Demand elasticities in promotional pricing: A theory-based analysis of empirical challenges

This paper develops a continuous-time model of selling in which a firm optimally offers price promotions in a market with static but heterogeneous consumer preferences. While consumer preferences are fixed, price promotions induce dynamic sorting behavior, causing price sensitivity to evolve over time. This dynamic response can create challenges for empirical analyses. We use the promotion-cycles model to examine these challenges for both experimental and observational settings. For experimental approaches, we show that failing to align interventions with the market’s equilibrium timing of promotions can lead to elasticity estimates that diverge from those naturally observed in the market. For observational methods, we demonstrate that – in the absence of price endogeneity – using lagged prices as instruments may introduce a spurious instrumentation bias that may be mistakenly attributed to endogeneity. We provide empirical guidance and show that, in most cases, such biases can be anticipated by directly examining how sales evolve during promotional cycles.