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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.

Suggested Citation

  • Karim Chalak, 2012. "Identification of Average Random Coefficients under Magnitude and Sign Restrictions on Confounding," Boston College Working Papers in Economics 816, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:816
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    References listed on IDEAS

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    1. James Heckman & Edward Vytlacil, 1998. "Instrumental Variables Methods for the Correlated Random Coefficient Model: Estimating the Average Rate of Return to Schooling When the Return is Correlated with Schooling," Journal of Human Resources, University of Wisconsin Press, vol. 33(4), pages 974-987.
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    4. 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.
    5. Peter Arcidiacono & Patrick Bayer & Aurel Hizmo, 2010. "Beyond Signaling and Human Capital: Education and the Revelation of Ability," American Economic Journal: Applied Economics, American Economic Association, vol. 2(4), pages 76-104, October.
    6. O. Ashenfelter & D. Card (ed.), 1999. "Handbook of Labor Economics," Handbook of Labor Economics, Elsevier, edition 1, volume 3, number 3.
    7. 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.
    8. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, vol. 56(2), pages 129-133, October.
    9. Victor Chernozhukov & Roberto Rigobon & Thomas M. Stoker, 2010. "Set identification and sensitivity analysis with Tobin regressors," Quantitative Economics, Econometric Society, vol. 1(2), pages 255-277, November.
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    Cited by:

    1. Galvao, Antonio F. & Montes-Rojas, Gabriel & Song, Suyong, 2017. "Endogeneity bias modeling using observables," Economics Letters, Elsevier, vol. 152(C), pages 41-45.

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    More about this item

    Keywords

    causality; confounding; endogeneity; omitted variable; partial identification; proxy;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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