The Measurement of Inequality: Reply
1979; American Economic Association; Volume: 69; Issue: 4 Linguagem: Inglês
ISSN
1944-7981
Autores Tópico(s)Economic theories and models
Resumoing from economic growth, we infer life cycle incomes from cross-section data by assuming that as a cohort ages it will occupy the income chairs now held by the older cohorts. But we also need information about the expected degree of intracohort mobility as a cohort ages. Zero mobility is indicated by perfect rank-order correlation of incomes across all years: a person occupying the nth income rank in his cohort at 30 would always occupy the nth income rank as the cohort moved through the life cycle. Individual life cycle curves would never cross and lifetime income inequality would be at a maximum, given the cohort income distributions. Under these conditions Wertz's ADJG or its proxy, the average of the cohort Ginis weighted by income shares, would closely measure lifetime inequality.5 Once we allow some intracohort mobility, lifetime inequality typically will drop, and if the rank-order transition matrix exhibits very high mobility, lifetime incomes will converge toward equality. Three recent studies show the importance of intracohort mobility for inequality. Bradley Schiller found that rank-order changes occurred across the entire range of the income scale and mobility could be viewed as a pervasive dynamic characteristic of our distribution. Donald Parsons' longitudinal income and autocorrelation study bears more directly on the issues raised here. Using male earnings from the National Longitudinal Surveys, Parsons found that: distribution of lifetime human wealth depends not only on the distribution of annual earnings but also on the consistency with which individuals maintain their economic position in the distribution from to year (p. 551). His results that the actual standard deviation 4By contrast, PG does not attempt to adjust actual incomes across cohorts to find the age-equivalent incomes since to do this properly requires knowledge of each individual's life cycle income; instead PG simply compares the average of the actual differences between two cohorts with the average of the ideal differences. This also seems crude, but with limited cross-section data it is less biased and provides better estimates of long-term inequality than does ADJG. 5For CPS income distributions, ADJG values are 97 percent of the weighted average of the cohort Ginis. This content downloaded from 157.55.39.186 on Tue, 12 Apr 2016 08:53:49 UTC All use subject to http://about.jstor.org/terms 676 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1979 of lifetime human wealth is only 60 percent of what the standard deviation would be if individuals were frozen into a given spot in the income distribution from one to the next (p. 559). This condition of zero mobility is, as we have seen, implicit in ADJG, and therefore Parsons' data indicate the degree of upward bias likely in ADJG. Finally, Parsons estimated the effect of high mobility: actual measure (standard deviation of lifetime earnings) is almost three times larger than it would be if earnings in each were generated by a random draw (p. 559). Lee Lillard's longitudinal study of human wealth reinforces these conclusions. Although his National Bureau of Economic Research sample of white males showed less income dispersion than family units, the relative spread which he found among the Gini coefficients has general significance. Lillard's cohort Ginis averaged .28 while the Gini of lifetime earnings was only .19. He states that Inequality in earnings at any stage of the life cycle for men over 30, as measured by either the coefficients of variation or the Gini coefficient is 50 percent larger than inequality in human wealth. This conclusion is not affected by changes in the discount rate (p. 49). Note that my estimate of lifetime income inequality for families in 1972 (using PG) was .239 while the average of the cohort Ginis was .334 and the Lorenz-Gini .359 (see my 1975 paper). The last two coefficients are 40 and 50 percent higher than PG, or alternatively, my PG figure and Lillard's Gini of lifetime inequality are both in the range of 67-72 percent of the conventional cross-section Gini coefficients. However, ADJG is .324 or 90 percent of G. Thus the longitudinal estimates of lifetime inequality offer striking confirmation that PG does not understate inequality but yields estimates in the correct range. These findings also enable us to resolve a question which has long puzzled researchers: why, if life cycle effects are important, do cohort Ginis average 90 percent of the overall Gini? The reason is now clear: the cohort Gini measure reveals what lifetime inequality would be if persons within a cohort were fixed in rank order throughout the life cycle of the cohort; hence it always overstates inequality in societies where significant intracohort mobility exists. Wertz's ADJG coefficient, as noted above, shares the same weakness. There remains one question. Why and how does PG yield closer estimates of lifetime inequality than ADJG although neither formula explicitly uses mobility data? The answer briefly is this: the investment in human capital and the stochastic process which generate a society's curved age-income profile also generate the variety of individual income profiles which determine the rankorder transition matrix. Larger mean income differences between age cohorts go hand in hand with increased mobility within a cohort as it moves across the parabolic life cycle path. The ADJG is invariant with respect to changes in the average age-income profile since mean income differences between cohorts are removed from the actual income differences (see Wertz, equation (2)). But PG responds in an appropriate way. Consider a square matrix, with age cohorts listed top and side, showing in each cell the average of the differences resulting from the income pairings. The main diagonal of the matrix will show the within-cohort pairings while the off-diagonal elements represent income pairings across cohorts (see my 1977 paper, p. 522, Table Ic, for a PG matrix in expected gain terms). Given a flat age-income profile, the PG and ADJG matrices will be the same. With a parabolic profile PG and ADJG will only be alike in the main diagonal; the offdiagonal elements of PG will be smaller than ADJG for the reason given by Wertz, namely I A l I B I ' I A B 1. The greater the mean income spread between cohorts, the greater the difference in the terms of the above inequality. The ADJG based on the right-hand term is unresponsive to changes in the shape of the life cycle curve and also to mobility; PG, however, varies directly with intracohort inequality and inversely with the mean difference between cohorts, and hence inversely with the degree of mobility. This is a valuable attribute in a coefficient with minimal data requirements, and the evidence from longitudinal income studies supports the conclusion that PG provides better estimates of lifetime inequality than other Gini formuThis content downloaded from 157.55.39.186 on Tue, 12 Apr 2016 08:53:49 UTC All use subject to http://about.jstor.org/terms VOL. 69 NO. 4 PAGLIN: MEASUREMENT OF INEQUALITY 677 las based on cross-section data. If equity judgments are conditioned by long-term rather than by transitory inequality, then PG can also be used as one element of an equity
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