Semiparametric quantile regression is employed to flexibly estimate sales response for frequently purchased consumer goods. Using retail store-level data, we compare the performance of models with and without monotonic smoothing for fit and prediction accuracy. We find that (a) flexible models with monotonicity constraints imposed on price effects dominate both in-sample and out-of-sample comparisons while being robust even at the boundaries of the price distribution when data is sparse; (b) quantile-based confidence intervals are much more accurate compared to least-squares-based intervals; (c) specifications reflecting that managers may not have exact knowledge about future competitive pricing perform extremely well.
