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Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices

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  • Kasahara, Hiroyuki
  • Shimotsu, Katsumi

Abstract

In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for unobserved heterogeneity. This paper studies nonparametric identifiability of type probabilities and type-specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work. Three elements emerge as the important determinants of identification; the time-dimension of panel data, the number of values the covariates can take, and the heterogeneity of the response of different types to changes in the covariates. For example, in a simple case, a time-dimension of T = 3 is sufficient for identification, provided that the number of values the covariates can take is no smaller than the number of types, and that the changes in the covariates induce sufficiently heterogeneous variations in the choice probabilities across types. Type-specific components are identifiable even when state dependence is present as long as the panel has a moderate time-dimension (T 6). We also develop a series logit estimator for finite mixture models of dynamic discrete choices and derive its convergence rate.

Suggested Citation

  • Kasahara, Hiroyuki & Shimotsu, Katsumi, 2006. "Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices," Queen's Economics Department Working Papers 273568, Queen's University - Department of Economics.
    • Handle: RePEc:ags:quedwp:273568
    DOI: 10.22004/ag.econ.273568
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    Cited by:

    1. is not listed on IDEAS
    2. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Sequential Estimation of Structural Models With a Fixed Point Constraint," Econometrica, Econometric Society, vol. 80(5), pages 2303-2319, September.
    3. Bound, John & Stinebrickner, Todd & Waidmann, Timothy, 2010. "Health, economic resources and the work decisions of older men," Journal of Econometrics, Elsevier, vol. 156(1), pages 106-129, May.
    4. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    5. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2008. "Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models," Journal of Econometrics, Elsevier, vol. 146(1), pages 92-106, September.

    More about this item

    Keywords

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    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
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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