Measurement Systems

Economic models often depend on quantities that are unobservable, either for privacy reasons or because they are difficult to measure. Examples of such variables include human capital (or ability), personal income, unobserved heterogeneity (such as con-sumer types), et cetera. This situation has historically been handled either by simply using observable imperfect proxies for each of the unobservables, or by assuming that such unobservables satisfy convenient conditional mean or independence assumptions that enable their elimination from the estimation problem. However, thanks to tre-mendous increases in both the amount of data available and computing power, it has become possible to take full advantage of recent formal methods to infer the statistical properties of unobservable variables from multiple imperfect measurements of them. The general framework used is the concept of measurement systems in which a vector of observed variables is expressed as a (possibly nonlinear or nonparametric) function of a vector of all unobserved variables (including unobserved error terms or dis-turbances that may have nonadditively separable affects). The framework empha-sizes important connections with related fields, such as nonlinear panel data, limited dependent variables, game theoretic models, dynamic models, and set identification. This review reports the progress made toward the central question of whether there exist plausible assumptions under which one can identify the joint distribution of the unobservables from the knowledge of the joint distribution of the observables. It also overviews empirical efforts aimed at exploiting such identification results to deliver novel findings that formally account for the unavoidable presence of unobservables. (JEL C30, C55, C57, D12, E21, E23, J24)

Automated summary

Economic models often rely on unobservable variables, which have historically been handled through imperfect proxies or assumptions. However, advances in data and computing power have made it possible to infer the statistical properties of these variables from multiple imperfect measurements. This article reviews progress in identifying the joint distribution of unobservable variables based on the joint distribution of observables, and discusses empirical efforts to exploit this identification for novel findings.