Back Calculating Nominal Wage Rates from Nominal Discount Rates: A Useful Exercise in Forensic Economic Analysis
Ireland, Thomas R., Journal of Legal Economics
The present value of any lost stream of earnings that is increasing over time can be calculated using a net discount rate or by using a specific nominal growth rate for earnings and a specific gross discount rate. Both approaches were declared legally acceptable in Jones & Laughlin Steel v. Pfeifer (1983), a United States Supreme Court decision that is the ruling federal case on such matters. In Pfeifer, the net discount rate method was referred to as the below market discount rate method and seemed to be the method preferred by Justice Stevens, who wrote the opinion. A similar strong preference for a below market discount rate was indicated in Culver II (1983), an important case in the 5th Circuit of the federal court system.' However, economists have long known that projecting specific rates and using a net rate, if both methods are used correctly, yield identical results. Samuels (1990) establishes the identity of the two methods by algebraic derivation but does not provide the kind of simple tabular example that would show this in a self-evident way to a judge. In its absence, such a demonstration has value in and of itself and is one purpose of this paper.
The second purpose of this paper is to show that such a derivation can be used to validate the reasonableness of a net discount rate being used by a forensic economist.2 Current nominal interest rates are market determined and based upon the market's expectations of the future, but there are no equivalent market based projections of expected rates of wage growth.3 As a result, estimates of future wage growth are often based on past wage growth. However, there is no agreement among forensic economists about the period of the past or the methods that should be used to estimate future wage increases. Past rates are history and cannot be used to accurately predict future rates in any systematic way (Havrilesky 1990). This paper shows how historical rates can be used to test the reasonableness of a given net discount rate without relying upon any specific past period or any particular methodology for projecting from that past period.
The third purpose of the back-calculation method relates to an unethical practice by forensic economists that this author has encountered in the past. An economist who wishes to disguise the fact that his wage growth/discount rate assumptions are different when working for plaintiffs than when working for defendants can hide those differences by switching between net discount rates and specific nominal rates when switching from plaintiff to defense sides of cases. The back-calculation method provides an easy mechanism for disclosing such practices.
The last purpose of this paper is to show how back calculated rate projections can be incorporated into the development of a loss distribution table that is reasonably easy for a jury to understand. A standard tactic of defense attorneys is to ask the plaintiff's economist to calculate the annual interest earned on his damages estimate. Usually, that value is close to or greater than the annual loss estimated for the first year of the fund. This has the potential to mislead jurors into believing that the present value is larger than it should be to replace all damages. This tactic can be countered by developing a loss distribution table that shows the jury the exact amount of the loss each year using a back calculated growth rate. The table begins with the present value of damages and calculates interest earned on the fund for each year. It then subtracts damage payments for that year, showing the balance in the fund at the end of the year. The table clearly shows that the end year balance declines to zero in the last year of projected losses. Thus, this table shows exactly how the fund works to replace the damage losses being projected. This can be very persuasive in redirect examination. Further, if this table is admitted into evidence, it can be very useful to the jury when the jurors actually make their trial decisions. …