One suggestion for coping with the Lucas critique of applied econometric research is to estimate the taste and technology parametersthat presumably underlie supply and demand curves. Proponents of this approach generally interpret economy-wide data on prices and quantities as the results of optimization problems solved by representative consumers and firms. Theoretical first-order conditions (normally linear)for interior solutions are then used to convert observed data intoestimates of the taste and technology parameters of representative agents.This brief paper points to a hazard in this type of research.Specifically, the new style of econometrics can lead to serious error if the economy-wide data are not in fact generated by interior optima of representative agents, but rather come from aggregating over agents that behave quite differently.In an example where the market-wide demand curve is smooth eventhough each individual's demand function is a step function, the procedures of the new econometrics are shown to lead to grievous errors even though all consumers optimize and the econometrician is assumed to know the precise form of the utility function. It is argued that this example is of quite general applicability, and that the simpler procedures of "old fashioned" econometrics may be less hazardous.