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Instrumental Variables Estimation of Nonparametric Models with Discrete Endogenous Regressors

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Mitali Das (Columbia University)

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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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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. 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. [Downloadable!] (restricted)
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  2. Poterba, James M & Venti, Steven F & Wise, David A, 1996. "How Retirement Saving Programs Increase Saving," Journal of Economic Perspectives, American Economic Association, vol. 10(4), pages 91-112, Fall. [Downloadable!] (restricted)
  3. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," Review of Economic Studies, Blackwell Publishing, vol. 70(1), pages 33-58, January.
  4. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, vol. 80(3), pages 313-36, June.
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  7. 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, Yale University. [Downloadable!]
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  8. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-59, July. [Downloadable!] (restricted)
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  9. Robinson, P M, 1976. "Instrumental Variables Estimation of Differential Equations," Econometrica, Econometric Society, vol. 44(4), pages 765-76, July. [Downloadable!] (restricted)
  10. Moffitt, Robert & Wolfe, Barbara L, 1992. "The Effect of the Medicaid Program on Welfare Participation and Labor Supply," The Review of Economics and Statistics, MIT Press, vol. 74(4), pages 615-26, November. [Downloadable!] (restricted)
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  11. 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. [Downloadable!] (restricted)
  12. Moffitt, Robert, 1983. "An Economic Model of Welfare Stigma," American Economic Review, American Economic Association, vol. 73(5), pages 1023-35, December. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
  2. Arthur Lewbel, 1997. "Coherence and Completeness of Structural Models Containing a Dummy Endogenous Variable," Boston College Working Papers in Economics 456, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
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  3. Hidehiko Ichimura & Christopher Taber, 2001. "Propensity-Score Matching with Instrumental Variables," American Economic Review, American Economic Association, vol. 91(2), pages 119-124, May. [Downloadable!] (restricted)
  4. Andrew Chesher, 2003. "Nonparametric identification under discrete variation," CeMMAP working papers CWP19/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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