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

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 tech- niques 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 esti- mator and show that its desparsified version is asymptotically normal under suit- able regularity conditions. The theoretical analysis of the paper is complemented by a simulation study and an empirical application to characteristic based asset pricing.