Are Net Discount Ratios Stationary? Evidence of Mean-reversion and Persistence

This article extends the debate initiated by Haslag, Nieswiadomy, and Slottje (1991, 1994) and Gamber and Sorensen (1994) in this journal about whether the net discount ratio can be described as a stationary process. Haslag, Nieswiadomy, and Slottje found discount ratios to be stationary. Gamber and Sorensen concluded that they are nonstationary; however, they identified the source of the nonstationarity as a single shift in the mean of the series. Using the Cochrane variance ratio and Campbell-Mankiw decomposition tests, the authors find that the net discount ratio follows a trend stationary process. However, to determine the degree or level of persistence, Lo’s Modified R/S Analysis (1991) is used. The authors find that the relative importance of any mean shift is a function of the duration of the discount period for expected earnings. INTRODUCTION Because forensic economists generally use historical averages to forecast the net discount ratio, an important question is whether net discount ratios are stationary over a sustained period of analysis. Shocks to a stationary time series may be temporary. If such is the case, the time series will revert to its long-term mean level (i.e., mean reversion) and the long-term forecast of a stationary time series will converge to its unconditional mean. In 1991, Haslag, Nieswiadomy, and Slottje generated results consistent with the hypothesis of a stationary discount ratio and concluded that a real net discount ratio can be used with confidence to forecast the present value of expected earnings. HowPatrick Hays and Max Schreiber are both associate professors of economics, finance, and international business, College of Business, Western Carolina University, Cullowhee, N.C. James E. Payne is associate professor, College of Business and Technology, Eastern Kentucky University, Richmond. Bradley T. Ewing is assistant professor of economics, Texas Tech University, Lubbock. Michael J. Piette is president, Analytical Economics, Inc., Tallahassee, Fla. 440 THE JOURNAL OF RISK AND INSURANCE ever, Gamber and Sorensen (1994) believed the Haslag, Nieswiadomy, and Slottje results were “critically dependent upon the specification of the unit root test they performed” and suggested their tests had not adequately eliminated the serial correlation from the residuals. Using alternative unit root tests with the higher number of lags, they found in favor of a nonstationary series; however, they noted that a single shift in the mean of the series appeared to be the source of the nonstationarity. Ultimately, Gamber and Sorensen argue that the optimal mean to apply in discounting should be the one enduring since the last shift and not the grand mean used in unit root (Dickey-Fuller) tests. In response to the comment by Gamber and Sorensen (1994), Haslag , Nieswiadomy, and Slottje (1994) present alternative unit root tests by Phillips and Perron (1988) and Stock and Watson (1988) that reject the null hypothesis of a unit root in the net discount ratio. Moreover, Haslag, Nieswiadomy, and Slottje (1994) contend that when data are expanded through the 1993 time period one observes the net discount ratio appears to be reverting to its full sample mean. Furthermore, they state, “In the case of the net discount ratio, the series has some persistence and can (temporarily) deviate from its mean for periods long enough to appear to have experienced a permanent shift. Indeed, an ‘optimal’ forecast of the net discount ratio should take this persistence into account” (1994, p. 57). A visual examination of Figure 1, a plot of the net discount ratio from 1964:2 through 1998:12, appears to support the Haslag, Nieswiadomy, and Slottje reply to Gamber and Sorensen. That is, the mean of the series was rising and approaching the overall mean in the original study in the 1964 through 1988 period. The shift to a lower mean between 1979:10 and 1980:1, which Gamber and Sorensen believed to be the source of the nonstationarity in the series, does appear to be a transient shift. However, this may have substantially affected the net discount ratio during the 1980 through 1988 period. Certainly no definitive statements should be made from a cursory visual examination of the series. The purpose of this article is to provide the forensic economist with empirical evidence as to the validity of the use of historical averages across a set of different discount periods. The practical question is whether the forensic economist can disregard temporary shifts in net discount ratios, and the underlying concern is the degree of persistence in these ratios. If the discount period for an evaluation is brief, then temporary “shocks” may be relevant and historical averages may prove to be inappropriate. However, for the more typical evaluations of 20 to 30 years, historical averages may prove to be appropriate if net discount ratios are deemed persistent. After testing for stationarity via Cochrane’s (1988) variance ratio and Campbell-Mankiw (1987) decomposition methods, the authors use Lo’s Modified R/S analysis1 to determine the time horizon(s) where temporary shocks/shifts would make the use of historical averages suspect. 1 Lo’s technique (1991) has been used in several studies regarding the degree of persistence in financial series. ARE NET DISCOUNT RATIOS STATIONARY? EVIDENCE OF MEAN REVERSION AND PERSISTENCE 441 FIGURE 1 Time Series Plots of Net Discount Ratio Series