Inference for Heterogeneous Effects using Low-Rank Estimation of Factor Slopes

TL;DR

This paper introduces a low-rank estimation method for panel data models with heterogeneous effects, enabling inference on individual and average effects by exploiting a factor structure in slopes.

Contribution

It proposes a multi-step estimation procedure using low-rank regularization, sample-splitting, and orthogonalization for inference in models with heterogeneous effects.

Findings

Estimator is asymptotically normal.

Method effectively estimates effects in simulations.

Applied to minimum wage and employment data.

Abstract

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.