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