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Identification of Average Random Coefficients under Magnitude and Sign Restrictions on Confounding

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  • Karim Chalak

    ()
    (Boston College)

Abstract

This paper studies measuring the average effects of X on Y in a structural system with random coefficients and confounding. We do not require (conditionally) exogenous regressors or instruments. Using proxies W for the confounders U, we ask how do the average direct effects of U on Y compare in magnitude and sign to those of U on W. Exogeneity and equi- or proportional confounding are limit cases yielding full identification. Alternatively, the elements of beta-hat are partially identified in a sharp bounded interval if W is sufficiently sensitive to U, and sharp upper or lower bounds may obtain otherwise. We extend this analysis to accommodate conditioning on covariates and a semiparametric separable specification as well as a panel structure and proxies included in the Y equation. After studying estimation and inference, we apply this method to study the financial return to education and the black-white wage gap.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 816.

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Date of creation: 04 Dec 2012
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Handle: RePEc:boc:bocoec:816

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Keywords: causality; confounding; endogeneity; omitted variable; partial identification; proxy;

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  1. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
  2. Jacob A. Mincer, 1974. "Schooling, Experience, and Earnings," NBER Books, National Bureau of Economic Research, Inc, number minc74-1.
  3. Jacob A. Mincer, 1974. "Introduction to "Schooling, Experience, and Earnings"," NBER Chapters, in: Schooling, Experience, and Earnings, pages 1-4 National Bureau of Economic Research, Inc.
  4. Jörg Stoye, 2008. "More on confidence intervals for partially identified parameters," CeMMAP working papers CWP11/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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