Identification of Probability Distributions with Misclassified Data

This paper addresses the problem of data errors in discrete variables. When data errors occur, the observed variable is a misclassified version of the variable of interest, whose distribution is not identified. For many years econometricians have conceptualized the problem through convolution and mixture models. This paper introduces the direct misclassification approach. The approach is based on the observation that in the presence of classification errors, the relation between the distribution of the true but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations, in which the coe.cient matrix is the matrix of misclassification probabilities. Formalizing the problem in these terms allows one to incorporate any prior information - e.g., validation studies, economic theory, social and cognitive psychology, or knowledge of the circumstances under which the data have been collected - into the analysis through sets of restrictions on the matrix of misclassification probabilities. Such information can have strong identifying power; the direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest. The method readily extends to drawing inference on parameters of the conditional distribution of an outcome variable when the conditioning variable is misclassified. It is easy to implement and often computationally tractable. A method for estimating the identification regions is given, and illustrated with an empirical analysis of the distribution of pension plan types using data from the Health and Retirement Study.

RDA

Misclassification/Identification Regions/Direct Misclassification Approach

10922