Panel Data Estimation of Individual Demand in Markets with Many Consumers

2026-06-09

AI Summary

This study addresses the challenge of accurately identifying individual-level demand in the presence of price endogeneity, a setting where conventional methods often fail. By integrating linear and random-coefficients demand models with a linear supply model, the authors employ a panel data differencing approach augmented with time fixed effects to control for simultaneity bias and aggregate macroeconomic dynamics. The analysis demonstrates that, provided the number of consumers in the market is sufficiently large and individual preference shocks are orthogonal to supply-side disturbances, standard panel estimators can yield approximately unbiased estimates of individual demand. This result establishes a novel theoretical foundation for the empirical identification of micro-level demand and meaningfully extends the applicability of panel data methods in structural demand estimation.

Abstract

The purpose of this paper is to consider whether and how panel data can be used to estimate individual demand, as opposed to market-level demand, while accounting for simultaneity resulting from prices being determined in markets. We consider linear demand models and random coefficient demand models, together with linear supply models. We find that the bias of individual demand estimates obtained using familiar panel data methods, like differencing, disappears as the number of consumers in each market grows, as long as the time-varying, i.e. idiosyncratic, component of preferences is orthogonal to the unobserved, time-varying component of supply. This approximate control is assumed in many panel discrete choice models and is plausible in other models where idiosyncratic preferences represent random variation in preferences over time. Macroeconomic effects can be allowed for by including regressors characterizing time effects, such as trends and time period dummies, or fixed time effects.

Problem

• panel data
• individual demand
• simultaneity
• price endogeneity
• demand estimation

Innovation

• panel data
• individual demand estimation
• simultaneity
• random coefficient models
• orthogonality condition