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Learning Markov Processes with Latent Variables From Longitudinal Data

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  • Jochmans, Koen
  • Higgins, Ayden

Abstract

We present a constructive proof of (nonparametric) identication of the parameters of a bivariate Markov chain when only one of the two random variables is observable. This setup generalizes the hidden Markov model in various useful directions, allowing for state dependence in the observables and allowing the transition kernel of the hidden Markov chain to depend on past observables. We give conditions under which the transition kernel and the distribution of the initial condition are both identied (up to a permutation of the latent states) from the joint distribution of four (or more) time-series observations.

Suggested Citation

  • Jochmans, Koen & Higgins, Ayden, 2022. "Learning Markov Processes with Latent Variables From Longitudinal Data," TSE Working Papers 22-1366, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:127401
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    References listed on IDEAS

    as
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    9. Higgins, Ayden & Jochmans, Koen, 2023. "Identification of mixtures of dynamic discrete choices," Journal of Econometrics, Elsevier, vol. 237(1).
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Dynamic discrete choice; finite mixture; Markov process; regime switching; state dependence;
    All these keywords.

    JEL classification:

    • 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

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