Adjusting for Family Composition and Size

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Adjusting for Family Composition and Size

• Module 4 Poverty Measurement and Analysis
• February, 2008

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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.

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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

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Differences in Needs

• Nutritional 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)

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The head-count ratio and equivalence scales  
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.
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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.

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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)

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Economies of Scale in Consumption

• Suppose money metric of consumers welfare has an
  elasticity of ? with respect to household size.
  Then welfare measure of a typical member of any
  household is measured in monetary terms by

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Economies of Scale in Consumption

• Suppose that ? is the proportion of household
  expenditure on purely private goods, and 1- ? is
  allocated to public goods.
• Then the correct monetary measure of per-capita
  welfare is
• Solving for ? yields
•  

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Economies of Scale in Consumption

• In Ecuador, average household size is 4.76.
• If ? 0.9 then ?0.8
• If ? 0.7 then ?0.51
• If average size 6
• ? 0.9 then ?0.77
• ? 0.7 then ?0.49 
• Problem, as with equivalence scales, is that
  there isnt a good way of estimating ?
• Best bet is sensitivity analysis again.
• (India Example)

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  The head-count ratio and economies of scale  
Source Drèze and Srinivasan (1997), Table 4.
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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)

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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.