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Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

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Author Info
Guido W. Imbens
Whitney K. Newey

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Abstract

This paper investigates identification and inference in a nonparametric structural model with instrumental variables and non-additive errors. We allow for non-additive errors because the unobserved heterogeneity in marginal returns that often motivates concerns about endogeneity of choices requires objective functions that are non-additive in observed and unobserved components. We formulate several independence and monotonicity conditions that are sufficient for identification of a number of objects of interest, including the average conditional response, the average structural function, as well as the full structural response function. For inference we propose a two-step series estimator. The first step consists of estimating the conditional distribution of the endogenous regressor given the instrument. In the second step the estimated conditional distribution function is used as a regressor in a nonlinear control function approach. We establish rates of convergence, asymptotic normality, and give a consistent asymptotic variance estimator.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0285.

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Date of creation: Nov 2002
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Handle: RePEc:nbr:nberte:0285

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  1. Andrew Chesher, 2002. "Local identification in nonseparable models," CeMMAP working papers CWP05/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  12. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November. [Downloadable!] (restricted)
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  14. repec:att:wimass:199217 is not listed on IDEAS
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  25. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May. [Downloadable!] (restricted)
  26. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-60, September.
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  27. J.D. Angrist & Guido W. Imbens & D.B. Rubin, 1993. "Identification of Causal Effects Using Instrumental Variables," NBER Technical Working Papers 0136, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  28. Charles F. Manski, 1993. "The Mixing Problem in Program Evaluation," NBER Technical Working Papers 0148, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  29. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier. [Downloadable!] (restricted)
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  31. repec:att:wimass:1920013 is not listed on IDEAS
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Cited by:
(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. Lingjie Ma & Roger Koenker, 2004. "Quantile regression methods for recursive structural equation models," CeMMAP working papers CWP01/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  2. Patrick Bajari & C. Lanier Benkard, 2001. "Demand Estimation With Heterogeneous Consumers and Unobserved Product Characteristics: A Hedonic Approach," NBER Technical Working Papers 0272, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society. [Downloadable!]
  4. Daniel McFadden, 2009. "The human side of mechanism design: a tribute to Leo Hurwicz and Jean-Jacque Laffont," Review of Economic Design, Springer, vol. 13(1), pages 77-100, April. [Downloadable!] (restricted)
  5. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics. [Downloadable!]
  6. Markus Frölich, 2006. "A Note on Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables," IZA Discussion Papers 2126, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  7. C. Lanier Benkard & Patrick Bajari, 2004. "Demand Estimation with Heterogeneous Consumers and Unobserved Product Characteristics: A Hedonic Approach," NBER Working Papers 10278, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  8. Sokbae Lee, 2004. "Endogeneity in Quantile Regression Models: A Control Function Approach," Econometric Society 2004 North American Summer Meetings 521, Econometric Society. [Downloadable!]
    Other versions:
  9. Patrick Bajari & C. Lanier Benkard, 2001. "Demand Estimation With Heterogeneous Consumers and Unobserved Product Characteristics: A Hedonic Approach," Working Papers 01010, Stanford University, Department of Economics. [Downloadable!]
  10. Christopher Timmins & Jennifer Murdock, 2006. "A Revealed Preference Approach to the Measurement of Congestion in Travel Cost Models," Working Papers tecipa-213, University of Toronto, Department of Economics. [Downloadable!]
  11. C. Lanier Benkard & Steven Berry, . "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: comment on B. Brown (1983) and Roehrig (1988)," Cowles Foundation Discussion Papers 1482, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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