Stochastic Specification and Maximum-Likelihood Estimation of the Linear Expenditure System

From the point of view of consumer demand theory the linear expenditure system (LES) provides a convenient model for representing consumer response to price and income and its linearity is one of its most attractive features. But when estimation problems are discussed, the descriptive adjective is more notable for its irony than its accuracy. Since Stone (1954) first calculated parameter estimates for the LES, some stochastic specifications for the system have been given. These specifications, however, ignore some of the requirements implied by economic theory and these methods of estimation lack desirable properties. This paper will deal with the problems of stochastic specification and maximum-likelihood estimation of the LES making full use of the restrictions of economic theory by assuming that the minimum required quantities for the commodities have a three-parameter multivariate lognormal distribution.