Time-Series Changes in Personal Income Inequality in the United States from 1939, with Projections to 1985

Abstract

Our commentators (henceforth P-S) cannot be faulted for pointing out a fact of which we are fully aware: the inclusion of the "weeks worked" variable in our model was not rigorous in the sense of explicitly formulating a dependence on human capital, labor supply, and other considerations. We preferred to leave this part of the story out for the time being. Work on this subject is only beginning at the NBER and elsewhere. The problems posed by P-S should be of value in such work. The specific functional form for the inclusion of weeks worked was adopted to facilitate the empirical application of the model. We phrased the insertion of W in a somewhat careless way in the beginning paragraph on our page 37. The sentence should read: "If E* is full-year earnings, actual annual earnings are Ei = E* W7, where W is the fraction of weeks worked during the year." Thus, r* is the full-time rate of return, and k, is defined as C,/E,*. At this level we do not see any particular problems arising with this formulation. The first sentence of the first paragraph on page 37 says, in effect, that the appropriate variables and parameters (including r and Eo) should be starred. Of course, there is no star on the left-hand side of our equation (4). It is calculated by P-S that our parameter estimates imply ko = 0.73, which is rather implausible. Actually, the appropriate coefficient of T is not r*k as they suggest, but r*ko + ko/ T* (1 + ko), as we show on page 38. The T' is the period of positive net investment, which is not assumed but implicit in the income profile. Its value is about 20 years. If so, ko = 0.44, and total "post-school year equivalents" of positive net investment K = 4.4, not 15 as P-S estimate. These estimates are not very secure, but not clearly outrageous. We should keep in mind that these as well as the "rate of return" estimates are not the main targets, but merely by-products of a much-simplified model whose purpose was to study time changes in the aggregate-income variance.