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Smoothed instrumental variables quantile regression, with estimation of quantile Euler equations

Listed author(s):
  • Luciano de Castro

    (University of Iowa)

  • Antonio F. Galvao

    (University of Arizona)

  • David M. Kaplan

    ()

    (University of Missouri)

This paper develops theory for feasible estimation and testing of finite-dimensional parameters identified by general conditional quantile restrictions. This includes instrumental variables nonlinear quantile regression as a special case, under much weaker assumptions than previously seen in the literature. More specifically, we consider a set of unconditional moments implied by the conditional quantile restrictions and provide conditions for local identification. Since estimators based on the sample moments are generally impossible to compute numerically in practice, we study a feasible estimator based on \emph{smoothed} sample moments. We establish consistency and asymptotic normality under general conditions that allow for weakly dependent data and nonlinear structural models, and we explore options for testing general nonlinear hypotheses.Simulations with iid and time series data illustrate the finite-sample properties of the estimators and tests. Our in-depth empirical application concerns the consumption Euler equation derived from quantile utility maximization. Advantages of the quantile Euler equation include robustness to fat tails, decoupling of risk attitude from the elasticity of intertemporal substitution, and log-linearization without any approximation error. For the four countries we examine, the quantile estimates of discount factor and elasticity of intertemporal substitution are economically reasonable for a range of quantiles just above the median, even when two-stage least squares estimates are not reasonable. Code is provided for all methods, simulations, and applications at the third author's website.

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File URL: https://economics.missouri.edu/sites/default/files/wp-files/dcgk_2017_sivqr_euler1.pdf
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Paper provided by Department of Economics, University of Missouri in its series Working Papers with number 1710.

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Length: 44 pages
Date of creation: 10 Jul 2017
Handle: RePEc:umc:wpaper:1710
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  1. Manski, C.F., 1988. "Ordinal Utility Models Of Decision Making Under Uncertainty," Working papers 363, Wisconsin Madison - Social Systems.
  2. Kaplan, David M. & Sun, Yixiao, 2017. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," Econometric Theory, Cambridge University Press, vol. 33(01), pages 105-157, February.
  3. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-265, April.
  4. Giovannetti, Bruno C., 2013. "Asset pricing under quantile utility maximization," Review of Financial Economics, Elsevier, vol. 22(4), pages 169-179.
  5. Alexis Akira Toda & Kieran Walsh, 2015. "The Double Power Law in Consumption and Implications for Testing Euler Equations," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1177-1200.
  6. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
  7. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  8. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, 03.
  9. Chen, Xiaohong & Liao, Zhipeng, 2015. "Sieve semiparametric two-step GMM under weak dependence," Journal of Econometrics, Elsevier, vol. 189(1), pages 163-186.
  10. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
  11. Toda, Alexis Akira & Walsh, Kieran James, 2016. "Fat Tails and Spurious Estimation of Consumption-Based Asset Pricing Models," MPRA Paper 78980, University Library of Munich, Germany.
  12. Kengo Kato, 2012. "Asymptotic normality of Powell’s kernel estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 255-273, April.
  13. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
  14. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
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