Research

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. I propose a computationally feasible two-step estimation procedure. In the first step, I use nuclear-norm regularization (NNR) 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. I establish the asymptotic properties of both the preliminary and iterative estimators. I 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 my empirical application, I apply the proposed approach to study the cross-market arbitrage behavior of U.S. nonfinancial firms.

In this paper, I develop a general framework for high-dimensional panel data models characterized by moment restrictions and interactive fixed effects. The framework allows both the number of parameters and the number of moment conditions to grow with the sample size, encompassing a broad class of linear and nonlinear specifications. I focus on settings with many covariates, among which only a small subset has a nonzero impact on the parameters of interest, and unobserved heterogeneity is captured by a low-rank component structured through latent factors and their loadings. This structure poses challenges for conventional sparse estimators such as Lasso, and for standard factor estimators like PCA. To address these issues, I propose a new generalized method of moments (GMM) procedure that combines ℓ₁ and nuclear-norm penalties. Under general conditions, the proposed estimator consistently recovers both the nonzero coefficients and the latent low-rank matrix in the presence of many moments. Monte Carlo simulations demonstrate good finite-sample performance.