Why Wrong Response Functions Predict Better and How to Detect Them

Many decisions depend on using the correct response function for marketing xpenditures. Empirical research sometimes justifies response functions based on predictive accuracy. This paper proves that there are always wrong response functions that predict better (on 4 criteria) than the true response function. The reason is not faulty estimation, simplicity, parsimony, fewer variables, the criterion for “better” or simple bias. Wrong functions use less concavity (deflated derivatives offset by inflated parameters) to hedge against (filter) observation error (and relevant sample information) for better predictions. True functions retain correct concavity (retaining all sample information) for better implications. However, whether predictions are vastly better or only barely better, hedging causes wrong implications. For example, hedging seriously underestimates optimal expenditures (not overestimates) because optimal decisions require accurate derivatives rather than accurate sales predictions. A potential solution for detecting wrong response functions is an out-sample test related to derivatives. This paper proves, with analytical proof and statistical simulation, that predictive tests using predictions of differences in sales (i.e., slope predictions) are better able to detect wrong response functions than traditional out-sample tests. Typical empirical analyses mask these findings because the true response function remains unobserved and, possibly, falsely inferred.