A transport-cost distance maps how airlines’ networks differ and recover: after COVID some seasonal supply patterns converged while geographic and route-length specializations remained distinct, offering a practical benchmarking and monitoring tool for analysts and regulators.

Main Finding

The paper develops an optimal-transport (OT) framework that represents each airline as a distribution of seat capacity or flight frequency over routes and uses route-level transportation costs to compute pairwise dissimilarities between carriers. OT-based indices capture multidimensional differences in network supply (seasonality, geographic proximity, route-length structure). Applied to 32 European airlines (2016–2025), the framework reveals heterogeneous and dimension-specific patterns of similarity, shows post‑pandemic convergence in some network dimensions and persistent differentiation in others, and yields a flexible tool for benchmarking, resilience assessment, and monitoring structural recovery after shocks.

Key Points

• Airlines are modeled as probability distributions of capacity/frequency over routes; pairwise dissimilarity is the OT (earth-mover) distance between these distributions under a chosen route cost.
• Three OT-based dissimilarity indices are introduced to highlight different supply dimensions:
  • Seasonal supply positioning — how carriers allocate capacity across seasonal time buckets.
  • Geographic market proximity — how overlapping or geographically close carriers’ routes are.
  • Route-length structure — differences in the distribution of route distances (short vs long haul).
• The OT framework goes beyond simple multimarket contact or aggregate concentration measures by accounting for heterogeneity in route networks and giving interpretable transport costs.
• Empirical application to European scheduled passenger flights (32 airlines, 2016–2025) shows:
  • Airline similarities are multidimensional and vary by carrier type and network features.
  • Longitudinal analysis (relative to a 2016 baseline) uncovers diverse adjustment trajectories across carriers.
  • After the COVID shock there is convergence in some network dimensions but persistent differentiation in others.
• Practical uses include forming peer groups for benchmarking, assessing resilience/recovery, and tracking medium-to-long-term structural change.

Data & Methods

• Data: route-level scheduled passenger flight data for 32 European airlines covering 2016–2025, represented as route-by-time distributions of either seat capacity or flight frequency.
• Representation: each airline-year (or airline-time unit) is treated as a discrete distribution over route nodes (or route-time nodes) with mass proportional to capacity/frequency.
• Cost specification: route-level transportation costs are defined to reflect the dimension of interest (e.g., geographic distance between route endpoints for market proximity; difference in route lengths for route-length structure; temporal distances for seasonality). These costs determine the amount of “work” required to reassign supply from one carrier’s network to another’s.
• Distance computation: pairwise OT distances (earth-mover type metrics) are computed between airline distributions using the specified cost matrix, producing interpretable dissimilarity indices for each dimension.
• Analysis:
  • Cross-sectional comparisons to reveal which carriers are similar on each dimension.
  • Longitudinal comparisons against a 2016 baseline to trace adjustment and recovery patterns over the 2016–2025 window.
  • Multidimensional comparisons to show that similarity depends on which network attribute is measured.
• (Methodological note) The framework is modular: the choice of cost metric and distributional granularity can be adapted to the research question (e.g., include season/time, airport clusters, or route attributes).

Implications for AI Economics

• Feature engineering for predictive models: OT distances provide interpretable, low-dimensional features capturing network similarity that can improve ML models predicting entry/exit, route launches, capacity changes, or competitive responses.
• Clustering and peer-group construction: OT-based indices enable economically meaningful clustering of carriers for benchmarking, transfer learning, or constructing synthetic control units (matching on network similarity rather than only market overlap).
• Treatment-effect heterogeneity and causal inference: OT distances serve as continuous similarity measures to stratify samples, form matched sets, or weight control units when estimating policy or shock impacts on carriers with similar network structures.
• Monitoring and anomaly detection: longitudinal OT measures can be used in automated monitoring systems (change-point detection, early-warning) to detect atypical network restructuring after shocks or strategic shifts.
• Market-structure and competition models: richer measures of carrier proximity improve empirical IO analyses (e.g., demand substitution, pricing competition) by replacing coarse multimarket-contact measures with transport-cost‑weighted distances that reflect actual capacity overlap.
• Model validation and synthetic data: OT metrics can evaluate similarity between simulated and real networks when training or validating generative models of airline networks or market outcomes.
• Computational considerations: OT computations can become costly on very large route sets; practical implementations may require approximation (e.g., entropy-regularized Sinkhorn methods) or aggregation (airport clusters, route bundling). AI economists should balance granularity and scalability when integrating OT features into ML pipelines.
• Policy and resilience assessment: regulators and analysts can use OT-based tracking to evaluate structural recovery after shocks (pandemics, fuel crises) and to identify persistent structural differences that may warrant intervention or targeted support.

Overall, the OT framework supplies a flexible, interpretable distance metric for airline network comparison that can be directly incorporated into AI/econometrics workflows for prediction, causal inference, clustering, and monitoring of structural change.