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

Author

Listed:
  • Xavier D'Haultf{oe}uille
  • Ao Wang
  • Philippe F'evrier
  • Lionel Wilner

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. Our price elasticity estimates are in line with those on airlines, but substantially higher, in absolute terms, 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.

Suggested Citation

  • Xavier D'Haultf{oe}uille & Ao Wang & Philippe F'evrier & Lionel Wilner, 2022. "Instrument-Free Demand Estimation Using Relative Prices Variation, with an Application to Railway Transportation," Papers 2206.04424, arXiv.org, revised Sep 2026.
    • Handle: RePEc:arx:papers:2206.04424
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    More about this item

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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