Measurement Error and Other Latent Variable Problems

计量误差在经济数据中普遍存在，这促使了对计量误差具有鲁棒性的计量经济学方法的发展。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学模型中的经典（即零均值）和非经典测量误差。然而，一些测量误差和更一般的潜变量模型尚未令人满意地涵盖在文献中，这种情况下，本项目的目的是解决。其中之一是所谓的Berkson型测量误差模型（例如，当重复测量或仪器变量可用时，与观测数据不相关但与真实未观测数据相关的误差）。在经济环境中，当报告数据的代理人试图根据他们的信息形成最佳预测时，这种类型的错误自然会出现。另一个与测量误差密切相关的被忽视的问题是非参数和不可分离因子模型的识别。因素模型（以其最简单的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，作为一种从大量不完美的代理中提取少量真实潜在因素的方法。拟议的工作大大扩展了因素模型的适用范围，并补充了非参数和不可分离的内生模型的积极文献。该项目的最后一个贡献是一个统一的方法来估计测量误差和更一般的潜变量模型，称为熵潜变量集成通过模拟（ELVIS）。这种方法透明地覆盖了点和集合识别模型，使研究人员能够自由地对不可观测的潜变量施加适当的限制，而无需明确指定不可观测的分布。所提出的方法是基于早期工作的PI贝叶斯指数倾斜经验似然（BETEL），它提供了一个正式的贝叶斯框架的时刻条件模型。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（阿利亚包括在Econometrica和Econometric Theory中的出版物），但该项目大大扩展和补充了这些早期的发现，以提供一套完整的针对潜在变量模型的统计工具。使用先进的功能和运营商为基础的方法，以解决完全非参数和不可分离的设置是一个关键的显着特点，拟议的工作。ELVIS-BETEL方法结合了各种技术（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），以产生广泛适用的推理方法。更广泛的影响：测量误差和潜变量的问题涉及到计量经济学，统计学和社会科学中的一个大社区。调查结果将通过在计量经济学和统计学会议上的介绍以及在这两个领域的期刊上发表论文而广泛传播。将在研究者的网站上公开提供一个实施拟议ELVIS估计方法的计算机程序。所提出的方法也将包括在PI的研究生课程中，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了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.