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Cross-Price Elasticity Estimation: Modern Methods Showcase

A comprehensive demonstration of state-of-the-art methods for estimating cross-price elasticities using Python's leading econometric and machine learning libraries.

Overview

This project implements working examples for cross-price elasticity estimation using:

  • EconML: Double ML, IV methods, Causal Forests, DR learners
  • PyBLP: BLP (Berry-Levinsohn-Pakes) random-coefficient logit demand models
  • LinearModels: High-dimensional panel regressions with fixed effects and IV/2SLS
  • Statsmodels: AIDS/QUAIDS demand systems
  • PyMC: Bayesian hierarchical elasticity models
  • Scikit-learn/XGBoost: DML pipelines with ML nuisance models

Installation

Recommended: Use a clean virtual environment to avoid dependency conflicts

# Create virtual environment
python -m venv elasticity_env

# Activate environment
source elasticity_env/bin/activate  # On macOS/Linux
# OR
elasticity_env\Scripts\activate     # On Windows

# Install packages
pip install -r requirements.txt

Quick activation (after setup):

# Use the provided script
source activate_env.sh

Quick Start

# Run all examples with comparison
python main_cross_price_elasticity.py

# Or run individual examples:
python data_preparation.py           # Generate synthetic data
python example_econml.py            # EconML causal ML methods
python example_pyblp.py             # PyBLP demand estimation
python example_linearmodels.py      # Panel data methods
python example_statsmodels_aids.py  # AIDS/QUAIDS systems
python example_pymc.py              # Bayesian hierarchical models
python example_sklearn_xgb_dml.py   # ML-based DML

Data

The project uses synthetic retail scanner data with:

  • Multiple products (substitutes and complements)
  • Multiple stores and markets
  • Time periods with seasonality
  • Price variations (promotions, regular prices)
  • Instrumental variables (cost shifters, competitor prices)
  • Consumer demographics for heterogeneous effects

Methods Demonstrated

1. EconML (Causal Machine Learning)

  • Double ML (DML): Flexible control for confounders using ML
  • IV Methods: Handling endogenous prices with ML first stages
  • Causal Forests: Heterogeneous treatment effects
  • DR Learners: Doubly robust estimation

2. PyBLP (Structural Demand)

  • Random Coefficients Logit: Flexible substitution patterns
  • Supply Side: Joint demand-supply estimation
  • Demographics: Consumer heterogeneity
  • Nested Logit: Category-based substitution

3. LinearModels (Panel Methods)

  • Fixed Effects: Entity and time fixed effects
  • 2SLS/IV: Instrumental variables for panels
  • Dynamic Panels: Lagged dependent variables
  • Heterogeneous Effects: Varying elasticities by group

4. Statsmodels (Demand Systems)

  • Linear AIDS: Almost Ideal Demand System
  • QUAIDS: Quadratic AIDS with flexible Engel curves
  • Restrictions: Homogeneity, symmetry, adding-up
  • Welfare Analysis: Consumer surplus calculations

5. PyMC (Bayesian Methods)

  • Hierarchical Models: Partial pooling across products
  • Cross-Price Effects: Full elasticity matrices
  • Varying Slopes: Market-specific elasticities
  • Time-Varying: Dynamic elasticity evolution

6. ML-Based DML

  • XGBoost DML: Gradient boosting for nuisances
  • LightGBM: High-dimensional features
  • Ensemble Methods: Combining multiple ML models
  • Neural Networks: Deep learning for non-linearities

Key Features

Elasticity Types Estimated

  • Own-price elasticities: Response of quantity to own price
  • Cross-price elasticities: Response to competitor prices
  • Income elasticities: Response to consumer income
  • Promotional elasticities: Impact of marketing

Methodological Advances

  • Endogeneity handling: IV, control functions, panel methods
  • Heterogeneity: Random coefficients, hierarchical models
  • Non-linearities: ML methods, polynomial terms
  • Uncertainty quantification: Bayesian posteriors, bootstrap

Output Files

Each method produces:

  • Elasticity estimates with confidence/credible intervals
  • Model diagnostics and convergence checks
  • Visualization plots (saved as PNG)
  • Comparison tables (CSV format)

Main outputs:

  • data/: Generated datasets in various formats
  • *.png: Visualization plots for each method
  • elasticity_comparison.csv: Summary comparison table
  • summary_comparison.png: Overall comparison plot

Results Interpretation

True Values (from data generation)

  • Own-price elasticity: -1.2
  • Within-category cross-price: 0.4 (substitutes)
  • Complement cross-price: -0.15
  • Unrelated products: 0.02

Method Selection Guide

Choose based on your needs:

Scenario Recommended Method
Causal inference focus EconML (DML, IV)
Rich substitution patterns PyBLP
Panel data LinearModels
Complete demand system AIDS/QUAIDS
Uncertainty quantification PyMC
High-dimensional controls XGBoost/LightGBM DML
Limited assumptions ML-based methods

Performance Notes

  • Full execution takes ~10-15 minutes on a modern machine
  • PyBLP and PyMC examples are computationally intensive
  • Reduce data size or iterations for faster testing

Technical Requirements

  • Python 3.8+
  • 8GB RAM minimum (16GB recommended)
  • Multi-core processor for parallel sampling

Troubleshooting

Common issues and solutions:

  1. Memory errors: Reduce number of markets/products in examples
  2. Convergence warnings: Increase iterations or adjust priors
  3. Import errors: Ensure all packages installed via pip install -r requirements.txt

Extensions

Possible extensions to explore:

  • Real data applications (scanner data, e-commerce)
  • Dynamic pricing strategies
  • Competition analysis
  • Demand forecasting
  • Optimal pricing algorithms

References

Key papers for each method:

  • DML: Chernozhukov et al. (2018) "Double/debiased machine learning"
  • BLP: Berry, Levinsohn & Pakes (1995) "Automobile prices in market equilibrium"
  • AIDS: Deaton & Muellbauer (1980) "An almost ideal demand system"
  • Causal Forests: Athey et al. (2019) "Generalized random forests"

License

MIT License - See LICENSE file for details

Contact

For questions or issues, please open a GitHub issue or contact the maintainers.

This showcase demonstrates modern econometric methods for elasticity estimation. The synthetic data and true parameters allow for method validation and comparison.