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 non-convex 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. To make our method readily applicable in practice, we also propose specific numerical algorithms for solving the involved optimization problems, establish their convergence, and provide their efficient implementation in our R package NNRPanel.

翻译：交互固定效应在标准线性面板模型中已被广泛用于控制异质性。尽管文献中已存在适用于非线性模型的类似固定效应估计量（Chen, Fernandez-Val 与 Weidner, 2021），但其实际应用受到严重制约，原因在于该方法的实现需解决高维非凸优化问题。本文在Chen、Fernandez-Val与Weidner（2021）理论分析基础上，提出一种新的计算高效估计量，该估计量在渐近意义上等价于原方法。与既有固定效应估计量不同，本方法无需求解高维非凸优化问题，可在大规模非线性面板数据中实现可行计算。我们提出的方法包含两个步骤：第一步，通过核范数正则化将优化问题凸化，获得包含固定效应在内的参数初步NNR估计量；第二步，以这些初步估计值为初始值，采用标准梯度下降法求解原始优化问题的全局最优解。为便于实际应用，我们还针对所涉优化问题提出具体数值算法，建立其收敛性证明，并在R包NNRPanel中提供高效实现方案。