Estimating Price Elasticity with Sparse Data: A Bayesian Approach

Abstract

Missing values and sparse data often challenge the reliability of statistical analysis in terms of biased parameter estimates and degraded confidence intervals, thereby leading to false inferences and suboptimal business decisions. To managers in the consumer data analytics field, the challenge faced by missing and limited data is nothing novel, and many powerful techniques of analysis and data management are available to them. However, the choice of adequate management practices is far from optimal. This chapter proposes an integrated approach by jointly treating the missing data and sparse data problems, using approximate Bayesian bootstrap (ABB) and Bayesian (HB) modeling. Therefore, the chapter addresses these two key challenges and corrects the bias formed, by extrapolating information from the sparse and missing data onto a large sample. The proposed method is illustrated by computation of price elasticity models for a leading consumer finance business on data that suffers from both missing and sparsity issues. The results presented illustrate the superiority of the model in taking better decisions in consumer data analytics. In contrast to the point estimate generated using traditional price elasticity models, the proposed model helps to make a better inference on the price elasticity estimates through a probability density function as it generates a distribution of price elasticity. Further expansion of the principle illustrated here will auger a powerful business optimization possibility and should be a fruitful area of future research.