Demand Models for Market-Level Data with Closed-Form Inverses

2026-10-07

AI Summary

This study addresses the challenges of demand model estimation and limited substitution patterns in market-level data by proposing a demand modeling framework based on closed-form inverse market share functions. Methodologically, drawing on generalized extreme value (GEV) theory, we construct generators that operate on market shares to accommodate overlapping nesting and multiple membership structures. By imposing utility maximization constraints, nonlinear models are transformed into linear instrumental variable (IV) regressions, enabling efficient estimation. This work overcomes the limitations of traditional Logit models by establishing a broader model class space than conventional additive random utility models, while maintaining strict consistency with utility maximization theory.

Abstract

We introduce a class of demand models for market-level data. The models can be estimated by linear instrumental variables regression while accommodating substitution patterns far richer than the logit and nested logit models they embed. They are built from closed-form inverse market share functions through a generator analogous to McFadden's generalized extreme value generating function, but acting on market shares. Constructive results allow arbitrary nesting structures, including overlapping nests and partial membership, yielding inverse-share analogs of generalized extreme value models. The class is consistent with utility maximization and strictly larger than the class of regular additive random utility models.

Problem

• demand models
• market-level data
• substitution patterns
• closed-form inverses
• instrumental variables regression

Innovation

• demand models
• closed-form inverses
• market share functions
• generalized extreme value
• instrumental variables regression