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Causal Forecasting for Pricing

Douglas Schultz, Johannes Stephan, Julian Sieber, Trudie Yeh, Manuel Kunz, Patrick Doupe, Tim Januschowski

TL;DR

The paper addresses pricing-driven demand forecasting by jointly predicting demand across price levels and extracting the causal effect of price on demand. It introduces the DML Forecaster, a three-component framework that combines transformer-based nuisance models (outcome and treatment) with an elasticity-aware effect model, trained via two-stage cross-fitting and ensemble inference. Empirical results show strong off-policy performance—where pricing policies differ from training data—while maintaining competitive on-policy accuracy, demonstrated on synthetic data and a large real-world fashion dataset. This causal-forecasting approach improves robustness to policy shifts and offers a practical path for price optimization in retail settings. The work advances pricing analytics by melding modern forecasting with causal inference, enabling more reliable counterfactual predictions under changing price policies.

Abstract

This paper proposes a novel method for demand forecasting in a pricing context. Here, modeling the causal relationship between price as an input variable to demand is crucial because retailers aim to set prices in a (profit) optimal manner in a downstream decision making problem. Our methods bring together the Double Machine Learning methodology for causal inference and state-of-the-art transformer-based forecasting models. In extensive empirical experiments, we show on the one hand that our method estimates the causal effect better in a fully controlled setting via synthetic, yet realistic data. On the other hand, we demonstrate on real-world data that our method outperforms forecasting methods in off-policy settings (i.e., when there's a change in the pricing policy) while only slightly trailing in the on-policy setting.

Causal Forecasting for Pricing

TL;DR

The paper addresses pricing-driven demand forecasting by jointly predicting demand across price levels and extracting the causal effect of price on demand. It introduces the DML Forecaster, a three-component framework that combines transformer-based nuisance models (outcome and treatment) with an elasticity-aware effect model, trained via two-stage cross-fitting and ensemble inference. Empirical results show strong off-policy performance—where pricing policies differ from training data—while maintaining competitive on-policy accuracy, demonstrated on synthetic data and a large real-world fashion dataset. This causal-forecasting approach improves robustness to policy shifts and offers a practical path for price optimization in retail settings. The work advances pricing analytics by melding modern forecasting with causal inference, enabling more reliable counterfactual predictions under changing price policies.

Abstract

This paper proposes a novel method for demand forecasting in a pricing context. Here, modeling the causal relationship between price as an input variable to demand is crucial because retailers aim to set prices in a (profit) optimal manner in a downstream decision making problem. Our methods bring together the Double Machine Learning methodology for causal inference and state-of-the-art transformer-based forecasting models. In extensive empirical experiments, we show on the one hand that our method estimates the causal effect better in a fully controlled setting via synthetic, yet realistic data. On the other hand, we demonstrate on real-world data that our method outperforms forecasting methods in off-policy settings (i.e., when there's a change in the pricing policy) while only slightly trailing in the on-policy setting.
Paper Structure (29 sections, 37 equations, 5 figures, 10 tables)

This paper contains 29 sections, 37 equations, 5 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Problem Setting and Background
  3. DML Forecaster
  4. The Nuisance Models
  5. The Effect Model
  6. Inference with the DML Forecaster
  7. Discussion: Departures from the DML Literature
  8. Experiments
  9. Baseline Models and Accuracy Metrics
  10. Hyperparameter Tuning
  11. Synthetic Dataset
  12. Real-World Data
  13. Experiments on Synthetic Data
  14. Model adaptations for this simulation study
  15. Results
  16. ...and 14 more sections

Figures (5)

  • Figure 1: The architecture of the DML Forecaster.
  • Figure 2: Synthetic demand time series (black), the associated realized discount (green) and off-policy forecasts for DML Forecaster (blue) as well as TF (cyan).
  • Figure 3: The improvement of the DML Forecaster (the more negative on the x-axis the more improvement) over TF increases with more elastic articles.
  • Figure 4: A scatter plot of discounts for articles on cyber week 2022 vs. two weeks prior. Each point represents a single article, and the units on the axes are the ratio of discount, with 0 being no discount and 1 being full discount.
  • Figure 5: A sample of the difference in forecasting error for the TF vs. DML Forecaster on cyber week 2022, measured on the off-policy experiment.