  In this paper we first propose a root-n-consistent Conditional Maximum
Likelihood (CML) estimator for all the common parameters in the panel logit
AR(p) model with strictly exogenous covariates and fixed effects. Our CML
estimator (CMLE) converges in probability faster and is more easily computed
than the kernel-weighted CMLE of Honor\'e and Kyriazidou (2000). Next, we
propose a root-n-consistent CMLE for the coefficients of the exogenous
covariates only. We also discuss new CMLEs for the panel logit AR(p) model
without covariates. Finally, we propose CMLEs for multinomial dynamic panel
logit models with and without covariates. All CMLEs are asymptotically normally
distributed.
