Boost Forecast Accuracy by 15% to Optimise Airline Pricing

In his blog post “Airline Revenue’s Blind Spot: An Exploration of Endogeneity with Dr. Stacey Mumbower, ADC-Consulting’s Marc Nientker explored pricing challenges especially in measuring price elasticity. Marc shared that confounding variables – or confounders for short – are a major pricing challenge. They arise when factors that influence price and sales are left out of the model – becoming omitted variables. These pesky nuisances distort elasticity estimates and so quietly drag down revenue.

Drawing from Marc’s presentation at AGIFORS in Warsaw 2025, this article dives deeper into the topic of tackling unobserved confounders and proposes a new solution that dramatically improves estimates.

Read on to learn:

• Common solutions like instrumental variables (IV) and double machine learning (DML) offer potential fixes, but each comes with practical limitations and strong assumptions that are difficult if not impossible to verify.
• Panel data with interactive fixed effects (IFE) provide a more flexible alternative that captures hidden influences by modelling how different itineraries respond to shared market change.
• With this approach, we have observed significantly improved elasticity estimates, which have translated into a +15% increase in forecasting accuracy, enabling our clients to achieve a substantial revenue uplift.

Airline pricing doesn’t happen in a vacuum. It lives in a chaotic ecosystem shaped by prices, sales trends, competitor behaviour, oil prices, geopolitical shifts, and macroeconomic conditions. These are just a few of the many confounding variables – hidden factors – that simultaneously affect both price and demand. Ignore them, and your willingness-to-pay (WTP) and price elasticity (PE) estimates will likely be too low.

Causal Pricing Elasticity Estimates

Traditional pricing models relied on observed correlations between price and demand. But they often missed the true, underlying cause-and-effect relationship. Well-established in statistics, causal PE models are now being used in airline pricing and revenue management (PRM) for better accuracy.

A causal PE model delivers market, flight, and cabin-level granularity, enabling pricing and revenue management (PRM) teams to better:

• Optimise discounts in high-sensitivity markets to drive volume without eroding margin.
• Protect high-margin segments where demand is inelastic by avoiding unnecessary price cuts.
• Target elastic zones with personalisation, upsell offers, or ancillary bundling to maximise yield.

Causal Pricing Methods

Two modern causal estimation methods currently dominate literature in airline PRM. Each come with their own drawbacks:

1. Instrumental Variables (IVs)
   Require using a variable that influences price but has no direct effect on demand. This “instrument” acts as a proxy to isolate the causal effect of price on demand.

However, finding such a variable is notoriously tricky – and without a valid one, hidden confounders can sneak in, quietly distorting results and undermining decision-making.

• Double Machine Learning (DML)
  Uses machine learning (ML) to predict both the treatment (e.g., price change) and the outcome (e.g., revenue). Then, it isolates what is left over. The unexplained variation is used to estimate the real causal impact.

However, its reliability hinges on careful model tuning and the assumption that all relevant confounders are observed. It’s a condition that, in practice, is often difficult to satisfy.

At ADC Consulting, we use generalised latent factor panel model approaches, specifically interactive fixed effects (IFE) models, as they offer a practical way to capture confounders without needing to see or measure them directly.

Panel Data and Interactive Fixed Effects

At ADC-Consulting, our causal price elasticity framework fuses panel data with IFE to account for the hidden forces shaping demand – without needing to observe them. Across multiple clients, this methodology has delivered sharper elasticity estimates resulting in validated gains of ~15% in forecasting accuracy and meaningful revenue impact. The secret: embracing the fact that confounders exist and building them into the model through the structure of the data itself.  Let’s break down the key components of the methodology!

Panel Data

Panel data tracks how multiple entities, such as routes, flights, or itineraries, behave over time. In airline pricing, this means observing how the same itinerary performs across different booking windows, travel dates, or demand cycles.

Each observation has two dimensions:

• Time (e.g., booking date, departure date)
• Entity (e.g., route, fare class, cabin, or itinerary)

This structure is powerful. It lets us separate what changes over time (like macro shocks or seasonal demand) from what varies across itineraries (like route-specific demand patterns or competition levels). In doing so, it provides a sharper lens to uncover causal relationships and hidden drivers of demand that would be invisible in a purely cross-sectional analysis.

The standard panel regression model looks like this:

𝑠_𝑖𝑡=𝑝_𝑖𝑡^′ 𝛽+𝑥_𝑖𝑡^′ 𝛾+𝜀_𝑖𝑡

Panel Data and Fixed Effects

To enhance estimation accuracy, you can incorporate fixed effects into your model. Fixed effects control for unobserved, time-invariant characteristics—such as a route’s inherent popularity—that could otherwise bias your results. They also account for time-specific shocks that impact all itineraries simultaneously, like major holidays or sudden shifts in demand. By absorbing these consistent and common influences, fixed effects help isolate the causal relationship between your variables of interest.

𝛼_𝑖: unobserved, time-invariant characteristics of each itinerary.

𝜉_𝑡: unobserved shocks that are common across all itineraries at a given time.

So, the model looks like this:

Panel model (fixed effects): 𝑠_𝑖𝑡=𝑝_𝑖𝑡^′ 𝛽+𝑥_𝑖𝑡^′ 𝛾+〖𝛼_𝑖+𝜉_𝑡+𝜀〗_𝑖𝑡

Even though the parameters 𝛼_𝑖 and 𝜉_𝑡 are unobserved, the model can be estimated through demeaning across the time and itinerary dimensions. It’s like saying: “Let’s look only at how things deviate from the average for each route and each day.”

However, there is a limitation to this approach. This method assumes that each itinerary is similarly impacted by the unobserved confounders. In the real-world, confounders affect different itineraries differently.

Panel Data and Interactive Fixed Effects

What if we extend the standard panel model by allowing different itineraries to react differently to the same external factors?

We could take a set of unobserved common shocks, such as market trends or macroeconomic events, and capture how strongly each itinerary responds to them. By combining these, the model would account for the different impact of shared confounders, making it more realistic in complex environments like airline pricing.

Imagine a competitor airline suddenly launching a high-frequency London to New York service. That market shock hits every itinerary in the corridor, but not uniformly. Economy seats may see a rush of lower-priced options and big volume swings, while Business-class fares, where schedule and service trump price, might remain relatively stable. By observing those different reactions to the same event, our IFE panel model learns each itinerary’s unique sensitivity to changes, without ever having to measure the competitor’s move directly.

So, we let  𝑓_𝑡=(𝑓_𝑡1,…, 𝑓_𝑡𝑟) represent a set of common confounders (factors) and let 𝜆_𝑖=(𝜆_𝑖1,…, 𝜆_𝑖𝑟) represent their heterogeneous impact (loadings)

Panel model + IFE model: 𝑠_𝑖𝑡=𝑝_𝑖𝑡^′ 𝛽+𝑥_𝑖𝑡^′ 𝛾+〖𝜆_𝑖^′ 𝑓_𝑡+𝜀〗_𝑖𝑡

A New Standard for Price Elasticity Estimation

Historically, uncorrected models underestimate price elasticity and so produce overly conservative demand forecasts. By incorporating interactive fixed effects to capture hidden influences, our IFE framework corrects this downward bias, providing elasticity estimates that better reflect true market responsiveness and drive the ~15% uplift in forecast accuracy.

Continue the Conversation

If you’re ready to enhance your pricing models, it’s time to explore these new approaches. Reach out to Vladimir Antsibor and Joël Gastelaars—we’d love to show you what it looks like in action.