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Working Paper
Approximately normal tests for equal predictive accuracy in nested models
Forecast evaluation often compares a parsimonious null model to a larger model that nests the null model. Under the null that the parsimonious model generates the data, the larger model introduces noise into its forecasts by estimating parameters whose population values are zero. We observe that the mean squared prediction error (MSPE) from the parsimonious model is therefore expected to be smaller than that of the larger model. We describe how to adjust MSPEs to account for this noise. We propose applying standard methods (West (1996)) to test whether the adjusted mean squared error ...
Working Paper
Some Evidence on Secular Drivers of US Safe Real Rates
We study long-run correlations between safe real interest rates in the United States and over 20 variables that have been hypothesized to influence real rates. The list of variables is motivated by the familiar intertermporal IS equation, by models of aggregate savings and investment, and by reduced form studies. We use annual data, mostly from 1890 to 2016. We find that safe real interest rates are correlated as expected with demographic measures. For example, the long-run correlation with labor force hours growth is positive, which is consistent with overlapping generations models. For ...
Conference Paper
Exchange rates and fundamentals
Standard economic models hold that exchange rates are influenced by fundamental variables such as relative money supplies, outputs, inflation rates and interest rates. Nonetheless, it has been well documented that such variables little help predict changes in floating exchange rates ? that is, exchange rates follow a random walk. We show that the data do exhibit a related link suggested by standard models - that the exchange rate helps predict fundamentals. We also show analytically that in a rational expectations present value model, an asset price manifests near random walk behavior if ...
Working Paper
Using out-of-sample mean squared prediction errors to test the Martingale difference hypothesis
We consider using out of sample mean squared prediction errors (MSPEs) to evaluate the null that a given series follows a zero mean martingale difference against the alternative that it is linearly predictable. Under the null of zero predictability, the population MSPE of the null ?no change? model equals that of the linear alternative. We show analytically and via simulations that despite this equality, the alternative model?s sample MSPE is expected to be greater than the null?s. We propose and evaluate an asymptotically normal test that properly accounts for the upward shift of the sample ...
Working Paper
Random Walk Forecasts of Stationary Processes Have Low Bias
We study the use of a zero mean first difference model to forecast the level of a scalar time series that is stationary in levels. Let bias be the average value of a series of forecast errors. Then the bias of forecasts from a misspecified ARMA model for the first difference of the series will tend to be smaller in magnitude than the bias of forecasts from a correctly specified model for the level of the series. Formally, let P be the number of forecasts. Then the bias from the first difference model has expectation zero and a variance that is O(1/P-squared), while the variance of the bias ...
Conference Paper
Model uncertainty and policy evaluation: some theory and empirics
This paper explores ways to integrate model uncertainty into policy evaluation. We first describe a general framework for the incorporation of model uncertainty into standard econometric calculations. This framework employs Bayesian model averaging methods that have begun to appear in a range of economic studies. Second, we illustrate these general ideas in the context of assessment of simple monetary policy rules for some standard New Keynesian specifications. The specifications vary in their treatment of expectations as well as in the dynamics of output and inflation. We conclude that the ...
Working Paper
A utility based comparison of some models of exchange rate volatility
When estimates of variances are used to make asset allocation decisions, underestimates of population variances lead to lower expected utility than equivalent overestimates: a utility based criterion is asymmetric, unlike standard criteria such as mean squared error. To illustrate how to estimate a utility based criterion, we use five bilateral weekly dollar exchange rates, 1973-1989, and the corresponding pair of Eurodeposit rates. Of homoskedastic, GARCH, autoregressive and nonparametric models for the conditional variance of each exchange rate, GARCH models tend to produce the highest ...