Measurement Error and Other Latent Variable Problems

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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.