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Estimation of Models With Multiple-Valued Explanatory Variables

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  • Alexandre Poirier
  • Nicolas L. Ziebarth

Abstract

We 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.

Suggested Citation

  • Alexandre Poirier & Nicolas L. Ziebarth, 2019. "Estimation of Models With Multiple-Valued Explanatory Variables," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 586-597, October.
    • Handle: RePEc:taf:jnlbes:v:37:y:2019:i:4:p:586-597
    DOI: 10.1080/07350015.2017.1391694
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    Cited by:

    1. Millimet, Daniel L., 2024. "(Don't) Walk This Way: The Econometrics of Crosswalks," IZA Discussion Papers 17154, Institute of Labor Economics (IZA).
    2. Krzysztof Karbownik & Anthony Wray, 2019. "Long-Run Consequences of Exposure to Natural Disasters," Journal of Labor Economics, University of Chicago Press, vol. 37(3), pages 949-1007.
    3. Sarada, Sarada & Andrews, Michael J. & Ziebarth, Nicolas L., 2019. "Changes in the demographics of American inventors, 1870–1940," Explorations in Economic History, Elsevier, vol. 74(C).
    4. Hwang, Sam Il Myoung & Squires, Munir, 2024. "Linked samples and measurement error in historical US census data," Explorations in Economic History, Elsevier, vol. 93(C).

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