Instrument-Free Demand Estimation Using Relative Prices Variation, with an Application to Railway Transportation

TL;DR

This paper introduces a novel demand estimation method that uses relative price variations over time without requiring cost shifters, applied to French railway data to evaluate pricing strategies and revenue management.

Contribution

It develops a new identification approach for demand estimation based on nonlinear difference-in-differences, applicable when cost shifters are unavailable and demand varies substantially.

Findings

Estimated price elasticities align with airline data, more negative than typical railway estimates.

Current revenue management performs comparably or better than uniform pricing.

Optimal pricing strategies could significantly increase revenue.

Abstract

We develop a new identification strategy for demand estimation when cost shifters may not be available and there are substantial variations in demand over time. This approaches relies on a kind of nonlinear difference-in-differences, in which price elasticities are identified by relating changes over time in relative purchases between two goods to changes in their relative prices. We apply this strategy to the context of French railway transportation and estimate price elasticities in line with those obtained on airlines, but more negative than those generally obtained on railway transportation. We then use our demand estimation to compare the current pricing with several counterfactual pricing strategies. Our results suggest similar or better performance of the actual revenue management compared to optimal uniform pricing, but also substantial losses compared to the optimal pricing strategy. Finally, we highlight the key role of revenue management in acquiring information when demand is uncertain.