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Unknown heterogeneity, the EC-EM algorithm, and Large T Approximation

El-Gamal, Mahmoud and Grether, David M. (1996) Unknown heterogeneity, the EC-EM algorithm, and Large T Approximation. Social Science Working Paper, 988. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20170815-150649504

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Abstract

We study a panel structure with n subjects/entities being observed over T periods. We consider a class of models for each subject's data generating process, and allow for unknown heterogeneity. In other words, we do not know how many types we have, what the types are, and which subjects belong to each type. We propose a large T approximation to the posterior mode on the unknowns through the Estimation/Classification (EC) algorithm of El-Gamal and Grether (1995) which is linear in n, T, and the unknown number of types. If our class of models (likelihood functions) allows for a consistent asymptotically normal estimator under the assumption of homogeneity (number of types = 1), then the estimators obtained by our EC algorithm inherit those asymptotic properties as T ↑ ∞ and then as n t ↑ ∞ (with a block-diagonal covariance matrix facilitating hypothesis-testing). We then propose a large T approximation to the EM algorithm to obtain posteriors on the subject classifications and diagnostics for the goodness of the large T approximation in the• EC stage. If the large T approximation does not seem to be appropriate, then we suggest the use of the more computationally costly EM algorithm, or the - even more costly - full Bayesian updating. We illustrate the procedure with two applications to experimental data on probability assessments within a class of Pro bit and a class of Tobit models.


Item Type:Report or Paper (Working Paper)
Additional Information:We acknowledge financial support from NSF grant #SBR-9320497 to the California Institute of Technology. We thank David Stephenson for programming assistance. We also thank participants at the CEME-NSF conference on microeconometrics in Madison, WI, June 1995 and in the econometrics workshops at Arizona, Columbia, Cornell, Northwestern, and Wisconsin, and audiences at Economic Science Association meetings, University of Amsterdam, Bayesian Research Conference at LA, and Behavioral Decision Making at MIT for many useful comments. Any remaining errors are, of course, our own.
Group:Social Science Working Papers
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Funding AgencyGrant Number
NSFSBR-9320497
Record Number:CaltechAUTHORS:20170815-150649504
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170815-150649504
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80435
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:15 Aug 2017 22:22
Last Modified:15 Aug 2017 22:22

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