Errata

Journal of Legal Economics, Mar 2008

David I. Rosenbaum and J. Michael Guthmann, "Net Discount Rates: Does Duration Matter?," Journal of Legal Economics, Volume 14, No. 2, pp.1-24.

Pages 19 and 20 should be replaced with the following:

test statistics when the base net discount rate is calculated over longer periods. The second element in the 2006 row, for example, shows that it takes six years beyond an 11-year duration before the mean net discount rate is different than the 11-year average net discount rate.

An N in Table 6 indicates that the net discount rate for the duration starting in that column is not statistically different from the net discount rate using a duration of as long as 25 years. Looking at the first row of the table, for example, the average net discount rates over durations between 19 and 24 years are not statistically different than the average net discount rate over a 25-year duration.

Consider the results in Table 6 for the year 2003. The 7 in the first column indicates that net discount rate using a 10-year duration is not statistically different from net discount rates using durations out through 17 years. However, the N in the seventh column shows that the net discount rate using a 16-year duration is not statistically different from net discount rates associated with using durations out through 25 years. Therefore, selecting a duration of 16 years effectively produces an average net discount rate that is not statistically different from net discount rates generated using durations ranging between 10 and 15 years or between 17 and 25 years. A 16-year duration encompasses results using 10-year through 25-year durations. The duration that encompasses both ends of the spectrum is the region shown in gray in Table 6.

In the 2001 row, the columns for 14-years and 15-years are the encompassing durations and thus are shaded elements. The net discount rate calculated in either year is not statistically different than discount rates calculated using durations between 10 and 13 or between 16 and 25 years. In the 2002 row, 15 years is the only encompassing duration. In the rows for 1997 through 1992, 18 years is always in the encompassing range. From row 1991 back to row 1989, the encompassing range is only 14 or 15 years.

The general conclusion from Table 6 is that over the time period 2006 through 1989, using durations between 14 and 18 years represents the net discount rate that encompasses the widest range of durations. In 15 of the 18 years over that period, the net discount rate associated with using a 14- year to 18-year duration is not statistically different than the net discount rate associated with using durations between 10 and 25 years. This range of five years, however, is fairly broad. In only one sample year - 1997 - are all five durations encompassing. Otherwise, observations from 1989 to 1991, as well as 1998 and later tend to cluster at the lower end of the range while observations between 1992 and 1996 tend to cluster at the higher end of the range. If the bands are narrowed to range between 15-year and 17-year durations, only 12 of the 18 sample years have an encompassing duration. If they are further narrowed to 16-year or 17-year durations, only eight have encompassing durations.

Conclusion

Economists have examined the proper duration to use when employing historical net discount rates as proxies for future net discount rates. Two tests were developed to investigate this issue. The first uses moving average net discount rates to examine the implications of duration. The results show that average net discount rates calculated over 10 years are not statistically different than net discount rates calculated over 11 through 25 years. These results indicate that duration may not be that important when using averages of historical net discount rates to calculate discount rates.

The second procedure tests the impacts of duration by disaggregating the moving averages. Results of this second procedure show that in about 80 percent of sample years, net discount rates calculated over approximately 14 years to 18 years encompass net discount rates calculated over durations ranging between 10 years and 25 years. This range is quite broad and observations tend to cluster at one end or the other. A narrower range finds durations that encompass results using between10-year and 25-year durations only about 45 percent of the time.

One can speculate on why there does not seem to be a more tightly packed range of encompassing durations. A number of papers have shown a trend break in net discount rates sometime in the late 1970s to early 1980s. Examination of the data show high net discount rates in the late 1980s as well. Both of these observations are indicative of some lack of stability in net discount rates. Another explanation may be non-stationarity of the net discount rate process. Some literature suggests non-stationarity, but those results are not conclusive. All in all, results from this analysis are less than definitive, setting the stage for further research in this area.