A Panel Data Approach to testing Anomaly Effects in Factor Pricing Models

There has been a large anomaly literature where firm specific characteristics such as leverage, past returns, dividend-yield, earnings-to-price ratios and book-to-market ratios as well as size help explain cross sectional returns. These anomalies that have been attributed to market inefficiency could be the result of a mis-specification of the underlying factor pricing model. The most popular approach to detecting these anomaly effects has been the two pass (TP) cross-sectional regression models, advanced by Black, Jensen and Scholes (1972) and Fama and MacBeth (1973). However, it is well-established that the TP method suffers from the errors in variables problem, because estimated betas are used in place of true betas in the second stage cross sectional regression. In this paper we address the issue of testing for factor price misspecification via the panel data approach. It is a salient fact that conventional approaches have completely ignored the benefits of using panel data techniques. Perhaps one of the main reasons for this neglect is that in factor pricing models, all betas are heterogeneous in the first pass time series regression. As a result there is no room for exploiting the panel dimension since there are no homogeneous coefficients to estimate. If our interest lies solely in testing the significance of these characteristics, we can show how to construct a theoretically coherent example to which panel data techniques dealing with both homogeneous and heterogeneous parameters can be applied. Panel-based anomaly tests have one clear advantage over TP-based tests; they are based on full information maximum likelihood estimates so that they do not suffer from the errors in variable problem and have all the usual asymptotic properties associated with likelihood tests. The empirical illustration shows the importance of market to book and market value in helping explain asset returns.