How Much Confidence Do We Have in Estimates of Future Net Discount Rates?

Abstract

A recent survey by Brookshire, et. al., (2006) suggests that forensic economists are mixed in their use of current versus historical data to estimate future net discount rates.1 Typically the choice is between a long-term average or simply the current prevailing rate.2 Cushing and Rosenbaum (2006) proposed an estimator that optimally uses the information in the past behavior of net discount rates to forecast future rates. Their optimal estimator is a weighted average of the current and long-term mean net discount rates with weights that depend on the degree of persistence in the net discount rate process and on the horizon over which one wishes to forecast future rates. Noting the practical impediments to calculating such an estimator, they proposed an alternate compromise estimator that equally weights the current net discount rate with a long-term average net discount rate. In this paper we extend that analysis by developing confidence intervals for the current, long-term average, optimal and compromise estimators. In particular, we develop both analytic and bootstrap estimates of 50% confidence intervals for all four estimators. The 50% boundary demarcates values that are more likely than not to occur. This serves two purposes. One is to shed light on error rates as is called for in Daubert (1993). The other is to help establish a reasonable degree of economic certainty in our net discount rate predictions. Results show that the boundaries vary by estimator and by forecast horizon. However, in almost all cases, the boundaries are within two percentage points of the point estimates. These boundaries generally narrow as the horizon increases. For the optimal and compromise estimators, the boundaries approach the point estimate plus or minus about one percentage point for a 20year horizon and beyond. Additional results show that the boundaries have remained quite stable over time, regardless of the estimator. Combining these results with earlier findings, the best range of predictions for the future net