This paper studies estimation and inference for linear quantile regression models with generated regressors. We suggest a practical two-step estimation procedure, where the generated regressors are computed in the first step. The asymptotic properties of the two-step estimator, namely, consistency and asymptotic normality are established. We show that the asymptotic variance-covariance matrix needs to be adjusted to account for the first-step estimation error. We propose a general estimator for the asymptotic variance-covariance, establish its consistency, and develop testing procedures for linear hypotheses in these models. Monte Carlo simulations to evaluate the finite-sample performance of the estimation and inference procedures are provided. Finally, we apply the proposed methods to study Engel curves for various commodities using data from the UK Family Expenditure Survey. We document strong heterogeneity in the estimated Engel curves along the conditional distribution of the budget share of each commodity. The empirical application also emphasizes that correctly estimating confidence intervals for the estimated Engel curves by the proposed estimator is of importance for inference.

中文翻译：

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使用生成的回归变量进行分位数回归

本文研究具有生成的回归变量的线性分位数回归模型的估计和推断。我们建议一种实用的两步估算程序，其中在第一步中计算生成的回归变量。建立了两步估计量的渐近性质，即一致性和渐近正态性。我们表明，需要调整渐近方差-协方差矩阵以解决第一步估计误差。我们提出渐近方差-协方差的一般估计量，建立其一致性，并为这些模型中的线性假设制定检验程序。提供了用于评估估计和推理程序的有限样本性能的蒙特卡洛模拟。最后，我们使用来自英国家庭支出调查的数据，将提出的方法用于研究各种商品的恩格尔曲线。我们记录了沿每种商品预算份额的有条件分布的估计恩格尔曲线中的强异质性。该经验应用还强调了，由所提出的估计器正确估计估计的恩格尔曲线的置信区间对于推断很重要。