Are Net Discount Ratios Stationary?: The Implications For Present Value Calculations Page: 505

                                
Are Net Discount Ratios Stationary?: The
Implications For Present Value Calculations
Joseph H. Haslag
Michael Nieswiadomy
D. J. Slottje
ABSTRACT
This article analyzes the relationship between real interest rates and real growth rates
in wages. The stationarity of these time series has been discussed in the literature.
However, since the net discount ratio, (1 + g,)/(1 + rt), is a nonlinear transformation, it
is not necessarily stationary even if the interest rate and growth rate in wages series are
each stationary. On the other hand, the net discount ratio may be stationary even if the
interest rate and growth rate series are both non- stationary. The significant finding of
this article is that this ratio is stationary. This conclusion appears robust since it holds
for at least four different Treasury securities analyzed: three month, six month, one
year, and three year. Therefore, a real net discount ratio, (1 + g)/(1 + rt), can be used
with confidence in constructing present value forecasts of expected earnings.
Estimating the present value of future lost earnings is a complicated
process. Some of the topics of recent research include methods of analyzing
expected earnings (Becker and Alter, 1987), the age-earnings life cycle (Lane
and Glennon, 1985; Lambrinos and Harmon, 1989), employee benefits
(Nieswiadomy and Slottje, 1988), disability effects (Nieswiadomy and
Silberberg, 1988), and the impact of state and federal taxes (Vernon, 1985).
However, the determination of the correct growth rate in wages and the
discount rate has received the most attention.
The purpose of this article is to explore the relationship between interest
rates and growth rates by testing for stationarity of the net discount ratio.'
The next section discusses methods used to calculate the discount rate and
growth rate. Then, unit root tests on the real growth rate in real wages, several
real interest rates, and several real net discount ratios are discussed. The
Joseph H. Haslag is Senior Economist at the Federal Reserve Bank of Dallas and Visiting
Assistant Professor of Economics at Southern Methodist University. Michael L. Nieswiadomy is
Associate Professor of Economics at the University of North Texas. Daniel J. Slottje is Associate
Professor of Economics at Southern Methodist University.
The authors would like to thank an anonymous referee for helpful comments.
'The other factors such as tax rates and age earnings profiles wich influence specific present
value calculations are not analyzed int his article. They do not significatly affect the conclusions.