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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 Microeconomics.ca Website in its series Micro Theory 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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Keywords: quantile regression; instrumental variables; weak identification;

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  1. Phillips, Peter C B, 1984. "The Exact Distribution of LIML: I," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 249-61, February.
  2. Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," The Journal of Business, University of Chicago Press, vol. 63(1), pages S125-40, January.
  3. Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-94, September.
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  13. Sakata, S., 1998. "Instrumental Variable Estimation Based on Mean Absolute Deviation," Papers 98-08, Michigan - Center for Research on Economic & Social Theory.
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  17. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
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