# The distribution of U.S. income and food expenditures.

The Distribution of U.S. Income and Food Expenditures

The Reagan years have been associated with the longest sustained peacetime economic expansion in our history. However, this expansion has not been without its critics. One frequent complaint is that current economic growth has favored higher income groups. Allegedly, wealthier members of society have been gaining an ever increasing share of total national income. This may have caused the distribution of income to become more and more unequal (Blackburn and Bloom 1987; Congressional Budget Office 1988; Ellwood and Levy 1988). While seldom voiced publicly, the strong relationship between food spending and income may imply that the distribution of food expenditures in this country has also become more unequal. Historically, food expenditures hold a prominent place in the United States as an indicator of household welfare. In fact, the percent of income spent on food was a pivotal variable in the construction of official U.S. poverty guidelines. Also, food spending continues to be the primary focus of many government programs, such as food stamps and school lunches. Despite the importance of food spending, study of intertemporal changes in the size distribution of food expenditures has been severely hampered by the lack of a nationally representative survey conducted on a continuous basis.

Beginning in 1980, however, the Bureau of Labor Statistics (BLS) has been conducting a Continuing Consumer Expenditure Survey (CCES). With the release of the 1985 survey, six survey years of data are available. This presents a unique opportunity to examine simultaneously food expenditure and income distributions over a continuous time frame with nationally representative data.

The primary purpose of this paper is to test for and to investigate any changes that may have occurred in both the income distribution and total food expenditure distribution. The empirical strategy is as follows. First, the null hypothesis that the distributions have not changed over time is tested. The alternative hypothesis includes all ways in which a distribution can change, such as by changes in means, variances, and asymmetries. Second, an interdistribution measure of relative economic affluence is estimated, and intradistribution inequality and the share of national food expenditures (income) received by income classes (i.e., asymmetry of the distributions and the manner in which this has changed) are examined. Third, the distributions are examined using the sociological theory of relative deprivation (Runciman 1966), and, finally, average propensities to spend for food are estimated.

BACKGROUND

In this study, analysis of income and food spending distributions differ in one important aspect. Studies of income distribution are concerned with the distribution of income across population units. The position taken here is that it is more insightful to study the distribution of food expenditures across income groups within a population than across population units per se (e.g., households or individuals). In other words, present interest centers on examining questions such as "How has the share of food expenditures of the poorest ten percent of the population changed?"

To formalize the discussion, first assume that adult equivalent household income, Y, is randomly distributed with probability density function, f(y), and mean [mu].(1) The probability distribution function (PDF) of income is

[Mathematical Expressions Omitted]

and represents the proportion of households having adult equivalent income less than or equal to Y.

The first moment distribution function (FMDF) of Y is

[Mathematical Expressions Omitted]

and represents the proportion of total adult equivalent incomes received by households having adult equivalent incomes less than or equal to Y. The relationship between F(Y) and [F. sub.1](Y) is called the Lorenz curve.

Assuming that [v.sub.i](Y) is the implied Engel relation for the ith commodity and [pi.sub.i] denotes the expenditure mean (per adult equivalent), then the FMDF for adult equivalent expenditure on the ith commodity is

[Mathematical Expressions Omitted]

and represents the proportion of total adult equivalent expenditures on the ith commodity by households having adult equivalent income less than or equal to Y. Kakwani and Podder (1976) define the concentration curve for the ith commodity as the relationship between F(Y) and [F.sub.1[v.sub.i(Y)]. Henceforth, the terms income and food expenditures refer to the variables on an adult equivalent basis and in real terms.

Lorenz and concentration curves can be estimated by a function developed by Kakwani and Podder (1976):

[Mathematical Expressions Omitted]

Where

[Mathematical Expressions Omitted]

are functions of the coordinates [(F(Y), F.sub.1(Y))] on the Lorenz curve. A, [alpha], and [Beta] are parameters to be estimated, and v is the equation error term (with zero mean and constant variance). Substituting

[alpha] = [Beta] + [Square root of 2]

[u] = [Beta] + [Square root of 2]

into (4) yields the equation of the concentration curve for the ith commodity.

The most commonly used measure of inequality within an income distribution is the Gini coefficient. A concentration ratio is the counterpart to the Gini coefficient and measures the departure of the concentration curve from the egalitarian line. These measures assess social welfare as a function of inequality and ignore other aspects of welfare, such as asymmetries and average affluence. Furthermore, they cannot offer a meaningful social ranking of distributions with different means.

Examining the shares of total food spending (income) received by income quintiles across time provides insight into which quintiles have "gained" or "lost" shares of total expenditures (income). This provides information on the shape of the distributions and the relative improvement (deterioration) in positions of households in different parts of the income distribution. The parameters of the Lorenz (concentration) curve ([alpha] and [Beta]) can be used to measure the skewness of a curve. If [alpha] < [Beta], the curve is skewed toward the left, and if [alpha] > [Beta], the curve is skewed to the right. If [alpha] = [Beta], the curve is symmetric. Therefore, as pointed out by Musgrove (1980), [alpha] - [Beta] is a measure of the skewness of a curve. For a given Gini coefficient (i.e., holding inequality constant), a Lorenz curve that is skewed to the left implies that households with lower incomes have a smaller share of total income than if the curve were symmetric or skewed to the right. For each individual curve, a two-tail t-test can be used to test the null hypothesis of symmetry (i.e., [alpha] = [Beta]).

Given populations [Q.sub.1], [Q.sub.2], . . . , [Q.sub.6] (1 = 1980, . . . , 6 = 1985), the null hypothesis that [Q.sub.1] and [Q.sub.2], for example, have identically distributed income variables (i.e., they are on average equally affluent) against the hypothesis that [Q.sub.2] is more affluent than [Q.sub.1] (given mean income is higher in [Q.sub.2] can be tested using a two-sample, one-sided Kolmogorov-Smirnov test. Given two random samples, [Q.sub.1] of size n and [Q.sub.2] of size m, the one-sided Kolmogorov-Smirnov statistic is

[Mathematical Expression Omitted]

where [F.sub.1](y) and [F.sub.2](y) are the PDFs for the two populations evaluated at the same level of real income. The large sample distribution of 4[KS.sup.2] mn/(m + n) is chi square with two degrees of freedom (Dagum 1980). For food expenditures, interest centers on testing whether the FMDFs (which are a type of cumulative distribution function) for any two given years are identical. That is, are food expenditures identically distributed across income groups over time. Thus, the corresponding test for food expenditures is [Mathematical Expression Omitted] where the FMDFs are evaluated at the same levels of real income.

The relative economic affluence (REA) statistic proposed by Dagum (1987) is used to measure the economic disparity between food spending (income) distributions over time. The REA statistic, denoted by D, measures the relative economic affluence of one population versus another when the populations have unequal mean expenditures (incomes). If a real difference between food expenditure (income) distributions exists, the statistic D will signal the existence of an effective discriminator even when the distributions are very close together. The relation D defines a strict partial ordering over a set of pairs of distributions. If the members of two populations, [Q.sub.1] and [Q.sub.2], are each grouped into the same k real income intervals, the distribution free estimator of D is defined by

[Mathematical Expression Omitted]

where

[Mathematical Expression Omitted]

where [X.sub.i]([Q.sub.1]) and [X.sub.j]([Q.sub.2]) are mean food expenditures (income) of the ith and jth intervals for [Q.sub.1] and [Q.sub.2], respectively. The [f.sub.1] (i) and [f.sub.2] (j) are the frequencies of the ith and jth intervals for populations [Q.sub.1] and [Q.sub.2.] D can be shown to be sensitive to the means, variances, and asymmetries of the distributions. As indicated by Dagum (1987), the statistical significance of the REA between two populations can be tested using the Kolmogorov-Smirnov test outlined above.

REAs are an important complement to intradistribution inequality measures because together they incorporate two social welfare preferences - the preference for less inequality within a population and more income (food expenditures) among its members. Thus, REAs and Gini ratios provide the basic information to perform welfare comparisons of income (expenditure) distributions with different means (Dagum 1987).

However, it is possible for an REA between two distributions to be very small (because they have almost equal means) but the distributions to be very dissimilar. That is, one has a large and the other a small Gini ratio (Dagum 1987). Hence, a strict ordering of distributions based on the two welfare criteria given above may require a model that simultaneously incorporates both criteria. This is because it is possible for one population to be more affluent than another and also have a higher Gini ratio.

One model, based on both inequality and the amount of the resource available, is the theory of relative deprivation. This sociological theory (Runciman 1966) states that the effect of deprivation that results from not having Z when others have it is an increasing function of the number of persons who do not have Z. The range of possible deprivation for each individual in society is (0,y*), where y* is the highest income in society. For any individual j, his income, yj, partitions total deprivation into two parts: (yj, y*), the range of income for which he is deprived, and (0,yj), the range of income for which he is satisfied. Yitzhaki (1979, 1982) formally quantified the theory and established its equivalence to utility theory. These results are based on an interpretation of utility theory that has not gained widespread support within the economics profession. In particular, the duality between relative deprivation and utility theory is based on the concept that utility is relative; that is, an individual evaluates a bundle of goods by comparing it to the consumption bundles of others. This school of thought, advocated by Kapteyn (1977), Kapteyn et al. (1980), and Van de Stadt et al. (1985), among others, run counter to most economic models that assume that individual utility functions are independent, i.e., they are not influenced by the behavior of others. The relative utility hypothesis relies, in many ways, on a cardinal utility function with interpersonal utility comparisons - propositions that are not assumed in standard utility and welfare theory, although the fields of psychology and sociology fully embrace the concept (Davis 1959; Helson 1964; Hyman and Singer 1968). Perhaps the best known example of an economic theory based on relative utility is Duesenberry's (1949) relative income hypothesis. In any event, the notion that utility is at least partially relative seems plausible, although readers will have to be their own judges of the merits of the relative deprivation hypothesis.

Given the above qualifiers, Yitzhaki shows that the degree of relative deprivation for the income range (y, y + dy) can be quantified by 1 - F(y), where F(y) is the cumulative income distribution, and 1 - F(Y) is the relative frequency of persons with incomes above y. He defines the relative satisfaction function of the jth person (which is the complement of the deprivation function) as

[Mathematical Expression Omitted]

that upon integration equals

[Mathematical Expression Omitted]

where u is the average income and [Sigma](yj) is the value of the Lorenz curve.

Society's degree of satisfaction (with an income distribution) can be defined as aggregate satisfaction or formally

[Mathematical Expression Omitted]

and using (12):

[Mathematical Expression Omitted]

where S is society's satisfaction with the existing income distribution, u is mean income, and GC is the Gini coefficient. This measure takes into account both inequality and changes in income levels and position. Thus, at a constant level of inequality, satisfaction is a monotonically increasing function of mean income in the society. Conversely, at a given mean income, satisfaction monotonically decreases as inequality increases. S is bounded between zero (total inequality) and u (total equality). Obviously, the measure is easily extended to food spending.

The Continuing Consumer Expenditure Survey (CCES) contains the most recent and continuous data available on food spending in American households. Six diary surveys have been publicly released (1980-1985), and each survey year is nationally representative. The data were obtained from a cross section of U.S. households reporting detailed information on purchases over a two-week period, together with socioeconomic data concerning the household units. The adult equivalent scales implicit in the U.S. poverty guidelines (Congressional Budget Office 1988) and scales developed by Brown and Johnson (1986) were used to adjust annual household gross income and total weekly food expenditures, respectively.(2) No single type of adult equivalent scale has gained universal acceptance. In fact, Gronau (1988, p. 1183) has written: "Adult equivalence scales have recently celebrated their first centenary, but the debate on how to estimate them and their welfare implications has not yet subsided." Given this fact, scales implicit in the poverty lines are frequently used (Congressional Budget Office 1988; Blackburn and Bloom 1987). Income was deflated by the CPI-XI (Congressional Budget Office 1988) and food expenditures by the CPI for total food (1980 as a base for both CPIs), and each year's data were aggregated into 25 income groups. [Tabular data omitted]

EMPIRICAL RESULTS

The REAs for income and food spending for all yearly pairwise comparisons between 1980 and 1985 are presented in Table 1. The deflated sample means for each of the variables and the Kolmogorov-Smirnov test statistics are also presented. The estimated coefficients for the Lorenz and food concentration curves for the years 1980 and 1985 are reported in Table 2 (estimates of the curves for the years 1981-1984 are available from the authors). In general, the estimated coefficients of both curves have relatively small standard errors, and the overall fits of the models to the data are good. Gini and concentration ratios are also presented in Table 2. Given the volume of empirical results, the following discussion only highlights the more important findings. [Tabular data omitted]

The Kolmogorov-Smirnov tests indicate that the null hypothesis of equally distributed income variables cannot be rejected at the five percent level for the pair 1983-1984. For all other pairs the hypothesis can be rejected. The same results were found for the food spending distributions.

After 1981 (note that income was higher in 1980 than 1981) and except for 1983-1984, the calculated REAs imply that the relative economic affluence of households (in terms of adult equivalent income) has increased each successive year. Consequently, if one is willing to make welfare comparisons based solely on relative economic affluence, this analysis indicates that after 1981 there has been a general improvement in the average affluence of U.S. households.

In terms of food spending, the REAs imply the following ranking of the distributions: 1985, 1980, 1982, 1983, 1984, and 1981. (Recall that REAs measure how much more affluent a population with a higher mean is than another. Note that adult equivalent food spending was higher in 1980 than in all years except 1985.) This is also the same ranking obtained if the distributions are ranked by mean expenditures for each year (a type of REA measure proposed by Vinod 1985). However, taking 1980 and 1985 as an example, the difference in the means is 42 cents, while the net economic affluence (i.e., [d.sub.1 - [p.sub.1]) is 52 cents. The difference occurs because an REA based on the difference in means is insensitive to changes in variances and asymmetries. [Tabular data omitted]

On the other hand, Gini coefficients indicate that inequality has increased in the distribution of income from 1980 to 1985, declining slightly between 1983 and 1984 before rising again. In particular, the Gini coefficient increased from 0.371 in 1980 to 0.414 in 1985 - an increase of 12 percent. Yearly changes in the food concentration ratios have the same pattern as the Gini ratios but with larger changes (this is examined below). For example, the concentration ratio increases from 0.149 in 1980 to 0.171 in 1985 - a 15 percent increase. While inequality increases at a slightly faster rate in the distribution of food spending than in the income distribution, the former has significantly less inequality. This is because of human subsistence requirements and government programs focusing on food spending (for example, food stamps and the Women, Infants, and Children Programs). Also, since the CCES is an expenditure survey, adjustments cannot be made for home production of food or commodity donation programs (e.g., the Temporary Emergency Food Assistance Program). Data that included information on these items would be likely to reduce the concentration ratios.

Basing welfare comparisons solely on inequality within a distribution, the income and food spending distributions are ranked in the following descending order: 1980, 1981, 1982, 1984, 1985, and 1983. This contrasts sharply with an ordering based on REAs. Clearly, in this situation the two welfare preferences, higher average affluence and inequality aversion, taken simultaneously do not provide a strict unambiguous ranking of distributions. This is because average economic affluence increased simultaneously with inequality.

The Yitzhaki measure of society's relative satisfaction with respect to the income and food spending distributions is presented in Table 3. This measure attempts to provide a strict ordering of distributions by unifying the welfare preferences of less inequality and more resources. However, recall that strong assumptions must be made to account for both welfare preferences simultaneously and to ensure a strict ordering of the distributions.

The measures were calculated using mean income (food expenditures) expressed in 1980 dollars and normalized on the calculated 1980 value for a given distribution. For example, the measure of society's satisfaction with the 1981 income distribution is 97.5, indicating that society is 2.5 percent less satisfied with the income distribution in 1981 versus 1980.

Society's apparent satisfaction with the distribution of income fell in 1981, rose in 1982, fell again in 1983, and rose in both 1984 and 1985. Despite higher mean incomes in both 1982 and 1983, satisfaction remained below 1980 levels because of increasing inequality. In both 1984 and 1985, satisfaction rose above 1980 levels, because increases in mean income were more than enough to compensate for increases in the Gini ratio.

For all years relative to 1980, society's apparent satisfaction with the distribution of food spending has declined - the measures following the same year-to-year pattern as the measures for income. However, unlike the income criterion, 1984 and 1985 satisfaction levels remain below that for 1980. These declines are caused by relatively flat or decreasing average per person real expenditures coupled with increasing concentration ratios.

Society's presumed satisfaction with both the income and food expenditure distributions as a percentage of the maximum attainable (i.e., if all members of society received mean income or food expenditures) show the same pattern - declining from 1980 through 1983, rising in 1984, and falling back in 1985. However, satisfaction with food spending was considerably higher than for income - over 80 percent versus about 60 percent for income. The high percent of the maximum attainable for food spending is a consequence of the small concentration ratios.

The relative satisfaction measures imply the following ranking of income distributions: 1985, 1980, 1982, 1983, 1984, and 1981. The ranking for food spending distributions is: 1980, 1985, 1982, 1981, 1984, and 1983. In general, these rankings are more in line with the rankings by REAs than by inequality measures.

The above analyses have attempted to examine distributions from the standpoint of the population or society in general. Attention now shifts to segments of the distributions. In particular, the share of national income (food spending) received by population quintiles and the percent of income they spend on food is examined. In 1980, the poorest 20 percent of the population received 4.78 percent of national income in contrast with 42.20 percent received by the wealthiest 20 percent of households. By 1985, the poorest 20 percent received 4.27 percent of national income and the wealthiest 20 percent received 45.59 percent, with the share received by the poorest quintile declining almost steadily from 1980 to 1985. In fact, all income quintiles except for the highest have lost their shares of national income from 1980 through 1985. This indicates that economic growth has generally favored the wealthier members of society.

Given the decline in income share received by all but the wealthiest population quintile, it is not surprising that the share of national food spending has declined for the lowest quintiles. For example, the lowest income quintile received 13.76 percent of national food spending in 1980, but this dropped to 12.77 in 1983 before rising to 13.33 in 1985. This contrasts with 28.81 percent received by the highest income quintile in 1985, up from 26.28 percent in 1980. As with national income, the share of total food spending received by all income quintiles, except the highest, has declined. The pattern of food spending shares received by the various quintiles tends to follow the patterns observed for income - underscoring the close relationship between food spending and income.

Expenditure elasticities were calculated using the estimated Lorenz and concentration curves (Kakwani and Podder 1976; Blaylock and Smallwood 1982) and are presented in Table 4 for various income levels. The elasticities are quite similar at the sample averages (0.33) and when estimated at the same real income level across surveys. This is evidence that the underlying Engel relationship has been stable, and, given the model in equation (3), this implies that the changes noted in the food spending distribution have been a function of changes in the income distribution. This is not surprising given the identical patterns in the changes in Gini and concentration ratios and the results of the Kolmogorov-Smirnov tests.

As noted above, if [alpha = beta], then a given Lorenz (concentration) curve is symmetric. Thus, a t-test can be used to test for symmetry. Results of t-tests indicate that the null hypothesis of symmetry cannot be accepted for any of the Lorenz curves at the 0.05 level of significance. The estimated coefficients for the individual Lorenz curves imply that the curves are skewed to the left in all cases, thereby implying that lower income households have a smaller share of income, for a given level of inequality, than if the curves were symmetric or skewed to the right. The null hypothesis of symmetry could not be rejected for the 1980, 1981, 1983, and 1984 concentration curves. The 1982 and 1985 curves were skewed to the right, implying that lower income households had a larger share of food expenditures, for a given level of inequality, than the symmetric curves.

Another measure of welfare, and one that played a critical role in the methodology underlying the formulation of the U.S. poverty guidelines, is the percent of income spent on food (i.e., the average propensity to spend on food out of income). The average propensities to spend (APS) on food at the sample averages and by quintiles for 1980 through 1985 are presented in Table 4. [Tabular data omitted]

As expected, the proportion of income spent on food declines rapidly across quintiles within each survey year. The APS within the lowest income quintile is 0.22 in 1980 and rises slightly to 0.23 in 1985. In general, the APS within a given quintile, except the lowest, is stable across surveys. The APS reaches a peak (0.24) in 1982 for the lowest quintile, suggesting that the 1982 recession may have affected lower income households more severely. Also, households in the poorest quintile (in terms of adult equivalent income) spent about 3 times as much of their incomes on food than the average household and about 5 times more than those in the highest quintile.

In real terms, both average income and food expenditures of households in the lower quintiles remained virtually unchanged between 1980 and 1985 but rose for households in the higher quintiles. This, together with stable APCs and higher total food expenditure elasticities at lower income than at higher income levels, has caused inequality to increase at a slightly faster rate in total food spending than income distribution. This also accounts, at least partially, for the relatively stable or slightly declining average food expenditures from 1980-1985 that, together with rising inequality, has lowered apparent satisfaction levels.

Before presenting some conclusions, it is useful to examine the changes in the demographic characteristics of the population subset in the lowest 20 percent of the income distribution from 1980 to 1985. During this period, the percent of the households in the lowest income quintile that are headed by a black increased modestly, the percent headed by a person over 64 years old declined about 7 percentage points (with a corresponding decline in the age of the household head), single parent households increased about 4 percentage points, and the percentage of single member households declined. This suggests that older households have been gaining affluence. Conversely, high divorce rates and increasing numbers of unwed mothers have increased the percentage of single parent households in the lowest income quintile.

SUMMARY AND CONCLUSIONS

Statistically significant changes have occurred in the income and food spending distributions during the first part of the 1980s. Total inequality within the income and food distributions, as measured by Gini coefficients and concentration ratios, has increased from 1980 to 1985. However, food spending is more equally distributed than income. This was expected because of subistence requirements and government efforts focusing on prodiving an adequate diet. Simultaneously with an increase in income inequality, the share of national income received by the lowest income quintile has dropped about 0.5 percentage points between 1980 and 1985 and risen over 3 percentage points for the highest quintile. The share of national income received by the middle quintiles also declined. Likewise, the share of national food expenditures received by the two lowest quintiles dropped about 1.5 percentage points and rose about 2.5 percentage points for the highest quintile between 1980 and 1985. On the other hand, REAs indicate a general improvement in the average affluence of the population. Thus apparent changes are a mixed blessing - increasing inequality but higher average affluence.

Using a measure developed by Yitzhaki, society's apparent satisfaction with the distributions of income and food spending was evaluated. This measure, based on the concept of relative utility, takes into consideration the "size of the pie" to be distributed as well as inequality. The measure indicates that society is more satisfied with the distribution of income in 1984 and 1985 than in prior years but less satisfied with the food spending distribution. On the other hand, in terms of the maximum attainable level of satisfaction, society is considerably more satisfied with the distribution of food spending than with the distribution of income.

Empirical results also suggest that economic growth in the 1980s has favored higher income households and that changes in the food spending distribution are primarily due to changes in the income distribution, not changes in the underlying Engel function.

REFERENCES

Blackburn, M. and D. Bloom (1987), "Earnings and Income Inequality in the United States," Population and Development Review, 13: 575-609. Blaylock, J. and D. Smallwood (1982), "Analysis of Income and Food Expenditure Distributions: A Flexible Approach," The Review of Economics and Statistics, 64: 104-109. Brown, M. and S. Johnson (1984), "Equivalent Scales, Scale Economics, and Food Stamp Allotments: Estimates from the Nationwide Food Consumption Survey, 1977-78," American Journal of Agricultural Economics, 66: 286-293. Congressional Budget Office (1988), Trends in Family Income, February. Dagum, C. (1980), "Inequality Measures Between Income Distributions with Applications," Econometrica, 48: 1791-1803. Dagum, C. (1987), "Measuring the Economic Affluence Between Populations of Income Receivers," Journal of Business and Economic Statistics, 5: 5-12. Davis, J. (1959), "A Formal Interpretation of the Theory of Relative Deprivatation," Sociometry, 22: 280-296. Duesenberry, J. (1949), Income, Saving and the Theory of Consumer Behavior, Cambridge, MA: Harvard University Press. Ellwood, D. and F. Levy (1988), "Trends in the Inequality of Permanent Incomes," paper presented at the annual meeting of the American Economic Association, New York, December. Gronau, R. (1988), "Consumption Technology and the Intrafamily Distribution of Resources: Adult Equivalence Scales Reexamined," Journal of Political Economy, 96: 1183-1205. Helson, H. (1964), Adaptation-Level Theory: An Experimental and Systematic Approach to Behavior, New York, NY: Harper Press. Hyman, H. and E. Singer (1968), Readings in Reference Group, Group Theory, and Research, New York, NY: The Free Press. Kakwani, N. (1978), "A New Method of Estimating Engel Elasticities," Journal of Econommetrics, 9: 103-110. Kakwani, N. and N. Podder (1976), "Efficient Estimation of the Lorenz Curve and Associated Inequality and Measures from Grouped Observations," Econometrica, 44: 137-148. Kapteyn, A. (1977), A Theory of Preference Formation, unpublished thesis, Leiden University, Leiden, The Netherlands. Kapteyn, A., J. Wansbeek, and J. Buyze (1980), "The Dynamics of Preference Formation," Journal of Economic Behavior and Organization, 1: 123-157. Musgrove, P. (1980), "Income Distribution and the Aggregate Consumption Function," Journal of Political Economy, 88: 504-525. Runciman, W. (1966), Relative Deprivation and Social Justice, London, England: Routledge and Kegan Paul. Smallwood, D., J. Blaylock, and J. Harris (1987), Food Spending in American Households, 1982-84. USDA, Economic Research Service, Statistical Bulletin 753. Van de Stadt, H., A. Kapteyn, S. Van de Geer (1985), "The Relativity of Utility: Evidence from Panel Data," The Review of Economics and Statistics, 67: 179-187. Vinod, H. (1985), "Measurement of Economic Distance Between Blacks and Whites," Journal of Business and Economic Statistics, 3: 78-88. Yitzhaki, S. (1979), "Relative Deprivation and the Gini Coefficient," Quarterly Journal of Economics, XCIII: 321-324. Yitzhaki, S. (1982), "Relative Deprivation and Economic Welfare," European Economic Review, 17: 99-113. The Journal of Consumer Affairs, Vol. 23, No. 2, 1989 0022-0078/0002-226 $1.50/0 (R) 1989 by The American Council on Consumer Interests

(1) The term "adult equivalent" means that household income (expenditures) has been adjusted by a set of adult equivalent scales. Adult equivalent scales are merely sophisticated methods of head counting that are used to adjust households budgets to permit welfare comparisons across households of different sizes. (2) The use of household gross income in lieu of net income was mandated by data considerations - net income was not reported on the 1980 and 1981 public use tapes. However, an examination of the 1982-1985 data (which included net income) indicates that only relatively small changes would occur in the empirical results if net income could be used instead of gross. The reason is that, for each year from 1982-1985, average net income as a percent of gross was almost constant at 90-91 percent and almost constant within quintiles across surveys (Smallwood, Blaylock, and Harris 1987). Sampling weights were used in all calculations.

James R. Blaylock and William N. Blisard are Agricultural Economists, USDA, Economic Research Service, Commodity Economics Division. Views expressed in this paper are not necessarily those of USDA or ERS. The authors wish to thank several anonymous reviewers and Richard C. Haidacher for helpful comments.

The Reagan years have been associated with the longest sustained peacetime economic expansion in our history. However, this expansion has not been without its critics. One frequent complaint is that current economic growth has favored higher income groups. Allegedly, wealthier members of society have been gaining an ever increasing share of total national income. This may have caused the distribution of income to become more and more unequal (Blackburn and Bloom 1987; Congressional Budget Office 1988; Ellwood and Levy 1988). While seldom voiced publicly, the strong relationship between food spending and income may imply that the distribution of food expenditures in this country has also become more unequal. Historically, food expenditures hold a prominent place in the United States as an indicator of household welfare. In fact, the percent of income spent on food was a pivotal variable in the construction of official U.S. poverty guidelines. Also, food spending continues to be the primary focus of many government programs, such as food stamps and school lunches. Despite the importance of food spending, study of intertemporal changes in the size distribution of food expenditures has been severely hampered by the lack of a nationally representative survey conducted on a continuous basis.

Beginning in 1980, however, the Bureau of Labor Statistics (BLS) has been conducting a Continuing Consumer Expenditure Survey (CCES). With the release of the 1985 survey, six survey years of data are available. This presents a unique opportunity to examine simultaneously food expenditure and income distributions over a continuous time frame with nationally representative data.

The primary purpose of this paper is to test for and to investigate any changes that may have occurred in both the income distribution and total food expenditure distribution. The empirical strategy is as follows. First, the null hypothesis that the distributions have not changed over time is tested. The alternative hypothesis includes all ways in which a distribution can change, such as by changes in means, variances, and asymmetries. Second, an interdistribution measure of relative economic affluence is estimated, and intradistribution inequality and the share of national food expenditures (income) received by income classes (i.e., asymmetry of the distributions and the manner in which this has changed) are examined. Third, the distributions are examined using the sociological theory of relative deprivation (Runciman 1966), and, finally, average propensities to spend for food are estimated.

BACKGROUND

In this study, analysis of income and food spending distributions differ in one important aspect. Studies of income distribution are concerned with the distribution of income across population units. The position taken here is that it is more insightful to study the distribution of food expenditures across income groups within a population than across population units per se (e.g., households or individuals). In other words, present interest centers on examining questions such as "How has the share of food expenditures of the poorest ten percent of the population changed?"

To formalize the discussion, first assume that adult equivalent household income, Y, is randomly distributed with probability density function, f(y), and mean [mu].(1) The probability distribution function (PDF) of income is

[Mathematical Expressions Omitted]

and represents the proportion of households having adult equivalent income less than or equal to Y.

The first moment distribution function (FMDF) of Y is

[Mathematical Expressions Omitted]

and represents the proportion of total adult equivalent incomes received by households having adult equivalent incomes less than or equal to Y. The relationship between F(Y) and [F. sub.1](Y) is called the Lorenz curve.

Assuming that [v.sub.i](Y) is the implied Engel relation for the ith commodity and [pi.sub.i] denotes the expenditure mean (per adult equivalent), then the FMDF for adult equivalent expenditure on the ith commodity is

[Mathematical Expressions Omitted]

and represents the proportion of total adult equivalent expenditures on the ith commodity by households having adult equivalent income less than or equal to Y. Kakwani and Podder (1976) define the concentration curve for the ith commodity as the relationship between F(Y) and [F.sub.1[v.sub.i(Y)]. Henceforth, the terms income and food expenditures refer to the variables on an adult equivalent basis and in real terms.

Lorenz and concentration curves can be estimated by a function developed by Kakwani and Podder (1976):

[Mathematical Expressions Omitted]

Where

[Mathematical Expressions Omitted]

are functions of the coordinates [(F(Y), F.sub.1(Y))] on the Lorenz curve. A, [alpha], and [Beta] are parameters to be estimated, and v is the equation error term (with zero mean and constant variance). Substituting

[alpha] = [Beta] + [Square root of 2]

[u] = [Beta] + [Square root of 2]

into (4) yields the equation of the concentration curve for the ith commodity.

The most commonly used measure of inequality within an income distribution is the Gini coefficient. A concentration ratio is the counterpart to the Gini coefficient and measures the departure of the concentration curve from the egalitarian line. These measures assess social welfare as a function of inequality and ignore other aspects of welfare, such as asymmetries and average affluence. Furthermore, they cannot offer a meaningful social ranking of distributions with different means.

Examining the shares of total food spending (income) received by income quintiles across time provides insight into which quintiles have "gained" or "lost" shares of total expenditures (income). This provides information on the shape of the distributions and the relative improvement (deterioration) in positions of households in different parts of the income distribution. The parameters of the Lorenz (concentration) curve ([alpha] and [Beta]) can be used to measure the skewness of a curve. If [alpha] < [Beta], the curve is skewed toward the left, and if [alpha] > [Beta], the curve is skewed to the right. If [alpha] = [Beta], the curve is symmetric. Therefore, as pointed out by Musgrove (1980), [alpha] - [Beta] is a measure of the skewness of a curve. For a given Gini coefficient (i.e., holding inequality constant), a Lorenz curve that is skewed to the left implies that households with lower incomes have a smaller share of total income than if the curve were symmetric or skewed to the right. For each individual curve, a two-tail t-test can be used to test the null hypothesis of symmetry (i.e., [alpha] = [Beta]).

Given populations [Q.sub.1], [Q.sub.2], . . . , [Q.sub.6] (1 = 1980, . . . , 6 = 1985), the null hypothesis that [Q.sub.1] and [Q.sub.2], for example, have identically distributed income variables (i.e., they are on average equally affluent) against the hypothesis that [Q.sub.2] is more affluent than [Q.sub.1] (given mean income is higher in [Q.sub.2] can be tested using a two-sample, one-sided Kolmogorov-Smirnov test. Given two random samples, [Q.sub.1] of size n and [Q.sub.2] of size m, the one-sided Kolmogorov-Smirnov statistic is

[Mathematical Expression Omitted]

where [F.sub.1](y) and [F.sub.2](y) are the PDFs for the two populations evaluated at the same level of real income. The large sample distribution of 4[KS.sup.2] mn/(m + n) is chi square with two degrees of freedom (Dagum 1980). For food expenditures, interest centers on testing whether the FMDFs (which are a type of cumulative distribution function) for any two given years are identical. That is, are food expenditures identically distributed across income groups over time. Thus, the corresponding test for food expenditures is [Mathematical Expression Omitted] where the FMDFs are evaluated at the same levels of real income.

The relative economic affluence (REA) statistic proposed by Dagum (1987) is used to measure the economic disparity between food spending (income) distributions over time. The REA statistic, denoted by D, measures the relative economic affluence of one population versus another when the populations have unequal mean expenditures (incomes). If a real difference between food expenditure (income) distributions exists, the statistic D will signal the existence of an effective discriminator even when the distributions are very close together. The relation D defines a strict partial ordering over a set of pairs of distributions. If the members of two populations, [Q.sub.1] and [Q.sub.2], are each grouped into the same k real income intervals, the distribution free estimator of D is defined by

[Mathematical Expression Omitted]

where

[Mathematical Expression Omitted]

where [X.sub.i]([Q.sub.1]) and [X.sub.j]([Q.sub.2]) are mean food expenditures (income) of the ith and jth intervals for [Q.sub.1] and [Q.sub.2], respectively. The [f.sub.1] (i) and [f.sub.2] (j) are the frequencies of the ith and jth intervals for populations [Q.sub.1] and [Q.sub.2.] D can be shown to be sensitive to the means, variances, and asymmetries of the distributions. As indicated by Dagum (1987), the statistical significance of the REA between two populations can be tested using the Kolmogorov-Smirnov test outlined above.

REAs are an important complement to intradistribution inequality measures because together they incorporate two social welfare preferences - the preference for less inequality within a population and more income (food expenditures) among its members. Thus, REAs and Gini ratios provide the basic information to perform welfare comparisons of income (expenditure) distributions with different means (Dagum 1987).

However, it is possible for an REA between two distributions to be very small (because they have almost equal means) but the distributions to be very dissimilar. That is, one has a large and the other a small Gini ratio (Dagum 1987). Hence, a strict ordering of distributions based on the two welfare criteria given above may require a model that simultaneously incorporates both criteria. This is because it is possible for one population to be more affluent than another and also have a higher Gini ratio.

One model, based on both inequality and the amount of the resource available, is the theory of relative deprivation. This sociological theory (Runciman 1966) states that the effect of deprivation that results from not having Z when others have it is an increasing function of the number of persons who do not have Z. The range of possible deprivation for each individual in society is (0,y*), where y* is the highest income in society. For any individual j, his income, yj, partitions total deprivation into two parts: (yj, y*), the range of income for which he is deprived, and (0,yj), the range of income for which he is satisfied. Yitzhaki (1979, 1982) formally quantified the theory and established its equivalence to utility theory. These results are based on an interpretation of utility theory that has not gained widespread support within the economics profession. In particular, the duality between relative deprivation and utility theory is based on the concept that utility is relative; that is, an individual evaluates a bundle of goods by comparing it to the consumption bundles of others. This school of thought, advocated by Kapteyn (1977), Kapteyn et al. (1980), and Van de Stadt et al. (1985), among others, run counter to most economic models that assume that individual utility functions are independent, i.e., they are not influenced by the behavior of others. The relative utility hypothesis relies, in many ways, on a cardinal utility function with interpersonal utility comparisons - propositions that are not assumed in standard utility and welfare theory, although the fields of psychology and sociology fully embrace the concept (Davis 1959; Helson 1964; Hyman and Singer 1968). Perhaps the best known example of an economic theory based on relative utility is Duesenberry's (1949) relative income hypothesis. In any event, the notion that utility is at least partially relative seems plausible, although readers will have to be their own judges of the merits of the relative deprivation hypothesis.

Given the above qualifiers, Yitzhaki shows that the degree of relative deprivation for the income range (y, y + dy) can be quantified by 1 - F(y), where F(y) is the cumulative income distribution, and 1 - F(Y) is the relative frequency of persons with incomes above y. He defines the relative satisfaction function of the jth person (which is the complement of the deprivation function) as

[Mathematical Expression Omitted]

that upon integration equals

[Mathematical Expression Omitted]

where u is the average income and [Sigma](yj) is the value of the Lorenz curve.

Society's degree of satisfaction (with an income distribution) can be defined as aggregate satisfaction or formally

[Mathematical Expression Omitted]

and using (12):

[Mathematical Expression Omitted]

where S is society's satisfaction with the existing income distribution, u is mean income, and GC is the Gini coefficient. This measure takes into account both inequality and changes in income levels and position. Thus, at a constant level of inequality, satisfaction is a monotonically increasing function of mean income in the society. Conversely, at a given mean income, satisfaction monotonically decreases as inequality increases. S is bounded between zero (total inequality) and u (total equality). Obviously, the measure is easily extended to food spending.

The Continuing Consumer Expenditure Survey (CCES) contains the most recent and continuous data available on food spending in American households. Six diary surveys have been publicly released (1980-1985), and each survey year is nationally representative. The data were obtained from a cross section of U.S. households reporting detailed information on purchases over a two-week period, together with socioeconomic data concerning the household units. The adult equivalent scales implicit in the U.S. poverty guidelines (Congressional Budget Office 1988) and scales developed by Brown and Johnson (1986) were used to adjust annual household gross income and total weekly food expenditures, respectively.(2) No single type of adult equivalent scale has gained universal acceptance. In fact, Gronau (1988, p. 1183) has written: "Adult equivalence scales have recently celebrated their first centenary, but the debate on how to estimate them and their welfare implications has not yet subsided." Given this fact, scales implicit in the poverty lines are frequently used (Congressional Budget Office 1988; Blackburn and Bloom 1987). Income was deflated by the CPI-XI (Congressional Budget Office 1988) and food expenditures by the CPI for total food (1980 as a base for both CPIs), and each year's data were aggregated into 25 income groups. [Tabular data omitted]

EMPIRICAL RESULTS

The REAs for income and food spending for all yearly pairwise comparisons between 1980 and 1985 are presented in Table 1. The deflated sample means for each of the variables and the Kolmogorov-Smirnov test statistics are also presented. The estimated coefficients for the Lorenz and food concentration curves for the years 1980 and 1985 are reported in Table 2 (estimates of the curves for the years 1981-1984 are available from the authors). In general, the estimated coefficients of both curves have relatively small standard errors, and the overall fits of the models to the data are good. Gini and concentration ratios are also presented in Table 2. Given the volume of empirical results, the following discussion only highlights the more important findings. [Tabular data omitted]

The Kolmogorov-Smirnov tests indicate that the null hypothesis of equally distributed income variables cannot be rejected at the five percent level for the pair 1983-1984. For all other pairs the hypothesis can be rejected. The same results were found for the food spending distributions.

After 1981 (note that income was higher in 1980 than 1981) and except for 1983-1984, the calculated REAs imply that the relative economic affluence of households (in terms of adult equivalent income) has increased each successive year. Consequently, if one is willing to make welfare comparisons based solely on relative economic affluence, this analysis indicates that after 1981 there has been a general improvement in the average affluence of U.S. households.

In terms of food spending, the REAs imply the following ranking of the distributions: 1985, 1980, 1982, 1983, 1984, and 1981. (Recall that REAs measure how much more affluent a population with a higher mean is than another. Note that adult equivalent food spending was higher in 1980 than in all years except 1985.) This is also the same ranking obtained if the distributions are ranked by mean expenditures for each year (a type of REA measure proposed by Vinod 1985). However, taking 1980 and 1985 as an example, the difference in the means is 42 cents, while the net economic affluence (i.e., [d.sub.1 - [p.sub.1]) is 52 cents. The difference occurs because an REA based on the difference in means is insensitive to changes in variances and asymmetries. [Tabular data omitted]

On the other hand, Gini coefficients indicate that inequality has increased in the distribution of income from 1980 to 1985, declining slightly between 1983 and 1984 before rising again. In particular, the Gini coefficient increased from 0.371 in 1980 to 0.414 in 1985 - an increase of 12 percent. Yearly changes in the food concentration ratios have the same pattern as the Gini ratios but with larger changes (this is examined below). For example, the concentration ratio increases from 0.149 in 1980 to 0.171 in 1985 - a 15 percent increase. While inequality increases at a slightly faster rate in the distribution of food spending than in the income distribution, the former has significantly less inequality. This is because of human subsistence requirements and government programs focusing on food spending (for example, food stamps and the Women, Infants, and Children Programs). Also, since the CCES is an expenditure survey, adjustments cannot be made for home production of food or commodity donation programs (e.g., the Temporary Emergency Food Assistance Program). Data that included information on these items would be likely to reduce the concentration ratios.

Basing welfare comparisons solely on inequality within a distribution, the income and food spending distributions are ranked in the following descending order: 1980, 1981, 1982, 1984, 1985, and 1983. This contrasts sharply with an ordering based on REAs. Clearly, in this situation the two welfare preferences, higher average affluence and inequality aversion, taken simultaneously do not provide a strict unambiguous ranking of distributions. This is because average economic affluence increased simultaneously with inequality.

The Yitzhaki measure of society's relative satisfaction with respect to the income and food spending distributions is presented in Table 3. This measure attempts to provide a strict ordering of distributions by unifying the welfare preferences of less inequality and more resources. However, recall that strong assumptions must be made to account for both welfare preferences simultaneously and to ensure a strict ordering of the distributions.

The measures were calculated using mean income (food expenditures) expressed in 1980 dollars and normalized on the calculated 1980 value for a given distribution. For example, the measure of society's satisfaction with the 1981 income distribution is 97.5, indicating that society is 2.5 percent less satisfied with the income distribution in 1981 versus 1980.

Society's apparent satisfaction with the distribution of income fell in 1981, rose in 1982, fell again in 1983, and rose in both 1984 and 1985. Despite higher mean incomes in both 1982 and 1983, satisfaction remained below 1980 levels because of increasing inequality. In both 1984 and 1985, satisfaction rose above 1980 levels, because increases in mean income were more than enough to compensate for increases in the Gini ratio.

For all years relative to 1980, society's apparent satisfaction with the distribution of food spending has declined - the measures following the same year-to-year pattern as the measures for income. However, unlike the income criterion, 1984 and 1985 satisfaction levels remain below that for 1980. These declines are caused by relatively flat or decreasing average per person real expenditures coupled with increasing concentration ratios.

Society's presumed satisfaction with both the income and food expenditure distributions as a percentage of the maximum attainable (i.e., if all members of society received mean income or food expenditures) show the same pattern - declining from 1980 through 1983, rising in 1984, and falling back in 1985. However, satisfaction with food spending was considerably higher than for income - over 80 percent versus about 60 percent for income. The high percent of the maximum attainable for food spending is a consequence of the small concentration ratios.

The relative satisfaction measures imply the following ranking of income distributions: 1985, 1980, 1982, 1983, 1984, and 1981. The ranking for food spending distributions is: 1980, 1985, 1982, 1981, 1984, and 1983. In general, these rankings are more in line with the rankings by REAs than by inequality measures.

The above analyses have attempted to examine distributions from the standpoint of the population or society in general. Attention now shifts to segments of the distributions. In particular, the share of national income (food spending) received by population quintiles and the percent of income they spend on food is examined. In 1980, the poorest 20 percent of the population received 4.78 percent of national income in contrast with 42.20 percent received by the wealthiest 20 percent of households. By 1985, the poorest 20 percent received 4.27 percent of national income and the wealthiest 20 percent received 45.59 percent, with the share received by the poorest quintile declining almost steadily from 1980 to 1985. In fact, all income quintiles except for the highest have lost their shares of national income from 1980 through 1985. This indicates that economic growth has generally favored the wealthier members of society.

Given the decline in income share received by all but the wealthiest population quintile, it is not surprising that the share of national food spending has declined for the lowest quintiles. For example, the lowest income quintile received 13.76 percent of national food spending in 1980, but this dropped to 12.77 in 1983 before rising to 13.33 in 1985. This contrasts with 28.81 percent received by the highest income quintile in 1985, up from 26.28 percent in 1980. As with national income, the share of total food spending received by all income quintiles, except the highest, has declined. The pattern of food spending shares received by the various quintiles tends to follow the patterns observed for income - underscoring the close relationship between food spending and income.

Expenditure elasticities were calculated using the estimated Lorenz and concentration curves (Kakwani and Podder 1976; Blaylock and Smallwood 1982) and are presented in Table 4 for various income levels. The elasticities are quite similar at the sample averages (0.33) and when estimated at the same real income level across surveys. This is evidence that the underlying Engel relationship has been stable, and, given the model in equation (3), this implies that the changes noted in the food spending distribution have been a function of changes in the income distribution. This is not surprising given the identical patterns in the changes in Gini and concentration ratios and the results of the Kolmogorov-Smirnov tests.

As noted above, if [alpha = beta], then a given Lorenz (concentration) curve is symmetric. Thus, a t-test can be used to test for symmetry. Results of t-tests indicate that the null hypothesis of symmetry cannot be accepted for any of the Lorenz curves at the 0.05 level of significance. The estimated coefficients for the individual Lorenz curves imply that the curves are skewed to the left in all cases, thereby implying that lower income households have a smaller share of income, for a given level of inequality, than if the curves were symmetric or skewed to the right. The null hypothesis of symmetry could not be rejected for the 1980, 1981, 1983, and 1984 concentration curves. The 1982 and 1985 curves were skewed to the right, implying that lower income households had a larger share of food expenditures, for a given level of inequality, than the symmetric curves.

Another measure of welfare, and one that played a critical role in the methodology underlying the formulation of the U.S. poverty guidelines, is the percent of income spent on food (i.e., the average propensity to spend on food out of income). The average propensities to spend (APS) on food at the sample averages and by quintiles for 1980 through 1985 are presented in Table 4. [Tabular data omitted]

As expected, the proportion of income spent on food declines rapidly across quintiles within each survey year. The APS within the lowest income quintile is 0.22 in 1980 and rises slightly to 0.23 in 1985. In general, the APS within a given quintile, except the lowest, is stable across surveys. The APS reaches a peak (0.24) in 1982 for the lowest quintile, suggesting that the 1982 recession may have affected lower income households more severely. Also, households in the poorest quintile (in terms of adult equivalent income) spent about 3 times as much of their incomes on food than the average household and about 5 times more than those in the highest quintile.

In real terms, both average income and food expenditures of households in the lower quintiles remained virtually unchanged between 1980 and 1985 but rose for households in the higher quintiles. This, together with stable APCs and higher total food expenditure elasticities at lower income than at higher income levels, has caused inequality to increase at a slightly faster rate in total food spending than income distribution. This also accounts, at least partially, for the relatively stable or slightly declining average food expenditures from 1980-1985 that, together with rising inequality, has lowered apparent satisfaction levels.

Before presenting some conclusions, it is useful to examine the changes in the demographic characteristics of the population subset in the lowest 20 percent of the income distribution from 1980 to 1985. During this period, the percent of the households in the lowest income quintile that are headed by a black increased modestly, the percent headed by a person over 64 years old declined about 7 percentage points (with a corresponding decline in the age of the household head), single parent households increased about 4 percentage points, and the percentage of single member households declined. This suggests that older households have been gaining affluence. Conversely, high divorce rates and increasing numbers of unwed mothers have increased the percentage of single parent households in the lowest income quintile.

SUMMARY AND CONCLUSIONS

Statistically significant changes have occurred in the income and food spending distributions during the first part of the 1980s. Total inequality within the income and food distributions, as measured by Gini coefficients and concentration ratios, has increased from 1980 to 1985. However, food spending is more equally distributed than income. This was expected because of subistence requirements and government efforts focusing on prodiving an adequate diet. Simultaneously with an increase in income inequality, the share of national income received by the lowest income quintile has dropped about 0.5 percentage points between 1980 and 1985 and risen over 3 percentage points for the highest quintile. The share of national income received by the middle quintiles also declined. Likewise, the share of national food expenditures received by the two lowest quintiles dropped about 1.5 percentage points and rose about 2.5 percentage points for the highest quintile between 1980 and 1985. On the other hand, REAs indicate a general improvement in the average affluence of the population. Thus apparent changes are a mixed blessing - increasing inequality but higher average affluence.

Using a measure developed by Yitzhaki, society's apparent satisfaction with the distributions of income and food spending was evaluated. This measure, based on the concept of relative utility, takes into consideration the "size of the pie" to be distributed as well as inequality. The measure indicates that society is more satisfied with the distribution of income in 1984 and 1985 than in prior years but less satisfied with the food spending distribution. On the other hand, in terms of the maximum attainable level of satisfaction, society is considerably more satisfied with the distribution of food spending than with the distribution of income.

Empirical results also suggest that economic growth in the 1980s has favored higher income households and that changes in the food spending distribution are primarily due to changes in the income distribution, not changes in the underlying Engel function.

REFERENCES

Blackburn, M. and D. Bloom (1987), "Earnings and Income Inequality in the United States," Population and Development Review, 13: 575-609. Blaylock, J. and D. Smallwood (1982), "Analysis of Income and Food Expenditure Distributions: A Flexible Approach," The Review of Economics and Statistics, 64: 104-109. Brown, M. and S. Johnson (1984), "Equivalent Scales, Scale Economics, and Food Stamp Allotments: Estimates from the Nationwide Food Consumption Survey, 1977-78," American Journal of Agricultural Economics, 66: 286-293. Congressional Budget Office (1988), Trends in Family Income, February. Dagum, C. (1980), "Inequality Measures Between Income Distributions with Applications," Econometrica, 48: 1791-1803. Dagum, C. (1987), "Measuring the Economic Affluence Between Populations of Income Receivers," Journal of Business and Economic Statistics, 5: 5-12. Davis, J. (1959), "A Formal Interpretation of the Theory of Relative Deprivatation," Sociometry, 22: 280-296. Duesenberry, J. (1949), Income, Saving and the Theory of Consumer Behavior, Cambridge, MA: Harvard University Press. Ellwood, D. and F. Levy (1988), "Trends in the Inequality of Permanent Incomes," paper presented at the annual meeting of the American Economic Association, New York, December. Gronau, R. (1988), "Consumption Technology and the Intrafamily Distribution of Resources: Adult Equivalence Scales Reexamined," Journal of Political Economy, 96: 1183-1205. Helson, H. (1964), Adaptation-Level Theory: An Experimental and Systematic Approach to Behavior, New York, NY: Harper Press. Hyman, H. and E. Singer (1968), Readings in Reference Group, Group Theory, and Research, New York, NY: The Free Press. Kakwani, N. (1978), "A New Method of Estimating Engel Elasticities," Journal of Econommetrics, 9: 103-110. Kakwani, N. and N. Podder (1976), "Efficient Estimation of the Lorenz Curve and Associated Inequality and Measures from Grouped Observations," Econometrica, 44: 137-148. Kapteyn, A. (1977), A Theory of Preference Formation, unpublished thesis, Leiden University, Leiden, The Netherlands. Kapteyn, A., J. Wansbeek, and J. Buyze (1980), "The Dynamics of Preference Formation," Journal of Economic Behavior and Organization, 1: 123-157. Musgrove, P. (1980), "Income Distribution and the Aggregate Consumption Function," Journal of Political Economy, 88: 504-525. Runciman, W. (1966), Relative Deprivation and Social Justice, London, England: Routledge and Kegan Paul. Smallwood, D., J. Blaylock, and J. Harris (1987), Food Spending in American Households, 1982-84. USDA, Economic Research Service, Statistical Bulletin 753. Van de Stadt, H., A. Kapteyn, S. Van de Geer (1985), "The Relativity of Utility: Evidence from Panel Data," The Review of Economics and Statistics, 67: 179-187. Vinod, H. (1985), "Measurement of Economic Distance Between Blacks and Whites," Journal of Business and Economic Statistics, 3: 78-88. Yitzhaki, S. (1979), "Relative Deprivation and the Gini Coefficient," Quarterly Journal of Economics, XCIII: 321-324. Yitzhaki, S. (1982), "Relative Deprivation and Economic Welfare," European Economic Review, 17: 99-113. The Journal of Consumer Affairs, Vol. 23, No. 2, 1989 0022-0078/0002-226 $1.50/0 (R) 1989 by The American Council on Consumer Interests

(1) The term "adult equivalent" means that household income (expenditures) has been adjusted by a set of adult equivalent scales. Adult equivalent scales are merely sophisticated methods of head counting that are used to adjust households budgets to permit welfare comparisons across households of different sizes. (2) The use of household gross income in lieu of net income was mandated by data considerations - net income was not reported on the 1980 and 1981 public use tapes. However, an examination of the 1982-1985 data (which included net income) indicates that only relatively small changes would occur in the empirical results if net income could be used instead of gross. The reason is that, for each year from 1982-1985, average net income as a percent of gross was almost constant at 90-91 percent and almost constant within quintiles across surveys (Smallwood, Blaylock, and Harris 1987). Sampling weights were used in all calculations.

James R. Blaylock and William N. Blisard are Agricultural Economists, USDA, Economic Research Service, Commodity Economics Division. Views expressed in this paper are not necessarily those of USDA or ERS. The authors wish to thank several anonymous reviewers and Richard C. Haidacher for helpful comments.

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Author: | Blaylock, James R.; Blisard, William N. |
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Publication: | Journal of Consumer Affairs |

Date: | Dec 22, 1989 |

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