Introduction

Equivalence scales – index numbers that attempt to measure the cost to a household of a change in its composition – are of considerable importance in the study of poverty and distribution and in the formulation of government policy. Yet there appears to be no consensus on what model of equivalence scales is the most appropriate, or whether, if at all, comparisons of household welfare can be based on household expenditure data. The reader is referred to Coulter, Cowell and Jenkins (1991) and Browning (1991) for recent surveys of the literature.

The model of equivalence scales usually attributed to Engel (1857) is perhaps the simplest and most easy to compute. It relies on the use of the share of food, sometimes broadly interpreted to include other necessities, as an indicator of household welfare. The equivalence scale is simply the ratio of expenditures that imply equal levels of the budget share of food for households of different demographic compositions. In general, it is impossible to test the assumption used to identify household welfare from household behaviour; it is only possible to test the implications for household demand of an identifying assumption. This makes rejections conclusive, but not acceptances.

The restriction on household demand implied by the Engel model have been explicitly spelled out by Deaton (1981) and, more recently, Browning (1988) and Blackorby and Donaldson (1988). In the absence of information on price variation it is not possible in this chapter to test these restrictions explicitly.