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.
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.
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, though 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 feasible for some models and data; 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 are either not available or very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Montecarlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries.
This paper is concerned with the interaction between price and inventory decisions in retailing firms and its implications for the dynamics of markups and the existence of sales promotions. We consider a model where a monopolistically competitive retailer decides price and inventories, and assumes lump-sum costs when placing orders or changing nominal prices. In this model, the existence of stockout probabilities ;Ind fixed ordering costs generate a cyclical price behaviour characterized by long periods without nominal price changes and short periods with very low prices (i.e. sales promotions). We estimate this model using a unique longitudinal dataset with information about retail and wholesale prices, inventories, orders, and sales for several brands in a supermarket chain. Based on the estimated model we perform several counterfactual experiments that show the important role that inventories and fixed ordering costs play in the dynamics of retail prices and the frequency of sales promotions in this dataset.5. The slope of m(s) depends on the sensitivity of the price elasticity of sales with respect to the stockout probability.
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.
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