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Local indirect least squares and average marginal effects in nonseparable structural systems

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  • Schennach, Susanne
  • White, Halbert
  • Chalak, Karim

Abstract

We study the scope of local indirect least squares (LILS) methods for nonparametrically estimating average marginal effects of an endogenous cause X on a response Y in triangular structural systems that need not exhibit linearity, separability, or monotonicity in scalar unobservables. One main finding is negative: in the fully nonseparable case, LILS methods cannot recover the average marginal effect. LILS methods can nevertheless test the hypothesis of no effect in the general nonseparable case. We provide new nonparametric asymptotic theory, treating both the traditional case of observed exogenous instruments Z and the case where one observes only error-laden proxies for Z.

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  • 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.
  • Handle: RePEc:eee:econom:v:166:y:2012:i:2:p:282-302
    DOI: 10.1016/j.jeconom.2011.09.041
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    1. Pedro Carneiro & James J. Heckman & Edward Vytlacil, 2010. "Evaluating Marginal Policy Changes and the Average Effect of Treatment for Individuals at the Margin," Econometrica, Econometric Society, vol. 78(1), pages 377-394, January.
    2. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    3. Hoderlein, Stefan & Winter, Joachim, 2010. "Structural measurement errors in nonseparable models," Journal of Econometrics, Elsevier, vol. 157(2), pages 432-440, August.
    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. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
    6. Karim Chalak & Halbert White, 2011. "Viewpoint: An extended class of instrumental variables for the estimation of causal effects," Canadian Journal of Economics, Canadian Economics Association, vol. 44(1), pages 1-51, February.
    7. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    8. 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.
    9. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
    10. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    11. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    12. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    13. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, September.
    14. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    15. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    16. Halbert White & Karim Chalak, 2008. "Identifying Structural Effects in Nonseparable Systems Using Covariates," Boston College Working Papers in Economics 734, Boston College Department of Economics.
    17. Richard Blundell & James L. Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    19. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    20. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    21. James Heckman, 1997. "Instrumental Variables: A Study of Implicit Behavioral Assumptions Used in Making Program Evaluations," Journal of Human Resources, University of Wisconsin Press, vol. 32(3), pages 441-462.
    22. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    23. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    24. Joseph G. Altonji & Rosa L. Matzkin, 2001. "Panel Data Estimators for Nonseparable Models with Endogenous Regressors," NBER Technical Working Papers 0267, National Bureau of Economic Research, Inc.
    25. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    26. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    27. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    28. Schennach, Susanne M., 2004. "Nonparametric Regression In The Presence Of Measurement Error," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1046-1093, December.
    29. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
    30. Bertail, Patrice & Haefke, Christian & Politis, D.N.Dimitris N. & White, Halbert, 2004. "Subsampling the distribution of diverging statistics with applications to finance," Journal of Econometrics, Elsevier, vol. 120(2), pages 295-326, June.
    31. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    32. Politis, Dimitris N. & Romano, Joseph P., 1999. "Multivariate Density Estimation with General Flat-Top Kernels of Infinite Order," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 1-25, January.
    33. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    34. Kristin F. Butcher & Anne Case, 1994. "The Effect of Sibling Sex Composition on Women's Education and Earnings," The Quarterly Journal of Economics, Oxford University Press, vol. 109(3), pages 531-563.
    35. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    36. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
    37. Karim Chalak & Halbert White, 2007. "An Extended Class of Instrumental Variables for the Estimation of Causal Effects," Boston College Working Papers in Economics 692, Boston College Department of Economics, revised 30 Nov 2009.
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    Cited by:

    1. Xavier d'Haultfoeuille & Stefan Hoderlein & Yuya Sasaki, 2013. "Nonlinear difference-in-differences in repeated cross sections with continuous treatments," CeMMAP working papers CWP40/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. James J. Heckman, 2010. "Building Bridges between Structural and Program Evaluation Approaches to Evaluating Policy," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 356-398, June.
    3. Joeri Smits & Jeffrey S. Racine, 2013. "Testing Exclusion Restrictions in Nonseparable Triangular Models," Department of Economics Working Papers 2013-02, McMaster University.
    4. James J. Heckman & John Eric Humphries & Gregory Veramendi, 2016. "Returns to Education: The Causal Effects of Education on Earnings, Health and Smoking," NBER Working Papers 22291, National Bureau of Economic Research, Inc.
    5. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    6. Taisuke Otsu & Luke Taylor, 2014. "Estimation of Nonseparable Models with Censored Dependent Variables and Endogenous Regressors," STICERD - Econometrics Paper Series 575, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. repec:cep:stiecm:/2014/575 is not listed on IDEAS
    8. Karun Adusumilli & Taisuke Otsu, 2015. "Nonparametric instrumental regression with errors in variables," STICERD - Econometrics Paper Series /2015/585, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Heckman, James J. & Humphries, John Eric & Veramendi, Gregory, 2016. "Dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 191(2), pages 276-292.
    10. Kasy, Maximilian, "undated". "Instrumental variables with unrestricted heterogeneity and continuous treatment - DON'T CITE! SEE ERRATUM BELOW," Working Paper 33257, Harvard University OpenScholar.
    11. Maximilian Kasy, 2014. "Instrumental Variables with Unrestricted Heterogeneity and Continuous Treatment," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1614-1636.
    12. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
    13. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. 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.

    More about this item

    Keywords

    Indirect least squares; Instrumental variables; Measurement error; Nonparametric estimator; Nonseparable structural equations;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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

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