Price/demand elasticity model from the Bayesian approach : The case of a Chilean retail company

Banque du Chili – Chili
Université Pontificale Catholique du Chili – Chili

Abstract : This project presents data from a Chilean retail firm to model elasticity from a Bayesian perspective. Elasticity measures the behavior of products based on price and demand. It can be obtained through linear regressions of the logarithm of prices and units sold. The problem arises with discounts, special days, etc. This temporal relationship causes biases in the estimates that the company compensates for by performing a chain of regres­sions. Bayesian statistics fixes a distribution for the parameters, and then, with plausibility, uses Bayes ’ rule to obtain a posteriori distribution. The project uses an a priori Normal-Gamma-Inverse to specify the linear regression model. For the application, we obtain the line level elasticities through the classical model and the product elasticities with the Bayesian model, incorporating the line information. Through a t-test we conclude that the average of the chain elasticities does not differ from those obtained by the Bayesian model. Therefore, by complementing the two points of view, we obtain good results that can be used in trade.

Keywords : elasticity, detail, frequentist, inference, normal-gamma-inverse.

JEL classification : C11, M21.