Information Criterion and Estimation of Misspecified Qualitative Choice Models

This paper investigates misspecified estimation and model selection criteria derived from the 'Information Criterion (see Akaike (1973))' for qualitative choice models. Four estimators for the 'Information Criterion' are derived for general qualitative choice models. Two of these estimators were previously derived by Akaike (1973) and Chow (1981) for arbitrary likelihood functions. The new estimators are derived by taking analytic expectations of the log likelihood function. A number of Monte Carlo experiments are performed using binominal logit models to investigate the behavior of the Information Criterion estimators with realistic sample sizes. The new analytic estimators are more accurate than the more general estimators , but they do not always perform as well in minimizing prediction or estimation error. Monte Carlo results also show that the usual asymptotic distribution properties of the maximum likelihood estimator are poor approximations for sample sizes as large as 1,000 observations with only two variables.