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Instrumental Variables Estimation of Nonparametric Models with Discrete Endogenous Regressors

  • Mitali Das

    (Columbia University)

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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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. Moffitt, Robert, 1983. "An Economic Model of Welfare Stigma," American Economic Review, American Economic Association, vol. 73(5), pages 1023-35, December.
  2. 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.
  3. Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Hausman, J.A. & Newey, W.K., 1992. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Working papers 93-2, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. James J. Heckman & Jeffrey Smith, 2000. "The Sensitivity of Experimental Impact Estimates (Evidence from the National JTPA Study)," NBER Chapters, in: Youth Employment and Joblessness in Advanced Countries, pages 331-356 National Bureau of Economic Research, Inc.
  6. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
  7. Robinson, P M, 1976. "Instrumental Variables Estimation of Differential Equations," Econometrica, Econometric Society, vol. 44(4), pages 765-76, July.
  8. 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.
  9. 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.
  10. 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.
  11. Donald W.K. Andrews & Yoon-Jae Whang, 1989. "Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality," Cowles Foundation Discussion Papers 925, Cowles Foundation for Research in Economics, Yale University.
  12. 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.
  13. 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.
  14. 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..
  15. 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.
  16. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-59, July.
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