Matthew J. Cushing

The indeterminacy of prices under interest rate pegging: The non-Ricardian case

Abstract This paper investigates the issue of price level indeterminacy under a pure interest rate peg in models that depart from standard Ricardian assumptions. Using a monetary version of Blanchards finite horizons model, I find wealth effects operating on government bonds are not sufficient to determine a unique price level. Next, I consider price determination under a non-Ricardian fiscal authority. I show that, if agents rationally perceive the possibility of fiscal default, the price level is again indeterminate. I conclude that departures from Ricardian equivalence are not sufficient to ensure a unique price level under a monetary policy of pure interest rate pegging.

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-

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

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

The Persistence of Shocks to Macroeconomic Time Series: Some Evidence From Economic Theory

This paper presents new estimates of persistence of shocks to quarterly labor income, monthly Treasury bill yields, and annual real common stock dividends. The authors replace orthogonality conditions involving near unit root instruments with restrictions on innovation variances implied by a generalized version of the permanent income hypothesis, a term structure model, and constant discount rate efficient markets model. Conditional on these theories, they obtain precise estimates of persistence without imposing arbitrary restrictions on the magnitude of the largest root. Shocks are more persistent than indicated by unrestricted trend stationary models but less persistent than implied by unit root models.

The Efficiency of Race- and Gender-Targeted Income Transfers

In this article, the authors quantify the potential efficiency gains from moving toward an income redistribution system that bases transfers on membership in demographic groups such as race and gender. They compute four measures of the marginal efficiency cost (MEC) of redistribution under a standard linear income tax and under a policy that tags specific demographic groups. The authors find that a tagging system can significantly lower the MEC of redistribution. At the margin, a system of tagging demographic groups achieves the goal of greater income equality at a significantly lower cost in terms of lost output.

Filtering as a Test of Specification

This paper generalizes the first differencing test proposed by C. I. Plosser, G. W. Schwert, and H. White to the case of finite one-sided polynomial filters. The authors demonstrate that the filtering test is asymptotically equivalent to a Hausman-Wu test. This provides a computationally simple way of performing the test and analyzing the tests power. The authors show that the choice of lag weights is nontrivial for filters of order greater than one. By examining the optimal choice of filter, the paper shows under what circumstances filtering tests will be powerful. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.