SMOOTHED ESTIMATING EQUATIONS FOR INSTRUMENTAL VARIABLES QUANTILE REGRESSION

By David M. Kaplan, Yixiao Sun. Econometric Theory, 2016

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The moment conditions or estimating equations for instrumental variables quantile regression involve the discontinuous indicator function. We instead use smoothed estimating equations (SEE), with bandwidth h. We show that the mean squared error (MSE) of the vector of the SEE is minimized for some h > 0, leading to smaller asymptotic MSE of the estimating equations and associated parameter estimators. The same MSE-optimal h also minimizes the higher-order type I error of a SEE-based χ2 test and increases size-adjusted power in large samples. Computation of the SEE estimator also becomes simpler and more reliable, especially with (more) endogenous regressors. Monte Carlo simulations demonstrate all of these superior properties in finite samples, and we apply our estimator to JTPA data. Smoothing the estimating equations is not just a technical operation for establishing Edgeworth expansions and bootstrap refinements; it also brings the real benefits of having more precise estimators and more powerful tests.

Subfields: Economics and Econometrics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/69b25e928a1ae16a68308b74da0f65aacc711bfc

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Citations in the corpus

Fast Calibrated Additive Quantile Regression (2017, methodology): “Following Kaplan and Sun (2017), we use d combinations u1, . . . , ud such that ujk = 1(k = j), which is equivalent to minimizing the trace of nh4BBT − hE(AAT), or the sum of its eigenvalues.”
Smoothing Quantile Regressions (2019, methodology): “moothing objective function Rb h(b;˝) put forth by Horowitz (1998) replaces the indicator in the check function by a kernel counterpart: Rb h(b;˝) := 1 n P n i=1 e i(b) h ˝ K e i(b)=h i . As noted by Kaplan and Sun (2017), the rst-order derivative of this objective function is Rb(1) h (b;˝) = 1 n Xn”
Corporate Governance, Incentives, and Tax Avoidance (2015, methodology): “First we considered quantile regression with instrumental variables (e.g., Frolich and Melly, 2012; Kaplan and Sun, 2013; Powell, 2013).”
Quantiles via moments (2019, methodology): “25We note that our estimates are even closer to the ones obtained using the fully automated plug-in estimator of Kaplan and Sun (2017). 26It is possible to combine the IVQR with the method proposed by Chernozhukov, Fernández-Val, and Galichon (2010) to obtain structural quantile functions that do no”