Academic journal article Journal of Risk and Insurance

Are Net Discount Rates Stationary? the Implications for Present Value Calculations: Comment

Academic journal article Journal of Risk and Insurance

Are Net Discount Rates Stationary? the Implications for Present Value Calculations: Comment

Article excerpt

Introduction

In a recent article in this Journal, Haslag, Nieswiadomy, and Slottje (1991) present evidence that the nonlinear net discount ratio over the 1964 through 1989 period is a stationary series. This is an important finding, since it implies not only that a stable relationship exists between the growth rate of wages and interest rates, but also that valid inferences about the population moments of the distribution of the net discount ratio can be drawn from these data. As a result, historical averages of the net discount rate can be used confidently to estimate the present value of future earnings.(1)

Although Haslag, Nieswiadomy, and Slottje do examine the robustness of their results to changes in the interest rate, they do not examine robustness with respect to changes in the form of the unit root test. As pointed out by Campbell and Perron (1991), the outcomes of unit root tests are often quite sensitive to the specification of the tests. In this comment, we reexamine the time series properties of the nonlinear version of the net discount ratio and find that the results of Haslag, Nieswiadomy, and Slottje are critically dependent upon the specification of the unit root test they performed. In particular, we find that their tests fail to adequately eliminate the serial correlation from the residuals. Moreover, once we eliminate the serial correlation from these tests, we fail to reject the null hypothesis of a unit root for all of the net discount ratios tested.

A unit root process is essentially a time series process that experiences a random change in its mean every time period. The standard augmented Dickey-Fuller procedure tests whether a time series has a constant mean or a mean that changes randomly with each new observation. Under certain circumstances, this battery of tests will falsely suggest that a series is a unit root process. In particular, as demonstrated by Perron (1990), it is possible to misidentify a time series that has a one-time shift in its mean as a unit root process even though it is stationary around its two separate means. This distinction is important for forecasting purposes. In the case of a unit root process, all of the information that is relevant for forecasting is contained in the most recent observation. In the case of a series that is stationary around a one-time shift in its mean, all of the observations made since the mean shift contain information about the possible future path of the series.

Although our augmented Dickey-Fuller tests appear to indicate the presence of a unit root in the net discount ratio, the graphical evidence suggests that there was a substantial shift in the mean of the series during the period 1977 through 1981. As a result of this mean shift, these tests might incorrectly identify the net discount ratios to be unit root processes. To investigate this possibility, we employ the procedure recommended by Zivot and Andrews (1992), which tests the null hypothesis of a unit root against the alternative hypothesis that the series is stationary around a one-time shift in its mean. Using this test, we reject the unit root hypothesis in favor of the alternative of a one-time mean shift for all of the net discount ratios tested.

Our results indicate that the nonlinear version of the net discount ratio is a nonstationary series over the entire 1964 through 1989 time period. However, the source of nonstationarity appears to be a one-time shift in the mean of the series. Once the shift in the mean is removed, the net discount ratio becomes stationary. The most important implication of this finding is that the optimal forecast for the net discount ratio is not its grand mean over the 1964 through 1989 time period, but rather the mean since its last shift.

Data, Methodology, and Results

Following Haslag, Nieswiadomy, and Slottje, we first construct four net discount ratios using monthly data on the growth rate of the real average hourly wage in the private nonagricultural sector and the ex post real return on four different Treasury security maturities. …

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