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 earnings-to-price ratio and book-to-market ratio as well as size help explain cross sectional returns. These anomalies that have been attributed to market inefficiency could be the result of a misspecification 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. However, it is well-established that the TP method suffers from the errors in variables problem, because estimated betas are used 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. Perhaps one of the main reasons for the neglect of benefits of using panel data technique is that in factor pricing models, all betas are heterogeneous in the first pass time series regression. However, if our interest lies solely in testing the significance of the firm's characteristics in factor pricing models, 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 book to market equity and market value in helping explain asset returns in the UK over 1968-2002 even in the three factor models.