Heterogeneity in dynamic discrete choice models

We consider dynamic discrete choice models with heterogeneity in both the levels parameter and the state dependence parameter. We …rst analyse the purchase of full fat milk using a long consumer panel (T > 100) on many households. The large T nature of the panel allows us to consistently estimate the parameters of each household separately. This analysis indicates strongly that the levels and Thanks are due to Bo Honoré, Manuel Arellano, Thierry Magnac and to the participants in the CAM workshop on ‘Limited dependent variable models’in July 2004 and a CEMFI seminar for helpful comments and discussion. This work was supported by the EU AGE RTN, HPRN-CT-2002-00235 and by the Danish National Research Foundation through its grant to CAM. the state dependence parameter are heterogeneous and dependently distributed. This empirical analysis motivates the theoretical analysis which considers the estimation of dynamic discrete choice models on short panels, allowing for more heterogeneity than is usually accounted for. The theoretical analysis considers a simple two state, …rst order Markov chain model without covariates in which both transition probabilities are heterogeneous. Using such a model we are able to derive small sample analytical results for bias and mean squared error. We discuss the maximum likelihood approach, a novel bias corrected version of the latter and we also develop a new estimator that minimises the integrated mean square error, which we term MIMSE. The attractions of the latter estimator are that it is very easy to compute, it is always identi…ed and it converges to maximum likelihood as T becomes large so that it inherits all of the desirable large sample properties of MLE. Our main …nding is that in almost all short panel contexts the MIMSE signi…cantly outperforms the other two estimators in terms of mean squared error.