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Estimating average marginal effects in nonseparable structural systems

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  • Susanne Schennach

    ()
    (Institute for Fiscal Studies and University of Chicago)

  • Halbert White
  • Karim Chalak

Abstract

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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Bibliographic Info

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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Cited by:
  1. Kasy, Maximilian, . "Instrumental variables with unrestricted heterogeneity and continuous treatment," Working Paper 33257, Harvard University OpenScholar.
  2. Joeri Smits & Jeffrey S. Racine, 2013. "Testing Exclusion Restrictions in Nonseparable Triangular Models," Department of Economics Working Papers 2013-02, McMaster University.
  3. 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.
  4. 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.
  5. Susanne Schennach, 2012. "Measurement error in nonlinear models- a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Stefan Hoderlein & Halbert White, 2009. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," CeMMAP working papers CWP33/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. James J. Heckman, 2010. "Building Bridges Between Structural and Program Evaluation Approaches to Evaluating Policy," NBER Working Papers 16110, National Bureau of Economic Research, Inc.
  8. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
  9. 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.
  10. 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.
  11. 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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