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The Multinomial Multiperiod Probit Model: Identification and Efficient Estimation

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  • Liesenfeld, Roman
  • Richard, Jean-François

Abstract

In this paper we discuss parameter identification and likelihood evaluation for multinomial multiperiod Probit models. It is shown in particular that the standard autoregressive specification used in the literature can be interpreted as a latent common factor model. However, this specification is not invariant with respect to the selection of the baseline category. Hence, we propose an alternative specification which is invariant with respect to such a selection and identifies coefficients characterizing the stationary covariance matrix which are not identified in the standard approach. For likelihood evaluation requiring high-dimensional truncated integration we propose to use a generic procedure known as Efficient Importance Sampling (EIS). A special case of our proposed EIS algorithm is the standard GHK probability simulator. To illustrate the relative performance of both procedures we perform a set Monte-Carlo experiments. Our results indicate substantial numerical e?ciency gains of the ML estimates based on GHK-EIS relative to ML estimates obtained by using GHK.

Suggested Citation

  • Liesenfeld, Roman & Richard, Jean-François, 2007. "The Multinomial Multiperiod Probit Model: Identification and Efficient Estimation," Economics Working Papers 2007-26, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:6340
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    Cited by:

    1. Aßmann, Christian, 2008. "Assessing the Effect of Current Account and Currency Crises on Economic Growth," Economics Working Papers 2008-01, Christian-Albrechts-University of Kiel, Department of Economics.

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    Keywords

    Discrete choice; Importance sampling; Monte-Carlo integration; Panel data; Parameter identification; Simulated maximum likelihood;

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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