How does awareness evolve when advertising stops? The role of memory

Extant models posit that awareness declines immediately and gradually after the cessation of advertising, whereas anecdotal evidence from managers suggests awareness stays constant for a while and then decays rapidly. This pattern arises because consumers remember advertisements for a finite time before they forget. Hence, we extend advertising models by incorporating the memory for ads. We conceptualize the role of memory as "delayed forgetting of ads" and capture it using delay differential equations, which exhibit richer dynamics and expand the class of dynamic models used in marketing. Analytically, we derive the 90% duration of advertising effects under various scenarios. Empirically, we analyze awareness evolution in the absence of advertising for the Peugeot car brand. We not only find strong support for the proposed model, but also estimate the memorability of Peugeot ads to be about 3 weeks. Moreover, if we ignore consumer memory as in the extant models, we would overstate the forgetting rate by 39%. Finally, we discuss managerial implications and identify new avenues for further research.