Which is the better measure of welfare - per capita consumption, or adult equivalent?

The following example illustrates the motivation for the question. Suppose you have two households, A and C. Household A comprises four adults, and household C comprises two adults and two small children. Suppose each household consumes $100 of food in one month, total. On a per-capita basis, this is $25 per capita in consumption for each member of both households. However, for household C, this measure of welfare actually underestimates the true welfare of the household. The reason is that the children do not need to consume as much as adults, so that a child that consumes $25 of food is much better of than an adult that consumes $25 worth of food. So even though the per-capita consumption of each household is the same, household C is actually better off – the per-capita consumption measure of welfare has underestimated the welfare of household C.

Consider another example. Lets look at small family S, which comprises 1 adult. He buys firewood to heat his home, which contains only himself, for $10. Family A also buys $10 worth of firewood to heat their home. The per-capita consumption of firewood is $10 for household S and $2.5 for household A. However, each member of each household enjoys the same amount of heat – there are economies of scale in heating the room (assume a one room house, since we are talking about poor households here. Maybe the larger household requires more firewood, but certainly not four times as much, if you believe that there are economies of scale here). In this case, the per-capita measure again underestimates the welfare of the larger household.

One option for adjusting for economies of scale and differing needs of household members is to use the adult equivalent scale, which assigns weights to household members to make the adjustment. More information on the adult equivalent scale can be found here: http://www.oecd.org/LongAbstract/0,3425,en_2649_33933_35411112_1_1_1_1,00.html and here: http://www.google.com/url?sa=t&source=web&cd=1&ved=0CBsQFjAA&url=http%3A%2F%2Fwww7.nationalacademies.org%2Fcnstat%2FPoverty_Equivalence_Scales_Betson_Paper_PDF.pdf&rct=j&q=adult%20equivalent%20scale&ei=uZvrTNCNHYWclgforpm0AQ&usg=AFQjCNHXrcw16y_WDjZIZQbzg0hhJx71qA&sig2=b4PKoKi--xVUvmepS7ICnA&cad=rja

I asked some colleagues about this, and I’ve summarized the discussion below.

The adult-equivalent approach makes sense. It seems that theoretically, adult equivalent consumption should always be used because it is a better estimate of individual welfare, assuming one knows the weights. It adjusts for economies of scale in consumption, as well as the fact that children need to consume less than adults. So adult equivalent does not underestimate welfare as much as per capita equivalent does. However, it has significant disadvantages:

1) There is no universally agreed upon standard or empirical way for how to assign weights to the household members. Many just use a best guess.
2) Using it would result in inconsistency with other measures of poverty, such as the poverty line, cutoff, etc. We should be consistent with how we have been measuring poverty.
3) It is more complex; it is harder to explain and administer

The per-capita method is simpler and more transparent, even though it may underestimate consumption of larger households. As a general rule, it is best to go with the equivalence scale that is currently in use.

Another criticism of using adult equivalent consumption as the dependent variable in PMT regressions is that the variables used to calculate adult equivalent from per-capita consumption are variables that appear on the right hand side of the regression. For example, household size and number of children may appear on the RHS, and these are used to adjust per-capita consumption to form adult equivalent consumption, which would go on the LHS. However, controlling for these variables in the regression does not fix the problem of per-capita consumption underestimating welfare (any thoughts on this, anyone?).

One colleague says that there is no right or wrong answer here, but suggests to use whichever equivalence scale (adult equiv or per-capita) that is currently in use in the context of interest.

One observation that I would like to contribute is that I have found that, at least in my experience, using per-capita rather than adult equivalent consumption has yielded regression estimates with greater explanatory power. This is important if you are trying to predict consumption for PMT.