This paper develops a new method for estimating the structural parameters of (discrete choice) dynamic programming problems. The method reduces the computational burden of estimating such models. We show the valuation functions characterizing the expected future utility associated with the choices often can be represented as an easily computed function of the state variables, structural parameters, and the probabilities of choosing alternative actions for states which are feasible in the future. Under certain conditions, nonparametric estimators of these probabilities can be formed from sample information on the relative frequencies of observed choices using observations with the same (or similar) state variables. Substituting the estimators for the true conditional choice probabilities in formulating optimal decision rules, we establish the consistency and asymptotic normality of the resulting structural parameter estimators. To illustrate our new method, we estimate a dynamic model of parental contraceptive choice and fertility using data from the National Fertility Survey. 1. See Eckstein and Wolpin (1989b) for a recent survey of this fast growing field. 497 498 REVIEW OF ECONOMIC STUDIES estimate the structural parameters of such models. Indeed, most of the studies cited above compute the valuation function using backwards recursion, not just once, but every time the parameters are evaluated in the estimation routine. Although several recent advances have been made that reduce these computational burdens (see Miller (1982, 1984), Wolpin (1984), Pakes (1986) and Rust (1987)), backwards recursion solutions remain extremely costly to implement. Such computational burdens have deterred researchers from estimating all but the most parsimonious specifications of structural models and from experimenting with alternative specifications. This limitation is potentially serious in light of findings, such as those of Flinn and Heckman (1982), which indicate that estimates for job search models appear very sensitive to alternative specifications of the model's underlying structure. This paper presents a new estimator for such models, called the Conditional Choice Probability (CCP) estimator. Our approach does not require econometricians to explicitly solve the valuation functions used to characterize optimal decision rules via backwards recursion methods. It is based on a new representation of the valuation function which is expressed in terms of the utility payoffs, choice probabilities, and probability transitions of choices and outcomes that remain feasible in future periods. Under conditions presented below, this representation can be exploited to estimate the model's structural parameters by employing non-parametric estimates of these future choice probabilities and probability transitions in place of their true values. Coupling our representation of valuation functions with the semiparametric estimation procedures we develop in this paper, makes tractable empirical investigations of a wide class of dynamic discrete ...

Moving the Goalposts: Addressing Limited Overlap in Estimation of Average Treatment Effects by Changing the Estimand *Estimation of average treatment effects under unconfoundedness or exogenous treatment assignment is often hampered by lack of overlap in the covariate distributions. This lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification. In such cases researchers have often used informal methods for trimming the sample. In this paper we develop a systematic approach to addressing such lack of overlap. We characterize optimal subsamples for which the average treatment effect can be estimated most precisely, as well as optimally weighted average treatment effects. Under some conditions the optimal selection rules depend solely on the propensity score. For a wide range of distributions a good approximation to the optimal rule is provided by the simple selection rule to drop all units with estimated propensity scores outside the range [0.1, 0.9].

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Newcomer, Arline Geronimus and participants in the Workshop on Low Income Populations at the Institute for Research on Poverty at the University of Wisconsin-Madison for helpful comments on an earlier draft and Frances Margolin, Hoda Makar, and Simon Hotz for their editorial assistance. We especially wish to thank Robert Willis for numerous helpful discussions during the course of this study. All remaining errors are the responsibility of the authors. The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research.