Weak separability and the estimation of elasticities in multistage demand systems

The necessary conditions for multistage budgeting to be at least approximately justified are reviewed, and the plausibility of these assumptions (i.e., weak separability and low variability of price indices with utility level) are discussed. Using no further assumptions, simple relationships between expenditure and price elasticities in different budgeting levels are derived. These results are applied to a three-stage model for Swedish food consumption, and it is shown that the assumptions are not inappropriate. Restricting the analysis to the last stage of a multistage budgeting process is also shown to lead to considerable errors, which could well have policy consequences.