Further results on the estimation of dynamic panel logit models with fixed effects

Abstract: 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. Honor\'e 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 the logit AR(1) model are linearly independent and span the set of valid moment functions, which is a 2^{T}-2T-dimensional linear subspace of the 2^{T}-dimensional vector space of real valued functions over the outcomes y element of {0,1}^{T}. We also prove that when p=2 and T element of {3,4,5}, there are, respectively, 2^{T}-4(T-1) and 2^{T}-(3T-2) linearly independent moment functions for the panel logit AR(2) models with and without covariates.