Estimation of Models With Multiple-Valued Explanatory Variables |
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Authors: | Alexandre Poirier Nicolas L Ziebarth |
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Institution: | 1. Department of Economics, University of Iowa, Iowa City, IA 52242 (alexandre-poirier@uiowa.edu);2. Department of Economics, Auburn University, Auburn, AL 36849, and NBER, Cambridge, MA 02138 (nicolas.lehmannziebarth@gmail.com) |
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Abstract: | ABSTRACTWe study estimation and inference when there are multiple values (“matches”) for the explanatory variables and only one of the matches is the correct one. This problem arises often when two datasets are linked together on the basis of information that does not uniquely identify regressor values. We offer a set of two intuitive conditions that ensure consistent inference using the average of the possible matches in a linear framework. The first condition is the exogeneity of the false match with respect to the regression error. The second condition is a notion of exchangeability between the true and false matches. Conditioning on the observed data, the probability that each match is correct is completely unrestricted. We perform a Monte Carlo study to investigate the estimator’s finite-sample performance relative to others proposed in the literature. Finally, we provide an empirical example revisiting a main area of application: the measurement of intergenerational elasticities in income. Supplementary materials for this article are available online. |
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Keywords: | Data combination Intergenerational elasticities Regression methods Statistical matching |
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