🤖 AI Summary
This paper addresses high-dimensional panel data models with interactive fixed effects. We propose a unified estimation and inference method applicable to both low-dimensional and ultra-high-dimensional settings (where $p gg N,T$). Methodologically, we extend the common correlated effects (CCE) approach to high dimensions by constructing a dimension-reduction projection operator based on cross-sectional averages of regressors to eliminate unobserved common factors. Subsequently, we develop a debiased Lasso estimator that achieves asymptotic normality—rigorously established under both large-$T$ and small-$T$ asymptotic frameworks—and attains the optimal convergence rate. Theoretical analysis guarantees valid statistical properties, including consistency, asymptotic normality, and oracle efficiency. Monte Carlo simulations and an empirical asset pricing application demonstrate the method’s effectiveness, robustness, and practical utility across diverse data-generating environments.
📝 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.
