Identification of structural dynamic discrete choice models

This paper presents new identification results for the class of structural dynamic discrete choice models that are built upon the framework of the structural discrete Markov decision processes proposed by Rust (1994). We demonstrate how to semiparametrically identify the deep structural parameters of interest in the case where utility function of one choice in the model is parametric but the distribution of unobserved heterogeneities is nonparametric. The proposed identification method does not rely on the availability of terminal period data and hence can be applied to infinite horizon structural dynamic models. For identification we assume availability of a continuous observed state variable that satisfies certain exclusion restrictions. If such excluded variable is accessible, we show that the structural dynamic discrete choice model is semiparametrically identified using the control function approach. This is a substantial revision of "Semiparametric identification of structural dynamic optimal stopping time models", CWP06/07.

Bayesian Estimation of Dynamic Discrete Choice Models

Structural estimation, Dynamic programming, MCMC

Dynamic Discrete Choice and Dynamic Treatment Effects

This paper considers semiparametric identification of structural dynamic discrete choice models and models for dynamic treatment effects. Time to treatment and counterfactual outcomes associated with treatment times are jointly analyzed. We examine the implicit assumptions of the dynamic treatment model using the structural model as a benchmark. For the structural model we show the gains from using cross equation restrictions connecting choices to associated measurements and outcomes. In the dynamic discrete choice model, we identify both subjective and objective outcomes, distinguishing ex post and ex ante outcomes. We show how to identify agent information sets.

Bounds on Parameters in Dynamic Discrete Choice Models

Identification of dynamic nonlinear panel data models is an important and delicate problem in econometrics. In this paper we provide insights that shed light on the identification of parameters of some commonly used models. Using this insight, we are able to show through simple calculations that point identification often fails in these models. On the other hand, these calculations also suggest that the model restricts the parameter to lie in a region that is very small in many cases, and the failure of point identification may therefore be of little practical importance in those cases. Although the emphasis is on identification, our techniques are constructive in that they can easily form the basis for consistent estimates of the identified sets.

Estimation of a dynamic discrete choice model of irreversible investment

In this paper we propose and estimate a dynamic structural model of fixed capital investment at the firm level. Our dataset consists of an unbalanced panel of Spanish manufacturing firms. Two important features are present in this dataset. There are periods in which firms decide not to invest and periods of large investment episodes. These empirical evidence of infrequent and lumpy investment provides evidence in favour of irreversibilities and nonconvex capital adjustment costs. We consider a dynamic discrete choice model of irreversible investment with a general specification of adjustment costs including convex and nonconvex components. We use a two stage estimation procedure. In a first stage, we obtain GMM estimates of technological parameters. In the second stage, we obtain partial maximum likelihood estimates for the adjustment cost parameters. The estimation strategy builds on the representation of conditional value functions as a computable function of conditional choice probabilities. It is in the line of structural estimation techniques which avoid the solution of the dynamic programming problem

Solving Dynamic Discrete Choice Models Using Smoothing and Sieve Methods

We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the Bellman operators defining the two functions. The random Bellman operators, and therefore also the corresponding solutions, are generally non-smooth which is undesirable. To circumvent this issue, we introduce a smoothed version of the random Bellman operator and solve for the corresponding smoothed value function using sieve methods. We show that one can avoid using sieves by generalizing and adapting the `self-approximating' method of Rust (1997) to our setting. We provide an asymptotic theory for the approximate solutions and show that they converge with root-N-rate, where $N$ is number of Monte Carlo draws, towards Gaussian processes. We examine their performance in practice through a set of numerical experiments and find that both methods perform well with the sieve method being particularly attractive in terms of computational speed and accuracy