Heterogeneous Response Functions in Advertising

De Fleur (1956) provides the earliest evidence of diminishing returns. He finds a common logarithmic pattern for leaflets dropped and message recalled in field experiment. Since then, many researchers have applied logarithmic or square root patterns to capture the effect of diminishing returns with their advertising response modeling across different media. But discussions with managers support the notion that the diminishing returns to incremental dollars spent on one medium (say, television) are not likely to be the same as those for equivalent dollars spent on other media (e.g., Print). But if diminishing returns indeed vary across media, how does that change the resulting allocation recommendation? To address this issue, we derive a dynamic model that captures the notion of differential diminishing returns and disentangles it from closely related notions of differential carryovers and differential ad effectiveness. Second, we develop a systematic method to estimate the model's parameters using market data and illustrate empirically that all three effects, diminishing returns, carryover and ad effectiveness vary across the four media employed. Finally, we investigate the normative implications for managerial decision-making. Here, we additionally account for varying media buying efficiencies across media. Taken together, the approach and its illustration should provide managers with a better toolkit to allocate their multimedia budgets.