Estimating Promotion Effects Using Big Data: A Partially Profiled LASSO Model With Endogeneity Correction

Retailers are interested in understanding which price promotions are profitable and which are not. However, simultaneously estimating the promotion effects of a large number of products on retailer sales and profits is technically challenging for both researchers and practitioners. To address this challenge, this study proposes a Partially Profiled Least Absolute Shrinkage and Selection Operator (Partially Profiled LASSO) model, which can estimate ultra-high-dimensional regression relationships at a low computational cost and control for the endogeneity of promotion depth. The model can flexibly incorporate the time-varying promotion effects and the cross-over effects among the promotions of different products. We conduct an empirical study using data provided by a large retailer over a five-month period. Our model efficiently identifies products with promotion effects and the promotion effects are significantly associated with certain promotion, product, and category characteristics. The results also show that our model with cross-over effects outperforms the benchmark models that are widely used to handle the high-dimensional predictor matrix (e.g., the standard LASSO and principal component regression methods). This paper contributes to the related literature on price promotion and marketing analytics in data-rich environments, and provides implications for retailers to make more informed promotion strategies.