Does the Stochastic Specification of the Linear Expenditure System Matter?

When income in a system of demand equations is defined as total expenditure, actual expenditure on any commodity must lie between zero and income, or equivalently, budget shares must lie between zero and one. But models for expenditures or shares are often the sum of deterministic components (predicted values), which are functions of prices and income, and disturbances, usually assumed multivariate normal. The predicted values ought to satisfy the same bounds as the dependent variables and will do so if the demand system is regular. But even then, the situation is theoretically inconsistent with unbounded disturbances and it has been proposed (Fry et al., 1996) that analysis be appropriately modified. In assessing how much practical difference this makes, the linear expenditure system (LES) is, for reasons described in the paper, the crucial case. We compare estimation methods for the LES, using Irish data from 1979-99 on some broadly defined commodities, and find that the differences are not of practical concern.