Measurement Systems
综述了如何利用多个不完美测量来推断不可观测变量统计性质的方法，强调与面板数据、博弈模型等领域的联系，并报告了识别不可观测变量联合分布的研究进展。
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 consumer “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 tremendous 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 “disturbances” that may have nonadditively separable affects). The framework emphasizes 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.