Estimation and Inference in High-Dimensional Panel Data Models with Interactive Fixed Effects

TL;DR

This paper introduces advanced econometric methods for estimating and making inferences in high-dimensional panel data models with interactive fixed effects, extending existing approaches to handle large numbers of regressors.

Contribution

It develops a novel estimation and inference framework that extends the common correlated effects approach to high-dimensional settings with many regressors, including cases where regressors outnumber observations.

Findings

Estimator achieves consistent estimation in high-dimensional settings.

Desparsified estimator is asymptotically normal under regularity conditions.

Method performs well in simulations and empirical asset pricing application.

Abstract

We develop new econometric methods for estimation and inference in high-dimensional panel data models with interactive fixed effects. Our approach can be regarded as a non-trivial extension of the very popular common correlated effects (CCE) approach. Roughly speaking, we proceed as follows: We first construct a projection device to eliminate the unobserved factors from the model by applying a dimensionality reduction transform to the matrix of cross-sectionally averaged covariates. The unknown parameters are then estimated by applying lasso techniques to the projected model. For inference purposes, we derive a desparsified version of our lasso-type estimator. While the original CCE approach is restricted to the low-dimensional case where the number of regressors is small and fixed, our methods can deal with both low- and high-dimensional situations where the number of regressors is large and may even exceed the overall sample size. We derive theory for our estimation and inference methods both in the large-T-case, where the time series length T tends to infinity, and in the small-T-case, where T is a fixed natural number. Specifically, we derive the convergence rate of our estimator and show that its desparsified version is asymptotically normal under suitable regularity conditions. The theoretical analysis of the paper is complemented by a simulation study and an empirical application to characteristic based asset pricing.