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.