Heterogeneity In Dynamic Discrete Choice Models

We consider dynamic discrete choice model with heterogeneity in both the levels parameter and the state dependence parameter. We first consider a simple two-state, first-order Markov chain model without covariates in which both transition probabilities are heterogeneous in a theoretical analysis. Using such a model we are able to derive exact small sample results for bias and mean squared error. 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. Our main finding is that in almost all short panel contexts the MIMSE significantly outperforms the other two estimators in terms of MSE. Then we extend the MIMSE estimator to allow for exogenous covariates. At last, I use the MIMSE estimator to process a new panel data in order to test the effectiveness of the estimator.