Tests for the validity of portfolio or group choice in financial and panel regressions

In the capital asset pricing model (CAPM), estimating beta consistently is important to obtain a consistent estimate of the price of risk. However, it is often found that the estimate of beta is sensitive to the choice of portfolios used in the estimation. This paper provides a new test to evaluate whether the choice of portfolios in typical asset price regressions is valid, in the sense that the portfolios satisfy two conditions: (i) the way the portfolios are formed are exogenous; and (ii) the choice of the group of assets to include in the portfolios provides enough information to identify the parameters of interest. Thus, checking the validity of the portfolio choice is an important pre-requisite to ensure consistent estimates of the parameters of the model. We illustrate the performance of the test in small samples via Monte Carlo simulations. The proposed test is also applicable to group and pseudo panel data models.