Abstract
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.
Work done for this paper was supported by the Stiftung Volks wagen werk, the Riksbankens Jubileumsfond, and grant SES-8607652 of the National Science Foundation. We are very grateful to an anonymous referee of this volume for useful comments.
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Notes
This is true if the u t are serially independent (see Barten, 1969). However, when the u t are autocorrelated, maximum-likelihood estimates may be conditional on the equation deleted. For a detailed argument, see Berndt and Savin (1975).
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Chipman, J.S., Tian, G. (1989). Stochastic Specification and Maximum-Likelihood Estimation of the Linear Expenditure System. In: Raj, B. (eds) Advances in Econometrics and Modelling. Advanced Studies in Theoretical and Applied Econometrics, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7819-6_9
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