02 The Pattern of Food Expenditures.docx

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1、 The Pattern of Food Expenditures Author(s)： 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 09:49 UTC JSTOR is a not-for-prof

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4、7.66.218.73 on Fri, 17 Mar 2017 09:49:13 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 th

5、at 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 t

6、erm “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 transformation of

7、the form xr = a + bx y = c + dy may close the differences between the savings curves for different places or different dates. Such a linear transformation expressing a translation and an expansion of the coordinates, it appears, reduces substantially the difference between the food expenditures of u

8、rban 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 transformation may be interpreted as measures of “level” which reflects secular changes in the standard of food consumption and of a

9、price?, in a general sense. The transformation 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 a

10、pproach 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 possib

11、le 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

12、 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

13、 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 regressi

14、ons 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 regressi

15、on 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 o

16、f 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

17、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 fam

18、ilies 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 expendi

19、ture 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 09:49:13 UTC All use subject to http:/about.jstor.org/terms ;45i $ 217 643 284 883 354 1118 406 1358 444 1631 486 1879 544 23

20、16 614 ;771 $ 338 832 354 i 75 426 1344474 1632 SiS 1925 560 2272 616 2790 723 ;792 $ 342 1324 S 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 Av

21、erage Income Average Expenditure For Food $ 592 $ 292 $ 3 5 $ 241 $ 3 4 $ 33 $ 313 $ 424 771 332 622 293 738 378 776 492 1065 4 3 856 352 I29 498 1243 6 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 5l 3480 1025

22、 2798 726 2625 683 13987 1710 4408 1100 3312 761 7595 1314 4247 847 6641 1085 * For method 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 in

23、tervals 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 (

24、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

25、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- to

26、n, 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. Childrens Bureau. The data for the two surveys coincide suf

27、ficiently, 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 Clerica

28、l 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 rel

29、ate 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 sec

30、ond 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 Seria

31、l 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 s

32、ize 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

33、 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 uniform practice and some method like the one described here must be de

34、veloped 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 EXPENDITUR

35、E 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 F

36、ood Income For Food 0330220612858I468QI347II222233333 00000000000s 055555555556 1234567890I4 III This content downloaded from 67.66.218.73 on Fri, 17 Mar 2017 09:49:13 UTC All use subject to http:/about.jstor.org/terms 2 00 THE REVIEW OF ECONOMICS AND STATISTICS the pattern of food expenditures in u

37、rban 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

38、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 transformations of the form = a + bx = c + dy which w

39、ill 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 transformations could be determined that conv

40、ert 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 transfor

41、med， 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 transformation. Similarly, an inflection point, where the direction of curvature changes, corresponds to an in

42、flection point in the curve that results from the transformation. 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

43、 federal employees, whereas the surveys for 1935-36, 1941, and 1944 included all occupational groups. The existing information 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 limi

44、ted 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 wer

45、e 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 de

46、rivative clearly has a form 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 observati

47、ons， 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

48、 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 s

49、ome 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