Testing capital asset pricing models using functional-coefficient panel data models with cross-sectional dependence

This paper proposes a functional-coefficient panel data model with cross-sectional dependence motivated by re-examining the empirical performance of conditional capital asset pricing model. In order to characterize the time-varying property of assets’ betas and alpha, our proposed model allows the betas to be unknown functions of some macroeconomic and financial instruments. Moreover, a common factor structure is introduced to characterize cross-sectional dependence which is an attractive feature under a panel data regression setting as different assets or portfolios may be affected by same unobserved shocks. Compared to the existing studies, such as the classic Fama–MacBeth two-step procedure, our model can achieve substantial efficiency gains for inference by adopting a one-step procedure using the entire sample rather than a single cross-sectional regression at each time point. We propose a local linear common correlated effects estimator for estimating time-varying betas by pooling the data. The consistency and asymptotic normality of the proposed estimators are established. Another methodological and empirical challenge in asset pricing is how to test the constancy of conditional betas and the significance of pricing errors, we echo this challenge by constructing an L2-norm statistic for functional-coefficient panel data models allowing for cross-sectional dependence. We show that the new test statistic has a limiting standard normal distribution under the null hypothesis. Finally, the method is applied to test the model in Fama and French (1993) using Fama–French 25 and 100 portfolios, sorted by size and book-to-market ratio, respectively, dated from July 1963 to July 2018.