利用因子斜率的低秩估计推断异质效应
Inference for Heterogeneous Effects using Low-Rank Estimation of Factor Slopes
摘要：
我们研究了具有一般异质效应的面板数据模型，其中允许斜率在个体和时间上变化。我们采用的关键降维假设是，异质斜率可以表示为具有因子结构，使得高维斜率矩阵是低秩的，因此可以使用低秩正则化回归进行估计。我们提供了一个简单的多步估计程序的异质性影响。该程序利用样本分裂和正交化，以适应以下使用惩罚低秩估计推理。我们正式验证所得到的估计是渐近正常的，允许简单的建设推论语句{个人的时间特异性的影响和横截面平均这些影响}。我们说明了所提出的方法在模拟实验中，并通过估计最低工资对就业的影响。
英文摘要：
We study a panel data model with general heterogeneous effects where slopes are allowed to vary across both individuals and over time. The key dimension reduction assumption we employ is that the heterogeneous slopes can be expressed as having a factor structure so that the high-dimensional slope matrix is low-rank and can thus be estimated using low-rank regularized regression. We provide a simple multi-step estimation procedure for the heterogeneous effects. The procedure makes use of sample-splitting and orthogonalization to accommodate inference following the use of penalized low-rank estimation. We formally verify that the resulting estimator is asymptotically normal allowing simple construction of inferential statements for {the individual-time-specific effects and for cross-sectional averages of these effects}. We illustrate the proposed method in simulation experiments and by estimating the effect of the minimum wage on employment.
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