A Monte Carlo study of bias corrections for panel probit models

Abstract

We examine bias corrections which have been proposed for the fixed effects panel probit model with exogenous regressors, using several different data generating processes to evaluate the performance of the estimators in different situations. We find a best estimator across all cases for coefficient estimates, but when the marginal effects are the quantity of interest no analytical correction is able to outperform the uncorrected maximum-likelihood estimator.

Keywords:

• bias correction
• panel probit
• marginal effects

AMS Subject Classification:

• C13
• C23

Acknowledgments

We would like to thank an anonymous referee and the associate editor for suggestions which have improved the paper.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1. Chamberlain [9] offers a third approach, a correlated random effects (CRE) model which assumes a parametric form of dependence between the two elements.

2. See [9,10] and discussion in [11].

3. To see this consider the joint likelihood of observations across an individual with all ‘failures’ $y_{it}=0\mathrm{\forall }t$, then by allowing ${\alpha }_i$ to decrease without bound the likelihood of this will converge to 1. Similarly, if $y_{it}=1\mathrm{\forall }t$ then the likelihood of these observations will increase to 1 as ${\alpha }_i\to \mathrm{\infty }$.

4. Also called common parameters in [12] to avoid confusion with other econometric uses of the phrase ‘structural parameters’.

5. This result is found again in [5,6] suggesting an error on Heckman's part.

6. Arellano and Hahn [13] and Arellano and Bonhomme [14] propose solutions for the case where T is large (or at least as large as N) so we do not consider these approaches here as we are interested in the case of large N and small T. Bartolucci and Nigro [15] propose solutions for the logit model. Perera et al. [16] develop saddle point approximation methods for testing serial correlation which could provide an alternative method to developing bias corrections for this situation. Our purpose in this paper is not to develop new bias correction methods, but rather to help the applied researcher evaluate the alternatives in the literature.

7. Unreported experiments found that large outliers occurred when the panel length was shorter, for example, $T=4$, which were then typically amplified by the analytical corrections being considered. This suggests FE estimators should not be used in such situations because of a significant lack of within-individual data.