New Choice Model Fixes Asymmetric Price Elasticity
A skewed multinomial probit model allows firms to better predict how consumers react differently to price hikes versus price cuts.
A new skewed multinomial probit (SMNP) model allows for asymmetric choice responses, correcting a flaw in standard models that assume consumers react identically to positive and negative shifts in variables like price. By using a multivariate skew-normal distribution for latent utilities, the model captures the reality that a price increase often triggers a different magnitude of customer churn than a price decrease triggers in new acquisitions.
This shift in modeling changes how companies calculate price elasticities. Standard models often produce misleading substitution predictions because they force a symmetric response. The SMNP model identifies alternative-specific skewness parameters, which means a business can now distinguish between a customer who is highly sensitive to a price hike but indifferent to a discount, and one who behaves the opposite way.
Retailers and service providers relying on demand estimation for dynamic pricing will find this more accurate for predicting substitution patterns. When a product's price rises, customers do not always migrate to the next cheapest alternative in a linear fashion. The SMNP model recovers these asymmetric patterns, providing a more precise map of where customers go when they leave a specific product.
Implementing this level of nuance previously created computational hurdles, specifically regarding identification and the disruption of Gaussian updating in Bayesian estimation. The researchers solved this using a covariance reparameterization and a double data-augmentation scheme. This makes the model computationally viable for large consumer datasets without sacrificing the flexible substitution patterns of the original probit framework.
Companies that manage complex product portfolios with high cross-elasticity are most exposed to these findings. If current models understate the pain of a price increase while overstating the gain of a promotion, the resulting revenue projections are fundamentally skewed. The SMNP model provides a mathematical path to align those projections with actual consumer behavior.
Market observers should watch for the integration of skew-normal distributions into commercial pricing software. The ability to produce economically meaningful differences in elasticity predictions suggests that traditional demand curves may be oversimplifying the risk of price adjustments.