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

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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.

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Bibliographic Info

Paper provided by University of Western Ontario, Department of Economics in its series UWO Department of Economics Working Papers with number 20065.

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Date of creation: 2006
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Handle: RePEc:uwo:uwowop:20065

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Postal: Department of Economics, Reference Centre, Social Science Centre, University of Western Ontario, London, Ontario, Canada N6A 5C2
Phone: 519-661-2111 Ext.85244
Web page: http://economics.uwo.ca/research/research_papers/department_working_papers.html

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Keywords: dynamic discrete choice models; finite mixture; nonparametric identification; panel data; sieve estimator; unobserved heterogeneity;

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Cited by:
  1. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2009. "Sequential Estimation of Structural Models with a Fixed Point Constraint," Discussion Papers 2009-18, Graduate School of Economics, Hitotsubashi University.
  2. John Bound & Todd Stinebrickner & Timothy Waidmann, 2007. "Health, Economic Resources and the Work Decisions of Older Men," University of Western Ontario, Economic Policy Research Institute Working Papers 20076, University of Western Ontario, Economic Policy Research Institute.
  3. Pedro Mira & Victor Aguirregabiria, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers wp2007_0711, CEMFI.
  4. 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.

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