A Linear Estimator for Factor-Augmented Fixed-T Panels With Endogenous Regressors

A novel method-of-moments approach is proposed for the estimation of factor-augmented panel data models with endogenous regressors when <i>T</i> is fixed. The underlying methodology involves approximating the unobserved common factors using observed factor proxies. The resulting moment conditions are linear in the parameters. The proposed approach addresses several issues which arise with existing nonlinear estimators that are available in fixed <i>T</i> panels, such as local minima-related problems, a sensitivity to particular normalization schemes, and a potential lack of global identification. We apply our approach to a large panel of households and estimate the price elasticity of urban water demand. A simulation study confirms that our approach performs well in finite samples.

本文提出一种新颖的矩估计法（Method of Moments），用于解决固定时间维度T下、带有内生解释变量的增因子面板数据模型的参数估计问题。该方法的核心逻辑是通过观测得到的因子代理变量（factor proxies），对不可观测共同因子（unobserved common factors）进行近似刻画。由此得到的矩条件关于模型参数呈线性形式。本文所提方法可有效解决现有固定T面板框架下非线性估计方法所存在的若干问题，包括局部极小值相关问题、对特定归一化方案的敏感性，以及潜在的全局识别缺失问题。我们将该方法应用于大规模家庭面板数据集，并据此估计了城市用水需求的价格弹性。最终通过模拟实验证实，该方法在有限样本情境下表现优异。