This paper considers the estimation of dynamic binary choice panel data models with fixed effects. It is shown that the modified maximum likelihood estimator (MMLE) used in this paper reduces the order of the bias in the maximum likelihood estimator from OðT À1 Þ to OðT À2 Þ, without increasing the asymptotic variance. No orthogonal reparametrization is needed. Monte Carlo simulations are used to evaluate its performance in finite samples where T is not large. In probit and logit models containing lags of the endogenous variable and exogenous variables, the estimator is found to have a small bias in a panel with eight periods. A distinctive advantage of the MMLE is its general applicability. Estimation and relevance of different policy parameters of interest in this kind of models are also addressed. r
In this paper, I consider the estimation of dynamic binary choice panel data models with fixed effects. I use a Modified Maximum Likelihood Estimator (MMLE) that reduces the order of the bias in the Maximum Likelihood Estimator from O(T-1) to O(T-2), without increasing the asymptotic variance. I evaluate its performance in finite samples where T is not large, using Monte Carlo simulations. In Probit and Logit models containing lags of the endogenous variable and exogenous variables, the estimator is found to have a small bias in a panel with eight periods. A distinctive advantage of the MMLE is its general applicability. Identification issues about policy parameters of interest that arise in this kind of models are also addressed. In contrast with linear models, parameters of interest typically depend on the distribution of the individual effects. I discuss the relevance of mean effects across individuals and show an instance in which the entire distribution is needed. Compared with simple MLE, simulation results show that MMLE improves significantly the estimation of the distribution of the effect of interest.
We consider dynamic discrete choice models with heterogeneity in both the levels parameter and the state dependence parameter. We first present an empirical analysis that motivates the theoretical analysis which follows. The theoretical analysis considers a simple two-state, first-order Markov chain model without covariates in which both transition probabilities are heterogeneous. Using such a model we are able to derive exact small sample results for bias and mean squared error (MSE). We discuss the maximum likelihood approach and derive two novel estimators. The first is a bias corrected version of the Maximum Likelihood Estimator (MLE) although the second, which we term MIMSE, minimizes the integrated mean square error. The MIMSE estimator is always well defined, has a closed-form expression and inherits the desirable large sample properties of the MLE. Our main finding is that in almost all short panel contexts the MIMSE significantly outperforms the other two estimators in terms of MSE. A final section extends the MIMSE estimator to allow for exogenous covariates. Copyright (C) The Author(s). Journal compilation (C) Royal Economic Society 2010.
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