Econometrica: Jul, 1972, Volume 40, Issue 4

The S-Branch Utility Tree: A Generalization of the Linear Expenditure System

https://doi.org/0012-9682(197207)40:4<737:TSUTAG>2.0.CO;2-I
p. 737-747

Dale Heien, Murray Brown

A utility tree is specified yielding a complete set of demand equations that subsumes the linear expenditure system as a special case. In contrast to the Stone-Geary system, it is shown that our S-branch model allows for Hicks-Allen complements, and it does not restrict the own-price elasticity. Moreover, it is not costly in terms of the additional parameters required. Maximum-likelihood estimates of the S-branch system are presented; these are derived by means of the Bard version of the Gauss-Newton algorithm. In this application to food expenditure data in the United States the use of the S-branch system avoids a potential misspecification which would have resulted from the application of the linear expenditure system.