BLP estimation using Laplace transformation and overlapping simulation draws

We derive the asymptotic distribution of parameters Berry et al. (1995) (BLP) model in a many markets setting which takes into account simulation noise under assumption overlapping draws. show that as long number draws R and T approach infinity, our estimator is m=min(R,T) consistent asymptotically normal. do not impose any relationship between rates at go to thus allowing for case R≪T. provide estimate variance can be used form valid confidence intervals. Instead directly minimizing BLP GMM objective function, we propose using Hamiltonian Markov Chain Monte Carlo methods implement Laplace-type equivalent estimator.