An Investigation of the Accuracy of the Clark Approximation for the Multinomial Probit Model

The Clark approximation, in which the maximum of two normally distributed random variables is approximated by a third normally distributed random variable, forms the basis of a relatively inexpensive technique for evaluating the choice probabilities of multinomial probit models. This paper reports the results of a series of numerical experiments in which the accuracy of probit computations based on the Clark approximation was investigated. In contrast to previous investigations, these experiments dealt with the accuracy of the results obtained when the Clark approximation is used for econometric estimation of the values of probit models' parameters and for prediction of choice probabilities using the estimated parameter values. It was found that the accuracy of the results obtained with the Clark approximation varies greatly from model to model. In many of the experiments the approximation performed quite satisfactorily, but in others it produced errors that probably would be causes for concern in practical work. It is difficult or impossible to judge the accuracy of results obtained using the Clark approximation without knowledge of the results that would be obtained using a computational technique that is known to be accurate. Consequently, in practical empirical work it often will not be possible to obtain reliable indicators of the Clark approximation's accuracy. However, it is likely that the errors resulting from use of the Clark approximation to estimate a probit model are small compared to the errors that would result from using the simpler logit model in a situation where the correct model specification is probit