Tractable Estimation of Nonlinear Panels with Interactive Fixed Effects

2025-11-19

AI Summary

To address the high-dimensional nonconvex optimization challenge in estimating interactive fixed effects for nonlinear panel models, this paper proposes an efficient two-step estimation method. In the first step, nuclear norm regularization (NNR) convexifies the original nonconvex objective, yielding a consistent initial estimator. In the second step, gradient descent is applied to the original (nonconvex) objective function, initialized at the NNR-based estimate, guaranteeing convergence to the global optimum. By circumventing direct optimization of the high-dimensional nonconvex problem, the method substantially improves computational efficiency and numerical stability. The resulting estimator is asymptotically equivalent to existing optimal estimators. Moreover, the procedure preserves standard inferential validity: conventional asymptotic theory applies, enabling straightforward construction of confidence intervals and hypothesis tests. This framework provides a practical, scalable tool for empirical analysis of large-scale nonlinear panel data.

Technology Category

• Search and Optimization: Non-convex Optimization
• Natural Language Processing: Learning & Optimization for NLP
• Machine Learning: Kernel Methods

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Developing computationally efficient estimator for nonlinear panel models
• Avoiding high-dimensional non-convex optimization in fixed effects estimation
• Enabling feasible computation for large nonlinear panel datasets

Innovation

• Convexify problem via nuclear norm regularization
• Use standard gradient descent for global solution
• Avoid high-dimensional non-convex optimization computationally