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

TL;DR

This paper introduces efficient inner-loop algorithms for static and dynamic BLP estimations, combining analytical solutions and acceleration techniques to reduce computation time and improve performance.

Contribution

It proposes novel methods including an outside option share term, analytical mean utility representation, and Anderson acceleration for faster BLP estimation.

Findings

Algorithms significantly reduce inner-loop iterations.

Numerical experiments demonstrate improved computational efficiency.

Methods are easy to implement and effective in practice.

Abstract

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.