This paper proposes a new family of specification tests and applies them to affine term structure models of the London Interbank Offered Rate (LIBOR)-swap curve. Contrary to Dai and Singleton (2000), the tests show that when standard estimation techniques are used, affine models do a poor job of forecasting volatility at the short end of the term structure. Improving the volatility forecast does not require different models; rather, it requires a different estimation technique. The paper distinguishes between two econometric procedures for identifying volatility. The 'cross-sectional' approach backs out volatility from a cross section of bond yields, and the 'time-series' approach imputes volatility from time-series variation in yields. For an affine model, the volatility implied by the time-series procedure passes the specification tests, while the cross-sectionally identified volatility does not. This is surprising, since under correct specification, the 'cross-sectional' approach is maximum likelihood. One explanation is that affine models are slightly misspecified; another is that bond yields do not span volatility, as in Collin-Dufresne and Goldstein (2002). , Oxford University Press.

[This paper proposes a new family of specification tests and applies them to affine term structure models of the London Interbank Offered Rate (LIBOR)-swap curve. Contrary to Dai and Singleton (2000), the tests show that when standard estimation techniques are used, affine models do a poor job of forecasting volatility at the short end of the term structure. Improving the volatility forecast does not require different models; rather, it requires a different estimation technique. The paper distinguishes between two econometric procedures for identifying volatility. The "cross-sectional" approach backs out volatility from a cross section of bond yields, and the "time-series" approach imputes volatility from time-series variation in yields. For an affine model, the volatility implied by the time-series procedure passes the specification tests, while the cross-sectionally identified volatility does not. This is surprising, since under correct specification, the "cross-sectional" approach is maximum likelihood. One explanation is that affine models are slightly misspecified; another is that bond yields do not span volatility, as in Collin-Dufresne and Goldstein (2002).]

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.]