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.

翻译：交互固定效应在线性面板模型中已被常规控制。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 与 Weidner，2021），但其在应用研究中的使用仍相当有限，因为其实现涉及求解高维非凸优化问题。本文通过提出一种新的计算高效估计量，补充了 Chen、Fernandez-Val 与 Weidner（2021）的理论分析，该估计量在渐近意义上等价于他们的估计量。与先前提出的固定效应估计量不同，我们的估计量避免了求解高维优化问题，可在大规模非线性面板中实际计算。我们提出的方法包含两个步骤：第一步，利用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核范数正则化估计量；第二步，以这些初步估计值为初始点，通过标准梯度下降法求解原始优化问题的全局解。因此，在实践中，研究者可直接将我们的计算高效估计量与 Chen、Fernandez-Val 与 Weidner（2021）提供的推断理论相结合，以构建置信区间并进行假设检验。