A Simulation-Based Information-Theoretic Estimator of Economic Models with Unobserved Variables

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One of the most difficult aspects of the empirical testing of economic models is the presence of variables that influence the behavior of the economic system under study but that are not observed by researchers. A considerable number of innovations in applied and theoretical economics have consisted of uncovering specific sets of assumptions that permit the determination of the parameters of interest, despite the presence of these unobservable, or latent, variables. The proposed research project devises a general methodology to handle such situations by combining two areas of research that have received a considerable attention in the statistics and economics literature over the past decade, namely, simulation-based and generalized empirical likelihood approaches. Simulation-based approaches offer the advantage of replacing tedious algebraic manipulations by a large number of simple calculations that can easily be handled by today's computers. Unfortunately, these approaches typically require researchers to make assumptions regarding the distribution of the unobservable variables. The present project avoids this limitation by employing techniques related to generalized empirical likelihood estimators which have been specifically aimed at replacing assumptions regarding the distribution of a variable by less restrictive assumptions regarding the moments of a variable, such as its mean or its variance. The approach is general, in the sense that it applies to any model that can be expressed in terms of (potentially nonlinear) moments, conditional mean or independence assumptions, in both identified and set-identified settings. The asymptotic, or large sample, properties of this new estimator for latent variable models are investigated. Also, the construction of the estimator has implications even in the absence of unobservable variables, as it suggests the use of an estimator closely related to, but not a member of, the widely studied generalized empirical likelihood family. In particular, the estimator combines the two most popular generalized empirical likelihoods, namely Empirical Likelihood and Exponential Tilting. The research project compares this new estimator, called exponentially tilted empirical likelihood, to existing estimators. The goal of this project is to enable researchers to employ more realistic economic models without being hindered by the complexity of the resulting equations, through the use of general-purpose numerical methods. It also furthers the ongoing search for statistical methods that make the best possible use of available data.