An Em Algorithm for Modelling Variably-aggregated Demand
GroseSimone
McLarenKeith
2017
The response of consumer demand to prices, income, and othercharacteristics is important for a range of policy issues. Naturally, the level of detail for which consumer behaviour can be estimated depends on the level of disaggregation of the available data. However, it is often the case that the available data is differently aggregated in different time periods, with the information available in later time periods usually being more detailed. The applied researcher is thus faced with choosing between detail, in which case the more highly aggregated data is ignored; or duration, in which case the data must be aggregated up to the "lowest common denominator". Furthermore, since parametric demand systems invariably involve a large number of parameters, with the number increasing at least linearly with the number of expenditure categories, it may well be that only the second option is feasible. That is, there is simply not enough data available at the finer aggregation level for the chosen model to be estimated.This paper develops an EM algorithm for the estimation of a consumerdemand 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.