Estimation of Consumer Demand Functions When the Observed Prices Are the Same for All Sample Units

With the advent of the almost ideal demand system (AIDS) of Deaton and Muellbauer, the estimation of consumer demand functions revolves around specifications that use flexible functional forms of the indirect utility function. This dual approach has put on the backburner the traditional primal approach because the direct utility function exists only in a latent state. The lack of explicit, analytical invertibility of either system, however, is an indication that focusing exclusively on the dual side of the consumer problem is equivalent to disregard potentially important and independent information residing with the primal side. This paper suggests that efficient estimates (in the sense of using all the available information) of the demand functions require the joint estimation of all the primal and dual relations. The specification of this objective assumes that risk-neutral households maximize their expected utility subject to their expected budget constraint. This theoretical framework leads to a two-step procedure that produces consistent and efficient estimates of the model’s parameters. The generality of the approach proposed here can handle also the frequently encountered case when all the sample units face the same observed commodity prices. Finally, we present a general solution of the nonlinear errors-in-variables problem with a novel estimation procedure that avoids the pitfalls of the traditional approach.