Fast and simple inner-loop algorithms of static / dynamic BLP estimations

This study investigates computationally efficient inner-loop algorithms for estimating static/dynamic BLP models. It provides the following ideas for reducing the number of inner-loop iterations: (1). Add a term relating to the outside option share in the BLP contraction mapping; (2). Analytically represent the mean product utilities as a function of value functions and solve for value functions (for dynamic BLP); (3). Combine an acceleration method of fixed-point iterations, especially the Anderson acceleration. They are independent and easy to implement. This study shows the good performance of these methods using numerical experiments.