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Specification Analysis of Structural Quantile Regression Models

  • Juan Carlos Escanciano
  • Chuan Goh

This paper introduces a broad family of tests for the hypothesis of linearity in parameters of functions that are identified by conditional quantile restrictions involving instrumental variables. These tests are tantamount to assessments of lack of fit for quantile regression models involving endogenous conditioning variables, and may be applied to assess the validity of post-estimation inferences regarding the counterfactual effect of endogenous treatments on the distribution of outcomes. We show that the use of an orthogonal projection on the tangent space of nuisance parameters at each quantile index improves power performance and facilitates the simulation of critical values via the application of simple multiplier-type bootstrap procedures. Monte Carlo evidence is included, along with an application to an empirical analysis of the structure of demand for a particular subsegment of the market for anti-bacterial drugs in India.

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Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-415.

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Length: 52 pages
Date of creation: 19 Nov 2010
Date of revision:
Handle: RePEc:tor:tecipa:tecipa-415
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  1. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
  2. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of semiparametric models when the criterion function is not smooth," LSE Research Online Documents on Economics 2167, London School of Economics and Political Science, LSE Library.
  3. Joel Horowitz & Sokbae Lee, 2007. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," CeMMAP working papers CWP02/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly, 2008. "Inference On Counterfactual Distributions," Boston University - Department of Economics - Working Papers Series wp2008-005, Boston University - Department of Economics.
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  7. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
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  14. Sakov, Anat & Bickel, Peter J., 2000. "An Edgeworth expansion for the m out of n bootstrapped median," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 217-223, September.
  15. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
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  17. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
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  20. Escanciano, J. Carlos, 2009. "On The Lack Of Power Of Omnibus Specification Tests," Econometric Theory, Cambridge University Press, vol. 25(01), pages 162-194, February.
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  24. Zheng, John Xu, 1998. "A Consistent Nonparametric Test Of Parametric Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 14(01), pages 123-138, February.
  25. Escanciano, J. Carlos, 2007. "Weak convergence of non-stationary multivariate marked processes with applications to martingale testing," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1321-1336, August.
  26. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
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  29. Blundell, Richard & Powell, James L., 2007. "Censored regression quantiles with endogenous regressors," Journal of Econometrics, Elsevier, vol. 141(1), pages 65-83, November.
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