The Present Value of Future Earnings: Contemporaneous Differentials and the Performance of Dedicated Portfolios

Abstract

Introduction Anderson and Roberts (A-R) (1989) offer evidence regarding the estimation of the present value of a worker's stream of future earnings. A-R addressed the issue of identifying the appropriate differential between the rate (r) at which the earnings stream should be discounted and the rate of growth (g) of that earnings stream. They concluded . . . that a benchmark after-tax net discount rate [i.e., (r-g)] of -0.5 percent would be appropriate for assessing awards for lost earnings for most cases. (p. 64). Bryan and Linke (B-L) (1988) reached a similar conclusion. Specifically, B-L investigated the use of portfolios of alternative composition, but with each dedicated to the replacement of an earnings stream. The earnings streams to be replaced were of varying duration over the 1953 through 1984 period. Each of these special-purpose portfolios is referred to as a dedicated portfolio. It turned out that dedicated portfolios consisting of U.S. Treasury securities of one-year constant maturity constituted the least cost means of providing for future earnings streams. The averages of the ex post or realized yields on dedicated portfolios and the ex post rates of growth in wages were approximately the same. The atypical differentials between interest rates and wage growth rates during the 1981 through 1988 period have raised questions regarding the robustness of A-R's and B-L's evidence that the appropriate differential is approximately zero. At first blush, it may seem plausible for litigants, juries and judges to review and compare recent data relating to the differential between interest rates and wages growth rates. We refer to such data as contemporaneous; that is, year-by-year, actual interest rates and actual rates of growth in wages as they move through time. The focus of this article is on a narrow, but timely, issue: namely, does information regarding interest rates and rates of growth in wages just prior to a loss period provide useful information regarding the present value of the future stream of wages during the loss period? The answer to this question is especially important during periods when the contemporaneous differential differs markedly from zero. [1] The Model In this section there is a discussion of the adjustment of the economy to discrepancies between the actual level of interest rates and rates of growth in wages. Within the context of such adjustments, a model is presented of the impact of contemporaneous differentials on the relation between returns on dedicated portfolios and growth rates in wages. Contemporaneous Interest Rates and Wages Growth It is common to define the nominal rate of interest (r) as the sum of the expected real rate (i) and an inflation premium (p).[.sup.2] Similarly, the rate of growth in wages (g) may be defined as the sum of the rate of growth in the marginal productivity of labor (f), and the rate of change in the general price level (p). The differential between i and f depends upon an economic relationship between the real rate of interest and the productivity of labor. That relationship rests, in turn, on a relation between the productivity of real capital and the productivity of labor. Relationships among the real rate of interest, the marginal productivity of labor, and the marginal productivity of real capital emerge from steady-state equilibrium conditions of the economy. The marginal productivity of capital is defined as r = mp[.sub.K]P[.sub.O]/P[.sub.K] (Where mp[.sub.K]P[.sub.O] = capital's marginal revenue product in constant prices, and P[.sub.K] = the price of capital).[3]The productivity of labor is defined as L = mp[.sub.L]P[.sub.O]/(W/i) (where mpLP[.sub.O] = labor's marginal revenue product in constant prices, and W = the nominal wage for labor).4 Using K to denote the capital stock, N for the number employed and T to denote the state of technology along with other factors affecting the productive process (e. …