Naive maximum likelihood estimation of binary logit models with fixed effects leads to unreliable inference due to the incidental parameter problem. We study the case of three-dimensional panel data, where the model includes three sets of additive and overlapping unobserved effects. This encompasses models for network panel data, where senders and receivers maintain bilateral relationships over time, and fixed effects account for unobserved heterogeneity at the sender-time, receiver-time, and sender-receiver levels. In an asymptotic framework, where all three panel dimensions grow large at constant relative rates, we characterize the leading bias of the naive estimator. The inference problem we identify is particularly severe, as it is not possible to balance the order of the bias and the standard deviation. As a consequence, the naive estimator has a degenerating asymptotic distribution, which exacerbates the inference problem relative to other fixed effects estimators studied in the literature. To resolve the inference problem, we derive explicit expressions to debias the fixed effects estimator.
Debiased Inference for Dynamic Nonlinear Panels with Multi-dimensional Heterogeneities
School of Economics, Xiamen University（厦门大学经济学院）；Wang Yanan Institute for Studies in Economics, Xiamen University（厦门大学王亚南经济研究院）；Institute for Advanced Economic Research, Dongbei University of Finance and Economics（东北财经大学高级经济研究院）
Further results on the estimation of dynamic panel logit models with fixed effects
Kitazawa (2013, 2016) showed that the common parameters in the panel logit AR(1) model with strictly exogenous covariates and fixed effects are estimable at the root-n rate using the Generalized Method of Moments . Honoré and Weidner (2020) extended his results in various directions: they found additional moment conditions for the logit AR(1) model and also considered estimation of logit AR(p) models with p>1. In this note we prove a conjecture in their paper and show that for given values of the initial condition, the covariates and the common parameters 2^{T}-2T of their moment functions for…
Difference-in-Differences with Time-varying Continuous Treatments using Double/Debiased Machine Learning
Queen Mary University of London（伦敦大学玛丽女王学院）；University of Fribourg（弗里堡大学）；Bates White Economic Consulting（贝茨怀特经济咨询公司）；University of California, Los Angeles（加州大学洛杉矶分校）
