Financial Variables and the Simulated Out‐of‐Sample Forecastability of U.S. Output Growth Since 1985: An Encompassing Approach

We reconsider the out-of-sample forecasting ability of a large number of financial variables with respect to real output growth over the 1985:1 1999:4 period. We show that models including financial variables display almost no forecasting ability relative to an autoregressive benchmark model over this period according to a mean squared forecast error metric. However, tests based on forecast encompassing indicate that many financial variables do, in fact, contain information that is useful for forecasting real output growth over the 1985:1-1999:4 out-of-sample period. Our results suggest that the extant literature exaggerates the demise of the forecasting power of financial variables with respect to real activity since the mid-1980s. (JEL C22, C53, E44, E32) I. INTRODUCTION It is widely documented that the ability of financial variables to forecast real output growth has broken down---especially since the mid-1980s--according to a mean squared forecast error (MSFE) criterion; see, for example, the recent study of Stock and Watson (2003). In this article, we use the concept of forecast encompassing to reexamine the out-of-sample forecasting ability of a large number of financial variables with respect to U.S. real output growth over the 1985:1-1999:4 period. By focusing on forecast encompassing, the present work complements Stock and Watson (2003), Thoma and Gray (1998), and other recent studies that rely primarily on a relative MSFE criterion to analyze the out-of-sample forecasting ability of financial variables. Forecast encompassing is closely related to the construction of optimal composite forecasts. (1) Consider two sets of out-of-sample forecasts of real output growth, one from an autoregressive distributed lag (ARDL) model that includes a financial variable and one from a simple autoregressive (AR) benchmark model, and consider forming an optimal composite forecast as a convex combination of the forecasts from the two models. If the optimal weight attached to the forecast from the ARDL model is zero, then the ARDL model does not contain information that is useful in the formation of the optimal composite forecast apart from the information already contained in the AR benchmark model. In this case, the AR model forecasts encompass the ARDL model forecasts. However, if the optimal weight attached to the ARDL model forecast is greater than zero, then the ARDL model does contain information useful for forecasting real output growth apart from that already contained in the AR benchmark model. Harvey et al. (1998) develop a test statistic for the null hypothesis that the optimal weight attached to one out-of-sample forecast is zero against the alternative hypothesis that the optimal weight is greater than zero. Clark and McCracken (2001) develop a variant of the Harvey et al. (1998) statistic that accounts for the parameter uncertainty inherent in the formation of forecasts and that Monte Carlo simulations show to be considerably more powerful in detecting forecasting ability than the original statistic. In our applications, we reconsider the forecasting power of 10 of the financial variables used in Stock and Watson (2003) with respect to U.S. real gross domestic product (GDP) and industrial production growth over the 1985: 1-1999:4 out-of-sample period. These are 10 of the most popular financial variables in the extant literature: M0, M1, M2, M3, federal funds rate, 3-month Treasury bill rate, term spread, default spread, real stock prices, and dividend yield. For each financial variable, we construct recursive out-of-sample forecasts of real output growth over the 1985:1-1999:4 period based on an ARDL model that includes a given financial variable as an explanatory variable. Following Stock and Watson (2003), we consider forecasts of both real GDP and industrial production growth. We use the Harvey and colleagues (1998) and Clark and McCracken (2001) statistics to test the null hypothesis that the out-of-sample forecasts of real output growth from an AR benchmark model encompass the forecasts from the ARDL model that includes a given financial variable. …