An EM Algorithm for Modelling Variably-Aggregated Demand.

This paper develops an EM algorithm for the estimation of a consumer demand system involving variably aggregated data. The methodology is based on the observation that more highly aggregated data does in fact contain information on the finer subcategories. It is therefore possible, under certain simplifying assumptions, to derive the distribution of the unobserved fine-level expenditures conditional on the observed but more highly aggregated data. The expectation of the log-likelihood is then taken with respect to this conditional distribution. Under the assumption of multivariate normality both these steps can be performed analytically, resulting in an EM criterion that can be maximised iteratively at comparatively little cost. The technique is applied to an ABS dataset containing historical information relating to private final consumption expenditures on up to 18 commodities.