The Multinomial Multiperiod Probit Model: Identification and Efficient Estimation

45 Pages Posted: 17 Sep 2007

See all articles by Roman Liesenfeld

Roman Liesenfeld

University of Cologne, Department of Economics

Jean-Francois Richard

University of Pittsburgh - Department of Economics

Date Written: September 5, 2007

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 efficiency gains of the ML estimates based on GHK-EIS relative to ML estimates obtained by using GHK.

Keywords: discrete choice, importance sampling, Monte-Carlo integration, panel data, parameter identification, simulated maximum likelihood

JEL Classification: C35, C15

Suggested Citation

Liesenfeld, Roman and Richard, Jean-Francois, The Multinomial Multiperiod Probit Model: Identification and Efficient Estimation (September 5, 2007). Available at SSRN: https://ssrn.com/abstract=1014605 or http://dx.doi.org/10.2139/ssrn.1014605

Roman Liesenfeld (Contact Author)

University of Cologne, Department of Economics ( email )

Albertus-Magnus-Platz
D-50931 Köln
Germany

Jean-Francois Richard

University of Pittsburgh - Department of Economics ( email )

4901 Wesley Posvar Hall
230 South Bouquet Street
Pittsburgh, PA 15260
United States
412-648-1750 (Phone)

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