Working Papers 1998 – Abstracts

4/98
A comparison of alternative estimators for binary panel probit models
Mark N. Harris; Lachlan R. Macquarie; Anthony J. Siouclis

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. In large samples, the Gibbs sampler was also found to perform well.

5/98
Modified likelihood and related methods of handling nuisance parameters in the linear regression model
Mizan R. Laskar and Maxwell L. King

In this paper, different approaches to dealing with nuisance parameters in likelihood based inference are presented and illustrated by reference to the linear regression model with nonspherical errors. The estimator of the error variance using each of the approaches is also derived from the linear regression model with spherical errors. We observe that many of these estimators are unbiased. A theoretical comparison of the likelihood functions is reported and we note that some of them are equivalent. Empirical evidence in the literature indicates that estimators based on the conditional profile likelihood and tests based on the marginal likelihood have better small sample properties compared to those based on other likelihood and message length functions.

6/98
Comparisons of estimators and tests based on modified likelihood and message length functions
Mizan R. Laskar and Maxwell L. King

The presence of nuisance parameters causes unexpected complications in econometric inference procedures. A number of modified likelihood and message length functions have been developed for better handling of nuisance parameters but all of them are not equally efficient. In this paper, we empirically compare different modified likelihood and message length functions in the context of estimation and testing of parameters from linear regression disturbances that follow either a first- order moving average or first-order autoregressive error processes. The results show that estimators based on the conditional profile likelihood and tests based on the marginal likelihood are best. If there is a minor identification problem, the sizes of the likelihood ratio and Wald tests based on simple message length functions are best. The true sizes of the Lagrange multiplier tests based on the message length functions are rather poor because the score functions of message length functions are biased.

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