Most econometric schemes to allow for heterogeneity in micro behaviour have two drawbacks: they do not …t the data and they rule out interesting economic models. In this paper we consider the time homogeneous …rst order For comments and useful suggestions, we thank three referees, Enrique Sentana, Whitney Newey, Ivan Fernandez-Val, Sara Ayo, and participants at seminars at Boston University; MIT/Harvard; Yale University; Nu¢eld (Oxford); IFS (London); CEMFI; Manchester; Columbia, CAM (Copenhagen) and a conference at the Tinbergen Institute. The second author gratefully acknowledges that this research was supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme, by grants ECO2012-31358, ECO2009-11165 and SEJ2006-05710 from the Spanish Minister of Education, MCINN (Consolider-Ingenio2010), Consejería de Educación de la Comunidad de Madrid (Excelecon project); he also thanks the Department of Economics at the MIT at which he conducted part of this research as visiting scholar.y The …rst draft was titled "Identi…cation of the dynamic discrete choice model" and was presented at the CAM Summer Workshop (University of Copenhagen) in July 2007.Markov (HFOM) model that allows for maximal heterogeneity. That is, the modelling of the heterogeneity does not impose anything on the data (except the HFOM assumption for each agent) and it allows for any theory model (that gives a HFOM process for an individual observable variable). 'Maximal' means that the joint distribution of initial values and the transition probabilities is unrestricted.We establish necessary and su¢cient conditions for generic local point identi…cation of our heterogeneity structure that are very easy to check, and we show how it depends on the length of the panel.We apply our techniques to a long panel of Danish workers who are very homogeneous in terms of observables. We show that individual unemployment dynamics are very heterogeneous, even for such a homogeneous group. We also show that the impact of cyclical variables on individual unemployment probabilities di¤ers widely across workers. Some workers have unemployment dynamics that are independent of the cycle whereas others are highly sensitive to macro shocks.