Corrigendum to “Equivalent-expenditure functions and equivalent-dependent equivalence scales”

Abstract

This note is to correct an error in Donaldson and Pendakur (2004) in this Journal. In bEquivalent-expenditure functions and expenditure-dependent equivalence scalesQ ,w e propose equivalence scales which are log-linear in expenditure and show that they are identifiable from behaviour under the maintained assumption of log-linearity. In the empirical work, we find the equivalence scales for families in comparison with single childless adults to be declining in expenditure. Equivalence scales which vary with expenditure allow expenditure-shares for children’s goods to depend on expenditure, and in the empirical work, we find the expenditure-share equation for children’s clothing to be declining in expenditure. In the empirical work, we estimated a 10-good quadratic almost ideal demand system over 60 price regimes to recover equivalence scales wherein one of the goods was children’s clothing. Unfortunately, we have since discovered that the children’s clothing data are only comparable for the first 45 price regimes in the data. In particular, in the data for the first 45 price regimes, children’s clothing is defined as clothing for children aged less than 14, but in the data for the last 15 price regimes, it is defined as clothing for children aged less than 4. To assess the importance of this error, we estimated two new demand systems: (1) a 9-good demand system which is identical to the original except that clothing for adults and clothing for children are pooled into a single good called dclothingT; and (2) a 10-good demand system which is identical to the original except that it is estimated on only cases facing the first 45 price regimes. We use the first new demand