Inference after discretizing time-varying unobserved heterogeneity

TL;DR

This paper develops a new inference method for linear panel data models with discretized, time-varying unobserved heterogeneity, addressing a gap in valid post-clustering inference without requiring exact group structures.

Contribution

It introduces a bias-reducing inference procedure based on double machine learning insights for models with nonseparable two-way heterogeneity, validated through theory and simulations.

Findings

The proposed method performs well asymptotically.

Simulations confirm the accuracy of the inference procedure.

Application to fiscal policy aligns with economic theory.

Abstract

Approximating time-varying unobserved heterogeneity by discrete types has become increasingly popular in economics. Yet, provably valid post-clustering inference for target parameters in models that do not impose an exact group structure is still lacking. This paper fills this gap in the leading case of a linear panel data model with nonseparable two-way unobserved heterogeneity. Building on insights from the double machine learning literature, we propose a simple inference procedure based on a bias-reducing moment. Asymptotic theory and simulations suggest excellent performance. In the application on fiscal policy we revisit, the novel approach yields conclusions in line with economic theory.