A General Method for Demand Inversion

TL;DR

This paper introduces a versatile numerical method for demand inversion in discrete choice models, transforming the problem into a convex optimization task that improves computational efficiency and robustness over existing algorithms.

Contribution

The paper develops a general convex optimization approach for demand inversion applicable to a wide class of discrete choice models, including BLP and pure characteristics models.

Findings

Outperforms the contraction mapping algorithm in simulations.

Remains robust with near-zero market shares.

Computational complexity comparable to convex programming.

Abstract

This paper describes a numerical method to solve for mean product qualities which equates the real market share to the market share predicted by a discrete choice model. The method covers a general class of discrete choice model, including the pure characteristics model in Berry and Pakes(2007) and the random coefficient logit model in Berry et al.(1995) (hereafter BLP). The method transforms the original market share inversion problem to an unconstrained convex minimization problem, so that any convex programming algorithm can be used to solve the inversion. Moreover, such results also imply that the computational complexity of inverting a demand model should be no more than that of a convex programming problem. In simulation examples, I show the method outperforms the contraction mapping algorithm in BLP. I also find the method remains robust in pure characteristics models with near-zero market shares.