Chipman, John S. and Tian, Guoqiang (1989): Stochastic Specification and Maximum-Likelihood Estimation of the Linear Expenditure System. Published in: Advanced Studies in Theoretical and Applied Econometrics , Vol. 15, (1989): pp. 131-142.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Stochastic Specification and Maximum-Likelihood Estimation of the Linear Expenditure System|
|Keywords:||Stochastic Specification; Maximum-Likelihood Estimation; Linear Expenditure System|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory|
|Depositing User:||Guoqiang Tian|
|Date Deposited:||17. Sep 2012 13:35|
|Last Modified:||18. Feb 2013 16:15|
Barten, A.B.:1964, ‘Consumer Demand Functions Under Conditions of Almost Additive Preferences’, Econometrica, 32, 1-38.
Barten, A.B.:1969, ‘Maximum-Likelihood Estimation of a Complete System of Demand Equations’, European Economic Review, 7-73.
Berndt, E. R., and N. E. Savin: 1975, ‘Estimation and Hypothesis Testing in Singular Equation Systems with Autoregressive Disturbances,’ Econometrica, 43, 937-957.
Block, H.D., and J. Marschak: 1960, ‘Random Orderings and Stochastic Theories of REsponse’, in I. Olkin et al. (eds.), Contributions to Probability and Statistics, Stanford University Press, Stanford, California, U.S.A., pp. 97-132.
Chipman, J. S.: 1960, ‘Stochastic Choice and Subjective Probability’, in D. Willner (ed.), Decisions, Values, and Groups, 1, Pergamon Press, New York, New York, U. S. A., pp. 70-95.
Chipman, J.S.:1985, ‘Estimation of Net-Import Demand Functions for the Federal Republic of. Germany, 1959-1982’, in H. Giersch (ed.), Probleme und Perspektiven der weltwirtschaftlichen Entwicklung, Dunker & Humblot, Berlin, Germany, pp. 197-213.
Chipman, J.S., and G. Tian: 1988, ‘Generalized Maximum-Likelihood Estimation of the Linear Expenditure System with Lognormal Distribution’, manuscript.
Christensen, L. R., D.W. Jorgenson, and L. J. Lau: 1975, ‘Transcendental Logarithmic Utility Functions’, American Economic Review, 65, 367-383.
Cohen, A.C.: 1951, ‘Estimating Parameters of Logarithmic-Normal Distributions by Maximum Likelihood’, Journal of the American Statistical Association, 46, 206-212.
Davidson, D., and J. Marschak: 1959, ‘Experimental Tests of a Stochastic Decision Theory’, in C. W. Churchman and P. Ratoosh (eds.), Measurement: Definitions and Theories, John Wiley & Sons, Inc., New York, New York, U.S.A., pp. 233-269.
Deaton, A. S.: 1975, Models and Projections of Demand in Post-War Britain, Chapman and Hall, London, England.