Estimating the Present Value of Future Income Losses: An Historical Simulation 1900-1982

Abstract

Estimating Present Value of Future Income Losses: An Historical Simulation 1900-1982: Comment A number of methods for estimating present value of lost future earnings to injured parties in tort litigation have been presented in this Journal during past decade. Professor Schilling (1985) uses historical simulation for all possible five, 12 and 30 year loss periods from 1900 through 1982 to compare performance of three valuation methods (1) to each other and to a benchmark estimate. He concluded that the 'Alaska' method is found to be best relative to benchmark although none of [three] methods performs very well in an absolute sense relative to benchmark estimate [p. 100]. We do not question Schilling's conclusion regarding superiority of Alaska method. There is good economic logic to explain this finding. However, we question whether his benchmark provides an appropriate standard for evaluating performance of alternative valuation methods. Estimating Present Value of Future Earnings The present value of a worker's future earnings can be represented as [Mathematical Expression Omitted] where [PV.sub.0] = present value of future earnings at t=0; WL = expected working life in years at t=0; [E.sub.0] = annual earnings rate at t=0; [g.sub.[alpha]] = rate of growth in earnings in period [alpha] ([alpha] = 1, 2, ..., WL); [d.sub.[alpha]] = discount rate in period [alpha] ([alpha] = 1, 2, ..., WL); and [pi] = multiplication operator. Using continuous compounding, an average growth rate (g) and discount rate (d), equation (1) converts into [PV.sub.0] = [E.sub.0][1 - [e.sub.-(d-g)(WL)]]/[[e.sub.(d-g)-1]]. (2) From equation (2) it is apparent that size of (d-g) differential, not expected levels of d and g, determines present value of a future stream of earnings. A strong covariance between nominal rates of growth in annual earnings of workers (g) and annual interest rates (d) is to be expected because of their common determinant, inflation, and because hire price for any factor of production embodies real interest rate. Historical earnings growth and interest rates data provide support for expected covariance between [d.sub.[alpha]] and [g.sub.[alpha]]; (2) moreover, over extended periods of time these same data show that (d-g) differential was not markedly different from zero. Thus, it is not surprising that Schilling found that Alaska Method outperformed two valuation methods employing averages of historical wage growth and discount rates. Nor it is surprising that he supports recent Model Periodic Payments of Judgment Act (National Conference of Commissioners on Uniform State Laws, 1982). This Act essentially adopts Alaska Method for its recommendation that tort awards be paid in installments over loss period with annual growth rate ([g.sub.[alpha]]) of installments set equal to yield on one-year U.S. Treasury securities (Henderson, 1980 and 1981, National Conference of Commissioners on Uniform State Laws, 1982). What is surprising as that Schilling concludes on basis of his simulation study that Alaska Method performs tolerably well for short (five-year) loss periods, but that it does not perform very well for longer (12 and 30 year) loss periods (National Conference of Commissioners on Uniform State Laws, 1982, p. 114). (3) It is our view that support for this conclusion relates to Schilling's benchmark estimation procedure. Schilling's Benchmark Valuation Estimate Schilling develops his benchmark present value estimates for all possible five, 12 and 30 year loss periods from 1900 through 1983 using perfect foresight. First, he estimated interest rates that would actually be available each year during an n-year loss period for zero coupon, high-grade corporate bonds with maturities from one to n (five, 12 or 30) years. …