短面板中的平稳误差与分位数回归
Stationary Errors and Quantile Regression in Short Panels
AI总结：
本文针对带无约束个体效应和时间平稳特异扰动的线性面板模型，提出一种两步最小距离固定T估计量，该估计量根-n一致且渐近正态，经蒙特卡洛实验验证表现良好。
AI中文摘要：
本文研究带有无约束个体效应和时间平稳特异扰动的线性面板模型。我们首先证明，在分位数模型中，平稳性是一个强约束。在具有分位数依赖斜率的线性条件分位数设定中，跨期条件残差分布的相等性通常会迫使斜率系数在分位数指数上保持恒定。因此，平稳误差模型识别的是一个共同位置系数，而非一组分位数特定的斜率效应。随后，我们开发了该共同系数的固定T估计量：对每个时期，我们将结果变量对全部解释变量历史进行横截面分位数回归。平稳性使得复合个体效应与扰动的分位数投影在跨期特定解释变量间保持一致。当T≥2时，所得投影系数的对角块与非对角块之间的差异可识别共同斜率。我们通过两步最小距离估计量整合所有此类约束，该估计量在固定T时满足根-n一致性与渐近正态性，允许个体内跨期存在无约束依赖，且无需估计个体效应。我们提供了一致的解析协方差估计量、聚类自助法以及对平稳性隐含的投影约束的过度识别检验。大量蒙特卡洛实验表明，该估计量在多种设定下表现良好。
英文摘要：
This paper studies a linear panel model with an unrestricted individual effect and a time- stationary idiosyncratic disturbance. We first show that stationarity is a strong restriction in a quantile model. In a linear conditional quantile specification with quantile-dependent slopes, equality of the conditional residual distributions across periods generically forces the slope coefficient to be constant over the quantile index. Thus, a stationary-error model identifies a common location coefficient rather than a collection of quantile-specific slope effects. We then develop a fixed-T estimator of this common coefficient. For each period, we run a cross- sectional quantile regression of the outcome on the full history of regressors. Stationarity makes the quantile projection of the composite individual effect and disturbance common across the period-specific regressions. Differences between diagonal and off-diagonal blocks of the resulting projection coefficients therefore identify the common slope whenever T>=2. We combine all such restrictions by a two-step minimum-distance estimator. The estimator is root-n-consistent and asymptotically normal with fixed T, permits unrestricted dependence across periods within an individual, and does not estimate the individual effects. We provide a consistent analytic covariance estimator, a cluster bootstrap, and an overidentification test of the projection restrictions implied by stationarity. Extensive Monte Carlo experiments show adequate performance under various designs.
