The Shape of Advertising Response Functions Revisited: A Model of Dynamic Probabilistic Thresholds

Prior work in marketing has suggested that advertising threshold effects-levels beneath which there is essentially no sales response-are rarely encountered in practice. Because advertising policies settle into effective ranges through early trial and error, thresholds cannot be observed directly, and arguments for their existence must be based primarily on a "statistical footprint," that is, on relative fits of a range of model types. To detect possible threshold effects, we formulate a switching regression model with two "regimes," in only one of which advertising is effective. Mediating the switch between the two regimes is a logistic function of category-specific dynamic variables (e.g., order of entry, time in market, number of competitors) and advertising levels, nesting a variety of alternative formulations, among them both standard concave and S-shaped responses. A sequence of comparisons among parametrically related models strongly suggests: that threshold effects exist; that market share response to advertising is not necessarily globally concave; that superior fit cannot be attributed to model flexibility alone; and that dynamic, environmental, competitive, and brand-specific factors can influence advertising effectiveness. These effects are evident in two evolving durables categories (SUVs and minivans), although not in the one mature, nondurable category (liquid detergent) studied.