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

经济模型的实证检验最困难的方面之一是存在影响所研究的经济系统行为的变量，但研究人员没有观察到这些变量。在应用经济学和理论经济学中，有相当多的创新是通过揭示特定的假设来确定感兴趣的参数，尽管存在这些不可观察的或潜在的变量。拟议的研究项目设计了一个通用的方法来处理这种情况，结合两个领域的研究，在统计和经济学文献中，在过去的十年中，得到了相当大的关注，即模拟为基础的和广义的经验似然方法。基于模拟的方法提供了用大量的简单计算来代替繁琐的代数操作的优点，这些计算可以很容易地被今天的计算机处理。不幸的是，这些方法通常需要研究人员对不可观测变量的分布做出假设。本项目避免了这一限制，采用技术相关的广义经验似然估计，已专门针对取代假设有关的变量的分布较少限制性的假设有关的一个变量的时刻，如其均值或方差。该方法是通用的，在这个意义上说，它适用于任何模型，可以表示在（潜在的非线性）的时刻，条件均值或独立的假设，在确定和设置确定的设置。研究了潜变量模型的新估计量的渐近性质或大样本性质。此外，即使在不存在不可观测变量的情况下，估计量的构建也会产生影响，因为它表明使用与广泛研究的广义经验似然家族密切相关但不是其成员的估计量。特别是，估计量结合了两个最流行的广义经验似然，即经验似然和指数倾斜。该研究项目将这种称为指数倾斜经验似然的新估计量与现有估计量进行了比较。 该项目的目标是使研究人员能够采用更现实的经济模型 而不受所得方程的复杂性的阻碍。它还推动了正在进行的寻找统计方法的工作，以便尽可能最好地利用现有数据。

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.