TY - JOUR
T1 - The stochastic specification of demand share equations
T2 - Restricting budget shares to the unit simplex
AU - Fry, Jane M.
AU - Fry, Tim R.L.
AU - McLaren, Keith R.
N1 - Funding Information:
Economists are often interested in estimating a system of equations that relate to shares of a total. Examples of this are the shares of individual demands in * Corresponding author. Part of this research was funded by the Australian Research Council (Grant Number A 79231646). The authors would like to thank participants at a Universityo f Manchester econometricsw orkshop and two anonymous referees for helpful comments and suggestions on this paper. All remaining errors and omissionsa re, however, solely the responsibilityo f the authors. Part of the research for this paper was undertaken while the first two authors were visitingt he Department of Econometrics, Manchester University.T he department's provision of resources and kind hospitality are gratefully acknowledged.
PY - 1996/8
Y1 - 1996/8
N2 - The traditional approach to estimating systems of share equations is to append a multivariate normal stochastic component to the deterministic component. The adding up restrictions are then exploited to delete one equation and estimation is carried out by maximum likelihood. Such an approach leads to an implied model which violates economic theory, as there remains a nonzero probability of shares being negative or greater than unity. In this paper we propose the use of a method from the statistics literature, compositional data analysis, and a distribution familiar to statisticians, the additive logistic normal, for the estimation of a system of demand share equations.
AB - The traditional approach to estimating systems of share equations is to append a multivariate normal stochastic component to the deterministic component. The adding up restrictions are then exploited to delete one equation and estimation is carried out by maximum likelihood. Such an approach leads to an implied model which violates economic theory, as there remains a nonzero probability of shares being negative or greater than unity. In this paper we propose the use of a method from the statistics literature, compositional data analysis, and a distribution familiar to statisticians, the additive logistic normal, for the estimation of a system of demand share equations.
KW - Additive logistic normal
KW - Demand share
KW - Dirichlet distribution
KW - Multivariate normality
KW - Simplex
KW - Stochastic
UR - http://www.scopus.com/inward/record.url?scp=0001101363&partnerID=8YFLogxK
U2 - 10.1016/S0304-4076(95)01727-5
DO - 10.1016/S0304-4076(95)01727-5
M3 - Article
AN - SCOPUS:0001101363
SN - 0304-4076
VL - 73
SP - 377
EP - 385
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -