Constructing the Welfare Aggregate

Part 2: Adjusting for Differences Across

Individuals

Bosnia and Herzegovina Poverty Analysis Workshop

September 17-21, 2007

Topics

Introduction1. Aggregation Issues2. Adjusting for differences across individuals

a) Cost of living differences– across regions– over time

b) Differences in household composition– economies of scale– equivalence scales

Concluding Observations

2a. Differences in cost of living (across regions )

Price indices summarize prices in different locations. One can use existing regional Consumer Price Indices or construct such indices: 1. Specify a basket for which prices should be

compared. The choice of basket depends on the type of analysis: Basket for the poverty line Average quantities or values of selected food

items in the country as a whole. Specific baskets for each region or each

household.

Differences in cost of living (regions, cont. )

2. Define “regions” for which indices are to be calculated (could be each entity; or could be larger groups such as urban North, urban South, rural North, rural South).

3. Calculate the cost of the basket for each region, using average prices observed in the region (either from household consumption data, or from community data which collects local level price information). Also calculate the national cost, with averages.

Differences in cost of living (regions, cont.)

4. Calculate the relative price index for each region, by taking the ratio of the regional index to the national index.

kregioninjitemofpricetheispWhere

qp

qp

P

kj

J

j

Nationj

Nationj

J

j

Nationj

kj

k

1

1

Differences in cost of living (over time)

When comparing two points in time, similarly, indices are based on the cost of the same basket of goods over time. The choice of the basket can either be that of any period, depending on the analysis.

tperiodatjitemofpricetheispWhere

qp

qp

P

tj

J

j

periodnceReferej

periodnceReferej

J

j

periodrenceRefej

tj

t

1

1

2b. Differences in household composition

A series of issues arise when calculating the aggregate, related to both the size and the composition of households. For instance,

1. Does a household of 4 need twice as much as a household of 2?

2. Do two households with the same number of members, but different composition (e.g. one with 5 adult men, and the other one with one adult woman and 4 little children) need the same amount to reach a certain level of welfare?

Some form of “normalization” should be used to allow comparison of households, in light of both size and composition.

Issue 1: Household size & economies of scale

a: Some goods and services are shared between members, like public goods within the household. (e.g. heating, cooking oil, housing, transportation means, etc.). The shared goods within the household are the root of economies of scale.

Question 1: Should we adjust the consumption or expenditure aggregate for household size, in order to be able to compare households and to compare the aggregate with the poverty line? Question 2: How to adjust?

Household size & economies of scale (cont.)

Problem: Should we adjust for economies of scale?

When a high share of budget is devoted to

“private” goods, such as food, the scope for economies of scale is small.

When a high share of budget is devoted to “public” goods (if price and quantity of housing, utilities, durable goods are high), economies of scale are likely to be larger.

Household size & economies of scale (cont.)

Look at the shares in the data, and decide whether to adjust. Note that in poorer countries, the economies of scale tend to be very small and no adjustments are usually made for economies of scale.

Note that, when not adjusting, one might overestimate the poverty of large households and underestimate that of small households. Need for sensitivity analysis

Household size & economies of scale (cont.)

Solution: How to adjust for economies of scale? If no adjustments are to be made for economies

of scale, divide the total household consumption or expenditure by the number of members. Total consumption is assumed to be equally divided, with no ‘gains’ from sharing consumption.

This is typically preferred in low or middle income countries.

Household

HouseholdIndividual N

ConsCons

Household size & economies of scale (cont.)

If adjustments are to be made, then, one can divide the total consumption of expenditure by N, where takes a value between 0 and 1.

0 if all goods consumed are public in the household, in which case each individual is assumed to consume the total consumption of the household

1 if we assume that no goods consumed are public in the household, in which case we fall back on the previous case.

)( Household

HouseholdIndividual N

ConsCons

Issue 2: Household composition & equivalence scales

Problem: It is usually assumed that children and the elderly need less than working age adults. Similarly, it is sometimes considered that women need less consumption than men.

Question 1: Should we adjust the consumption or expenditure aggregate for household composition in order to compare households and to compare the aggregate with the poverty line?Question 2: How to adjust?

Household composition (equivalence scales)

Solution: Should we adjust for household composition?

If children/elderly are as “expensive” as adults despite their lower nutritional requirement (e.g. because of very high costs for education or health), less need for adjustment.

If a high share of the expenses go to goods that are needed by all in the same quantity (heat, housing, etc.), less need for adjustment.

If a high share of the expenses go to goods that are needed in different quantities, more need for adjustment.

Household composition (equivalence scales)

Look at the information available and decide whether to adjust.

Note that in low-income countries, the differences in needs tend to be higher than in high or middle income countries.

Note that, when not adjusting, one might overestimate the poverty of households with numerous children and underestimate that of households with few children. Need for sensitivity analysis

Household composition (equivalence scales)

Solution: How to adjust? If no adjustments are to be made for differences

in need, then simply divide the total household consumption or expenditure by the number of members. Total consumption is assumed to be equally divided, with all members having the same gains.

Household

HouseholdIndividual N

ConsCons

Household composition (equivalence scales)

If adjustments are to be made, one uses equivalence scales. The scales calculates the number of “equivalent adult” in the household. One then divides the total consumption by the “number of adult equivalent”. One can decide on the different categories and calculate the “weight” given to each category on different basis. An equivalence scale typically looks like:

)5.0x(

)8.0x()1x(

15underChildren

WomenAdultmaleAdultAdultsEquivalent

N

NNN

Household size and composition: Summary

There are also scales that take both household size and household composition into account. An example is the OECD scale.

The first adult is given a weight of 1. The other adults are given a weight of 0.7, to reflect

economies of scale. Children are given a weight of 0.5 to reflect their

presumably lower needs.

)5.0x(

7.0x1)-(1

15underChildren

AdultsAdultsEquivalent

N

NN

Equivalence scales in practice Several choices:

Normative (e.g., nutritionists) Empirical (subjective/ behavioral) Arbitrary (e.g., administrative, per

capita)

Equivalence scales - empirical The general formula

N = (A+*C)

where A is the number of adults in the

household, K is the number of children, is the cost of children relative to an

adult and is the economies of scale parameter

Equivalence scales – empirical

To estimate economies of scale: Behavioral - Lanjouw and Ravallion based on the

distinction between public and private goods within the household:

x/n =*x/n + (1-)*x The average welfare is the weighted sum of two

parts: (a) average consumption of private goods, rival

in consumption; and (b) total consumption of public goods, non-rival

in consumption. Solving for , the equation becomes: = -ln(1-+/n)/ln(n)

Equivalence scales – empirical To estimate the cost of children

relative to adults: Rothbarth - households with the same

level of per adult expenditures on goods consumed only by adults are equally well-off

Concluding Observations

1. Sensitivity Analysis: Are conclusions robust to choices made? (components of consumption, cost of living adjustments, equivalence scales? etc.)

2. Supplementary Indicators: Non-income measures (e.g. health status, education, access to services, empowerment, etc.)