A Comparison of Alternative Estimators for Binary Panel Probit Models* Mark N. Harris Melbourne Institute of Applied Economic and Social Research The University of Melbourne
Lachlan R. Macquarie and Anthony J. Siouclis Department of Econometrics and Business Statistics Monash University
Melbourne Institute Working Paper No. 3/00 ISSN 1328-4991 ISBN 0 7340 1483 X February 2000
* We are extremely grateful to Tim Fry, Ritchard Longmire and Rosi Doran for helpful guidance and suggestions. We are also greatly indebted to Sid Chib for making the Gibbs sampler Gauss code available to us. All remaining errors are our own. Abstract: Recent advances in computing power have brought the use of computer intensive estimation methods of binary panel data models within the reach of the applied researcher. The aim of this paper is to apply some of these techniques to a marketing data set and compare the results. In addition, their small sample performance is examined via Monte Carlo simulation experiments. The first estimation technique used was maximum likelihood estimation of the cross section probit (ignoring heterogeneity). The remaining techniques estimated the binary panel probit model using: standard maximum likelihood; the Solomon-Cox approximation to this likelihood; and finally, the Gibbs sampler to obtain Bayesian estimates. The results suggested that, in most cases, standard maximum likelihood estimation of the binary panel probit model was the preferred technique primarily because it is readily available to applied practitioners. Although when the variance of the heterogeneity term is small, the computational simplicity of the Solomon-Cox approximation may prove attractive. When the sample size was increased, the Gibbs sampler was also found to perform well.
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