Low-Rank Estimation of Nonlinear Panel Data Models

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.