Two-Pass Cross-Sectional Regression of Factor Pricing Models: Minimum Distance Approach

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Abstract
The two-pass cross-sectional regression method has been widely used to evaluate linear factor pricing models. One drawback of the studies based on this method is that statistical inferences are often made ignoring potential conditional heteroskedasticity or/and autocorrelation in asset returns and factors. Based on an econometric framework called minimum distance (MD), this paper derives the asymptotic variance matrices of two-pass estimator under general assumptions. The MD method we consider is as simple as the traditional two-pass method. However, it has several desirable properties. First, we find an MD estimator whose asymptotic distribution is robust to conditional heteroskedasticity or/and autocorrelation in asset returns. Despite this robustness, the MD estimator has smaller asymptotic standard errors than other two-pass estimators popularly used in the literature. Second, we obtain a simple chi-statistic for model misspecification test, which has a simple form similar to the usual generalized method of moments tests. We also discuss the link between the MD method and the other methods such as generalized least squares and maximum likelihood. A limited empirical exercise is conducted to demonstrate the empirical relevance of the MD method.

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