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Estimating average marginal effects in nonseparable structural systems

  • Susanne Schennach

    ()

    (Institute for Fiscal Studies and University of Chicago)

  • Halbert White
  • Karim Chalak

We provide nonparametric estimators of derivative ratio-based average marginal effects of an endogenous cause, X, on a response of interest, Y , for a system of recursive structural equations. The system need not exhibit linearity, separability, or monotonicity. Our estimators are local indirect least squares estimators analogous to those of Heckman and Vytlacil (1999, 2001) who treat a latent index model involving a binary X. We treat the traditional case of an observed exogenous instrument (OXI)and the case where one observes error-laden proxies for an unobserved exogenous instrument (PXI). For PXI, we develop and apply new results for estimating densities and expectations conditional on mismeasured variables. For both OXI and PXI, we use infnite order flat-top kernels to obtain uniformly convergent and asymptotically normal nonparametric estimators of instrument-conditioned effects, as well as root-n consistent and asymptotically normal estimators of average effects.

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File URL: http://cemmap.ifs.org.uk/wps/cwp3107.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP31/07.

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Date of creation: Dec 2007
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Handle: RePEc:ifs:cemmap:31/07
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  6. 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.
  7. James J. Heckman & Edward J. Vytlacil, 2000. "Local Instrumental Variables," NBER Technical Working Papers 0252, National Bureau of Economic Research, Inc.
  8. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
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  18. Hoderlein, Stefan & Winter, Joachim, 2009. "Structural Measurement Errors in Nonseparable Models," Discussion Papers in Economics 9192, University of Munich, Department of Economics.
  19. 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.
  20. Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
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  26. Stefan Hoderlein, 2009. "How Many Consumers are Rational?," Boston College Working Papers in Economics 748, Boston College Department of Economics.
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  28. Susanne M. Schennach, 2004. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometric Society 2004 North American Summer Meetings 602, Econometric Society.
  29. Schennach, Susanne M., 2004. "Nonparametric Regression In The Presence Of Measurement Error," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1046-1093, December.
  30. 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, 07.
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  35. 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.
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