SMOOTHED ESTIMATING EQUATIONS FOR INSTRUMENTAL VARIABLES QUANTILE REGRESSION
针对工具变量分位数回归中估计方程含不连续指示函数的问题，提出平滑估计方程方法，通过选择最优带宽减小均方误差，提升估计精度和检验功效，并在JTPA数据中验证。
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 χ 2 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.