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Instrumental Variables Estimation and Weak-Identification-Robust Inference Based on a Conditional Quantile Restriction

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  • Marmer, Vadim
  • Sakata, Shinichi

Abstract

Extending the L1-IV approach proposed by Sakata (1997, 2007), we develop a new method, named the $rho_{tau}$-IV estimation, to estimate structural equations based on the conditional quantile restriction imposed on the error terms. We study the asymptotic behavior of the proposed estimator and show how to make statistical inferences on the regression parameters. Given practical importance of weak identification, a highlight of the paper is a proposal of a test robust to the weak identification. The statistics used in our method can be viewed as a natural counterpart of the Anderson and Rubin's (1949) statistic in the $rho_{tau}$-IV estimation.

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Bibliographic Info

Paper provided by Vancouver School of Economics in its series Microeconomics.ca working papers with number vadim_marmer-2011-26.

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Length: 34 pages
Date of creation: 28 Sep 2011
Date of revision: 28 Sep 2011
Handle: RePEc:ubc:pmicro:vadim_marmer-2011-26

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Web page: http://www.economics.ubc.ca/

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Keywords: quantile regression; instrumental variables; weak identification;

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  1. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
  2. Donald W.K. Andrews, 1990. "Generic Uniform Convergence," Cowles Foundation Discussion Papers 940, Cowles Foundation for Research in Economics, Yale University.
  3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, November.
  4. Peter C.B. Phillips, 1983. "The Exact Distribution of LIML: II," Cowles Foundation Discussion Papers 663, Cowles Foundation for Research in Economics, Yale University.
  5. Charles R. Nelson & Richard Startz, 1988. "The Distribution of the Instrumental Variables Estimator and Its t-RatioWhen the Instrument is a Poor One," NBER Technical Working Papers 0069, National Bureau of Economic Research, Inc.
  6. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  7. Sakata, Shinichi, 2007. "Instrumental variable estimation based on conditional median restriction," Journal of Econometrics, Elsevier, vol. 141(2), pages 350-382, December.
  8. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  9. Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-94, September.
  10. Sakata, S., 1998. "Instrumental Variable Estimation Based on Mean Absolute Deviation," Papers 98-08, Michigan - Center for Research on Economic & Social Theory.
  11. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
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Cited by:
  1. Victor Chernozhukov & Christian Hansen, 2013. "Quantile models with endogeneity," CeMMAP working papers CWP25/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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