  We show that a dynamic logit model for binary panel data allowing for state
dependence and unobserved heterogeneity may be accurately approximated by a
quadratic exponential model, the parameters of which have the same
interpretation that they have in the true model. We also show how we can
eliminate the parameters for the unobserved heterogeneity from the
approximating model by conditioning on the total scores, i.e. sum of the
response variables for any individual in the panel. This allows to construct an
approximate conditional likelihood for the dynamic logit model, by maximizing
which we can estimate the parameters for the covariates and the state
dependence. This estimator is very simple to compute and, by means of a
simulation study, we show that it is competitive in terms of efficiency with
the estimator of Honore' & Kyriazidou (2000). Finally, we outline the extension
of the proposed approach to the case of more elaborated structures for the
state dependence and to that of categorical response variables with more than
two levels.
