In many public policy problems, we need to estimate the way in which policy changes affect people's behavior. In the analysis of tax and subsidy reform, which is the topic of this paper, we need to know how tax-induced price changes affect the amounts that people buy of the taxed goods. We present various economic and statistical approaches to obtaining the estimates that are required. We consider the structural methods that are standard in economics, where the behavior and welfare of individual agents are simultaneously captured by the specification of utility functions whose parameters are to be estimated. We argue that these methods are less useful than alternatives that directly consider the derivatives of the regression function of average behavior. We consider both parametric and nonparametric estimators of these derivatives in the context of price reform for foods in Pakistan, focussing on the advantages and disadvantages of "average derivative estimation" (ADE) as proposed by Hardle and Stoker (1989) and Stoker (1991). Average derivative estimation is attractive in principle because it directly estimates the statistics that are required for policy analysis. In the practical case considered here, neither technique is a clear winner; each has strengths and weaknesses.