THE EFFECT OF MODEL MISSPECIFICATION ON TESTS OF THE EFFICIENT MARKET HYPOTHESIS

Abstract

TESTS OF THE Efficient Market Hypothesis (EMH) are in general weak tests. The null hypothesis has always been that the market is efficient with no specific alternative of inefficiency. Thus, the power of these tests is not known. The tests usually rely on a certain market model without questioning the validity of the model that was used. A misspecified model may provide test statistics that indicate that the market is efficient when it is not efficient and vice versa. The possibility that the EMH has not been rejected because the wrong market model was used, was never adequately considered. This paper is concerned with the theoretical effect of model misspecification on tests of the efficient market hypothesis. Since tests of the EMH usually use a certain market model, the conclusions are based on the assumption that the model is correctly specified. By deriving the possible biases due to model misspecification, we are actually concerned with the power (or validity) of the EMH tests. Tests of the EMH generally proceed in two stages: First, we estimate the relevant parameters using a certain market model; second, we use the estimated parameters for prediction and use the prediction errors, also called residuals,' to test market efficiency. The statistical properties of the parameters, estimated in the first stage, depend on how well the market model describes the true underlying stochastic process. Serious misspecifications may yield biased and/or inefficient parameter estimates. This in turn may result in biased and/or inefficient estimates of the residuals in the second stage. The extent to which these misspecifications affect our conclusion about market efficiency depends on the way we use these residuals in testing the EMH. Under certain circumstances (to be specified later) the misspecifications, no matter how serious, will not affect our conclusions with regard to market efficiency. In the remainder of this paper we first consider general cases of misspecification, their effect on parameter estimates and on residual estimates. Then we consider the effects of misspecification in some specific cases. Finally we present the effect of ,B changes on residual estimates.