This paper considers estimation of a dynamic discrete choice model with second order state dependence in the presence of strictly exogenous time-varying explanatory variables. We propose a new method for estimating such models, and a small Monte Carlo study suggests that the method performs well in practice. The method is used to test for duration dependence in labour market spells for young people in France. The novelty in the application is that we are able to control for time-varying explanatory variables. In a discrete time duration model, duration dependence will result in second order state dependence, and the paper therefore also adds to the literature on estimation of duration models with unobserved heterogeneity.