Econometrica: Jan 2014, Volume 82, Issue 1

Entropic Latent Variable Integration via Simulation

https://doi.org/10.3982/ECTA9748
p. 345-385

Susanne M. Schennach

This paper introduces a general method to convert a model defined by moment conditions that involve both observed and unobserved variables into equivalent moment conditions that involve only observable variables. This task can be accomplished without introducing infinite‐dimensional nuisance parameters using a least favorable entropy‐maximizing distribution. We demonstrate, through examples and simulations, that this approach covers a wide class of latent variables models, including some game‐theoretic models and models with limited dependent variables, interval‐valued data, errors‐in‐variables, or combinations thereof. Both point‐ and set‐identified models are transparently covered. In the latter case, the method also complements the recent literature on generic set‐inference methods by providing the moment conditions needed to construct a generalized method of moments‐type objective function for a wide class of models. Extensions of the method that cover conditional moments, independence restrictions, and some state‐space models are also given.

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Supplement to "Entropic Latent Variable Integration via Simulation"

This supplement includes (i) proofs omitted from the main text, (ii) additional simulation examples, (iii) an extended notion of the identified set, (iv) difficulties associated with the use of alternative discrepancies, (v) inference methods, (vi) computational details of the implementation of the method in the paper, (vii) relationships with earlier information-theoretic and entropy-based methods.

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Supplement to "Entropic Latent Variable Integration via Simulation"

This zip file contains the replication files for the manuscript.

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