Adjusting for Family Composition and Size

Module 4: Poverty Measurement and Analysis

February, 2008

Adjusting for Family Composition and Size

Ultimate goal is to arrive at a money metric of individual welfare.Consumption (and income) aggregates are usually constructed at the level of the household.Convention is to divide household consumption by the number of family members to arrive at a measure of per capita consumption.This approach sidesteps two issues: Different people may have different needs The cost per person of reaching a certain welfare

level may be lower in large households than small ones.

Differences in needs

In principle equivalence scales can be used to adjust for differences in needs. E.g. If a child needs half as much as an adult,

then a two adult - two child household will consist of three equivalent adults.

If the total consumption of household is 120 then equivalent-consumption will equal 40. All four individuals will be allocated this equivalent-consumption.  

Where do equivalence scales come from? Huge range of candidate scales

Differences in NeedsNutritional scales – derived from health studies. At best can be used to deflate food expenditures. Behavioral scales – econometric estimates based on observed allocations. Major difficulties with identification. For example, if we observe that female children get less, do they need less? Or is it that they are systematically discriminated against?Little guidance as to which scales are best. One option to conduct sensitivity analysis. (India example)

The head-count ratio and equivalence scales Household Type

Equivalence scales

  (1,1,1) (1,1,0.6) (1,0.8,0.6) (1,0.7,0.4)

All households 63.4 63.2 62.9 63.8

Male-headed 63.8 63.6 63.5 64.5

Female-headed

57.7 57.4 54.3 52.7

Widow-headed 58.3 61.9 58.2 58.6

Extended; male-headed

68.2 69.5 67.6 67.4

Source: Drèze and Srinivasan (1997), Table 3.Note: The equivalence scales are written as triplets indicating the weights for ‘adult male’, ‘adult female’ and ‘child’, in that order.

Differences in Needs

We often find that poverty profiles do not change much as a result of equivalence scale adjustments.

 Use of per capita welfare measure may not be too misleading

 This is an empirical question that needs to be checked on a case-by-case basis.

Economies of Scale in Consumption

The use of a per capita measure of consumption imposes an assumption of no economies of scale in consumption.

Where might such economies come from? Consumption of public goods within the household

(radio, water pump) Bulk purchase discounts on perishable food items Economies in food preparation (fuel, time)

Economies of Scale in Consumption

Suppose money metric of consumer’s welfare has an elasticity of θ with respect to household size. Then welfare measure of a typical member of any household is measured in monetary terms by:

n

xx *

Economies of Scale in Consumption

Suppose that ρ is the proportion of household expenditure on purely private goods, and 1- ρ is allocated to public goods.

Then the correct monetary measure of per-capita welfare is:

Solving for θ yields:

 

xn

x

n

x)1()(

)ln(

)1ln(

nn

Economies of Scale in Consumption

In Ecuador, average household size is 4.76. If ρ =0.9 then θ=0.8 If ρ =0.7 then θ=0.51

If average size = 6 ρ =0.9 then θ=0.77 ρ =0.7 then θ=0.49 

Problem, as with equivalence scales, is that there isn’t a good way of estimating θBest bet is sensitivity analysis again.(India Example)

 The head-count ratio and economies of scale 

Household Type

Mean size

Economies of scale parameter θ

1 0.8 0.6 0.4

All households

5.35 63.4 59.6 54.5 49.5

Male-headed

5.56 63.8 59.4 53.9 48.6

Female-headed

3.60 57.7 61.6 62.0 62.6

Widow-headed

3.32 58.3 63.8 65.1 66.2

Extended; male-headed

6.78 68.2 60.3 51.0 43.5

Source: Drèze and Srinivasan (1997), Table 4.

Economies of Scale in Consumption

Message now is that the per capita assumption is not innocuous. Conclusions as to the relative poverty of large households (many children) versus small (elderly) are usually quite sensitive. Big issue in regions (ECA) where there are big

debates regarding public spending priorities (pensions versus child benefits)

Note, over time, economies of scale parameters could evolve (Lanjouw, et al, 2004)

Further reading

Deaton, A. and Paxson, C. (1998) ‘Economies of Scale, Household Size and the Demand for Food’, Journal of Political Economy, 106(5): 897-930.Lanjouw, P.F. and Ravallion, M. (1995): Poverty and Household Size, Economic Journal, Vol 105, No. 433.Lanjouw, J., Lanjouw, P., Milanovic, B., and Paternostro, S. (2004) Economies of Scale and Poverty: the Impact of Relative Price Shifts During Economic Transition, Economics of Transition 12(3) 509-536.