# **II.** Measured Poverty Under Alternative Consumption Definitions

We consider here a range of poverty indicators and two alternative approaches to setting a poverty line, both of which build on Engel's Law. We set out the simplest case of moving from food expenditure, F, alone as the welfare indicator to a more comprehensive measure, Y, which includes food plus non-food expenditures: _Y=F+NF._ Both food and non-food are continuous and monotonic functions of total expenditure: _F=ffY), NF=g(Y)._ It will be convenient below to define the inverse function _Y_ = _f -' (F) = k(F)._ We shall make use of the following assumptions: _Al) f'20 - 'Ž0._ _A2) g'20_ _A3) k'>0 (Engels Law)._ By Al, food expenditure is increasing in total expenditures. A2 implies that the samne for non-food expenditures while A3 implies that total expenditures increase at an increasing rate with food. The latter implies that the budget share devoted to food declines as total expenditures increase.

Let z denote the "food poverty line", which is the cost of purchasing a minimum food consumption basket. Typically, this line provides for a nutritional intake considered to be just adequate given the consumption patterns of low income households. The "final poverty line" allows for a certain amount of "essential" non-food spending over and above what is necessary to meet a person's nutritional requirements. Because it is difficult to set objective criteria as to what constitutes essential non-food consumption, the non-food component of the final poverty line is usually obtained by scaling up, by some factor, the food poverty line. We apply two commonly implemented approaches for deriving the final poverty line. The first, which we denote the "traditional" poverty line, T(z), scales up the food poverty line, z, by the non-food budget share of those households whose food expenditures exactly meet the food poverty line. Thus:

## _T(z) =k(z)._

The "austere" poverty line, A(z), has been proposed by Ravallion (1994a) as an alternative. It adds to the food poverty line the amount normally spent on non-food items by those households whose _total_ expenditure, Y, is just equal to the food poverty line. Because this group of households is sacrificing essential food consumption in order to acquire a certain number of non-food items, Ravallion argues that these must be essential<sup>6</sup> . Thus: If _h(F)_ is the probability density function of food spending in a sample then measured poverty, with food expenditure as the welfare measure, can be written as: where _PF(F,_ z) is a household poverty indicator. Now let Z denote one of the final poverty lines, T(z) or A(z). Then measured poverty, with total expenditure as the welfare measure, can be written as: 6 These two approaches are described in detail in Ravallion (1994a). Variants have been implemented in practice. For example, the 'traditional" approach resembles that adopted in setting the official poverty lines in the United States and India (Deaton, 1995), although usually average non-food shares of a reference population have been taken rather than the estimated non-food share of a household whose food expenditures exactly meet the food poverty line. Bidani and Ravallion (1994) apply the "austere' poverty line in a study of Indonesia. See also several recent World Bank poverty assessments, for example, the _Ecuador Poverty Report_ (World Bank, 1995). It should be noted that holding the poverty line constant (in real terms) across data sets remains by far the most common practice. All of the biases discussed below pertaining to the 'austere" poverty line would hold even more strongly with a constant poverty line.

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