Historical Averages, Units Roots and Future Net Discount Rates: A Comprehensive Estimator

The forensic economics literature hosts a continuing debate about the appropriateness of using historical verses current rates to predict future net discount rates. If the net discount rate series is stationary, which means that shocks are transitory and the series reverts to a long-term mean value, estimates based on historical values are reasonable. Alternatively, if the series exhibits a unit root, then past observations have questionable predictive value and the best predictor of the next period’s discount rate depends mainly on the current net discount rate. Several analyses have been performed to examine the stationarity of net discount rates, and the literature is mixed in its conclusions. Whether the series is found to be stationary depends on the period and measures observed, as well as the type of statistical tests performed. The inherent uncertainty over the existence of a unit root does not help the practitioner choose between the long-term average and the current net discount rate as an appropriate estimator. We derive an alternative estimator of future net discount rates based on the statistical properties of the underlying series. The estimator depends on both the length of the forecast horizon and the rate at which a time series converges to its equilibrium level in response to a shock (or its degree of persistence). For long forecast horizons, the estimator tends to resemble the longterm average. For short forecast horizons, the estimator more nearly resembles the current value. Similarly, if the degree of persistence is large (it converges slowly), the estimator tends to resemble the current rate whereas if persistence is low (it converges quickly), the estimator more nearly resembles the longterm average. In an important special case, where the net discount rate follows a first-order autoregressive process, the optimal estimator is a weighted average of the current net discount rate and the long-term mean of the net discount rate process. The use of a data-based, weighted average optimal estimator has certain advantages. From a theoretical standpoint, the optimal estimator is more efficient than either the long-term average or the current net discount rate. Benchmark estimates suggest that the forecast error variance using the optimal estimator is less than half that of the long-term average or current net dis-