Partial Identification of Probability Distributions with Misclassified Data

Francesca Molinari

Working Papers from Cornell University, Center for Analytic Economics

Abstract: 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. Inferential problems caused by data errors have been conceptualized 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 coefficient 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--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. A method for estimating the identification regions and construct their confidence sets is given, and illustrated with an empirical analysis of the distribution of pension plan types using data from the Health and Retirement Study.

JEL-codes: C10 C13 C14 J26 (search for similar items in EconPapers)
Date: 2005-04
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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Related works:
Journal Article: Partial identification of probability distributions with misclassified data (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:ecl:corcae:05-10

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