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Instrumental Variables Estimation of Nonparametric Models with Discrete Endogenous Regressors

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  • Mitali Das

    (Columbia University)

Abstract

This paper presents new instrumental variables estimators for nonparametric models with discrete endogenous regressors. The model specification is sufficiently general to include structural models, triangular simultaneous equations and certain models of measurement error. One motivation of the model specification is program evaluation problems, which arise frequently in empirical policy applications. Restricting the analysis to discrete endogenous regressors is an integral component of the analysis since a similar model with continuously distributed endogenous regressors is ill-posed and cannot be identified. The central contribution of this paper is a consistent two-step nonparametric instrumental variables estimator of the model. Large sample results, including global convergence rates and asmptotic normality are also provided. Discreteness of the regressors is shown to produce an additive representation of the model which leads to a simple verifiable condition for identification, and a restriction that is imposed in estimation. The proposed nonparametric two-step IV estimator is based on series estimation, which is particularly amenable to additive models, and yields efficiency gains in imposing additivity. The first step constitutes nonparametric estimation of the instrument, while the second step constructs the IV estimator from a linear combination of an instrument matrix and a matrix of the regression covariates. Nonparametric estimation of the instruments permits bypassing the specification of conditional distributions, but is heuristic, and does not affect the subsequent large sample results of the estimator. Linear functionals of the estimator are shown to be asymptotically normal, including root-n-consistent when certain regularity conditions hold.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1008.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1008

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  1. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
  2. James J. Heckman & Jeffrey A. Smith, 1997. "The Sensitivity of Experimental Impact Estimates: Evidence from the National JTPA Study," NBER Working Papers 6105, National Bureau of Economic Research, Inc.
  3. James M. Poterba & Steven F. Venti & David A. Wise, 1996. "How Retirement Saving Programs Increase Saving," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 91-112, Fall.
  4. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
  5. Robinson, P M, 1976. "Instrumental Variables Estimation of Differential Equations," Econometrica, Econometric Society, vol. 44(4), pages 765-76, July.
  6. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
  7. Ahn, Hyungtaik, 1995. "Nonparametric two-stage estimation of conditional choice probabilities in a binary choice model under uncertainty," Journal of Econometrics, Elsevier, vol. 67(2), pages 337-378, June.
  8. Hausman, Jerry A & Newey, Whitney K, 1995. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Econometrica, Econometric Society, vol. 63(6), pages 1445-76, November.
  9. Joshua Angrist, 1989. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," Working Papers 631, Princeton University, Department of Economics, Industrial Relations Section..
  10. Moffitt, Robert, 1983. "An Economic Model of Welfare Stigma," American Economic Review, American Economic Association, vol. 73(5), pages 1023-35, December.
  11. Donald W.K. Andrews, 1988. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Cowles Foundation Discussion Papers 874R, Cowles Foundation for Research in Economics, Yale University, revised May 1989.
  12. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-59, July.
  13. Andrews, Donald W.K. & Whang, Yoon-Jae, 1990. "Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality," Econometric Theory, Cambridge University Press, vol. 6(04), pages 466-479, December.
  14. Chevalier, Judith A, 1995. "Capital Structure and Product-Market Competition: Empirical Evidence from the Supermarket Industry," American Economic Review, American Economic Association, vol. 85(3), pages 415-35, June.
  15. Robert Moffitt & Barbara Wolfe, 1990. "The Effect of the Medicaid Program on Welfare Participation and Labor Supply," NBER Working Papers 3286, National Bureau of Economic Research, Inc.
  16. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 33-58.
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Cited by:
  1. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
  2. Andrew Chesher, 2004. "Identification in additive error models with discrete endogenous variables," CeMMAP working papers CWP11/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Arthur Lewbel, 2007. "Coherency And Completeness Of Structural Models Containing A Dummy Endogenous Variable," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1379-1392, November.
  4. Christopher Taber & Hidehiko Ichimura, 2001. "Propensity-Score Matching with Instrumental Variables," American Economic Review, American Economic Association, vol. 91(2), pages 119-124, May.

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