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02 The Pattern of Food Expenditures.docx

The Pattern of Food Expenditures Authors Dorothy S. Brady and Helen A. Barber Source The Review of Economics and Statistics, Vol. 30, No. 3 Aug., 1948, pp. 198-206 Published by The MIT Press Stable URL http//www.jstor.org/stable/1926749 Accessed 17-03-2017 0949 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use ination technology and tools to increase productivity and facilitate new s of scholarship. For more ination about JSTOR, please contact supportjstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms Conditions of Use, available at http//about.jstor.org/terms The MIT Press is collaborating with JSTOR to digitize, preserve and extend access to The Review of Economics and Statistics This content downloaded from 67.66.218.73 on Fri, 17 Mar 2017 094913 UTC All use subject to http//about.jstor.org/terms THE PATTERN OF FOOD EXPENDITURES Dorothy S. Brady and Helen A. Barber INTRODUCTION AND SUMMARY IN a discussion of a paper on the correlation between savings and the income distribution, Simon Kuznets noted that the savings curves for different places or different dates can be de- scribed as differing with respect to level and with respect to slope.1 This description holds as well when savings are compared in terms of relative income position as when savings are related to current dollar income. If the term “level” is defined as a difference in position that can be eliminated by a translation of the coordinates, and the term slope defined as a difference in scale that can be eliminated by an expansion or contraction of the coordinate units，Mr. Kuznets’ observations imply that a transation of the xr a bx y’ c dy may close the differences between the savings curves for different places or different dates. Such a linear transation expressing a translation and an expansion of the coordinates, it appears, reduces substantially the difference between the food expenditures of urban families in relation to income for the surveys made between 1901 and 1944 throughout the range of incomes up to the sixth or seventh decile. The parameters of the transation may be interpreted as measures of “level” which reflects secular changes in the standard of food consumption and of aprice, in a general sense. The transation also reduces the differences between income distributions and thus describes a correspondence between the food expenditure curve and the income distribution. FOOD EXPENDITURE AND INCOME The food expenditure curve was chosen for the examination of this approach for two rea- 1 Simon Kuznets, “Comment on Dorothy S. Brady and [198 ] sons. The variation between the food curves, food expenditures expressed as a percentage of income, is reduced in general more than the savings curves when correlated with relative income position.2 Secondly， it is now possible to eliminate the variation due to family size from the data by a fairly accurate adjustment procedure.3 For this study the observed data on average food expenditures by income bracket were all standardized to the corresponding figure for 3.5 persons as the average size of family. The average size 3.5 persons was se Rose D. Friedman, ‘Savings and the Income Distribution， ’ ’’ Studies in Income and Wealth, Volume io National Bureau of Economic Research, New York, 1947. 2 Rose D. Friedman initiated the study of the food expenditure curves and other group curves in this manner in order to trace, if possible, the changes in consumption pattern that are associated with changes in the position of the curve for total expenditures or its complement, total savings. Some tentative results of this study are being prepared for publication. 3 The adjustment procedure is based on a study of the regressions of food expenditures on family size at the same income bracket for all the surveys, from 1901 to date, that have tabulated food expenditures by income and size of family. The regressions are logarithmic, log y a b log x, where y is the food expenditure and x is the size of family. The regression coefficient, b, varies from about 0.25 to 0.50 and appears to center around Ys, the value taken pro tem as the average. While in the lower and middle income brackets there appears no tendency for the values of uby, to change systematically with income, at the highest incomes observed the values of all tend to be above the average. It is possible that the values of “6” increase at first slowly and then more and more rapidly with income, but this interaction, which may be due to an increasing proportion of adults in families of each size, say 4 persons, as the income is increased, remains to be explored. For the purposes of this study, the average value of Yz was accepted as applicable throughout the entire range of incomes. The adjustment factor was accordingly based on the relation between the mean and the mean cube root for the size of family as determined by the distributions of families by size within income brackets observed in recent surveys. The relationship found is purely empirical and applies only to urban families. The mean cube root y is related to the mean x as follows y .1138 log -f .8731 This relation provides the basis for adjusting the observed average expenditure on food for the observed average size of family to the average food expenditure for any other average size. This content downloaded from 67.66.218.73 on Fri, 17 Mar 2017 094913 UTC All use subject to http//about.jstor.org/terms ;45i 217 643 284 883 354 1118 406 1358 444 1631 486 1879 544 2316 614 ;771 338 832 354 i〇 75 426 1344474 1632 SiS 1925 560 2272 616 2790 723 ;792 342 1324 S〇 i 1835 651 2641 840 3469 920 4320 1089 1934 f 1935-36 4 1941 TT 1944 Average Income Average Expenditure For Food Average Income Average Expenditure For Food Average Income Average Expenditure For Food Average Income Average Expenditure For Food 592 292 3〇 5 241 3〇 4 33〇 313 424 771 332 622 293 738 378 776 492 1065 4〇 3 856 352 I29〇 498 1243 6〇 I 1343 459 1090 413 1764 604 1779 736 1633 519 1324 467 2448 716 2259 855 1929 567 1686 537 3757 837 2757 948 2250 625 2150 614 6575 I〇 5l 3480 1025 2798 726 2625 683 13987 1710 4408 1100 3312 761 7595 1314 4247 847 6641 1085 * For of standardizing the data for family size, see text, t Eighteenth Annual Report of the Commissioner of Labor “Cost of Living and the Retail Prices of Food,” 1903. Average income taken as the midpoint of the intervals except for the class 1,200, which was estimated from the average income of the entire sample. The data relate to urban communities of all sizes. t Great Britain Board of Trade, “Cost of Living in American Towns,’’ 1911. The averages for the North and the South, nationality and racial groups shown separately in the report were weighted together using the census proportions for the North and South, white and negro groups and the survey proportions for the nationality groups. The data relate to wage-earner families in large cities. U. S. Bureau of Labor Statistics Bulletin 357, nCost of Living in the United States.” The data relate to wage-earner families in cities of all sizes. || Special tabulation of the data collected by the U. S. Bureau of Labor Statistics for the study of ‘‘Cost of Living of Federai Employees in Five Cities, in 1927-28 presented in Leven, Moulton, and Warbur- ton, Americas Capacity to Consume. The lowest observation for the average income 792 is from special tabulations, presented in the same source, of the data from the study of the Welfare of the Children of Maintenance-of-Way Employees,” U. S. Children’s Bureau. The data for the two surveys coincide sufficiently, when standardized for family size, at the average incomes between 1300 and 1400 and between 1800 and 1900 to justify this “splicing.” The data relate to five large cities. f U. S. Bureau of Labor Statistics Bulletins 636, 639, 640, 641, aMoney Disbursements of Wage-Earners and Clerical Workers, 1934- 36.n The data for the city surveys relating to the year 1934 were combined and represent white families in large cities outside of the New York City area. ** National Resources Planning Board, “Family Expenditures in the United States, Statistical Tables and Appendixes.” The data relate to all occupational groups in urban communities of all sizes. ft U S. Bureau of Labor Statistics Bulletin 822， “Family Spending and Saving in Wartime.” The data on annual food expenditures in 1941 were adjusted on the basis of a comparison with the reports on weekly food expenditures in the second quarter of 1942, which indicated that at the income levels above 2500, annual food expenditures in 1941 had been reported at the expenditure level prevailing in April- June, 1942. The data apply to all occupational groups in urban communities of all sizes. U. S. Bureau of Labor Statistics Serial No. R 1818， “Expenditures and Savings of City Families in 1944.” THE PATTERN OF FOOD EXPENDITURES lected because that value was close to the average size of family in the greater part of the income classes in the 1935-36 study. The advantages of eliminating the influence of differences in family size outweigh the errors that may result from using a tentative adjustment procedure. In every family expenditure study in this country, the average size of family increases with the family income, and the relation between family size and income differs from survey to survey. The relationship between expenditures and income is accordingly 199 confounded with the relationship between expenditures and the size of family, unless the data are tabulated separately by size of family and income. This， unfortunately, has not been a uni practice and some like the one described here must be developed in order to allow for the study of the changes overtime in the influence of income on expenditures independent of the size of family. The data on food expenditures standardized to the constant average size of family are shown in Table 1. They represent in general TABLE 1. THE FOOD EXPENDITURE CURVE AVERAGE EXPENDITURES FOR FOOD AT SPECIFIED DATES AMONG URBAN FAMILIES, AVERAGING 3.5 PERSONS BY INCOME LEVEL 19011 19091 1918 1927-2811 Average Average Average Average Average Expenditure Average Expenditure Average Expenditure AverageExpenditure Income For Food Income For Food Income For Food Income For Food 0330220612858I468QI347II222233333 00000000000s 055555555556 1234567890I4 III This content downloaded from 67.66.218.73 on Fri, 17 Mar 2017 094913 UTC All use subject to http//about.jstor.org/terms 2 00 THE REVIEW OF ECONOMICS AND STATISTICS the pattern of food expenditures in urban communities between 1901 and 1944. The investigations providing these data differed considerably with respect to survey technique and population coverage, and these differences without doubt influence quantitative comparisons of the data. Until systematic procedures are developed for measuring their influence on consumption, the various factors affecting the comparability of the data from the different studies can only be recognized in appraising the results of the analysis.4 CHARACTERISTICS OF THE FOOD EXPENDITURE CURVE There are many transations of the a bx c dy which will bring the food expenditure curves approximately into coincidence, so that statistical tests would reveal a significant decrease in the differences between the curves. Thus, if the curves are represented by linear regressions ， an indefinite number of transations could be determined that convert one line into the position of another, unless some criterion is introduced that is equivalent to matching two pairs of observations. To identify corresponding points on two food expenditure curves requires an examination of the curves for characteristics that do not change when they are transed， that is moved horizontally and vertically with an expansion or contraction of the scales. Thus the maximum point in a curve corresponds with the maximum on the curve obtained through a transation. Similarly, an inflection point, where the direction of curvature changes, corresponds to an inflection point in the curve that results from the transation. In order to study the characteristics of the food expendi- 4 The chief difference between the surveys is in population coverage. The surveys for 1901, 1909, 1918, and 1934 were limited to the “wage-earner” group, the 1927-28 survey to federal employees, whereas the surveys for 1935-36, 1941, and 1944 included all occupational groups. The existing ination which reveals no evidence of occupational differences in food expenditures, given the same income and size of family, comes from the 193S-36 survey and therefore is too limited for generalization. The surveys for 1909, 1927-28, and 1934 apply to large cities, the others to all cities. The data available, chiefly from the 1935-36 survey, reveal a distinct difference in the food consumption pattern in large cities and in small. ture curve, the first three derivatives were estimated by calculating the successive divided differences and associating them with the successive midpoints between the averages on the income scale Tables 2, 3, and 4. The first derivative measures the rate of change of expenditures with income at each point on the income scale. The first derivative clearly has a resembling a frequency curve in the most recent periods， 1935-36, 1941， and 1944. It rises to a maximum and then falls as incomes are increased. In the earlier surveys, 1901， 1909, 1918，and 1927- 28 ， the first derivative in general declines through the range of observations， but the first two values differ less than the second and third. The question whether a maximum on the first derivative appears near the lowest end of observational range may be decided by an examination of the estimates of the second derivative. The second derivative measures the rate of change in the first derivative with income at each point on the income scale. It is the ‘‘acceleration’’ of the expenditure curve. In most of the surveys，the second derivative of the food expenditure curve declines from a positive value to a negative minimum, then rises and flattens off, perhaps approaching some small negative constant value. In the “neighborhood” of the minimum， the curve describing the second derivative is fairly symmetric like a parabola. By accepting this symmetry as general, a zero value can be found for all the surveys, either by interpolation or extrapolation. This assumption leads to postulating the existence of a maximum in the first derivative for all surveys, since at the maximum of a function its rate of change becomes zero in passing from a positive value to a negative value. Th