Academic journal article Journal of Risk and Insurance

An Empirical Analysis of Five Models for Forecasting Lost Future Earnings

Academic journal article Journal of Risk and Insurance

An Empirical Analysis of Five Models for Forecasting Lost Future Earnings

Article excerpt


To fairly compensate an accident victim whose earning capacity has been impaired, it is important to obtain reliable estimates of lost future income. In litigation seeking to resolve this earning potential, different approaches can be used. This article aims, through empirical analysis, to find a model that most accurately predicts lost future earnings. Five models--each employing certain assumptions and having different implications--are tested.

The use of the deterministic exponential model in damage cases to establish lost future earning capacity assumes that the plaintiff's annual loss (Y) following the date of trial will increase over time (t) at a constant percentage rate. This process is described by the linear differential equation,

(1/Y)dY/dt = a, (1)

where a is the percentage rate of change in Y. This equation is obtained from the exponential equation,

Y(t) = Y(0)exp|at~, (2)

where Y(0), which is known, is the individual's base year earnings. (The base year in a lawsuit for lost future earnings is the year preceding the date of trial.) Equation (2) traces the path that annual earnings follow when the wage earner's annual employment hours are constant over time and his or her wage per hour grows at a constant percentage rate.

Because the plaintiff in a damage case is entitled only to compensatory damages that represent the present value of future losses, equation (2) is modified to permit discounting of future values to present value. The equation

|Mathematical Expression Omitted~,

where r = an annual rate of discount,

m = the expected number of remaining years of the ith individual's worklife, and

Y(t) = the individual's lost future earnings in year t, yields the present value (|P.sub.i~) of the individual's lost future earning capacity.

Research into the measurement of lost future earnings in damage cases has addressed the theoretical implications of variations of equation (2). One of these variations is the offset model, which is exponential in structure, with the discount rate equal to the growth rate of lost earnings. Setting these rates equal to each other, in effect, causes the parameter a in the above equations to equal zero. Hence,

Y(t) = Y(0).

The offset model is attractive for use in damage cases because of the simplicity with which the issue of lost future earnings can be organized for presentation to a jury (Lambrinos and Harmon, 1989, p. 734).

In another variation of equation (2), the deterministic exponential model is modified to help ensure that the individual's projected losses track an "appropriate" inverted U-shaped lifetime annual earnings curve. The hypothesis that an individual's earnings follow such a path is a central tenet of human capital theory (see, for example, Hoffman, 1979, and Welch, 1975).

Lambrinos and Harmon (1989) measure the predictive accuracy of these variations of the exponential model. Their data set comprises economic and demographic profiles of 812 continuously employed household heads. These profiles include annual earnings for 1968 through 1983. This data set is a subset of the University of Michigan's Panel Study of Income Dynamics (PSID), an ongoing, multiyear, economic, and demographic study of a sample of household heads and others. These data are reported in Morgan and Duncan (1988).

Using the individual's 1968-1970 earnings, Lambrinos and Harmon predict the present value of the individual's 1971-1983 earnings with two models. The predicted values generated by each model are then compared to the discounted value of the individual's actual 1971-1983 earnings in order to measure the accuracy of the forecasts generated in the 812 cases by each of the models. The authors conclude, on the basis of the results of root mean squared error and other statistical tests, that the exponential model, with the age-earnings adjustment, predicts more accurately than the offset model in the 812 cases. …

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