Some Notes on Sample Selection Models

Sample selection problems are pervasive when working with micro economic models and datasets of individuals, households or firms. During the last three decades, there have been very significant developments in this area of econometrics. Different type of models have been proposed and used in empirical applications. And new estimation and inference methods, both parametric and semiparametric, have been developed. These notes provide a brief introduction to this large literature.Sample selection. Censored regression model. Truncated regression model. Treatment effects. Semiparametric methods.

Estimation of Dynamic Discrete Games Using the Nested Pseudo Likelihood Algorithm: Code and Application

This document describes program code for the solution and estimation of dynamic discrete games of incomplete information using the Nested Pseudo Likelihood (NPL) method in Aguirregabiria and Mira (2007). The code is illustrated using a dynamic game of store location by retail chains, and actual data from McDonalds and Burger King.Estimation of Dynamic Games; Nested Pseudo Likelihood Algorithm; Program Code

Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games

Empirically studying dynamic competition in oligopoly markets requires dealing with large states spaces and tackling difficult computational problems, while handling heterogeneity and multiple equilibria. In this paper, we discuss some of the ways recent work in Industrial Organization has dealt with these challenges. We illustrate problems and proposed solutions using as examples recent work on dynamic demand for differentiated products and on dynamic games of oligopoly competition. Our discussion of dynamic demand focuses on models for storable and durable goods and surveys how researchers have used the \Industrial Organization; Oligopoly competition; Dynamic demand; Dynamic games; Estimation; Counterfactual experiments; Multiple equilibria; Inclusive values; Unobserved heterogeneity.

Nonparametric Identification of Behavioral Responses to Counterfactual Policy Interventions in Dynamic Discrete Decision Processes

This paper deals with identification in Markov dynamic discrete decision processes. It shows the nonparametric identification of the behavioral responses to counterfactual policy interventions that modify the one- period utility function.Dynamic discrete decision processes, Identification, Counterfactual policy experiments.

Another Look at the Identification of Dynamic Discrete Decision Processes

This paper presents an econometric approach to estimate the behavioral effects of counterfactual policy experiments in the context of dynamic decision models where the current utility function and the distribution of unobservables are nonparametrically specified. Previous studies have shown that the identification of the current utility function in dynamic decision models requires of stronger assumptions than in static decision models. We show in this paper that knowledge of the current utility function (or of a 'normalized' utility function) is not necessary to identify counterfactual choice probabilities in dynamic models. To identify these counterfactuals we need the probability distribution of the unobservables and the difference between the present value of choosing always the same alternative and the present value of deviating one period from this strategy. We show that both functions are identified from the factual choice probabilities under similar conditions as in static decision models. Based on this result we propose a nonparametric procedure to estimate the behavioral effects of counterfactual experiments in dynamic decision models. We apply this method to evaluate the effects of an investment subsidy program in the context of a model of machine replacement.Dynamic discrete decision processes; Nonparametric Identification; Counterfactual experiments.

Comment: The Identification Power of Equilibrium in Simple Games

This paper studies the identification of structural parameters in dynamic games when we replace the assumption of Markov Perfect Equilibrium (MPE) with weaker conditions such as rational behavior and rationalizability. The identification of players' time discount factors is of especial interest. I present identification results for a simple two-periods/two-players dynamic game of market entry-exit. Under the assumption of level-2 rationality (i.e., players are rational and they know that they are rational), a exclusion restriction and a large-support condition on one of the exogenous explanatory variables are sufficient for point-identification of all the structural parameters.Identification, Empirical dynamic discrete games, Rational behavior, Rationalizability.

A Method for Implementing Counterfactual Experiments in Models with Multiple Equilibria

This paper proposes a method for implementing counterfactual experiments in estimated models that have multiple equilibria. The method assumes that the researcher does not know the equilibrium selection mechanism and wants to impose minimum restrictions on it. Our key assumption is that the equilibrium selection function does not jump discontinuously between equilibria as we change marginally the structural parameters of the model. Under this assumption, we show that, although the equilibrium selection function is unknown, the researcher can obtain an approximation of this function in a neighborhood of the estimated values of the structural parameters. Under the additional assumption that the counterfactual equilibrium is stable, this approximation can be combined with iterations in the equilibrium mapping to obtain the exact counterfactual equilibrium. We illustrate the differences between our approach and other methods, such as the selection of a counterfactual equilibrium that is closer to the equilibrium in the data, and equilibrium mapping iterations using the equilibrium in the data as the initial value. We show that, in general, these alternative methods are not consistent with the assumption that the equilibrium selection mechanism is continuous with respect to the structural parameters.Structural models with multiple equilibria; Counterfactual experiments; Equilibrium selection.

Another Look at the Identification of Dynamic Discrete Decision Processes: With an Application to Retirement Behavior

This paper deals with the estimation of the behavioral and welfare effects of counterfactual policy interventions in dynamic structural models where all the primitive functions are nonparametrically specified (i.e., preferences, technology, transition rules, and distribution of unobserved variables). It proves the nonparametric identification of agents' decision rules, before and after the policy intervention, and of the change in agents' welfare. Based on these results we propose a nonparametric procedure to estimate the behavioral and welfare effects of a general class of counterfactual policy interventions. The nonparametric estimator can be used to construct a test of the validity of a particular parametric specification. We apply this method to evaluate hypothetical reforms in the rules of a public pension system using a model of retirement behavior and a sample of workers in Sweden.Dynamic discrete decision processes; Nonparametric identification; Counterfactual policy interventions; Retirement behavior.

Econometric Issues and Methods in the Estimation of Production Functions

This paper discusses the main econometric issues in the identification and estimation of production functions, and reviews recent methods. The main emphasis of the paper is in explaining the role of different identifying assumptions used in alternative estimation methods.Production Function Estimation. Dynamic Panel Data Models. Endogeneity. Sample Selection.

Pseudo Maximum Likelihood Estimation of Structural Models Involving Fixed-Point Problems

This paper deals with the estimation of structural econometric models where the probability distribution of endogenous variables is implicitly defined as an equilibrium of a fixed-point problem. It proposes a pseudo maximum likelihood procedure and studies its asymptotic properties.