Regular Alternatives to the Almost Ideal Demand System

While the Almost Ideal Demand System has received increasing attention in empirical studies of consumer demand, the fact that the underlying PIGLOG (and PIGL) cost function is not globally regular has often led to violation of concavity in the estimated Slutsky matrix. This violation typically occurs at many points within the actual sample. Although the estimating form of AIDS is attractive, it is also obvious that it can be at best a local approximation to a regular form since, beyond an arbitrarily restrictive regularity region, the implied AIDS shares must fall outside the (0,1) interval. This paper suggests a modification to the PIGLOG class of preferences which preserves regularity in a much wider region of expenditure-price space. The Modified AIDS, termed MAIDS, may be shown to contain AIDS as a local linear approximation. Because MAIDS is not a member of the Generalised Linear class of cost functions, it does not have the exact aggregation properties of AIDS. Instead of employing a representative individual approach to aggregation, we explicitly aggregate over individuals and parameterize on certain macro averages in order to apply the model to available macro data. The resulting MACRO MAIDS form contains all the parameter restrictions of MICRO MAIDS together with some additional terms which arise explicitly through the aggregation. We compare the estimated MACRO MAIDS with AIDS and demonstrate the improved regularity features.