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; we also provide an R package for empirical implementation.

翻译：交互固定效应在线性面板模型中常被用于控制不可观测的异质性。尽管文献中已存在针对非线性模型的类似固定效应估计量（Chen, Fernandez-Val 和 Weidner, 2021），但由于其实现涉及求解高维非凸问题，该估计量在实际研究中应用有限。本文对Chen、Fernandez-Val和Weidner（2021）的理论分析进行补充，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。与以往提出的固定效应估计量不同，我们的估计量无需求解高维优化问题，可在大规模非线性面板中高效计算。所提方法包含两步：第一步，通过核范数正则化将优化问题凸化，获得包括固定效应在内的参数初步NNR估计量；第二步，以这些初步估计为初始值，采用标准梯度下降法求解原始优化问题的全局解。实际应用中，可结合本文的计算高效估计量与Chen、Fernandez-Val和Weidner（2021）的推断理论构建置信区间并进行假设检验；我们同时提供R包供实证应用。