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

对经济模型进行实证检验最困难的方面之一是，存在影响所研究经济系统行为的变量，但研究人员没有观察到这些变量。应用经济学和理论经济学中相当多的创新包括揭示特定的假设集，这些假设允许确定感兴趣的参数，尽管存在这些不可观察的或潜在的变量。拟议的研究项目结合了过去十年来在统计学和经济学文献中受到极大关注的两个研究领域，即基于模拟的方法和广义经验似然方法，从而设计了一种处理这种情况的一般方法。基于模拟的方法的优点是用大量简单的计算取代了乏味的代数操作，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。本项目通过采用与广义经验似然估计器有关的技术来避免这一限制，这些技术的具体目的是用关于变量的矩的限制性较低的假设来取代关于变量分布的假设，例如变量的均值或方差。这种方法是一般的，因为它适用于在识别和集合识别的环境中都可以用(潜在的非线性)矩、条件平均或独立假设来表示的任何模型。研究了这种新的潜变量模型估计量的渐近或大样本性质。此外，即使在没有不可观测变量的情况下，估计量的构造也有意义，因为它表明使用了与被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，该估计器结合了两种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器与现有的估计器进行了比较。这个项目的目标是通过使用通用的数值方法，使研究人员能够采用更现实的经济模型，而不会受到由此产生的方程的复杂性的阻碍。它还进一步推动了目前对尽可能最大限度地利用现有数据的统计方法的探索。

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.