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.

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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.

SUMMARYThis paper estimates a dynamic ordered probit model of self-assessed health with two fixed effects: one in the linear index equation and one in the cut-points. This robustly controls for heterogeneity in unobserved health status and in reporting behavior, although we cannot separate both sources of heterogeneity. We find important state dependence effects, and small but significant effects of income and other socioeconomic variables. Having dynamics and flexibly accounting for unobserved heterogeneity matters for those estimates. We also contribute to the bias correction literature in nonlinear panel models by comparing and applying two of the existing proposals to our model.

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.

SUMMARYWe propose a simple dynamic stochastic model of sterilization and contraceptive use and we estimate its structural parameters using a sample of married couples from the 1995 Spanish Family and Fertility Survey. The estimated structural model improves on previous studies in terms of its ability to rationalize observed behaviour. Allowing for simple forms of permanent unobserved heterogeneity across couples in their ability to conceive has important implications for estimates of utility and cost parameters. Estimates of child valuation parameters imply that most Spanish couples would have two children, but significant deviations from this goal are brought about by imperfect and costly fertility control. We perform simulations to quantify the impact on fertility of the availability of sterilization and other technologies which improve fertility control.