This paper proposes a new nested algorithm (NPL) for the estimation of a class of discrete Markov decision models and studies its statistical and computational properties. Our method is based on a representation of the solution of the dynamic programming problem in the space of conditional choice probabilities. When the NPL algorithm is initialized with consistent nonparametric estimates of conditional choice probabilities, successive iterations return a sequence of estimators of the structural parameters which we call K-stage policy iteration estimators. We show that the sequence includes as extreme cases a Hotz-Miller estimator (for K = 1) and Rust's nested fixed point estimator (in the limit when K → ). Furthermore, the asymptotic distribution of all the estimators in the sequence is the same and equal to that of the maximum likelihood estimator. We illustrate the performance of our method with several examples based on Rust's bus replacement model. Monte Carlo experiments reveal a trade-off between finite sample precision and computational cost in the sequence of policy iteration estimators.

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This paper studies the estimation of dynamic discrete games of incomplete information. Two main econometric issues appear in the estimation of these models: the indeterminacy problem associated with the existence of multiple equilibria and the computational burden in the solution of the game. We propose a class of pseudo maximum likelihood (PML) estimators that deals with these problems, and we study the asymptotic and finite sample properties of several estimators in this class. We first focus on two-step PML estimators, which, although they are attractive for their computational simplicity, have some important limitations: they are seriously biased in small samples; they require consistent nonparametric estimators of players' choice probabilities in the first step, which are not always available; and they are asymptotically inefficient. Second, we show that a recursive extension of the two-step PML, which we call nested pseudo likelihood (NPL), addresses those drawbacks at a relatively small additional computational cost. The NPL estimator is particularly useful in applications where consistent nonparametric estimates of choice probabilities either are not available or are very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Monte Carlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries. Copyright The Econometric Society 2007.

Internet: www.cemfi.es We would like to thank Olympia Bover and Agar Brugiavini for insightful discussions and Manuel Arellano and Stephane Bonhomme for useful conversations. This work also benefited from the comments of seminar participants at AbstractWe study the prevalence of informal caregiving to elderly parents by their mature daughters in Europe and the effect of intense (daily) caregiving and parental health on the employment status of the daughters. We group the data from the first two waves of SHARE into three country pools (North, Central and South) which strongly differ in the availability of public formal care services and female labour market attachment. We use a time allocation model to provide a link to an empirical IV-treatment effects framework and to interpret parameters of interest and differences in results across country pools and subgroups of daughters. We estimate the average effect of parental disability on employment and daily care-giving choices of daughters and the ratio of these effects which is a Local Average Treatment effect of daily care on labour supply under exclusion restrictions. We find that there is a clear and robust North-South gradient in the (positive) effect of parental ill-health on the probability of daily care-giving. The aggregate loss of employment that can be attributed to daily informal caregiving seems negligible in northern and central European countries but not in southern countries. Large and significant impacts are found for particular combinations of daughter characteristics and parental disability conditions. The effects linked to longitudinal variation in the health of parents are stronger than those linked to cross-sectional variation.

This paper reviews methods for the estimation of dynamic discrete choice structural models and discusses related econometric issues. We consider single agent models, competitive equilibrium models and dynamic games. The methods are illustrated with descriptions of empirical studies which have applied these techniques to problems in different areas of economics. Programming codes for the estimation methods are available in a companion web page.