Measurement Error and Other Latent Variable Problems

测量误差在经济数据中普遍存在，这促使计量经济学方法的发展对测量误差具有鲁棒性。在早期的工作中，研究者设计了这样的方法来处理各种计量经济模型中的经典（即零平均值）和非经典测量误差。然而，一些测量误差和更一般的潜在变量模型尚未在文献中得到令人满意的覆盖，这是本项目旨在解决的情况。其中之一是所谓的伯克森型测量误差模型（例如，当重复测量或仪器变量可用时，与观测数据无关但与真实未观测数据相关的误差）。这种类型的错误在经济环境中自然出现，当报告数据的代理试图在给定其信息的情况下形成最佳可能的预测器时。与测量误差密切相关的另一个被忽视的问题是非参数和不可分离因子模型的识别。因子模型（以其最简单、线性和可分离的形式）在经济学和社会科学中有着悠久的历史，是一种从大量不完美代理中提取少量真正潜在因素的方法。提出的工作大大扩展了因子模型的适用范围，并补充了非参数和不可分离内生模型的现有文献。这个项目的最后贡献是一个统一的方法来估计测量误差和更一般的潜在变量模型，称为通过模拟的熵潜在变量集成（ELVIS）。这种方法透明地涵盖了点识别和集识别模型，使研究人员能够以（条件）矩条件或独立性的形式自由地对不可观察的潜在变量施加适当的限制，而不必明确指定不可观察的分布。所提出的方法是基于PI在贝叶斯指数倾斜经验似然（BETEL）上的早期工作，BETEL为力矩条件模型提供了正式的贝叶斯框架。正确处理测量误差和其他潜在变量的存在是计量经济学和统计学中一个长期和广泛研究的问题。虽然在PI的早期工作中已经解决了某些类型的测量误差（特别是在《计量经济学》和《计量经济学理论》上发表），但该项目大大扩展和补充了这些早期的发现，提供了一套完整的针对潜在变量模型的统计工具。使用先进的基于函数和算子的方法来解决完全非参数和不可分离的设置是所提出工作的一个关键区别特征。ELVIS-BETEL方法结合了一系列广泛的技术（例如基于模拟的方法，熵最大化，非参数贝叶斯方法和经验似然），以产生一种广泛适用的推理方法。更广泛的影响：测量误差和潜在变量的问题涉及到计量经济学、统计学和一般社会科学中的一个大社区。除了在这两个领域的期刊上发表论文外，研究结果还将通过在计量经济学和统计学会议上发表报告的方式广泛传播。将在研究者的网站上公开提供一个执行拟议的ELVIS估计方法的计算机程序。所提出的方法也将被纳入PI的研究生课程，该课程涵盖了广泛的测量误差分析和经验似然方法，从而为新一代研究人员提供更准确地分析经济数据的强大工具。

Measurement error is pervasive in economic data, which motivates the development of econometric methods that are robust to measurement error. In earlier work, the investigator devised such methods to handle classical (i.e. zero mean) and nonclassical measurement error in a wide variety of econometric models. However, a number of measurement error and more general latent variable models have yet to be satisfactorily covered in the literature, a situation this project aims to address. One of them is the so-called Berkson-type measurement error model (e.g. an error that is uncorrelated with the observed data but correlated with the true unobserved data) when repeated measurements or instrumental variables are available. This type of error arises naturally in economic settings when the agents reporting the data attempt to form the best possible predictor given their information. Another overlooked problem closely tied to measurement error is the identification of nonparametric and nonseparable factor models. Factor models (in their simplest, linear and separable, form) have a long history in economics and in the social sciences as a way to extract a small number of true latent factors from a large number of imperfect proxies. The proposed work considerably extends factor models' range of applicability and complements the active literature on nonparametric and nonseparable endogenous models. This project's last contribution is a unified approach to the estimation of measurement error and more general latent variables models, called Entropic Latent Variable Integration via Simulation (ELVIS). This method transparently covers both point- and set-identified models and enables researchers to freely impose suitable restrictions on the unobservable latent variables taking the form of (conditional) moment conditions or independence without having to explicitly specify the distribution of the unobservables. The proposed approach is based upon earlier work by the PI on the Bayesian Exponentially Tilted Empirical Likelihood (BETEL), which provides a formal Bayesian framework for moment condition models. Properly handling the presence of measurement error and other latent variables is a longstanding and extensively studied problem in econometrics and statistics. While some types of measurement error have been addressed in the PI's earlier work (which led, inter alia, to publications in Econometrica and Econometric Theory), this project considerably extends and complements these earlier findings to provide a complete set of statistical tools targeting latent variables models. The use of advanced functional- and operator-based methods to address fully nonparametric and nonseparable settings is a key distinguishing feature of the proposed work. The ELVIS-BETEL method combines of a wide array of techniques (e.g. simulation-based approaches, entropy maximization, nonparametric Bayesian methods and empirical likelihood) in order to yield a widely applicable inference method. Broader Impacts: The issues of measurement error and latent variables concern a large community within econometrics, statistics and the social sciences in general. The findings will be disseminated broadly through presentations at both econometrics and statistics conferences, in addition to publishing papers in journals of both fields. A computer program implementing the proposed ELVIS estimation method will be made publicly available on the investigator's web site. The proposed methods will also be included in the PI's graduate class, which covers a wide range of measurement error analysis and empirical likelihood methods, thus providing a new generation of researchers with powerful tools to more accurately analyze economic data.