PDF Ebook Efficient Tests of Stock Return Predictability
Tests of the predictability of stock returns may be invalid when the predictor variable is persistent and its innovations are highly correlated with returns. This paper develops a pretest to determine whether the conventional test leads to incorrect inference and an efficient test of predictability that always leads to correct inference. Although the conventional t-test is highly misleading for the dividend-price and the smoothed earnings-price ratios, we find evidence for predictability using our test. We also find evidence for predictability with the short rate and the long-short yield spread, for which the conventional t-test leads to correct inference.
Numerous studies in the last two decades have asked whether stock returns can be predicted by financial variables such as the dividend-price ratio, the earnings-price ratio, and various measures of the interest rate. 1 The econometric method used in a typical study is an OLS regression of stock returns onto the lag of the financial variable. The main finding of such regressions is that the t-statistic is typically greater than two and sometimes greater than three. Using conventional critical values for the t-test, one would conclude that there is strong evidence for the predictability of returns.
This statistical inference of course relies on first-order asymptotic distribution theory, which implies that the t-statistic is approximately standard normal in large samples. However, both simulation and analytical studies have shown that the large-sample theory provides a poor approximation to the actual finite-sample distribution of test statistics when the predictor variable is persistent and its innovations are highly correlated with returns (see Mankiw and Shapiro (1986), Elliott and Stock (1994), and Stambaugh (1999).
To be concrete, suppose the log dividend-price ratio is used to predict returns. Even if we were to know on prior grounds that the dividend-price ratio is stationary, a time series plot (or more formally a unit root test) shows that it is highly persistent, much like a nonstationary process. Since first-order asymptotics fails when the regressor is nonstationary, it provides a poor approximation in finite samples when the regressor is persistent. Elliott and Stock (1994, Table 1) provide Monte Carlo evidence which suggests that the size distortion of the one-sided t-test is approximately 20 percentage points for plausible parameter values and sample size in the dividend-price ratio regression. 2 They propose an alternative asymptotic framework in which the regressor is modeled as having a local-to-unit root, which provides an accurate approximation to the finite-sample distribution.
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PDF Ebook Efficient Tests of Stock Return Predictability
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