Tractable Estimation of Nonlinear Panels with Interactive Fixed Effects

TL;DR

This paper introduces a computationally efficient estimator for nonlinear panel models with interactive fixed effects, making such models more practical for large datasets by avoiding complex high-dimensional optimization.

Contribution

It proposes a new two-step estimator that convexifies the problem with nuclear norm regularization and then finds the global solution via gradient descent, improving computational feasibility.

Findings

Estimator is asymptotically equivalent to existing methods.

Method is feasible for large nonlinear panels.

Provides an R package for implementation.

Abstract

Interactive fixed effects are routinely controlled for in linear panel models. While an analogous fixed effects (FE) estimator for nonlinear models has been available in the literature (Chen, Fernandez-Val and Weidner, 2021), it sees much more limited use in applied research because its implementation involves solving a high-dimensional non-convex problem. In this paper, we complement the theoretical analysis of Chen, Fernandez-Val and Weidner (2021) by providing a new computationally efficient estimator that is asymptotically equivalent to their estimator. Unlike the previously proposed FE estimator, our estimator avoids solving a high-dimensional optimization problem and can be feasibly computed in large nonlinear panels. Our proposed method involves two steps. In the first step, we convexify the optimization problem using nuclear norm regularization (NNR) and obtain preliminary NNR estimators of the parameters, including the fixed effects. Then, we find the global solution of the original optimization problem using a standard gradient descent method initialized at these preliminary estimates. Thus, in practice, one can simply combine our computationally efficient estimator with the inferential theory provided in Chen, Fernandez-Val and Weidner (2021) to construct confidence intervals and perform hypothesis testing; we also provide an R package for empirical implementation.