When estimating finance panel regressions, it is common practice to adjust standard errors for correlation either across firms or across time. These procedures are valid only if the residuals are correlated either across time or across firms, but not across both. This paper shows that it is very easy to calculate standard errors that are robust to simultaneous correlation along two dimensions, such as firms and time. The covariance estimator is equal to the estimator that clusters by firm, plus the estimator that clusters by time, minus the usual heteroskedasticity-robust ordinary least squares (OLS) covariance matrix. Any statistical package with a clustering command can be used to easily calculate these standard errors.

Goyal and Welch (2007) argue that the historical average excess stock return forecasts future excess stock returns better than regressions of excess returns on predictor variables. In this article, we show that many predictive regressions beat the historical average return, once weak restrictions are imposed on the signs of coefficients and return forecasts. The out-of-sample explanatory power is small, but nonetheless is economically meaningful for mean-variance investors. Even better results can be obtained by imposing the restrictions of steady-state valuation models, thereby removing the need to estimate the average from a short sample of volatile stock returns.

[Goyal and Welch (2007) argue that the historical average excess stock return forecasts future excess stock returns better than regressions of excess returns on predictor variables. In this article, we show that many predictive regressions beat the historical average return, once weak restrictions are imposed on the signs of coefficients and return forecasts. The out-of-sample explanatory power is small, but nonetheless is economically meaningful for mean-variance investors. Even better results can be obtained by imposing the restrictions of steady-state valuation models, thereby removing the need to estimate the average from a short sample of volatile stock returns.]