. The purpose of the analysis is to estimate the regression of Cip (the systematic part of Ci) on Cp (the systematic part of C), . = . + . C1p B01 Ble (5) where Boi = aOi — ali aOV/al and Bi = ali/al' Since no data provide with Ci and Cp, they are substituted by Ci and C, p and the demand relationship can be derived from (4) Ci = Boi + Bic + Ni (6) Where Wi = Vi - BiU' Bias in B1 is expected if it is esti- mated by the 1east—squares method since C and Wi have com— !non elements Bi’ hence they are not mutually independent. qflie bias will be eliminated by using Y as an instrumental Varfiiable, since "Corufluence Analysis by Means of Lag Moments and Other Methods Of' Confluence Analysis," Econometrica, IX (January, 1941), 1-24; R- C. Greary, "Determination of Linear Relations Between Syste- matic Parts of Variables with Errors of Observation, the Varian- ces of Which Are Unknown," Econometrica, XVII (January, 1949), 30‘58; J. Durbin, ”Errors in Variables," Review of the Inter- when Statistical Institute, XXII (1954), 23—32; and D. J. Sargan, "Estimation of Economic Relationships Using Instrumental Variables," Econometrica, XXVI (July, 1958), 393—415. ——~——_—. cov (CiX) 511 ali'd ali .=————=———-= =—-=B. 1 1 cov (C,Y) al al-d al where Biis the estimate of the parameterll, and cov (Ci,Y) _ cov(C,Y)_ cov(Y ,Y) ali=——;al=._——’ d=__p_._ l cov (C,Y) var(Y) var(Y) It should be noted that Friedman56 in fact suggests that the income elasticities for individual commodities should be estimated by using the ratio ali/al' His perma— nent income hypothesis consists of three equations: (7) C = KY p p Y = Yp + Yt (8) C - Cp + Ct (9) where Cp stands for permanent consumption, Yp permanent in— come, K constant, Yt transitory income, and 0t transitory con- sumption. Each of the variables in the above equations is in the same period of time. In addition, Friedman makes the assumption that Cov (Yp’Yt) = Cov (Ct’ Yp) = Cov (Ct’ Yt) = 0 (10) = = 11 and EYt ECt o ( ) Although Liviatan's analysis makes use of equations (8) and (9) and assumption (11), it does not make use of aSsumptions (7) and (10). 56M. Friedman, op. cit., pp. 206—207. - “JV ‘ 36 Although the method of instrumental variables is capable of eliminating the bias, it should be realized that it involves a loss of efficiency in the sense that the vari- ance of B is usually greater than that of the regression coefficient, b, of original least—squares procedure.57 Thus an instrumental variable is not desirable unless the bias found in the ordinary least—squares estimators, but elimina- lted by this method, is found to outweigh the concomitant loss in efficiency. Liviatan has developed a testing criteria for determining which method is preferable, which involves a fairly simple computation.58 The test statistic n (bi — Bi)2 2 is chi—square distribution i=1 Var (b.—B.) 1 1 with (n — 1) degree of freedom, where Var(bi — Bi) = Var (W) l 2 1 - I) = Var (b) (2—- — I). If the 1" N~Var (C) r cY cY 57If Var (W) is constant, J. D. Sargan, op. cit., has shown the asymptotic variances of B and b are: Var (W) Var (W) 1 Var (b) = —————-——— , and Var (B) = ————————— ° 2 N'Var (C) N-Var (C) r cY Where N denotes the sample size, and rCY the correlation COeITicient between C and Y. Hence Var (b) 2 -—-=rcy : 1 Bar (B) FOI‘ a slightly different proof, see J. Durbin, o . cit., pp. 26—27. 58 N. Liviatan, op. cit., pp. 346—348. For the compu— tation of the variance of the difference between b and B, and the; similar test, see J. Durbin, op. cit., pp. 27—28. 37 null hypothesis that the bias is due to errors of observa— tion only be accepted, then the least—squares method is to be used, and if the hypothesis be rejected, the method of instrumental variable will be applied. As the coefficients of determination between C and Y are almost one in our cross-section estimation, we can directly employ the method of instrumental variables in this study. If the above linear equations are expressed in double— logarithmic form,59 the Bi are expenditure elasticities. How— ever, they can be interpreted as the income elasticities if we are willing to accept Friedman's basic hypothesis that the elasticity of the systematic part of total expenditure with respect to the economic concept of income is unitary.6O Though Bi are expenditure elasticities, they are derived by the regressions of measured total consumption and individual item expenditures on measured income, so they can be computed from cross—section data available, which are classified by income groups and give average values of income, total expen- diture, and expenditures on individual items for such groups. 59The above basic statistical analysis does not change if the equations are in logarithmic form. 6OSee M. Friedman, Op. cit., pp. 206—207. Let nC. - Y be elasticity of 1p p expenditure on commodity i with respect to permanent income Yp, then n n n n C. - y = c_ . c . c . y . = . = , 1p p 1p p p p’ Hence Cip Yp Cip Cp Bl 38 It should be noted that the statistical model of in— strumental variables discussed above eliminates the biases only under the assumption that family size is constant. Bias may arise if family size is not introduced into the equations since it is usually a variable in cross—section data. How— ever, when the family size N is used as independent variable, in addition to C or Y, in a least—squareSanalysis, the co- effecient of N will usually be biased for N is correlated with C or Y. These biases can be eliminated by using the method of instrumental variables since the above simple in— strumental variable equations are readily extended to multiple regression with the same statistical analysis.61 Thus we can obtain the consistent estimates of the "true” parameters by using both Y and N as instrumental variables. Unfortunately, the estimation of family size elasticity from the multiple instrumental variable equations is still not clear. We can— not but estimate family size elasticity by the original multiple regression equation. It should be realized that not all the data under this study have been available for families of different size. To those data that are not classified according to family size but provide average size of families in a given income group, the average total expenditure and individual expendi— ture in a given income class are sometimes adjusted by family Size elasticities by a number of researchers in order to eliIninate the family size effect. However, those methods of 61A simple proof using matrix has been done by J. Durbin, op. cit., p. 39 adjustment are only approximate, and in view of the fact that there is little difference in the average family size in each income group in our data, we decline to do the adjustment. Although the cross-section data of income and expenditure, based on per household, are readily transformed to a per capita basis, it is believed that the conversion into per capita basis is worse than the approximate adjustment by family size elasticities, for the relationship between family size and expenditure is far from proportional. Bias in the parameters estimated probably exists if family size variable is not included in the estimating equation. The bias, how— ever, is believed to be very small, if any. Each observation is weighted by the number of house— holds on which it is based.62 The parameters estimated would be biased if the estimate equation is not thus weighted, since the middle income classes contain a larger number of households than both the low and high income groups and the elasticities of demand are generally higher for the poor and lower for the rich. It is probably better to divide the in— come level into three or five classes and to estimate the parameters from each income class separately. However, we do not assume it necessary to do so because omitting the open-ended upper and lower classes and weighting by the house— luold number is believed to remove the bias. 62Because the grouped data were used, the number of ObEServations in the computations was the number of income or tOt:al expenditure classes which entered the estimating equa— ticnis but not the number of households covered in the surveys. 40 Form of the Equation Guidance by economic theory as to the form of equa- tion to be fitted to the available data is limited. As noted in the last section, the values of the parameters estimated depend partly on the from of equation that has been used, and the choice of the mathematical form of demand equation has been regarded as very important by econometricians. The func- tional form, however, is limited to three main types, y;§., the linear, semi—logarithmic, and double—logarithmic. 63 but Linear forms were used by Allen and Bowley, have seldom been used since, because of the essential non— negativity of consumption though these forms satisfy the additivity criterion and are very convenient for computation. After a careful examination of the possible forms of equations that could be used for family survey data, Prais and Houthakker conclude that semi—logarithmic form is better than double-logarithmic form, since the latter yields con— stant elasticities, which is not consistent with the generally accepted view that the income elasticity of total expenditure tends to decline as income increases.6u They also conclude that the semi—logarithmic function is most suited for neces— 65 sities and the double—logarithmic function for luxuries. 63R. G. D. Allen and A. L. Bowley, op. cit. 6&8. J. Prais and H.S. Houthakker, op. cit, p. 97—98. 65Differences for the two classes of commodities (necessities and luxuries) also are suggested by other demand analysts. In particular, H. Wold and L. Jureen, op. cit. P- G. Champernowne, "Discussion on H. S. Houthakker, the Econometrics of Family Budget,” Journal of Royal Statistical 41 Nevertheless, Houthakker later uses double-logarithmic form in his study of the international household expenditure patterns, regardless of necessities and luxuries, on the grounds that, in addition to its absence of the defect of the linear function, it allows more freedom in dealing with mul- tiple currencies and an easier introduction of the effects of 66 family size. Double-logarithmic form also has the advantage of somewhat greater flexibility than other forms. It should, however, be pointed out that the former method has the Society, Series A, CXV (Part I, 1952), has suggested that the two functions: for necessities, and II }_J I (D f(Z) for luxuries. II N f(Z) But the concept of necessities and luxuries is not clear. Some goods are necessity for rich people but they may be luxury for the poor. This is also applied to the rich and poor countries; while many consumer goods are regarded as necessity in the United States, they are probably luxury for the underdeveloped countries. A number of goods appear as luxuries and then become semi—luxuries or even necessi- ties as incomes rise and prices fall. Because of this phe- nomenon and because of the consideration that a saturation level of consumption exists at very high level of incomes, Aitchison and Brown have developed a so-called sigmoid .Engel curve, which implies that a consumer good acts as a luxury at low income and as a necessity at high income. IFor this, see J. Aitchison and J. A. C. Brown, "A Synthesis (if Engel Curve Theory," The Review of Economic Studies, XXII (1954-1955), 34-46; also their ngnormal Distribution (Cam— txridge, England: Cambridge University Press, 1957). 66H. S. Houthakker, op. cit. 42 difficulty of satisfying the additivity criterion. But this does not matter, because its discrepancy is in fact likely to be very small.67 In discussing the logarithmic form in economic analy— sis, Foote notes: From a statistical viewpoint, logarithmic equation should be used when (1) the relationships between the variables are believed to be multiplicative rather than additive, (2) the relations are believed to be more stable in percentage than in absolute terms, and (3) the unexplained residuals are believed to be more uniform over the range of the independent variables when expressed in percentage rather than absolute terms. To some ex—' tent, these items are different aspects of the same thing. The last two conditions are more likely to hold for analyses based on undeflated data than for those based on deflate 8data, although they might hold in either in— stance. Though the most appropriate form of demand equation has not been agreed upon by econometricians, the majority of demand analysts prefer the logarithmic form. In virtue of the above discussion and of nature of data under this study, we have not hesitated in choosing the double—logarithmic form in estimating demand parameters in this study. 67As shown by H. S. Houthakker, ”The Econometrics of ..," op. cit., p. 6, if . n . C = a.°Cbl, where 2 Ci = C, then C - Eai-Cbl i e(l—ZaiCbl) tend to be zero for i a ccnisiderable range of values of C, since the regression furnztions are fitted to observations which themselves satisfy true adding—up condition. 68Richard J. Foote, op. cit., p. 37. 43 Time—Series Equations As to the equations used to estimate the parameter from time—series data, the statistical techniques for the demand analysis show little change. Following the tradi— tional approach, parameters from time series are estimated by the equation69: = A y Bil YBi2 P Cil Q Ci2 R C13 (12) qti i t t—l t t t where qi denotes per household amount demand for commodity i, Yt per household current real income, Yt—l per household preceding year's real income (Y and Y also stand for the t t—l permanent income estimated by Friedman's method of weighted moving average of disposable income), Pt own price, and Qt other price level, and Rt competitive or complementary good's price level. In the logarithmic form and treating P as a ' dependent variable, equation (12) becomes 1 1 B11 log P1: = (5_ ) log Ai + (C. ) log qti — (57—)log Yt 11 11 11 ; B. C. ' C. - (—£g) log Y - (—lg)log Q - (—$;)log R (13) C. t—I C. t C. t 11 11 11 69This is the same as the equation used by J. Tobin, op. cit. Richard Stone, op. cit. uses an equation similar to this. He ignores preceding years income effect but intro— ‘ duces time to denote the changes in tastes and habit in his regression equation. We decline to use a time variable; the reasons have been given fully in H. Wold and L. Jureen, pp. cit., pp. 240—242. Among other things, a time variable in time—series equation does not eliminate serial correlation. 44 In combining time—series and cross-section analysis, Bi = B. +Bi are taken from cross—section estimates, then equation 11 2 (13) can be written: log P = hO + hl (log qti — Bi log Yt) + h (log Yt — log Y t 2 t-1) + h3 log Qt + h4 log R (14) t The parameters in equations (12) and (13) can be derived from the coefficients in equation (14) as follows: Another way of combining information from time series and cross section is stated as follows:70 In terms of the logarithms of the variables, substitute B. = B. - B. , so 11 1 12 the equation (14) can be written: log qti — Bi log Yt = log Ai - Bi2(log Yt — log Yt—l) + Cil log Pt + Ci2 log Qt + Ci3 log Rt (15) What then are the differences between the estimates by equations (14) and (15)? Which one represents the better demand relationship? While we will estimate the parameters by both equations, it is argued that suitability of equation depends on a country's economic condition. 70This method was used by Richard Stone in his The Measurement of . . ., op. cit., while the preceding method using own price as regressand was used by J. Tobin, op. cit. 45 In the case of Japan, a regression of quantity on price seems more suitable for the demand for food, since Japan is not self-sufficient in food supply.71 However, evidence shows that the absolute magnitudes of the elasticities are usually larger when price is used as a dependent variable in a "pure" time—series equation (Table 2). There are many reasons why the absolute values of the estimated regression coefficients depend upon whether price or quantity is treated as dependent, as shown by Orcutt, 72 and Harberger.73 They show, in particular, that either the errors of measurement in the independent vari— ables or the shifts in the functions being estimated can cause bias in least—squares estimate, and Harberger concludes that the estimates by using price as a dependent variable can be regarded as ”upper limits” and the estimates by treating quantity as a dependent variable as ”lower limits” to the "ture" parameter. If this conclusion is true, equation (15) should be preferred to equation (14), since, as shown at the beginning of this section, price elastici— ties are usually larger by conditional regression than by 71For this argument see L. R. Klein, op. cit,, p. 73. 72Guy H. Orcutt, "Measurement of Price Elasticities in International Trade," Review of Economics and Statistics, XXXII (May, 1950), 117-132. 73Arnold C. Harberger, ”Review of Stone's The Measure- merit of Consumers' Expenditure and Behavior in the United Kiri dom 1920—1938, Vol. I," Econometrica, XXIII (April, 1955), 2174-218, and "Introduction" in A. C. Harberger (ed.), The Denuand for Durable Goods_(The University of Chicago Press, 1950), pp. 3—26. lIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII:—____________________________________________ 46 TABLE 2.-—A comparison of elasticities estimated using price and quantity as the dependent variable in the least—squares equation* Commodity and Price Income Study Period Elasticities Elasticities Food: Girshick-Haavelmoa 1922—1941 (1) _037 .28 (2) -.56 .34 Burkb 1922—1941 (1) - 2o .24 (2) — 29 .30 ; Food (Livestock Products): FoxC 1922—1941 (1) —.56 .47 (2) -.61 .51 Frenchd 1919—1941 (1) --45 -53 (2) _-71 .58 * (1) denotes least—squares equation using quantity of demand as the dependent variable, and (2) indicates the retail price of the commodity treated as dependent. aM. A. Girshick and Trygve Haavelmo, "Statistical Analysis of the Demand for Food: Examples of Simultaneous Estimation of Structural Equation,” Econometrica, XV (April, 1947), 79-110- bM. C. Burk, "Changes in the Demand for Food from 1341—1950,” Journal of Farm Economics, XXXIII (August, 1951), 2 1-298. . OK. A. Fox, "Factors Affecting Farm Income, Farm 1 Prices, and Food Consumption," Agricultural Economic Research 1 (July, 1951). ’ dB. L. French, "The Statistical Determination of the Denuand for Meat," Econometrica,XX (January, 1952), 96. 47 "pure" time—series least—squares equation. In other words, price elasticities would be beyond the ”upper limits" to the "true" parameters by combining cross-section and time— series technique. 1 CHAPTER III ANALYSIS OF CROSS-SECTION DATA In this chapter, the empirical results of the cross- section data, obtained by applying the techniques given in the preceding chapter, will be analyzed. Section 1 analyzes the empirical results from the National Survey of Family Income and Expenditure (hereafter referred to N§FIE), Attempts are made to utilize these data to investigate the classification bias and the influence of the following vari— ables on expenditures for basic living materials: income, family size, type of dwelling house, number of earners per household, occupation, region, city size, and urban—rural differences. In Section 2, the income elasticities of basic living materials estimated from the Annual Report on Famiiy Ipcome and Egpenditure Survey (hereafter referred to as ARFIES) are analyzed and the stability of the elasticities Over time is tested. The Farm Households Economy Survey (hereafter referred to as FEES) is analyzed in Section 3. Furthermore, by comparing the income elasticities among four occupations in Section 1 and those between farm house- .hOlds and urban worker households in the third section, we MdLll be able to test the permanent income hypothesis. Ffixually, the analyses of this chapter are summarized in the last section. 48 49 In all the cross-section equations, each observation was weighted by the number of households on which it was based, and the open-ended upper and lower classes were omitted.1 Income here is defined as the gross income plus in— come in kind minus non-living expenditures such as all taxes, social security, and others. Total expenditure is the ori- ginal living expenditure plus income in kind when available. In EEEEE, in kind information on income, total expenditure, and food is provided. ARFIES did not survey income in kind for 1951 and 1952. However,since 1953, it gave income in kind on broad categories such as food, housing, fuel and light, and clothing, in addition to total income in kind. lhcome in kind on every item was recorded in EEEE. Since incomesin kind are usually an extremely small proportion of total expenditure, and since more than half of them are food, it is believed that biases in the parameters estimated are negligible, even if the in kind data on individual expendi- ture items other than total food were not available. With regard to other categories of consumption, fish includes fresh fish and dried and salted fish, and vegetables include fresh, dried, and seaweed. Subsidiary food is the aggregate of fish, meat, milk, eggs, vegetables, processed food, and condiments. L lNevertheless, both of the open—ended classes in FHES weree included in the computations. This was done on the grounds th51t income was classified into eight classes only in the sur- VGS’S, and that the number of families in both extreme ends Wer‘e as many as those in other income classes. 50 Differences in demand for basic living materials among ten occupations, eight regions, four city sizes, four numbers of earners, and five types of dwelling house, as well as the stability of the demand over time, are exten- sively investigated by employing dummy variables.2 In applying the dummy variables to test the regression coef- ficients, two alternative assumptions could be made: (1) consumption levels (Y—axis intercepts or the coefficients of the constant terms) are different among the sample groups, but they have the same income elasticity; (2) the sample groups differ only in their income elasticity, and have the same level of consumption. Since the results of the p-test of the coefficients obtained by the two alternative assump— tions were identical in every case, only the p—test of the estimates by the second assumption appears in the tables. However, the results are applicable to those estimated by the-first assumption. The B1 in the tables denote the expenditure elasti— cities estimated by the method of instrumental variable, i.e., the elasticity of a particular consumption category with re- spect to measured income divided by the elasticity of total expenditure with respect to measured income. All the other results shown in the tables are obtained by regression equa- tixJns. As was noted before, the variance of B is simply that Of"the coefficient estimated by original least—squares method 2For a note on the method of dummy variables in pracztical application, see Appendix A. 51 divided by the R2 (coefficient of determination) of the total expenditure on measured income. Since the coefficient of determination is nearly one in every case, the standard errors of Bi do not appear in the tables. All the tests in the tables are two—tailed p—tests. NATIONAL SURVEY OF FAMILY INCOME AND EXPENDITURE The simple instrumental variable regressions of cross—section analysis are log 01 = log a0 + a i 11 log Y (i = 1,2, ...,n) log C = log a0 + a1 log Y (16) where Ci stands for expenditure on the ith commodity, Y the n recorded income, and C = 2 Ci‘ Liviatan has shown that B1 = i=1 ali/al are the consistent estimates of the expenditure elas- ticities, as stated in the preceding chapter. Because the grouped data are used, a problem arises of whether the table classified by income or by total expenditure should be used in fitting the above equations. Although ali/al are the estimates of expenditure elasticities and it seems as though it would be more reliable to use the table classified by total expenditure, it should be realized that income is treated as an explanatory variable in each regression equa— tion above. According to Friedman,3 the table classified by income classes should be used while fitting the regression 3M. Friedman, op. cit., pp. 200—201. 52 of measured C on measured Y. On the other hand, in fitting the regression of measured Y on measured C, we are supposed to use the table classified by total expenditure classes. Thus it is more appropriate to use the table classified by income groups in fitting the above equations. Next, let us compare the estimates by the method of instrumental variables with those by the least—squares re- gressions. In the previous studies, only Prais and Houth- akker“ employed both income and expenditure as independent variables. They computed elasticities with respect to both Y and C in a double—logarithmic form of the least—squares regression based on the British surveys of 1937—1939. To make the comparison of the parameters estimated by using alternatively the methods of instrumental variables and least—squares, Liviatan computes Bi and claims that the least-squares bias is not negligible, as given in Table 3. Among other things, the considerable differences between B. and bi in the table can be traced to two factors: (1) the sample size was quite small—-the total number of families was only 1,361; and (2) the income data used by Prais and Houthakker were poor—-they had only the "income of the head of household” of the ”middle class sample." Our estimates of All Households (All Japan, urban and rural) from the tables classified by income classes and by total expenditure groups are shown in Table 4, while the ”S. J. Prais and H. S. Houthakker, op. cit., p. 102. 53 TABLE 3.—-Estimates of Engel curves using least-squares.and instrumental variables methods by Prais and Houthakker, and by Liviatan* Expenditure ali bi B = 3;; = a1i Group (1) <1) <2) 1 al 1'17 Farinaceous .47 .33 .40 Dairy .36 .26 .31 Vegetables .55 .40 .47 Fruit .75 .55 .64 Fish .79 .57 .68 Meat .60 .44 .51 Rent .83 .49 .71 Fuel .95 .73 .81 Clothing 1.35 1.24 1.15 Durables ~ 1.94 1.77 1.66 Literary 1.36 1.05 1.16 Vice 1.78 .61 .67 *This-table was adOpted from Nissan Liviatan, pp. cit., Table l (p. 342.) ali and bi are elasticities with respect to income and total expenditure respectively, by using the least-squares method, estimated by Prais and Houthakker. 5 estimates of Worker and General Households are given in Appendix B. Table 4 shows that income elasticities (Column 1) are smaller than the corresponding expenditures elastici— ties (Column 3) when they are estimated from the tables classified by income classes, and the opposite is ture when they are estimated from the tables classified by total ex- penditure groups. The reason for this can be easily explained by the relationship nCiY = nCiC . nCY, where nCiY is the ‘— 5A11 households are the summation of Worker and General Households. For the definition of these households, See Appendix 0. Urban is equivalent to all pp; which roughly (Borresponds to the English terminology of city, and rural Iincludes all machi and mura which are about the size of town and vi llage . 54 TABLE 4.--A comparison of the elasticities estimated from the tables classified by income group and by total expenditure classes, all households* Estimated from the Tables Classified by Income Classes Estimated from the Tables Classified by Total Expenditure Cl asses ny COl(l)/ai nE ny col(4)/ai ”E (l) (2) (3) (4) (5) (6) All Japan Total Expenditures .7804 1.1382 Food .5861 .7510 .7508 .8085 .7103 .7105 Cereals .3467 .4443 .4443 .5088 .4470 .4476 Subsidiary Food .6697 .8581 .8580 .8758 .7695 .7697 Cakes, Candies, Fruits and Beverages .8063 1.0332 1.0310 1.0779 .9470 .9471 Food Prepared Outside Household 1.1412 1.4623 1.4577 1.4974 1.3156 1.3168 Housing .8589 1.1006 1.0996 1.5268 1.3414 1.3410 Rent .2358 .3022 .2956 .5910 .5192 .5165 Repairs & Improvements 1.1498 1.4733 1.4773 2.0196 1.7744 1.7754 Furniture & Utensils 1.1542 1.4790 1.4788 2.0405 1.7927 1.7933 Fuel and Light .6824 .8744 .8751 .9291 .8163 .8172 Clothing 1.0295 1.3192 1.3177 1.5578 1.3687 1.3687 Urban Total Expenditures 7781 1.1364 Food 5896 .7577 .7569 .8050 .7084 .7086 Cereals 3677 .4726 .4717 .5309 .4672 .4676 Subsidiary Food 6458 .8300 .8296 .8448 .7434 .7435 Cakes, Candies, Fruits and Beverages .8005 1.0288 1.0264 1.0747 .9457 .9464 Food Prepared Outside Household l 0456 1.3438 1.3367 1.3773 1.2120 1.2138 Housing 7857 1.0098 1.0087 1.4200 1.2496 1.2482 Rent 0701 .0901 .0806 .4072 .3583 .3545 Repairs & Improvements 1 3006 1.6715 1.6802 2.0250 1.7819 1.7837 Furniture & Utensils l 1416 1.4672 1.4681 2.1037 1.8512 1.8514 Fuel and Light .6654 .8552 .8553 .9096 .8004 .8016 Clothing 1 0592 l 3613 1.3622 1.6136 1.4199 1.4209 Rural Total Expenditures .7697 1.1935 Food .5494 .7138 .7147 .8171 .6846 .6839 Cereals .3259 .4234 .4255 .5273 .4418 .4428 Subsidiary Food .6529 .8483 .8484 .9212 .7718 .7700 Cakes, Candies, Fruits & Beverages .8064 1.0477 1.0467 1.1399 .9551 .9524 Food Prepared Outside Household 1.0497 1.3638 1.3618 1.4847 1.2440 1.2425 fkmasing .9546 1.2402 1.2349 1.8344 1.5370 1.5397 IQent. .1840 .2391 .2354 .5431 .4550 .4369 Repairs & Improvements 1.0553 1.3711 1.3603 2.3530 1.9715 1.9807 PHJrniture & Utensils 1.1911 1.5475 1.5439 2.0948 1.7552 1.7563 Fuefil and Light .6681 .8680 .8715 .9909 .8302 .8258 Clc>tfliing .9872 1.2826 1.2787 1.5814 1.3250 1.3230 R The left side was estimated from NSFIE Vol. (1), Table 1-1, and the rigllt: hand side from the same source, Table 2-1. my denotes the income elasticity and the expenditure elasticity. ”El 55 elasticity of expenditure on commodity i with respect to income, nCiC the elasticity of expenditure on commodity i with respect to total expenditure, nCY the elasticity of total expenditure on income. WhethernCiY is greater or smaller than nCiC depends upon the magnitude ofrby. If we assume that C = c (Y) as in the resultant table, which is classified by income classes, the nCY is usually less than unity, for the data showed that during the short period of the survey the increase in the rate of total expenditure is smaller than that of income. Hence nCiY is smaller than nCiC. On the contrary, if the assumption that income is the function of total expenditure be made, the table classified by total expenditure is the proper one to be used andnCY is supposed to be greater than one so that nCiY is larger than its corresponding nCiC. The E1 from both classifications show little differ— ence from their corresponding bi' Since the B1 have been shown to be the consistent estimate of the "true" parameters, this indicates that the least-squares regression may be a suitable method in demand analysis if the sample size is suf- ficiently large. While the B1 of food (except cereals) and fuel and light from the tables classified by income classes are slightly larger than the corresponding Bi from the tables classified by total expenditure groups, the B1 of housing, clothing, and their components tend to be smaller. A slight difference between the estimates from these two tables of different classifications is expected, for among other things, 56 the number of households in each table is not exactly the same.' For instance, although there are 42,841 households in "All Japan" in the tables classifying consumer units by both income and total expenditure groups, by excluding both open- ended classes from computation, 41,786 households in the former and 42,554 households in the latter actually entered the estimating equations. For the reason given earlier, and because all other resultant tables classified by total ex- penditure classes do not provide income information, the rest of our results are based exclusively on the tables classi— fying consumer units by income groups. To carry the analysis of classification bias further, the tables classified by income, by family size, and those croSs-classified by income and family size are utilized. In Table 5, 0y denotes income elasticity and UN family size elasticity. Columns (1) — (4) are estimated from the table classified by income, columns (5) - (8) by family size, and columns (9) — (12) by both income and family size. 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Whether Bi’ estimated by a simple instrumental variable method (or a least—squares regression), are greater or smaller than the corresponding elasticities obtained by the equations including family size, depends on the Sign of the family size elasticities. So much for the classification bias. In order to know the demand conditions of the households other than farmers and fishers, the resultant table of All Households6 (A11 Japan) has been used to estimate the elasticity of demand with respect to income. The results of this estima— tion are set out in Table 7. All of the coefficients of income are significantly different from zero at better than 1 percent level by two—tailed t—test. Of the twenty—seven items (including group totals and sub—totals), only one shows a negative elasticity, while eleven show elasticities between 0 and l and fifteen show elasticities greater than one. The ordersof magnitude of the elasticities are generally what we expected them to be. It is natural to find that the elasticity of demand for barley shows a negative sign because it is regarded as a less desired item among cereals. It is also natural that the elasticity is lowest in cereals, and high in those goods such as meat, milk and eggs, and food 6 Single household was excluded from the estimation. 61 ”moo.vsoo. osm.H Asfio.vomo.fl Asso.voos.flu mpomocm Hmcomsmm “woo.vzoo. wom.H Ammo.vflmo.fi AHoH.vwmm.Hu mmSBOHo Amfio.vooo. oam.o Aooo.oomo.fl Ammo.vmmo.fiu mcflBQOHo Amfio.oooo. saw. Aofio.vmoo. Asoo.vomo. pawfla a floss Aomo.vmoo. oss.fi Azoo.v:mo.fl Amom.vsfim.mu mfiflmcooo o asapflcaom Ammo.voso. ms:.H Aozo.vomo.fi ”mam.vomz.mu mpqmsm>ososH a msfloamm Aooo.voom. mom. Aoso.vomm. Aomm.voas.fl scam Ammo.vosm. HoH.H Ammo.oomw. Asmfi.voom.u mcflmsom Ammo.oowo. mo:.a Aoqo.VH:H.H Amom.vs:m.mu oHoammsom ooflmpso cosmaopm boom Aofio.vmoo. soo.H Afimo.vomo. Afioo.voflm.fiu mommpo>om OHHOSOOHmm afloonoooa Asflo.vmoo. smo.fi Asflo.omoo. 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Zoos. :24 32 123.123. .ooooo.- 338.. .329. 333.- 3:8. 328. .ooosof .Somof .moooo. omqom. 284 28.80 12.3323. :38. 338. :28. .SSo. .233. .225. $88.. 338.. 238. :33. $34 coo... .mmmo.vmohm. .Nvmoo. .momoo. cosmoo. omwmoo. .omooo.u «ommoo.l cmmooo. «mHooo. UmHmoo.u mHooo. Hmoo.H manuaucouxm Hench 0H m m m o m e m N H mm acoumcou coHummsuoo coHumanouo coHumazuoo :oHumnsuoo acaumaaouo coHummsuoO coHuoasouo :oHumasuoo coHummsouo coHummzuoo .cmamo HHm .mcoHummzuoo emu mGOEm quUaumMHw OEOUEH mo mmucmummeu :H mmHnaHua> >EEdU mcha ummu wnu a0 mustmmaI.vH uqmdh 79 The'ny for food in occupations (5), (6) and (7) is significantly greater than that in occupation (l) at the 1 percent level. This can be explained by the quality vari- ance of the food consumed since occupation (1) involved more physical labor than the other three occupations, hence this group consumed a larger quantity of food but the limi— tation of income forced them to purchase food of lower quality. This relationship can be seen more clearly by comparing the elasticity for food between occupation (l) and occupation (8). While the ny for food is not different between the two occupations, occupation (8) has a signifi- cantly samller ny for cereals and larger ny for subsidiary food than occupation (l) at the 1 percent level. As rice is the major item of cereals, the test of the difference in the consumption of cereals among the ten occupational groups is identical with the case of rice except that the level of significance is a little altered in occupation (5). The ny for cereals in occupation (l) is only smaller than that in occupations(2), (5) and (6). While the higher ny for the latter two occupations can perhaps be attributed to their consumption of higher quality cereals in consequence of their higher income level, the large fly for cereals in occupation (2) seems due to this group having the lowest income level and living in a relatively underfed condition. Thus, when their income increased, they spent a relatively larger pro— portion of it on the basic materials of subsistence. 80 Besides cereals, subsidary food is the major item of food: fish, meat, milk and eggs are the three most im- portant items of subsidiary food. As mentioned above, laborers consumed a larger quantity of food than other people. But, because of their low income they were unable to spend a larger proportion of their increased income on fish, meat, milk and eggs as other people did. Thus, the difference of the ”y for fish between occupations (l) and (2) is not significant while the ”y for fish in all other occupations is greater than that in occupation (l)——in many cases the coefficients are significantly different at the 1 percent level.v In the case of meat, ny in occupation (2) is smaller than that in occupation (l) at the 1 percent level of significance. All the other occupations have the "y significantly different from occupation (l) at the l per- cent level except the coefficient of occupation (9) shows no difference from occupation (l). The results of the t—test of milk and eggs are identical with those of the meat with the level of significance changed slightly only for occupa— tions (5), (6) and (10). As to the results of the tftest of the differences in ”y for the rest of the food items between occuaption (l) and other occupations, the reader is referred to Table 14. The “y for housing in occupations (3) and (4) are significantly greater than that of occupation (1) while that in occupations (7), (8) and (9) are not significantly dif- ferent from zero. The ”y of the other five occupations are 81 significantly smaller than that of occupation (l) at the l or 5 percent level. The ”y for rent in occupation (l) is larger than that in all other occupations with the excep— tion of occupations (3) and (4). Special attention is directed to the fact that “y for housing and its components (rent, repairs and improvements, and furniture and utensils) in occupations (3) and (4) are all markedly greater than occupation (l), and those in occupations (2), (5) and (6) usually appear significantly larger than the corresponding figures in occupation (l). The factor causing these dif— ferences was pointed out in the discussion of the type of dwelling house: failure to estimate the rent value of owned and issued houses. It is quite unfortunate that the cross—classified data of the type of dwelling houses and occupations are not available. However, from the following table (Table 15) we can assume that households of occupations (3) and (4) lived in issued houses, a large prOportion of laborers in rented houses and rooms, and that general house- holds usually tended to have their own houses. It should be noted that the smaller ny for housing in occupation (2) than in occupation (l) was caused by the former's lower level of income rather than by type of dwelling houses, since it is supposed that a relatively larger proportion of the households of both occupations rent house or room. Thus the different patterns of expenditure on housing and its components among the occupational groups can be attributed to the type of dwelling houses; this effect is in turn caused 82 H amH :H ooo.m o moa.m omsom boome : mmo o moo.H o Hoo.o Eoom ooooom H mmm o Hao.H o on.H ooozo mHoHHooo Hm on.m so mom.o mm ooo.m ooozo mHopm>Hsm mm oom.m om o::.m am omm.HH omoom ooooom mm amm.mH m: Hom.mH mo ooH.om omoom ooozo ooH Hoo.aH ooH omH.om ooH Hoo.m: Hooos .m onosomsom m moHosomsom m moHosomsom ao sooSsz ao sooSsz ao sooSsz moHonomsom Hmsosow moHosomsom soxsoz moHosomsom HH< .swomw HHHa on» wsoSm moHozomsos ao sooSss on» ao QOHpsoHspmHQII.mH mqm that their income elasticities of clothing are almost the saune as those in occupations (6) and (8). It should be mentioned that the above dummy vari- alfiles enabled us to test the equality of either the constant teIun in occupation (l) and other occupations or the income eljisticity in occupation (l) and other occupations. Another way' of testing the equality of the regression coefficients (bcyth constant term and income elasticity for all occupations) is ‘to pool the data without using dummy variables. The pro- ceChire and the results of this test are shown in Appendix E. Next, the regional variations in demand for basic ljwning materials were investigated. The country is divided intca forty-six political regions, and income and expenditure infxarmation is readily available for each region. Yet, be- causse the work of combining the resultant tables into several geographical regions is beyond the s00pe of this study, only eigkrt political regions were selected to represent various geo— grapfliical locations. The criteria for choosing these eight Pegixons were that they covered every part of the country and that; a relatively larger number of households were surveyed irleach region. Consequently, various parts of the country WEPEE represented by the following eight regions: Region 1: Hokkaido (north) Region 2: Iwate Ken (north—east) Region 3: Niigata Ken (mid—west) Region 4: Tokyo To (mid-east) 85 Region 5: Osaka Fu (south—east) Region 6: Hiroshima (south-west) Region 7: Ehime Ken (south) Region 8: Fukuoka Ken (far south) Dummy variables were employed in this investigation, arui Tokyo To, which contains Tokyo——the most populous city ir1 the world--was taken as a base in the estimating equations. TTne results are shown in Table 16. Region proves to be a highly significant factor in thee demand for basic living materials. Only the n for total exqaenditure in Hokkaido is significantly greater than that in (Tokyo. While the ”y for food in three regions is not dif- ferwent from Tokyo's, that in the other four regions appears to toe significantly smaller at better than the 10 percent levral. Because of the relatively higher level of income and wesisernized way of eating, it is natural to find that Tokyo has 'the smallafi;elasticities for cereals and rice, and the larwgest elasticities for bread. The elasticities for other fOCKi and subsidiary food in Tokyo are larger than those in othen? regions except Region 6, which contains Japan's second lfllwgest city, Osaka. Tokyo's demand elasticities for in- Cfififlidual items of food other than cereals, fish, condiments, EHKi alcoholic beverages are also the largest except in a few minor cases. It is interesting to note that the elasticities for fish in all other regions are significantly greater than TOKYO'S at the 10 percent level in one case and at the 1 percent level in the rest, and the demand for alcoholic bever— ages does not show significant differences among the regions. .osoN Sosa ucosoaaHp aHucmoHchme uoc mH OB oaxoe Sosa ucosmaaHo # .Ho>oH mom cmcu smuuoh um 09 oaxoe Sosa usmsoaaHo >Hucm0HamcmHm o .Ho>oH WOH smzu swuuon um 09 oaxoe Sosa ucwswaaHp mHucmoHaHsmHm n .Ho>oH mm cons souuoo um 08 oxxoe Sosa ucosoaaHo aHucmoHchmHm m .Ho>oH wH can» swuuon um Hoe oaxoev v conmm Sosa ucmsoaaHp >Hucm0HchmHm s 86 .moumSHumw a0 msosso osmocmum osu osm m ao usmHs ocu ou monocucosmm CH smwmmm LUHLB mossmHa one "ouoz Homoo.vmomm. «mHHo.| momoo.u ovooo.n #Hmoo. somoo.u moooo.l muMOHo... vmmo.H mmom.H| muooaam Hmcomsom Amomo.VOHom. hmooo.u #HHoo. omHoo.| *mooo. smomo. #Hmoo. «ommo. vooo.H mmmm.H| mosuoHO Avooo.vamm. mmoHo.| mNHoo.| #Hmoo.n #mHoo. ommHo. *mHoo. sHoHo. mono.H Hmvm.Hn mcHnuoHU AmHmo.vmmHm. sommo.| «mmmo.| ¥HVHo.n HOHoo. cmooo. omooo. smmvo. ammo. vooH. uLqu o Hons AmHmH.VOHHm. oHooo.n #vmoo. movoo. momoo. vamo. *mNoo.| «have. ommo.H momm.H mHHmcouD o osSHHcsss Hoovm.vmmom. #NVHo.I momHo.| mooHo.I bommo.| mmmmo. 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Qmmoo.n ammoo.u smooo.n #VHoo. mHooo.| #mooo.n #Hooo. Nmom. onmv.H boom Hommo.vHHoo. «whoo.l mmmoo.| ovmoo.u #mHoo.| *mmoo.| #mooo.| «mooo. moms. Nmmo.H ossuHocwaxm Hmuos Amy oxosxsm oSHLm oSHcmost mxmmo mummHHz ousBH ooHoxxo: oaxoe ucwumcou mm m m o m m N H v conom :onom coHoom :onom :onom :onom sonwm conom .moHansm> meedp mCHms mconos ucmHo onu sea poumEHumw moHuHoHumMHw oEoocHI|.oH mqmde 87 Tokyo's elasticities for housing and its components are the largest except for repairs and improvements in Region 3 and furniture and utensils in Regions 1 and 3. Tokyo's elasticities for these latter two groups are a little larger only in three instances, but in the majority of cases they are no different from other regions. On the whole, the regions containing a larger city or cities tend to have large elasticities for food and housing. As could be expected, the regional differences in the demand for fuel and light, clothing, and clothes are mainly affected by climate. The elasticities for these three items are highest in the far north and gradually re— duce toward south. However, the demand elasticity for per- sonal effects does not follow this pattern; while the elasticity in the north and far south arm; significantly less than Tokyo's at the 5 percent and 1 percent level, respectively, the differences of the elasticity of Tokyo and other regions are not significantly different from zero. The effects of city size and urban-rural differences will be discussed briefly. The analysis of geographical variations in consumer demand usually covers the effects of region, city size, and urban-rural conditions within the country. Indeed, the effects of the three variations generally are closely related to each other. While our investigation of the effect of city size on the demand for basic living materials was limited to worker households, the preceding regional effects analyses were based on all 88 households. However, the results of the two analyses are similar to each other in the sense that the consumption pattern of the larger city is comparable to that of the region that contains a relatively larger city or cities. Data for the following four cities sizes were available: Size A: Six major cities with population of 900,000 or more—— Tokyo, Osaka, Nagoya, Kyoto, Yokohama, and Kobe. Size B: Middle city--48 cities with population between 150,000 and 899,999. Size C: Small city A--206 cities with population between 50,000 and 149,999. Size D: Small city B-—284 cities with population of less than 50,000. As size A's dummy variable was omitted in the re— gression equations, the results of the t-test are almost the same as those of the regional variations where Tokyo To was taken as a base. The reason is that Tokyo To in- cluded the city,Tokyo, whose population was more than twice as much as the second largest city, Osaka. The results of the city size estimations appear in Table 17. The bigger the city size,the larger the income elasticity for total expenditure tends to be. The income elasticities for total food and for the following food items are significantly larger in the size A city than in the other sizes at the 1 percent level, and the magnitudes of the elasticities are positively associated 89 TABLE 17.-—lncome elasticities estimated for four city sizes using dummy variables worker households Constant City City City City —2 . . . . R Size Size Size Size A B C D Total Expenditure .5717 .8643 .0029a —.0035a -.0050* .9890(.0169) Food 1.4338 .5906 .0040* -.0057* -.0074* .9863(.0130) Cereals 2.0586 .3261 .0097* .0081* .0090* .9137(.0186) Rice 2.0105 .3179 .0132* .0109* .0126* .9113(.0189) Barley 3.4254 -.4082 .0749* .0941* .1060* .8315(.0937) Bread —.9628 .7812 .0344* —.0411* -.0572* .9497(.0411) Other Food .6798 .7271 .0109* -.0137* -.0178* .9883(.0152) Subsidiary Food .8336 .6551 .0093* -.0127* -.0161* .9858(.0152) Fish .2143 .6252 .0035b —.0002# —.0014# .9672(.0212) Meat -1.6576 1.0181 .0232* —.0232* -.0381* .9820(.0278) Milk & Eggs -1.1010 .9127 .0195* -.0222* -.0300* .9520(.0403) Vegetables .3915 .5974 .0095* -.0139* -.0203* .9792(.0172) Processed Food .9804 .4606 .0132* -.0185* -.0203* .9587(.0199) Condiments .5708 .5162 .0044* .0082* .0076* .9579(.0197) Cakes, Candies, Fruits & Beverages -.4571 .8307 .0089* —.0054a -.0080* .9631(.0302) Cakes & Candies -.7838 .7986 .0125* -.0053a -.0079a .9589(.0308) Fruits -1.0380 .8424 .0032c -.0040c -.0071* .9742(.0254) Alcoholic ' Beverage —1.l316 .8394 .0044# -.0010# -.0008# .8430(.0660) Non-Alcoholic Beverage -1.5636 .8794 .0190* -.0150* -.0218* .9623(.0335) Food Prepared Outside Household -1.9256 1.0919 .0254* —.0390* -.0552* .9706(.0397) Housing .5762 .8930 .0038# -.0101* -.0177* .9326(.0455) Rent 2.8193 .0443 .0212* -.0539* -.0812* .8072(.0624) Repairs and Improvements -4.6715 1.6264 .0041# .0180c .0435* .7928(.1500) Furniture and Utensils -3.1968 1.3643 .0229* .0327* .0234* .9054(.0807) Fuel & Light -.2972 .7526 .0076* -.0068* -.0016# .9776(.0214) Clothing -1.7516 1.1651 .0012# .0036c .0063a .9786(.0314) Clothes -1.9136 1.1650 .0030# .0076a .0104* .9681(.0384) Personal effects -2.2851 1.1706 .0021# —.0050b -.0026# .9762(.0336) The figures which appear in the parentheses to the right of R2 are the standard errors of estimates. Notes: * Significantly different from city size (A) at better than 1% level. a Significantly different from city size (A) at better than 5% level. b Significantly different from city size (A) at better than 10% level. c Significantly different from city size (A) at better than 20% level. # Difference from city size (A) is not significantly different from zero. 9O 9: bread, other food, subsidiary food, with the size of city meat, milk and eggs, vegetables, processed food, non-alcoholic beverages, and food prepared outside the household. The income elasticity for fruits is also positively affected by the size of city. Size A's income elasticities for cereals, rice, barley, and condiments are significantly smaller than any other city size at the 1 percent level. Size A's income elasticity for cakes and candies is markedly greater than any other city size. Size B's ”y for fish is significantly greater at the 10 percent level than that in size A while the latter is not different from the two smaller city sizes. Although size A's my for alcoholic beverages is slightly larger than the other city sizes, the result of the tftest indicates that the disparities between them are not significantly different from zero. While the expenditure on housing and rent is posi— tively related to size of city, expenditure on repairs and improvements has the Opposite association. It is difficult to say whether the demand elasticity for furniture and utensils is negatively affected by the city size although size A's my for this item is significantly smaller than that in any other size of city at the 1 percent level. The size rankings, from the largest to the smallest, are C, B, D, and A. As to fuel and light, size A is not significantly different g 9That is, the larger the city, the larger the income Elasticity was estimated. The only exception to this positive association is the elasticity for non-alcoholic beverages Which is larger for size C than for size B. 91 from size D while its elasticity is smaller than size B's and greater than size C's, each at the 1 percent level of significance. The negative association between the size of city and the income elasticity for repairs and improvements as well as the small correlation between the size of city and_furniture and utensils, and fuel and light might be caused by the fact that a larger proportion of households in the larger city lived in rented houses which sometimes furnished reparis and improvements, furniture and utensils, and fuel and light. When the size of city grows bigger, the coefficients of clothing and clothes become smaller. The city size seems to have little effect on the demand for personal effects although ny in size C is smaller than that in size A at the 10 percent level of significance. Defining urban as including the four sizes of city in the preceding analysis of city size and rural as all the towns and villages, we found when worker households are di- vided into urban and rural, the urban-rural and city size variations in the expenditures on basic living materials are identical except that levels of significance are slightly different in a few items (that is, urban acted as larger cities and rural as smaller ones). Thus in thoSe items the bigger cities have significantly larger regression co— efficients than.smaller cities, it follows that urban has Significantly larger coefficients than rural and the converse is also true. 92 .o Scum ncoumoaHo aHucmoHchmHm no: mH cons: Sosa oocwsoaaHo : .Ho>oH mom och cosh souuon um cons: SOso ucouoaaHp mHucmoHchmHm o .Ho>oH moH may soon souumo us amass Sosa newscaaHo mHucooHchmHm n .Ho>oH mm oz» cage souuoh no cons: Sosa scouoaoHp aHucmoHchmHm m .Hm>oH oH we» coon Henson no cubs: Sena ucosmaaHo xHucmuHoHcmHm « "ouoz cmoo.u .mvo.| .omo.n «omo.| aomo.u ammo.| Hmssm mHv.HI mmo.mn Nvm.Hu ooH.Hn omo.~| vmm.H| cons: mmm. omH.H moo.H mom. 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HqH.I Hmm.u mmm.u ucmuwcou ucmHH o Hons awHumm amoo. omoo. xmoo. .moo. .ooo. .ooo. cvoo. omoo. «moo. Honda mom.Ha mHm.m mHm.mu mvo. moo. oqo. meo.H ovH.N omm.H cons: Hmm. mmm.H va.H ooo. omv. vow. ooe. omm. com. ucmumcoo OHDMHCHDL WUCOEflUCOU mUHm ammo. sovo. «omo. .wHo.I «MHo.I «mHo.I Umoo. mmoo. «moo. Hmssm 0H~.Hu mmm.v omo.mu ooo. moo. moo. vmm.H oom.~ oom.H cans: mom. omm.H mmN.H mmm. vow. mHm. vmm. mmm. mom. quumcou msHmmom room mHmmumU oommoQOsm como.l «omo.» «omo.| .vmo.| .Hmo.u «Hmo.| «moo.| «voo.| «woo.n Hmssm NmH.m Hoe.m om~.m mom. moH. mom. mom.H mmv.H wov.H cons: mNH. vmo. va. moo. ovo. 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HooH.vooo. moHnouomo> AoHo.oooo. . .H . .n Hoo. . . lmoo.oooo. o . . . . iooH.ooom. . .L. . .1. moon o xHHz .ooo.oooo. ammo loom AoHo oooo . moo. ooo H ooo H iaoo.oooo. i.oo vooo Ammo Como looH..ooo.1 ANHH Como . ivoH Loom w one: ieHo.oooo. ioHo.oHoo. imHo.oooo. moo. Hoo. moo. Homo.oooe. ioHo.oooo. ioHo.oomo. iooo.vooo. iHoo.oHoo. looo.ommH.H roam AeHo.oooo. imHo.oooo. ioHo.oooo. Hoo. oHo. ooo. imHo.oooo. ieHo.oooo. Ammo.oooo. looo.oHHo.H Aooo.oooe.H looo.oooo.H moooo onoHonosm ioHo.oHom. lmHo.vooo. isHo.oHoo. soa. woo. omo. lHoo.ooeo. imHo.oooo. Ammo.oooo. iooo.ooHo.H iooo.oon.H iooo.omom.H moooo nosoo Ammo.oeoo. Ammo.ooeo. 11 oem. omo. 11 iHoo.vooo. lomo.oooo. 11 ANVH.oHoo.1 looH.omoo.1 11 ooooo loco..HHo. Homo.oeoo. 1- Hoo.1 oHo.1 11 lmoo.oeoo. iHao.ooom. 11 loom.omoo.m iHoH.oooo.o 11 ooHuom HHHo.oHoo. Hooo.oooo. 11 on. oom. 11 ioHo.oooo. looo.cooo. 11 Amoo.ooom.o ieqo.oomo.o 11 oon HoHo.oHom. AHHo.omoo. AoHo.oooo. oem. ooo. oHo. AoHo.vooo. ioHo.cooo. Ammo..ooo. iooo.ooom.o immo.ooom.o AHoH.oooo.H mHoouoo AoHo.oooo. lmHo.vooo. ioHo.oeom. ooo. moo. moo. iHoo.oooo. ioHo.oooH. imoo.oome. Homo.oooo.H Looo.oooo.H Hooo.oooo.H oooo immo.ceoo. AHNo.oHom. HmHo.oooo. 11 11 11 immo.oooa. 14H:.ooma. Aomo.omoo. imeH.oooo.H looH.oomH.H HeNH.ooom.o ousuHocodxm Houos oooH oooH HooH oooH oooH Hoos oomH HoeH Hmos oooH oooH HooH a muc.umcou 1m .L 1.: s1 «.NomH oso .ommH .HmmH .Amvaozomzoc smxuOBV mwaam< a0 mmumEHummll.mH m4m<fi 96 by year estimations are equivalent to assuming that both intercepts and income elasticities are different each year. Owing to the availability of less items in 1951 and 1952 and owing to the difference between the classifications of these two years and the rest of the years, estimations by dummy variables were done separately for 12 years (1951- 1962) and 10 years (1953—1962). The results of the tests are presented in Table 20 and Table 21, respectively. It is evident from Table 20 that the elasticity of total expenditure tends to decrease over time. The elasti- city in the first two and last two years is significantly smaller and larger, reSpectively, than that in 1958 at the 1 percent level. The ”y for food has a similar tendency. From pervious results we know that the income elasticity for cereals is usually the lowest, and that for meat, milk and eggs the highest among all the food items. Since during this period Japan's national income had risen rapidly, we might expect that the elasticity for cereals would decrease and that for meat, milk and eggs increase. Although this table shows that the ny for these two items are in accord with our expectation, the elasticity for cereals in 1951 is markedly smaller than 1958, and that in 1952 not significantly dif— ferent from 1958. This might be a result of the different Classifications of the first two years and the years after 1953. The coefficients for vegetables in 1958 are smaller than all other years except for 1951 and 1952 at the 1 percent level of significance. 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Q0000. 00000. 00m0. 00000.1 30000.1 90000.1 U0m00.1 20000.1 «0000.1 «0000.1 0000.0 quuHUcmmxm 0muoa Amy m000 0000 0000 0000 0000 0000 0000 0000 0000 0000 m000 0000 acmumcoo m ummw NI .mo0QM0um> >EED¢ 0:00: m000 on 0000 EOuw mv0oc¢wsoz away: 000 UwumE0ummw mw0u000umm0w mEoucH 11.0w mqmde I —_... . .-.- 98 factor in determining the expenditures on fish and food prepared outside the household. The elasticity for housing in those years preceding 1958 is significantly smaller than that in 1958, which in turn is significantly smaller at the 1 percent level than that of those years afterward. As to fuel and light, the elasticities in the first two years are significantly smaller, and those in the last years significantly larger than the elasticity in 1958 at the 1 percent level, and those of the rest of years (other than 1957) are not dif— ferent from that in 1958 at the 20 percent level. The com— parison of the elasticity for clothing in 1958 with those in other years is rather erratic. The elasticities in the years 1955, 1959, and 1960 are not much different from 1958, and those in the other years (except 1957) are significantly larger than 1958 at either the 1 percent or 5 percent level. The results estimated by excluding 1951 and 1952 are presented in Table 21. Let us compare the income elas— ticities in 1953, 1958, and 1962. At the 1 percent level the elasticities for food, meat and milk and eggs, beverages, housing, rent,and total expenditure in 1958 are significantly greater than in 1953 except that in the case of total expen— diture the level of significance is 10 percent, and signifi- cantly smaller than in 1962. On the other hand,the 1958 income elasticities for cereals and barley are significantly Smaller than those of 1953 and larger than those of 1962. If we disregard a few exceptions (that is, ny's of the later 99 years are slightly larger than the ny'S of the early years) of the income elasticities between the three years, it can be generalized that the income elasticities for the above six items increase through time and that those for cereals and barley are negatively related to time. The income elasticities for fuel and light in 1958 are not significantly different from that in the period from 1953 to 1956 and in 1959, and is significantly smaller than ijl 1957 at the 5 percent level and in the last three years (1960-1962) at the 1 percent level. The elasticity for vegetables in 1958 is smaller than that in any other year at the 1 percent level of significance. The elasticity for fish, cakes and candies and fruits in 1953—1955, 1961, and 1962 is markedly larger than that in 1958, which is not much different from that in the other years. The ”y for clothing in 1953, 195“, 1956, 1957, 1961, and 1962 is significantly greater at the l per— cent level than that in 1958, which shows no difference from the other three years at the 20 percent level of signifi- cance. The elasticity for clothes in 1958 is significantly smaller than that in 1953, 195“, 1961, and 1962 at the l to 5 percent level, but greater than that in 1955-1957 at the 5 to 20 percent level and not different from that in 1959 and.l960 at the 20 percent level. While the elasticity for personal effects in 1958 is significantly smaller than that in the previous years, it shows no significant difference from that in the years afterward at the 20 percent level. lOO FARM HOUSEHOLDS ECONOMY SURVEYS The information on basic living materials for farm households was either classified by income group or cross- classified by income group and family size. We have shown in our previous analysis (in Section 1 of this chapter) that it is more reliable to estimate family size elasticity from the table cross—classified by income class and family size. The resultant tables of this cross-classification were available for three years from 1960 to 1962, and since the parameters estimated are not much different for these years, only the estimates in 1962 are shown in Table 22. In order to show the effects of family size on the demand for basic living materials, the table gives the re— sults estimated both by simple regressions (with income only as the explanatory variable) and by multiple regressions (with income and family size as explanatory variables). The coefficients of determination are usually improved when they were estimated by the multiple regression equations, especially for food and cereals because family size plays an important role in determining the demand for basic living materials. If family size elasticity for a given item is positive, its income elasticity estimated by multiple regression is smaller than the corresponding figure estimated by using income alone as the independent variable. However, the coefficient 0f the constant term is larger than the corresponding coef— ficient obtained by simple regression. When family size elasticity is negative, the converse is true. 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Hem. mme. wee. mgSBHecmgxm 0mpoe mo0ocmmsom m©0onmmsom m00osomsom m00o£mmsom m00onomsom m00ogomsom pmxhoz smog: 500m poxpoz smog: 800m Loxpoz 20903 Spam m. .m , mp0o0pm00m mEoocH mmm0 .nmLoE mo 000.0m wo Qo0pm0SQOQ m 3003 mm0p0o mnp C0v m00onomson 00x00: c003 m00onmmzoc Epww mo mm0p0o0pmm0m 680020 mo com000QEoo 1.3 Repairs and improvements,V furni- ture and utensils,W clothing,X y clothes, and personal effectsZ aThe magnitudes of the expenditure elasticity es- timated for rent dispersed widelygof the 16 estimates two were slightly greater than 0.5 and four were be- tween zero and 0.1. bHowever, of the 31 estimates, two were a little more than 0.6 and four were less than 0.3-—two of the estimates by the multiple regression were as small as 0.02 and 0.05. CThree of the 16 estimates were beyond this range. dOf the 16 estimates four were not in this range. eOne of the 16 estimates was 0.M5. 112 f0f the 30 estimates one was 0.55 and two—thirds were between 0.65 and 0.75. gOne of the four estimates was 0.9“. h Three of the 27 estimates were a little larger than 0.9. lOne of the 17 estimates was 0.95. JTwo of the 16 estimates were slightly outside this range. kThree of the 36 estimates were slightly larger than 0.9. 1Three of the 13 estimates were slightly greater than 1.10. mohe of the 28 estimates was 1.23. n0f the 1A estimates two were slightly less than 0.8 and another one was 1.11. 0One of the 1M estimates was 1.25. p0f the 14 estimates three were very near 0.8 and another three were larger than the upper limit. three of the 14 estimates were beyond the upper limit. rTwo of the 12 estimates were smaller than the lower limit. 8Two of the 12 estimates were 0.93 and another one was 0.91. t0f the 29 estimates one was 0.97 and eight were beyond the upper limit. u0f the 31 estimates five were slightly smaller than 1.1 and the other five outside the upper limit. V0f the 26 estimates two were less than 1.3, six- teen between 1.5 and 2.0 and six greater than 2.0. WFive of the 28 estimates were slightly smaller than 1.3. XEight of the 31 estimates were very near 1.3. ySix of the 14 estimates were slightly smaller than 1.3. ZFour of the 14 estimates were 1.22, 1.26, 1.27, and 1.29. 113 The family size elasticities estimated from the re- sultant tables cross-classified by income and family size are summarized in Table 26. TABLE 26.--Summary of the family size elasticities for basic living materials. Individual Commodity and Groups of Commodities rl<0 Meat, milk and eggs, alcoholic bever— ages, food prepared outside the household, housing, rent, repairs and improvements, furniture and utensils, clothing,* clothes. 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Ho 0 280000 llllllllllllllllllll 0“ uowmmwh £UH3 NUHUHUMMHU OORHm «DODGHHEOUVII.5N Hflnflfi 129 elasticities and the values of E2 are smaller whenever per— manent income instead of the measured income is used.9 One of the reasons for this phenomenon undoubtedly is that the method of measuring permanent income was unsatisfactory-— it was derived by a constant weight of the disposable in— comes of the current year and the past two years, and it consisted of only ten consecutive yearly observations. Because of the limitation of the measured income data, the Inethod of a weighted moving average of disposable income arm.a number of past years incomes with the weights expo— ‘tentially declining and other methods are not suitable to calculate the expected income series.10 However, when both permanent and transitory income erutered the estimating equations, the results improved con- sfixierably——in the majority of cases, the permanent income eliisticities became larger and their standard errors smaller, arui the values of E2 tended to be slightly greater than the cortresponding estimates obtained by using disposable income. Of the sixteen individual goods and groups of goods listed hi Table 27, housing,repairs and improvements, furniture and 9Not only are the expected income elasticities smaller thar1 their disposable income elasticities, but also the standard errors of the expected income elasticities are usually considerably larger than those of disposable income elasticities so that in many cases the permanent income elas— ticities are insignificantly different from zero. 10For explanations of other methods of measuring Permanent income, see Paul Taubman, "Permanent and Transi— tory Income Effects," The Review of Economics and Statistics, XLVII (February, 1965), 38—H3. 130 Lytensils, and clothing can probably be regarded as durable gxaods. Although permanent income was generally a much better tnariable than transitory income in determining the demand for ncni-durable goods in the sense that the elasticity of perma- ruent income was greater, its standard error smaller, and its {wartial correlation coefficient larger than those of transi- txyry income, the superiority of permanent income usually dimi— rrished in the demand for durable goods. In fact, in some analyses of the demand for durable cxnnmodities, elasticity of transitory income became more sig- rrificant and its partial correlation coefficient larger than the corresponding estimates obtained for permanent income. Despite the fact that the simplest method was used to derive the parmanent income series and that a time series of only 10 observations was analyzed, the results seem to run in the direction of Smith's finding that, while the permanent income fmqmothesis is verified with respect to non—durable goods, trarnsitory income is an important variable in explaining the 11 eXpenditures on durable commodities. 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II maemm.ve0o.0l mmm. 0o.v U mv.0 0m0o.vvwv. 20mmm.vmme.l In ufiosm.vsm0. #Amev.vvvm.u Nmm. m0.m U mm.0 Av0o.vmem. elomm.vmmm.n In 00mmm.vnov. ul0hv.v0mv.l tflvm0.vemm. nm.m m mC0LUO0U 0:000 a 0m5m m:0mso: @mm. Aomo.vmme. I: I: ¢A0mo.vovo.< ofimmm.vomo.0n 900sm.vmom. om.m poom a t Amv >00o0umo0m E009 ucU mm m0000d .mtoom pwum0w0 uo :mwo0um uwnuo 00¢: oOHuQICBO oEoocH ucmumcoU >u0toEEOU 00 .m o» uowmmwu LU03 >u0o0umm0m wo0um .0>o>usm >Eocoom mt0ozomso: Euwzc Nom0 ou 0mm0.mm00om oE0u co m0o0uoumE o:0>00 00mph mom wwwx0mcm pcmaooll.mm m0m<9 142 year's income or permanent income variables are not presented in the table. However, it is worthwhile to mention the esti- mates obtained by using permanent incomelLI as an explanatory variable. In contrast to the results obtained by using dis— posable income versus permanent income in the preceding section, all the income elasticities estimated for various commodities from farm households data are greater and the standard errors of the estimates smaller, also the goodness of fit usually improves whenever permanent income replaces disposable income as the independent variable. When both permanent and transitory incomes are introduced in the equa- tions, the results, which are similar to those from GRFIES in last section, show clearly that the expenditures on con- sumer non-durable goods such as food and its components are almost solely determined by permanent income, and that tran- sitory income appears to be more important than permanent income in explaining the demand for such durable goods as housing and clothing. A general analysis of the results as well as a com— mentary on the individual groups of commodities in Table 28 are given below. The values of R2 are pretty high using the original least-squares regressions, but the values become extremely low except for two groups (meat and milk and eggs, and fuel and light) when the parameters are estimated by the method 1“The method of estimating permanent income here was the same as that in last section. 143 of combining information from cross section and time series. About one half of the pure time-series income elasticities are larger than their correSponding cross-section estimates. Only four out of the thirty-one own-price elasticities have the wrong sign. All the signs of the cross-elasticities with respect to "all other prices” are positive. Similar to the analysis in the preceding section, a great majority of the sums of the elasticities are significantly different from zero. And among 31 equations, four have the positive serial correlation at the 5 percent level of significance. A test of the collinearity between income and prices shows that of the 37 correlation coefficients between income and price, only one is positively and twenty are negatively significant at the 5 percent level. Eggg.——When only "all other prices" is included, the time—series income elasticity is slightly less than the cross-section elasticity; but when the prices of housing and clothing are introduced, the income elasticity drOps to one half and is not significant. All the four own—price elas— ticities have the right signs and two of them as well as "all other prices" elasticity are insignificant. The cross— elasticities for food with respect to housing show positive sign but are not significant. Food and clothing are comple— ments at the 10 percent level of significance. Cereals.-—The time-series income elasticities are larger than the elasticity obtained from cross section but not significantly different from zero. All the own—price 144 elasticities are not significant. Both fish and meat, milk and eggs appear to be a complement to cereals and signifi- cant atbetter than the 20 percent level. Figh.--The values of R2 reduce from 0.82 to almost zero when the original time—series regressions are replaced by the conditional regressions. The income elasticities estimated from pure time series are about as large as the cross—section estimate and are significant. One half of the own-price elasticities carry the wrong sign and all but one of the price elasticities are not significantly different from zero. Although the "all other prices" elasticities are larger than unity, they are not significant as compared with their standard errors. In contrast to one's expectation, fish and meat, milk and eggs turn out to be complements. Meat, milk and eggs.--Regardless of which method is 2 used in estimating the demand parameters, the values of R are very high. The time-series income elasticities are twice as large as the elasticity obtained from budget survey and all are significant at better than the 1 percent level. Also both own-price and "all other prices” elasticities are quite large and significant. The cross—elasticity with respect to fish is positive as expected, and as large as 1.3 but less than its standard error. Housing.-—By the combined technique, the estimated values of R2 are only a little more than one-half of those estimated by the original time-series regressions. The time-series income elasticities are larger than the cross- 145 section elasticity and are significant. The own-price elas- ticities have the right sign and are insignificant, but when related prices are introduced, the price elasticities become about 4.5 times larger and positive. While the cross-elas— ticities with respect to food do not differ significantly from zero, food and fuel and light appear to be well-marked complements. Fuel and light.—-The income elasticities estimated from time series are much smaller than the cross-section estimate. Both the own-price elasticities and the cross- elasticities with respect to "all other prices" are greater than unity and highly significant. Clothing.——When the original least—squares regres- :sions are employed, the estimated values of R2 are near Linity but the R2 become negative and not significantly dif— Iferent from zero by use of the conditional regressions. CPhe demand elasticites estimated by the two methods are Clifferent considerably; the time-series income elasticities Eirwe less than one half of the cross-section estimate and the <3vvn0price elasticities obtained from the combined technique Elr‘e-much smaller than those estimated by the original least— EsCanares regressions and not significantly different from zero. 3 UIVIMARY In estimating the demand elasticities for 16 commo- Cififties from GRFIES and for 7 items from FHES, both the ori- E:'535-.:t'1.511 least-squares regression and the method of combining jLI'TI-I‘ormation from cross section and from time series were used. 146 When the original least—squares method was used,very high values of R2 were generally obtained for all but a few esti- mating equations. On the contrary, when the combined tech— nique was employed, the values diminished in a great majority of cases and many of them became extremely low. In many cases, the income elasticities estimated from the pure time series were considerably different from the cross-section estimates. The differences depended on the kind of commodity and on whether the prices of related goods were introduced. Roughly one half of the pure time- series income elasticities were larger than their corres- ponding elasticities obtained from the budget survey. The income elasticities for those "superior" goods estimated by the original least—squares tended to be especially large. Of all the own-price elasticities about one-quarter load implausible signs; generally such signs were obtained for l . . . <3ereals, condiments, hous1ng, rent, and furniture and uten- ESils. Besides, half the own-price elasticities were not sig- rlificantly different from zero. Although all the "all other Ixrices" elasticities estimated from FHES had positive signs, Cune—half of the elasticities obtained from GRFIES turned out ‘tco be negative. Many of the elasticities with respect to "all other prices" did not differ significantly from zero. :Elu general, the magnitude of the price elasticities estimated t>§y use of conditional regressions wzis larger and more \_ 15However, the sign for cereals estimated from GRFIES Ciluring the ten—year period (1953—1962) was negative. 147 TABLE 29 -—Summary of demand elastiCIties based on time series data. Individual Commodity and Group of Commodities "All Other Prices" Cross-Elasticitie with respect ' - - « Income Own-Price - - - ' f Commodities in Cross—Section Income Pure Time Series . ' ' ' PlastiCities to the Price 0 _ glggilgftles ElaSt1Cities ElaSCICLtleS FlaStICItles in the Paéenth8515 A R re airs & . ‘2-0 t0 '1-5 imgrovements vegetables (fish)‘a alcoholic furniture & fish (meat, milk,.& 9995)“? _1.5 to .1,0 beverages.g utensils“ condiments (fish) fuelsliqht'? processed food.d housinq‘ f°°d(°1°th'“9"“ fereals _1_(_) to -0,8 fuel&1iqht*1. (fish, meat and milk arid t clothingflk eggs), cereals (other foodL & fuel a light (hou51n9)‘ ‘5 ' food (housing) (clothin9,‘ & — cereals ' cereals food . . °~5 t0 0 vegetabiesfi vegetables,c processed food (fish).' cakes cakesscan ies & candies 5 fruits (alcoholic s fruits, & beverages, non—alcoholic Clothinq' beverages)‘ l to 0.5 cereals, processed cereals,“ rish,‘ condi- cereals,‘b food (housing)," food (fuel & food, & rent ments,C cakes&candies & condimentse light), hou51ng (food)' . fruits,d fuel & lightf housin (food),* fuel a light (food) to 1.0 food, fish, veqe- food,a fish,“ a pro- food,“ condi- cereals (meat, milk & eggs),‘I tables, cakes & cessed food ments, alco- processed food (meat, milk & candies & fruits, holic beverages. eggs),"c a fuel 8 light alcoholic beverages, (housing)” fuel 5 light 1.0 to 1.5 meatsmilk&oggs, non- alcoholic beverages9 fish,” a rent* rent (repairs & improvements), alcoholic beverages,, fuel a light (food)' housing, fuelsliqht,7 clothing 1.1 to 2.0 repairs 5 improve- meat & milk & eqqs' ments, furniture & utenSils 2 .0 to 3.0 meat 5 milk 8 egos.“ vegetables (meat, milk 5 non—alcoholic eggs)‘ beverages C>Ver 3,0 furniture & utensils housing,‘ repairs 5 Lhicertain improvements‘ housing (1.0 to 2.2) rent {—0.8 to _1 9) . Ego? (0.1 to cereals (f0.7 fish (meat, milk 5 eggs) (0.8 repairs 5 1m rovém At ")' {15h to ‘1-5)f154* to 1.9),. meat 5 milk & 8395 p 0 s (0.9 to '2.”), (0.9 to ~O'9)I (fish) (0.9 to 2.8), alco- (1.0 to 1.8), clothing meat, milk & (0.5 to 2.3) meatsmilkseggs holic beverages (non alcoholic qus (0.3 to (5.4 to -O.S), beverages)(1.0 to 1.7), non- -3.3), non— cakesscandiess alcoholic beverages (alcoholic alcoholic fruits' (1.1 to beverages) (0.2 to -3.9) beverages (4.7 0.4), non-alco- housing (fuel a light) (:0.9 to —l.2), holic beverages to -2.8), housing (food)' hou51ng (3.1 (-0.01 t9 5.2, (0.5 to -0.2), furniture 6 t: g0.7). rent fuel 8 llqht utensils (rent) (0.9 to -O.9) f . 'to -n.1). (0.6 to 2.0); clothing (food) {-.9 to —0.8), urniture & clothing (1-3 clothing (housing) (1 1 t0 UtenSIIS (1.8 to -O.4) —1.S) . to -1.1) \1 . _ . ____l- ..._ -‘H_ ‘ x_ —__ __ __ ‘._._ __ _ _ . __1________._g ' Denotes the estimate From GRFIES. U Denotes the estimate from FHES (those without these two notations include hcth surveys), one was lightly loss than zero. one was 0 c I\. a one of the five estimates was n_2n, B 1 b one was slightly lar or than zero. ‘ i one W33 -0.fi. C one was a little 105: than 20:0. 5 one was 0.6, C« 3 one was -0.6. d one was 0.35. C one W35 '0-7 and another one -n 3 one was 0‘7' e one was 0.92. d one was —n,3_ ' ' C one was 0,4, f one was 1.1. o d one was —o,2_ f 0 two of the five estimates were ~0.9 and -2 0 two of the five estimates were -3 0 one was ~0.4 D . one was-0,9, one was—0.2. ._J-- lu8 significant than those obtained by the alternative method. Many of the cross-elasticities with respect to the prices of competitive or complementary goods were in accord with our expectation. But in several cases the relationships were surprising. The demand elasticities for various goods in Tables 27 and 28 are summarized in Table 29. For the sake of seeing ‘more clearly how the pure time-series income elasticities differ from the cross—section estimates, the cross-section income elasticities entering the conditional regressions were also included in the table. Those commodities whose demand elasticities estimated from various equations were too dif- ferent to be included in a specific range were put in the category labeled ”uncertain." While the analysis of GRFIES showed that disposable income seemed to be a better variable than permanent income in explaining the consumption of almost all the basic living materials, the converse might be true for Efl§§ When both permanent income and transitory income entered the same equa— tion, the results of the estimation from both surveys indi— cated that, while permanent income was the sole variable in determining the demand for nondurable goods, the transitory income seemed more important in explaining the expenditures on consumer durabkecommodities. CHAPTER V REVIEW AND CONCLUSIONS In this study, the statistical consumer demand func- tions for basic living materials in Japan have been derived. The analysis was develOped by a two-step process. First, the budget survey data were utilized to esti- Inate the elasticities of income and family size for the demand for basic living materials by the method of instru— Inental variables and by the least-squares regressions. IDummy variables were employed to investigate the differences in expenditures on basic living materials among different group samples, as well as the stability of the demand over time. Second, the expenditure elasticities obtained from thee cross-section analysis were combined with the time- SeI’ieS information to estimate the elasticities with respect to own—price, "all other prices," and related goods prices. Aliso the income elasticities and other demand elasticities ‘Nelre estimated by the original least—squares regressions. Throughout the study, the estimating equations are ir1 double-logarithmic form. Despite its non-additivity and Other defects, this form is the best in respect to goodness of‘ fit, ease of estimation, and flexibility. 1M9 150 In cross—section analysis, the magnitude of the ex- penditure elasticities was found to depend on whether the resultant table classified by income or by total expendi— ture was used in fitting the estimation equation. The ex- penditure elasticities estimated by the method of instrumen— tal variables using measured income as the instrumental variable were very little different from those obtained by the least—squares regressions using total expenditure as an explanatory variable, but they were considerably larger than the income elasticities obtained by least—squares regressions. Since the expenditure elasticity obtained from the instru— mental variables method has been shown to be the consistent estimate of the "true” parameters and, since it can be inter- preted as the permanent income elasticity, the least—squares regression bias in estimating expenditure elasticity is pro— bably negligible with sufficiently large sample size, and ‘the income elasticity by the least-squares regression tends tCD be underestimated. As was expected, family size is an important variable irl determining expenditures on the demand for basic living mélterials, especially for total food and some of its compo— ‘ nents. The results of the analysis seem to confirm the gEEneral view that in order to derive more reliable estimates 0:? income and family size elasticities, the resultant table cPoss—classified by both income and number of household rmEmbers should be used. 151 Because estimations of the rent values of owned and issued houses were far from complete, the pattern of expendi- tures on rent and housing was quite different between these two types of dwelling houses and rented house and room. Be- sides, the demand for repairs and improvements and for fuel and light is significantly different among various types of dwelling houses because the expenditures of the types of dwelling houses other than owned house on these items were either unnecessary or partly included in rent. Although income and total expenditure were incorrectly measured due to the poor data on rent, the estimates of the demand elas— ticities for other items except housing were probably not affected since rent comprised a very small component of income and total expenditure. Occupational differences in the patterns of expen— diture on housing and its components were due to the type of dwelling house, whose effect was in turn caused by the fact that the rent values of owned and issued houses were poorly measured. The demand for other items of basic living mater- ials was, on the whole, considerably different among occu- pational groups, and usually several reasons can be found to explain their differences. Number of earners per household did affect the demand for basic living materials, but actually it was due to the close positive relationship between family size and number of earners. It may be safe to say that the effect of number of earners per se on the analysis of the demand for basic li- ving materials can be ignored. 152 The expenditures on basic living materials showed a great deal of difference among various regions. The regions containing a larger city or cities obviously have the ten- dency to have large demand elasticities for food and housing. The regional variations in the consumption of fuel and light, clothing, and clothes were mainly determined by climate. The analysis of geographical variations in consumer demand included the effects of region, city size, and urban-rural conditions within the country since the effects of the three variations usually are closely associated with one another. The results of the city size and regional variation analyses were closely related to each other in the sense that the expenditure pattern of the larger city is similar to that of the region containing a relatively larger city or cities. The negative association between the city size and the mag- nitude of the income elasticity for repairs and improvements as well as the small correlation between city size and the income elasticities for furniture and utensils and for fuel and light was probably due to the fact that a larger number of households in the larger city lived in rented houses and rooms which might furnish repairs and improvements, furniture and utensils, and fuel and light. It was also found that urban—rural and city size variations in the consumption pat- terns were the same in the sense that urban areas acted like larger cities and rural areas like smaller ones. 153 The permanent income hypothesis as applied to indi— vidual categories of consumption was tested by comparing the income elasticities estimated for different types of sample groups from cross-section data. On the basis of the hypo- thesis, the elasticity of expenditure on any particular category of consumption with respect to measured income for a group of families that have stable incomes is supposed to be higher than that for the group whose incomes fluctuate. ‘The results of the analysis, however, did not provide con- vincing evidence for the hypothesis. It was found that the Inagnitude of the income elasticity for a particular item of consumption was influenced not only by the fluctuation of income, prevailing prices, tastes and preferences, but also by many other factors such as income level, family size, llome ownership, availability of electricity and income dis— tI‘ibution. Certainly, the permanent income hypothesis can— rlot be rejected on the basis of this crude cross-section teSt, but it does indicate that Friedman's method of testing tile permanent income hypothesis with respect to individual gc>ods is inadequate. In time—series analysis, permanent income was esti— Inated by constant weighting of the current and past two lyears' disposable incomes. Permanent income was found to be a better variable than disposable income in determining the expenditures on basic living materials for farm households, bLTt disposable income turned out to be the better one for urban households. Whenever transitory income was introduced 15“ along with permanent income in the equation, the results always appeared to be better than those estimated by using disposable income alone as an independent variable. It was also found that expenditures on non—durable goods were deter— mined almost solely by permanent income, and that the tran— sitory income seemed more important than permanent income in explaining the consumption of consumer durable goods. Income elasticities estimated from the pure time- series equations were, in the majority of cases, consider- ably different from their corresponding cross—section esti- mates. Generally speaking, for those items whose cross- section estimates of income or expenditure elasticities were relatively low, the magnitude of the income elasticities estimated by the pure time-series equations tended to be much lower than the cross—section estimates. In addition, those commodities that had relatively high cross—section estimates usually tended to have much larger time—series income elasticities. However, the income elasticities esti—. mated by the pure time-series equation depended, in many cases, on whether the prices of related goods were included in the equations. Despite the divergence between the income elasticities from cross section and from time series, the order of magnitudes of the income and expenditure elasti- cities resulting from both analyses contained few surprises. Except for a few cases, the values of E2 usually were quite high when the demand relationship was fitted by the original least—squares, but the values diminished in 155 almost all the cases when the method of combining information from cross section and from time series was employed; many of them turned out to be surprisingly low. The price elastici— ties and their standard errors estimated by the conditional regression tended to be larger than those obtained from the original least-squares. The own-price elasticities for a few items carried implausible signs, but for most of the commodities the elas— ticities had the right signs. Half the own-price elasti- cities were not significantly different from zero. The "all other prices" elasticities for all the commodities for farm households had positive signs but about one half of the elasticities obtained for urban households carried negative signs. Many of the "all other prices” elasticities were not statistically different from zero. Furthermore, many of the cross-elasticities with respect to the prices of related goods had the expected signs and their magnitudes seemed reasonable, yet surprising relationships were found in quite a few cases. More than one half of the cross-elasticities did not differ significantly from zero. Although this study of the demand for basic living materials has been based on somewhat imperfect data and has utilized relatively simple methods, the analyses given in the preceding chapters show that the pattern of consumers' behavior in quantitative terms can be outlined roughly. In the great majority of cases, the results obtained are those expected. 156 With regard to the deeper investigation of consumer behavior and to the problem of obtaining more reliable esti- mates of the demand parameters, two aspects of improvement should be considered: One concerns data and the other con— cerns the technique of combining information from cross section and from time series. As to the data, several points should be made: (1) Although the data used in this study covered an unusually large number of households, they are grouped data. It is beyond doubt that the original data on individual fami- lies are better for research purposes. (2) If data for individual families were unavailable, the grouped data classifying consumer units by total expen— diture should give the average income in each class. This would enable us to estimate permanent consumption and would be invaluable information for studying the consumption pattern. (3) To make it possible to study the joint effects of many variables, the survey data should be a multiple cross- classification by a number of variables, say, occupation of household head, region, and type of dwelling house, in addi— tion to income and family size. (A) Although the data used in the time—series analysis were repeated surveys of twelve consecutive years, only a small number of the same households were surveyed for each successive two years. The re—interview data based on the same families for at least two years would doubtless provide in— formation of great value for the cross—section test of perma- nent income hypothesis. 157 (5) In relation to the preceding problem, it would be desirable to have data that provide information on income change from one year to the other, since the consumption pattern of families that have a certain level of real income for some time may be different from that of other households that have only just reached that level. (6) More family characteristics should be covered in the survey and made available to research workers. The method of combining information from cross—section data and from time series has been used to overcome the multi- collinearity problem encountered in time—series analysis. However, the combined method is not based on a sound theo- retical framework, and utilizing cross-section parameter esti- mates jointly with time series is questionable because time- series and cross-section data are influenced by so many different factors. The results we obtained by using the conditional regression and the pure time-series equation dif— fered considerably in many cases; the former approach appears to be inferior to the latter in terms of goodness of fit and the standard error of estimates. Of course, the combination of cross-section with time—series analysis seems highly ad— vantageous, and the analysis of consumer behavior should be consistent with both types of data. Nevertheless, additional effort should be directed to seeking more appropriate tech— niques for combining the information from cross section and time series. 158 The results of time-series analysis do not seem to be as satisfactory as those of cross—section analysis. One of the defects of time—series analysis was the short time span covered. In the course of the investigation, some ideas on overcoming the problem of small number of observations in time-series estimates have come to mind. First, data were available for 28 cities with popu- lations of 50,000 or more in the urban budget survey. If data were combined by an appropriate method and analyzed for, say, ten years, there would be 280 observations. In addition to the large number of observations, another advantage of this combination is that it might be possible to test whether there are structural differences among regions and cities. Second, quarterly or monthly data could be used instead of the yearly observations. This approach may yield useful estimates and may also make it possible to test the monthly or seasonal fluctuation in the demand for consumer goods. 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"The Early History of Empirical Studies of Consumer Behavior," Journal of Political Economy, LXII (April, 195M), pp. 95-113. Stone, Richard. "The Analysis of Market Demand: An Outline of Methods and Results,” Review of the International Statistics Institute, XVI (1948), pp. 23—35. "The Demand for Food in the U. K. Before the War," Metroeconomica, 111 (1951-1952), pp. 8-28. Summers, Robert. "A Note on Least Squares Bias in House— hold Expenditure Analysis," Econometrica, XXVII (January, 1959), pp. 121-126. Taubman, Paul. "Permanent and Transitory Income Effects," The Review of Economics and Statistics, XLVII (February, 1965), pp. 38-43. Tobin, James. "A Statistical Demand Function for Food in the U. S. A.” Royal Statistical Society Journal, Series A, CXIII (Part II, 1950), pp. 113-140. Watson, G. S. and E. J. Hannan. "Serial Correlation in Regression Analysis, II," Biometrika, XLII (1956), pp. 436—448. ' Wold, Herman and P. Faxey. ”On the Specification Error in Regression Analysis," Annals of Mathematical Statistics, XXVIII (1957), pp. 265—267. Unpublished Thesis Sparks, Willard R. Estimates of the Demand for Food from Consumer Panel Data, Unpublished Doctoral Disser— tation. Michigan State University, 1961. Japan, ,Japan, Japan, Japan, Japan, 166 Public Documents Bureau of Statistics, Office of the Prime Minister. 1959 National Survey of Family Income and Expenditure. Bureau of Statistics, Office of the Prime Minister. Annual Report on Family Income and Expenditure Survey, 1951-1962 (Kakei Chbsa H6koku). Bureau of Statistics, Office of the Prime Minister. General Report on the Family Income and Expenditure Surveyyrl946-1962. Department of Agriculture and Forestry. Farm House- holds Economy Survey, 1951—1962. Bureau of Economic Planning. National Income White Paper. APPENDICES APPENDIX A ON THE PRACTICAL APPLICATION OF THE DUMMY VARIABLES Let X1, X2, . . . , XlO be the variables of ten occupations, where X = .{1 if observation in occupation i, i 0 otherwise. Let us assume that the occupations differ only in their level of consumption (the Y-axis intercepts), and have the same marginal propensity to consume, then the model is C = bl + ale + ... + aIOXIO + BY + U (l) where C is consumption, Y income, and U error term. It is impossible to estimate the parameters in (1) since the matrix of sum of squares and cross products is singular. There are two alternative ways to fit the equa— tion: one way is to make use of all dummy variables without computing the over-all constant term, b in the regression; l) the other way is to omit one of the dummy variables and include the over-all term in the regression. In the latter case, the over—all constant term is actually the coefficient of the dummy variable omitted. While the first method estimates each occupational expected value, the second method 168 169 estimates both the expected value of the occupation whose dummy variable was omitted and the differences of the former value and the expected values of the other occupations whose dummy variables were included in the regression (or, they measure occupational shifts in the regression of C on Y as deviations from the intercept of the occupation whose dummy variable was omitted). Although the estimates and their interpretation differ between the two methods, the parameters estimated by the two ways make no essential dif— ference—— the results for one are readily derived from those obtained for the other.1 Let dl,d2, . . , le be the coef— ficients obtained by the no over—all constant term method, and X be omitted, and b the over-all constant term in I 1 the second method, then d = b 1 1, and di = a1 + bl, i = 2, 3, . . ., 10. Most researchers are primarily more interested in the second method of estimation than in the first one. To test whether the intercepts of the occupational group are the same is to apply a pftest to see whether ai is signifi— cantly different from zero.2 For those equations taking logarithmic form, the dummy variables should take values of ten and one instead of one and zero, respectively, for 1For the mathematical proof of this identity, see Arthur S. Goldberger, Econometric Theory (John Wiley and Sons, Inc., New York, 1964), pp. 210—221. 2For this point, see Robert L. Gustafson, ”The Use and Interpretation of 'Dummy Variables' in Regression," Michigan State University, East Lansing, 1962 (mimeo). 170 the log of zero is minus infinity, the log of ten is one and the log of one is zero. Alternatively, if we wish to assume that the inter- cept is the same but the slopes are different, and suppose that the first dummy variable is omitted, then the model is C = b2 + fOY + f222 + ... + flOZIO + U (2) Where Z. = X.Y. l i This equation should be fitted by the second method above, and the interpretation of the result follows the last model. If one makes the further assumption that the impact of the occupation was to make the intercepts and the slopes of the consumption different, then one might write + h Y + h X + + h Z G = b3 + g2X2 + + gloxlO o 2 2 °°' 10 lO+U (3) But the results of this equation are exactly the same as those estimated by ten separate regressions without using dummy variables, since equation (3) breaks the sample into 3 ten original samples of occupations. 3This has been shown by Arthur S. Goldberger, pp. cit., pp. 225—226. APPENDIX B-1.--A comparison of the elasticities estimated from the tables classi- Jf71 fied by income group and by total expenditure class, worker household. Estimated from the Tables Classified by Income Classes Estimated from the Tables Classified by Total Expenditure Classes ny col(1)/ai ”E ny 001(4)/ai ”E (1) (2) (3) (4) (5) (6) A11 Japan Total Expenditures .8701 1.1444 Food .5947 .6835 .6821 .7568 .6613 .6588 Cereals .2899 .3332 .3334 .4221 .3688 .3667 Subsidiary Food .6911 .7943 .7921 .8380 .7323 .7295 Cakes, Candies, Fruits and Beverages .8481 .9747 .9664 1.0213 .8924 .8857 Food Prepared Outside Household 1.2625 1.4510 1.4384 1.4693 1.2839 1.2716 Housing .9874 1.1348 1.1297 1.5548 1.3586 1.3638 Rent .2354 .2705 .2561 .5164 .4512 .4368 Repairs & Improvements 1.4806 1.7016 1.7057 2.2391 1.9566 1.9625 Furniture & Utensils 1.3106 1.5063 1.4929 2.0743 1.8126 1.8217 Fuel and Light .7778 .8939 .8932 1.0136 .8857 .8842 Clothing 1.1139 1.2813 1.2795 1.4991 1.3099 1.3081 Urban Total Expenditures .8720 1.1577 Food .5987 .6866 .6845 .7679 .6633 .6614 Cereals .3152 .3615 .3610 .4560 .3939 .3921 Subsidiary Food .6709 .7694 .7668 .8244 .7121 .7105 Cakes, Candies, Fruits and Beverages .8333 .9556 .9473 1.0188 .8800 .8754 Food Prepared Outside Household 1.1518 1.3209 1.3066 1.3918 1.2022 1.1923 Housing .9098 1.0433 1.0400 1.4652 1.2656 1.2706 Rent .0889 .1019 .0876 .3714 .3208 .3108 Repairs & Improvements 1.5755 1.8068 1.8164 2.2155 1.9137 1.9211 Furniture & Utensils 1.3254 1.5200 1.5035 2.1585 1.8645 1.8717 Fuel and Light .7603 .8719 .8716 .9988 .8627 .8624 Clothing 1.1679 1.3393 1.3387 1.5740 1.3596 1.3577 Rural Total Expenditures .8559 1.1364 Food .5544 .6477 .6470 .7095 .6243 .6181 Cereals .2569 .3002 .3006 .3946 .3472 .3433 Subsidiary Food .6677 .7801 .7789 .8238 .7249 .7176 Cakes, Candies, Fruits and Beverages .8618 1.0069 .0010 1.0473 .9216 .9057 Food Prepared Outside Household 1.2767 1.4916 1.4832 1.3657 1.2018 1.1788 Housing 1.1381 1.3297 1.3203 1.7982 1.5824 1.5962 Rent .0172 .0201 -.0018 .2814 .2476 .2064 Repairs & Improvements 1.5164 1.7717 1.7610 2.6050 2.2923 2.3022 Furniture & "tensile 1.3223 1.5449 1.5312 2.0414 1.7964 1.8101 Fuel and Light .7628 .8912 .8888 1.0334 .9093 .9011 Clothing 1.0128 1.1833 1.1787 1.4239 1.2530 1.2467 172 APPENDIX B-2.-—A comparison of the elasticities estimated from the tables classi- fied by income group and by total expenditure class, general households. Estimated from the Tables Classified by Total Expenditure Classes ny col(4)/ai n Estimated from the Tables Classified by Income Classes ny col(l)/ai n E E (1) (2) (3) (4) (5) (6) A11 Japan Total Expenditures .6945 1.1120 Food .5745 .8272 .8268 .8531 .7672 .9675 Cereals .3892 .5604 .5602 .5920 .5324 .5333 Subsidiary Food .6458 .9299 .9295 ..9073 .8159 .8161 Cakes, Candies, Fruits and Beverages .7657 1.1025 1.1018 1.1231 1.0100 1.0100 Food Prepared Outside Household 1.0292 1.4819 1.4790 1.4969 1.3461 1.3464 Housing .7320 1.0540 1.0581 1.4359 1.2913 1.2924 Rent .2503 .3604 .3629 .5976 .5374 .5418 Repairs & Improvements .8112 1.1680 1.1715 1.7497 1.5735 1.5758 Furniture & Utensils 1.0059 1.4484 1.4542 1.9313 1.7368 1.7367 Fuel and Light .5926 .8533 .8537 .8590 .7725 .7741 Clothing .9484 1.3656 1.3638 1.5888 1.4288 1.4290 Urban Total Expenditures .6871 1.1088 Food .5727 .8335 .8316 .8404 .7579 .7579 Cereals .4008 .5833 .5799 .6060 .5465 .5459 Subsidiary Food .6123 .8911 .8903 .8644 .7796 .7793 Cakes, Candies, Fruits and Beverages .7656 1.1142 1.1126 1.1286 1.0179 1.0180 Food Prepared Outside Household .9644 1.4036 1.3974 1.3637 1.2300 1.2292 Housing .6698 .9748 .9793 1.3366 1.2054 1.2067 Rent .0732 .1065 .1044 .3816 .3442 .3442 Repairs & Improvements .9910 1.4423 1.4489 1.7907 1.6150 1.6209 Furniture & Utensils .9775 1.4226 1.4353 2.0169 1.8188 1.8189 Fuel and Light .5623 .8184 .8170 .8284 .7471 .7493 Clothing .9588 1.3954 1.3973 1.6567 1.4941 1.4950 Rural Total Expenditures .6887 1.1891 Food .5451 .7915 .7916 .8977 .7549 .7552 Cereals .3811 .5534 .5590 .6415 .5395 .5431 Subsidiary Food .6396 .9287 .9276 .9896 .8322 .8308 Cakes, Candies, Fruits and Beverages .7591 1.1022 1.1017 1.2000 1.0092 1.0090 Food Prepared Outside Household .7787 1.1307 1.1198 1.5791 1.3280 1.3213 Housing .7474 1.0854 1.0906 1.7095 1.4376 1.4389 Rent. .2874 .4173 .4178 .7356 .6186 .6024 Repairs & Improvements .6153 .8934 .8904 1.9559 1.6449 1.6521 Furniture & Utensils 1.0288 1.4938 1.5067 1.9474 1.6377 1.6367 Fuel and Light .5999 .8711 .8713 .9617 .8088 .8052 Clothing .9609 1.3952 1.3942 1.6285 1.3695 1.3755 173 APPENDIX C.-—Occupation classification table. W2?” Manual Other Code Classification Definition Exam lea Clerical p House- Laborers holds This group includes the physical Coal sorters, Draftsmen, Metal 1"} laborers Who are employe 1n finishers, Electro-communication 2 1 Regular Laborers governmental or non-governmental operators Drivers Crews Con- _S corporations with a ong term ' . ’ ’ ,3 contract. ductors, Dehverymen, Shopmen, Sweepers, Guards, Servants, Car- 'g This group includes the physical penters, Domestic day maids etc. : Tern orary and laborers who are employed in a g 2 p ‘or :9 Day Laborers corporations with daily or thirty g and less day’s contract. 1'3 This group‘ includes the wage- Typists, Telephone operators, loyed in N C1 ks s t‘ h d u Non-governmental earners o are emp “5.533 er ' _ ec1on ea . A: m 3 Employees :ifgpgovfilonsrp‘igltsalginschgdigorziesd Physmans, Architects, Judges, 36 E en a e in clerical, technical or SIhOOI teachers, Pol1cemen, Cap ' o administrative business. tams, Railway conductors, Press- 3 ‘ men, Traveling salesmen, Pho- Th1s grou inCiUdES the W389 tographers, Radio announcers etc. '3 Governmental earners w o are employed in ': 4 governmental offices, hospitals or .2 Employees schools and engage in clerical, 0 technical or administrative busi- ness. This group includes managerial Ci r stores, Candystores, Haber- staffs of unincorporated or incor- das cries, Picture story tellers, Merchants and porated manufacturing, wholesale, Peddlers, Brokers, Pedicabmen, 5 Craftsmen retail or services who employ four Pawnshops, Barber’hoss ops, or less employees. Mounters, Carpenters, Scaffold workers Shoe shining laborers, Gardeners etc. - This group includes managerial Private hospital managers, Private Managerial Staffs staffs of unincorporated manufac- school managers, Dance man- 6 of Unincorporated turing, wholesale, retail or services agers etc. Enterprises wlhoees employ five or more em- P0 - This group includes managerial Presidents, Directors, Inspectors, Managerial Staffs staffs of incorporated manufactur- Trust tees, Ministers, Governors. 7 of Incorporated ing, wholesale, retail or services Prefecturai governors, Parliament- Enter rises who employ five or more em- ary vice ministers, Mayors etc. p ployees. 5; This group includes the workers Adovocates, Accountants and tax .3 who nppl specigl skill or knowl- attorneys, Medical practioners, - edge to t eir jo s. M1dwives, Priests, Painters, e 8 Professmnals Writers, Fortune tellers, Com- i=1 1 posers, Scriveners, Flower ar- ; rangement teachers etc. ‘ — 5 This grou includes those who can Models, Professional athletes, not be cassified in any one of Actors and actoresses. Assembly- 9 Others grou s mentioned above. men etc. P — , Housemaids Housebo s tuden Without etc. ' y ’ S ts 10 Occupation Unpaid Family 11 Workers Source: 1959 National Survey of Family Income and Expenditure, Bureau of Statistics, Japan. Office of the Prime Minister, 174 :oHummsooo sconce: Logo mnosuo Amy mawcoflmmomoum Amy momflumuouco poumuomnoocfl mo mwmmum Hwfinommcmz are momfinmnouco pouMHOQHOUCflc: mo mmwmum Hmfluommcmz va coEmummuo paw mucmnonoz Amv mooonmEo useficno>ow Avv mmomoamso accessosomuaoz Ame mnemonma map mumuomeoe “NV muononma Hoasmom AHV "mBOHHOw me one mcoflummsooo sou one mmv.a 5mm.H mom.H omm.H Hav.a mmm.a mmm.H mvm.a omv.H mom.H muoowmm HMCOmHom mwo.a 5mm. mum. mna. mow.a vmm.H mho.a oom.H mvo.a nmm.a monuoHo HNN.H omm. mmm.a mma. hem.a owm.H «NH.H «Hm.H vom.a omN.H mcflzuoHo vvm. mmh. mew. vam. men. vmm. man. mmm. mmm. awn. unmflq a doom mov.a mmm.a omv.H mmw.a mnm.a wmv.a moo.a mmm.a mmm.a wem.a maflmcoub a ousuflcusm omm.H hum.m mmo.H mmm.~ vem.a moa.a vw¢.H mam.a omv.m mnm.a mucoeo>oumEH a whammom me.a vom.a mmo.a omv.a ova.a mmo.H mam. mmm. Hem.a NNN.H mcwmsom nmm.a vam.a nmm.a chm. Hmm.a Ham.a OHN.H mom.a mmm.a vmv.a paosomsom opHmuso poucmoum poem mum. Nmm. mmo.a mam.a voo.H me.H Hem. mom. mmm.a mNo.H mommuo>om owaonooamlcoz who.a nmm.a mom. mam. mmw. mmo.a mun. mam. mmN.H mvm.a mommuo>om Ofiaozooag vwm. omo.H mvm.a omm. mvm. vmo.H «mm. mam. Hmo.a vwm. muwsum Nam. moa.a mmo.a Hmn. mmo.H mmo.a Nmm. vam. mmm. mam. moflpcmo a moxmo Ham. BNN.H mvo.H Hum. mam. moa.H omm. Hmm. >NH.H mmo.a mommuo>om w muflsum .mmHGGMU .moxmu mmm. owe. mew. eve. was. moo. Hum. mvm. mmm. 5mm. mucoEHUcou wen. mam. Hem. now. mmm. mmm. who. «am. nmn. was. poom commoooum mam. haw. 0mm. was. com. hem. mm». mmn. mmm. man. moanmuomo> ovm.a mmm.a mmm.a nmm. ova.a vam.a mom. Hmm. mov.a Nwo.a wmmm w xaflz wmm.a Hmm.a How. omm. nmm. vmm.a nmo.H hHH.H vmm.H mvm.a use: mmw. how. one. vmm. «mm. vmw. own. mmm. mom. omm. swam vam. evw. Nmm. omm. mmm. Hmm. mmn. mmn. Nmm. mmm. boom auwflbflmnsm who. moo. an.H mmm. mmb. va.H mam. ohm. mmH.H owo.a pcoum ham. mma. mmm. mmm. Hmw. moo. Nmm. Hmm. Hue. nmm. ooflm vom. mom. mum. mmm. Hmo. Hmm. nmm. sum. new. com. mamouou men. mmm. mmm. mmn. oam. Hmm. mm». who. has. mmn. poom Aoav Amy Amy Any Amy Amv Avv Amy Amy AHV coflummsooo mcoflummsooo sou CH wamflnoume mcfi>fla Uflmmn mo Hm ocBII.Q xHszmm< APPENDIX E TESTS OF THE EQUALITY OF COEFFICIENTS AMONG TEN OCCUPATIONS As the following statistic for the tests of the equality of regression coefficients is based on the assump— tion that the population from which the dependent variables were drawn has a constant variance, we use Barlett's method1 to test the variances homogeneity of the regression equations for ten occupations. The results of the tests are presented in Table E-l. Since the significant values of F(9,oo) at the 1 percent and 5 percent are 2.41 and 1.88 respectively, the variances of all the commodities except barley, alcoholic beverages, and rent are equal over the regressions of the occupational groups. The test of the equality of the consumption level and income elasticity is given by the following statistic2 SSR —SSRd N—sm F(k (s—l), N-sm) = e ' SSRd k(s—l) 1M. S. Bartlett, "Some Examples of Statistical Methods of Research in Agriculture and Applied Biology," Supplement—Journal of Royal Statistical Sociepy, V (1957). 2This formula is developed by Willard R. Sparks, Estimates of the Demand for Food from Consumer Panel Data (Ph.D. Dissertation, Michigan State University, 1961) For the statistical proof of this formula, see his Appendix B. Where there are only two regressions, for the test of equality of regression coefficients, see Gregory C. Chow, ”Tests of Equality Between Sets of Coefficients in Two Linear Regres— sions," Econometrica, XXVIII (July, 1960), 591-605. 175 “““~'-haa=—I-—-——-—--~--+— ~~ — —- 176 :H.H om.a m:.a em. m:.a mfl.m m:.w ms.a mm.H HH.H wo.m mm.H sm.a :m.H mpooeeo HoCOmpom meseoao assesses phone a Hose mHHmcopz a oLSpHcgsm meoEo>onoEH w mnflooom pcom mcflmzom paocomsoc oewm Ipso ponomono pooh omopo>ob . QHHoeooaolcoz owono>oo OHHOQOOH¢ mpflsnm moflpcoo w moxoo mowono>ob s messes .mexeo mm. mm.m ms. aa.m aw.a Hm. mo.H mm.H so. m:.m so. am. :m.H Hm. mpcoefiocoo poop commooooogm moabopowo> moms a sea: sees swam poop assessmesm poop spree eoogm hoagom oon maoonoo boom oQSpHpcogxm flopoe gossma .mvm co modao> oopSQEoo moflpflUoEEoo Aowzma .mvm mo mosao> popsmEoo meesaeoesoo mCOHmmonwon one go mpflocoonoc .mQOHpoQSOOO go» go moocoflno> one mo OHpmeopmlm mo moSHo> possessouu.aum mamae where: SSRe denotes the sum of squares of the residuals obtained by the hypothesis that regression coefficients are equal; SSRd, the sum of squares of the residuals obtained by the hypothesis that regression coefficients are different; N, the total number of observations; ' s, the number of regression equation; k, the number of sets of coefficients in a set of s regressions to be tested; m, the number of parameters to be estimated in each re- gression equation. The results of this test are given in Table E—2. This test shows that the regression coefficients of less than half of the commodities are different among the ten occupational groups at the 1 percent level. Occupational differences in consumer behavior are marked in most of the food, fuel and light, and personal effects, and the demand for a few food items, housing and clothing is generally the same for each occupation. 178 pcoonoo H one po psoofleflcmflm monocop* .Ho>oH pcoogoa OH one no bemoamflcwfim .o Ugo .Ho>oa .Amaa .mavm we easmapapm ewes are *ma.m mo. on. *mm.m mm. mm. 2.. mm. a? a as. mm. *mw.m :w. 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