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<p>Ancillary seat pricing requires estimating willingness-to-pay (WTP) from transaction logs in which offered prices are unobserved for non-purchases and operationally distorted for purchases. We develop a two-stage approach. <i>Synthetic Offer Reconstruction</i> (SOR) reverses known loyalty and operational pricing rules around the filed base price to recover a price-exposure feature for every passenger. A <i>Proximal Causal Inference</i> (PCI) refinement then estimates the price-purchase relationship with a cross-fitted two-stage sieve bridge, using operational variables as upstream proxies and leave-one-out within-flight statistics as downstream proxies for the latent exposure regime. We evaluate on synthetic airline data containing an unobserved flight-level confounder, over 100 random seeds, against an oracle restricted to the same price grid, alongside qualitative evidence from real operational airline data supporting the reconstruction and proxy choices. When training and deployment regimes coincide, the bridge matches a direct gradient-boosted baseline. When the confounder distribution shifts between training and deployment, it recovers 90–<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(93\%\)</EquationSource> </InlineEquation> of oracle revenue versus roughly <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(86\%\)</EquationSource> </InlineEquation> for the baseline and an inverse-probability-weighting benchmark. We further document a <i>calibration paradox</i>: supplying the same proxies to a flexible classifier as ordinary covariates attains the best observed calibration on held-out data, yet collapses to a near-fixed-price policy capturing only 74–<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(84\%\)</EquationSource> </InlineEquation> of oracle revenue in the synthetic evaluation. Structural use of proxy information through the bridge’s moment condition - not proxy availability itself - is what yields transportable WTP estimates under missing-not-at-random price exposure.</p>

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Willingness-to-pay estimation for airline ancillary seats under censored price exposure

  • 期刊论文

  • 发表日期：

    2026年7月2日

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  • Kevin Duijndam,
  • Ger Koole,
  • Tim von Lücken,
  • Rob Van Der Mei

摘要

Ancillary seat pricing requires estimating willingness-to-pay (WTP) from transaction logs in which offered prices are unobserved for non-purchases and operationally distorted for purchases. We develop a two-stage approach. Synthetic Offer Reconstruction (SOR) reverses known loyalty and operational pricing rules around the filed base price to recover a price-exposure feature for every passenger. A Proximal Causal Inference (PCI) refinement then estimates the price-purchase relationship with a cross-fitted two-stage sieve bridge, using operational variables as upstream proxies and leave-one-out within-flight statistics as downstream proxies for the latent exposure regime. We evaluate on synthetic airline data containing an unobserved flight-level confounder, over 100 random seeds, against an oracle restricted to the same price grid, alongside qualitative evidence from real operational airline data supporting the reconstruction and proxy choices. When training and deployment regimes coincide, the bridge matches a direct gradient-boosted baseline. When the confounder distribution shifts between training and deployment, it recovers 90– \(93\%\) of oracle revenue versus roughly \(86\%\) for the baseline and an inverse-probability-weighting benchmark. We further document a calibration paradox: supplying the same proxies to a flexible classifier as ordinary covariates attains the best observed calibration on held-out data, yet collapses to a near-fixed-price policy capturing only 74– \(84\%\) of oracle revenue in the synthetic evaluation. Structural use of proxy information through the bridge’s moment condition - not proxy availability itself - is what yields transportable WTP estimates under missing-not-at-random price exposure.