Estimation Under Profit-Driven Loss Functions

Consider the problem of estimating a price-sensitivity parameter in a demand model. Depending on the context in which the estimate will be used, traditional squared-error loss may be inappropriate. The authors consider the situation in which the estimate will be used by a manufacturer to set the price. Effectively, the manufacturer's goal of profit maximization induces a loss function that turns out to be asymmetric. Estimates that perform well with respect to such loss functions are obtained. A real example is considered in which, compared to traditional estimation under squared-error loss, this approach leads to smaller price-sensitivity estimates, suggesting higher optimal prices.