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Rationalizable Counterfactual Choice Probabilities in Dynamic Binary Choice Processes

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  • Xun Tang

    () (Department of Economics, University of Pennsylvania)

Abstract

We address two issues in nonparametric structural analyses of dynamic binary choice processes (DBCP). First, the DBCP is not testable and decision makers’ single-period payoffs (SPP) cannot be identified even when the distribution of unobservable states (USV) is known. Numerical examples show setting SPP from one choice to arbitrary utility levels to identify that from the other can lead to errors in predicting choice probabilities under counterfactual state transitions. We propose two solutions. First, if a data generating process (DGP) has exogenous variations in observable state transitions, the DBCP becomes testable and SPP is identified. Second, exogenous economic restrictions on SPP (such as ranking of states by SPP, or shape restrictions) can be used to recover the identified set of rationalizable counterfactual choice probabilities (RCCP) that are consistent with model restrictions. The other (more challenging) motivating issue is that when the USV distribution is not known, misspecification of the distribution in structural estimation leads to errors in counterfactual predictions. We introduce a simple algorithm based on linear programming to recover sharp bounds on RCCP. This approach exploits the fact that some stochastic restrictions on USV (such as independence from observable states) and economic restrictions on SPP can be represented (without loss of information for counterfactual analyses) as linear restrictions on SPP and distributional parameters of USV. We use numerical examples to illustrate the algorithm and show sizes of identified sets of RCCP can be quite small relative to the outcome space.

Suggested Citation

  • Xun Tang, 2009. "Rationalizable Counterfactual Choice Probabilities in Dynamic Binary Choice Processes," PIER Working Paper Archive 09-022, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:09-022
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    References listed on IDEAS

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    Keywords

    Dynamic discrete choice models; counterfactual outcomes; rationalizability; non-parametric and semiparametric identification;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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