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Conditional Moment Restrictions and Triangular Simultaneous Equations

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  • Jinyong Hahn

    (University of California, Los Angeles)

  • Geert Ridder

    (University of Southern California)

Abstract

It is shown that in a nonparametric nonseparable triangular system, the conditional moment restriction (CMR) does not identify the average structural function (ASF). The CMR identifies the ASF only if the model is structurally separable in observable covariates and unobservable random errors. This excludes, for instance, random coefficient models in which the CMR in general does not identify the average response. An implication of our results is that empirical researchers should use methods other than CMR if they want to estimate the average response in models that are not additively separable. © 2011 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Suggested Citation

  • Jinyong Hahn & Geert Ridder, 2011. "Conditional Moment Restrictions and Triangular Simultaneous Equations," The Review of Economics and Statistics, MIT Press, vol. 93(2), pages 683-689, May.
  • Handle: RePEc:tpr:restat:v:93:y:2011:i:2:p:683-689
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    References listed on IDEAS

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    1. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    2. Susanne Schennach & Halbert White & Karim Chalak, 2007. "Local Indirect Least Squares and Average Marginal Effects in Nonseparable Structural Systems," Boston College Working Papers in Economics 680, Boston College Department of Economics, revised 26 Dec 2009.
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    4. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    5. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 499-527.
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    7. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
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    Cited by:

    1. Kasy, Maximilian, "undated". "Instrumental variables with unrestricted heterogeneity and continuous treatment - DON'T CITE! SEE ERRATUM BELOW," Working Paper 33257, Harvard University OpenScholar.
    2. Schennach, Susanne & White, Halbert & Chalak, Karim, 2012. "Local indirect least squares and average marginal effects in nonseparable structural systems," Journal of Econometrics, Elsevier, vol. 166(2), pages 282-302.
    3. Jinhyun Lee, 2013. "A Consistent Nonparametric Bootstrap Test of Exogeneity," Discussion Paper Series, Department of Economics 201316, Department of Economics, University of St. Andrews.
    4. Lee, Jinhyun, 2013. "Sharp Bounds on Heterogeneous Individual Treatment Responses," SIRE Discussion Papers 2013-89, Scottish Institute for Research in Economics (SIRE).
    5. Maximilian Kasy, 2014. "Instrumental Variables with Unrestricted Heterogeneity and Continuous Treatment," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1614-1636.
    6. Lee, Jinhyun, 2013. "A Consistent Nonparametric Bootstrap Test of Exogeneity," SIRE Discussion Papers 2013-95, Scottish Institute for Research in Economics (SIRE).
    7. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
    8. Jinhyun Lee, 2013. "Sharp Bounds on Heterogeneous Individual Treatment Responses," Discussion Paper Series, Department of Economics 201310, Department of Economics, University of St. Andrews.
    9. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    10. repec:eee:econom:v:200:y:2017:i:2:p:238-250 is not listed on IDEAS

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