  This study investigates computationally efficient inner-loop algorithms for
estimating static/dynamic BLP models. It provides the following ideas to reduce
the number of inner-loop iterations: (1). Add a term concerning the outside
option share in the BLP contraction mapping; (2). Analytically represent mean
product utilities as a function of value functions and solve for the value
functions (for dynamic BLP); (3-1). Combine the spectral/SQUAREM algorithm;
(3-2). Choice of the step sizes. They are independent and easy to implement.
This study shows good performance of these methods by numerical experiments.
