An Econometric Framework for Estimating the Joint Elasticity of Advertising and Promotions on Retail Sales

Abstract

Contemporary media fragmentation and heightened marketing accountability necessitate quantifying the contribution of each marketing dollar to sales, including the joint effects of advertising and price promotions. Standard Marketing Mix Models (MMM), estimated on observational time series, remain correlational and leave a causal gap, especially when campaigns and discounts are executed concurrently. The intended audience for this framework includes both academic researchers and industry practitioners, with particular emphasis on data scientists and analytics professionals working in e-commerce, retail media, and digital marketing. For these readers, the model is designed to be readily implementable within contemporary data science pipelines, leveraging familiar tools such as regression-based modeling, regularization, hyperparameter search, and out-of-sample validation to support scalable, reproducible, and decision-relevant MMM applications. A log-log model is specified in which weekly log sales are regressed on channel-specific adstocked spends (Koyck formulation) and promotions, augmented with multiplicative interactions Adstock×Promo. Decay parameters are constrained by funnel theory (Video: 0.6–0.8; Display: 0.4–0.6; SP/SB/SD: 0.3–0.5) and selected via grid search using AIC/BIC and out-of-sample RMSE under a 70/30 chronological split. Controls capture seasonality and trading peaks. Diagnostics include VIF (<10), White’s test, and DW/ACF with AR(1) errors when indicated; robustness is assessed via Ridge/Lasso. Elasticities are computed at sample means. The empirical setting is a retailer case study spanning five channels (Video, Display, Sponsored Products, Sponsored Brands, Sponsored Display) plus total promotional discounts. Elasticities along the funnel for each of the owned channels are also large and meaningful: Promo 0.28-0.36, SP 0.22-0.28, SB 0.20-0.26, Display 0.15-0.20, Video 0.10-0.14, SD 0.08-0.12. All interaction point estimates are meaningful showing interference SP×Promo ?0.05 to ?0.08 SB×Promo ?0.04 to ?0.07 Display×Promo ?0.03 to ?0.05 SD×Promo ?0.01 to ?0.03 Video×Promo ? ?0.02 to 0.00. Budget Simulation: Allocate 60-68% of budget to advertising and 32-40% to promotions. For the advertising budget, allocate 30-35% to SP, 20-25% to SB, 18-22% to display advertising, and 12-16% to video advertising. Operationally, stacking deep discounts with lower-funnel bursts depresses marginal ROI, whereas staggering upper/mid-funnel activity 1–2 weeks before promotions improves outcomes. The framework quantifies negative joint elasticities between promotions and most ad channels in retail e-commerce, challenging maximal pressure strategies. Sequenced execution, rather than synchronous peaks, maximizes incremental sales and ROI. Limitations include observational endogeneity and linear response assumptions; future research should integrate hierarchical Bayesian adstock, causal identification (e.g., IV, RDD, geo-experiments), nonlinear saturation functions, and uncertainty-aware budget optimization.