Nonparametric Testing for Anomaly Effects in Empirical Asset Pricing Models

In this paper we propose a class of nonparametric tests for anomaly effects in empirical asset pricing models in the framework of nonparametric panel data models with interactive fixed effects. Our approach has two prominent features: one is the adoption of nonparametric functional form to capture the anomaly effects of some asset-specific characteristics, and the other is the flexible treatment of both observed/constructed and unobserved common factors. By estimating the unknown factors, betas, and nonparametric function simultaneously, our setup is robust to misspecification of functional form and common factors and avoids the well-known “error-in-variable” (EIV) problem associated with the commonly used two-pass (TP) procedure. We apply our method to a publicly available data set and divide the full sample into three subsamples. Our empirical results show that size and book-to-market ratio affect the excess returns of portfolios significantly for the full sample and two of the three subsamples in all five factor pricing models under investigation. In particular, nonparametric component is significantly different from zero, meaning that the constructed common factors (e.g., small minus big (SMB) and high minus low (HML)) cannot capture all the size and book-to-market ratio effects. We also find strong evidence of nonlinearity of the anomaly effects in the Fama-French 3-factor model and the augmented 4-factor and 5-factor models in the full sample and two of the three subsamples.