We consider dynamic discrete choice models with heterogeneity in both the levels parameter and the state dependence parameter. We first 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 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, first 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 identified 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 finding is that in almost all short panel contexts the MIMSE significantly outperforms the other two estimators in terms of mean squared error.
