An Application of the Bootstrap Method to the Analysis of Squared, Standardized Market Model Prediction Errors/Discussion

A study is undertaken to examine significance tests on squared, standardized market model prediction errors as performed in some information content studies. In considering the effect of departures from normality on the distribution theory for standardized market model prediction errors, it is demonstrated that for large estimation samples and leptokurtic disturbances, the normal theory formula for the variance of squared prediction errors underestimates the true variances. A simulation experiment is then performed that proves the empirical relevance of the bias in the normal formula theory for sample sizes and degrees of leptokurtosis that occur in market-based research. The nonparametric bootstrap method of Efron (1979) appears well-suited to this problem. Analysis reveals that, while the bootstrap standard errors perform poorly in this role, ''bootstrap p values'' solve the problem of biased inferences. Patell's (1976) earnings forecast data are used to demonstrate the approach. Discussion centers on the relative advantages of the bootstrap approach, its application, and alternative approaches.