Low-Rank Estimation of Nonlinear Panel Data Models

TL;DR

This paper develops a novel two-step estimation method for nonlinear panel data models with interactive fixed effects, combining nuclear-norm regularization and iterative inference to improve estimation accuracy and factor determination.

Contribution

It introduces a general framework for parameter estimation in nonlinear panel models with non-convex objectives, including a new two-step procedure and asymptotic analysis.

Findings

Effective in determining the number of factors

Improves convergence rate of coefficient estimators

Demonstrates accuracy through Monte Carlo simulations

Abstract

This paper investigates nonlinear panel regression models with interactive fixed effects and introduces a general framework for parameter estimation under potentially non-convex objective functions. We propose a computationally feasible two-step estimation procedure. In the first step, nuclear-norm regularization (NNR) is used to obtain preliminary estimators of the coefficients of interest, factors, and factor loadings. The second step involves an iterative procedure for post-NNR inference, improving the convergence rate of the coefficient estimator. We establish the asymptotic properties of both the preliminary and iterative estimators. We also study the determination of the number of factors. Monte Carlo simulations demonstrate the effectiveness of the proposed methods in determining the number of factors and estimating the model parameters. In our empirical application, we apply the proposed approach to study the cross-market arbitrage behavior of U.S. nonfinancial firms.