Part I: Measuring Poverty, Inequality, and the Growth Elasticity of Poverty

Week of 08/31: Measuring Poverty and Inequality | Week of 9/07: Understanding Pro-poor Growth: Measurement and Implications

Three Aspects of Welfare

1. Poverty - the level effect.

2. Inequality - the distribution effect.

3. Vulnerability - the risk element relating to the probability of becoming poor (if you are nonpoor) or falling deeper into poverty due to adverse shocks

1. Measuring Poverty

Any poverty measure involves three essential elements:

A. An indicator of well-being at the individual/household level.

B. A poverty line: a threshold of well-being below which an individual/household is considered to be poor.

C. A poverty statistic: a formula to summarize poverty at the aggregate level (country, region, ethnic group, etc)

(Should also fulfill certain desirable statistical properties)

1.A. Indicators of Well-being

• What are widely used measures in poverty analysis?

• Why do economists prefer consumption expenditure to income as an indicator of well-being?

• Monetary measures of well-being are widely used. They are obtained from Household Income and Consumption Expenditure Surveys

  • (These surveys are designed to be nationally representative — following some form of random sampling.)

• In the context of developing countries, economists prefer consumption expenditure to income because:

  • income doesn’t take into account access to goods and basic services

  • income is more susceptible to measurement errors as compared to expenditure (respondents more honest in reporting expenditure vs income)

  • income tends to be more volatile due to seasonality of economic activities like agriculture, tourism, etc..

1.B. A Poverty Line

• What is an absolute poverty line?

• How is it determined?

• An absolute poverty line is based on BASIC NEEDS to achieve a minimum acceptable standard of living. (Specifically, it captures the ability to afford enough food for a normal life, which is about 2000 calories per person per day.)

• It is determined by looking at looking at the average household expenditure corresponding to actual baskets of food that provide 2000 calories per person per day.

• The poverty line should be adjusted to taking into account inflation.

1.B. Poverty Line

• What is a relative poverty line?

• Where are they often used?

• A relative poverty line is defined in reference to the national average income (Ex: 50% of the national mean income in European countries).

• Relative poverty lines are often used in developed countries where social inclusion is a major concern relative to access to food.

1.C. The Foster-Greer-Thorbecke (FGT) Poverty Index

• What type of measures are the FGT indices?

• What does it mean that the FGT poverty indices are additively decomposable?

• The FGT poverty measures are moneymetric (using monetary poverty line).

• Indices are additively decomposable: a property where the poverty measures can be calculated for different sub-samples and then aggregated for higher units of analysis.

1.C. The FGT Poverty Index

1. What is the Head Count Ratio (P0)?

2. What is it measuring, and how is it estimated in practice?

The Head Count Ratio (P0): Measures the percentage of the relevant population (country, region, locality) living below a given poverty line z, where z>0.

P0 = q / n

• q: is the number of individuals whose income is below the poverty line (z)

• n: total population

In practice, P0 is estimated based on nationally representative sample of households instead of counting all poor people.

1.C. The FGT Poverty Index

What are the most important drawbacks of the Head Count Ratio (P0)?

• If the poverty line is relative, then P0 could increase even as the average income of the poor increases. (Relative poverty could still rise while absolute poverty falls. Imagine the income of the average poor person increasing by 3% while the national average income rises by 8%).

• P0 is not sensitive to the income shortfall of the poor (even if we take an absolute poverty line). For a given q and n, P0 can remain the same even when the income of the poor declines.

(Similarly, an increase in income among the poor may not change P0 as long as their income remains below the poverty line.)

1.C The FGT Poverty Index

1. What is The Poverty Gap (P1)?

2. What does it measure

3. What does I₀ stand for?

• P1 takes into account how far each poor person’s income (yi) falls short of the poverty line (z).

• It is expressed as the sum of the income shortfall of all poor people relative to the poverty line (z) divided by total population (n).

• I0 = z-ybar/z is the average income shortfall of the poor relative to the poverty line, and ybar is the average income of the poor.

• P1 also indicates the financial burden to society as a whole (in per capita terms) of bringing every poor person’s income up to the poverty line (The total financial resources needed to do so can be calculated as P1*z*n).

1.C The FGT Poverty Index

What is the key drawback of The Poverty Gap (P1)?

It gives equal weight to all income shortfalls of the poor.

(In other words, P1 is not sensitive to inequality among the poor)

1.C. The FGT Poverty Index

1. What is the Severity of Poverty (P2)?

2. What does it measure?

3. What does a reduction in P2 mean?

• P2 (also called the square poverty gap) measures the depth of poverty by giving more weight to the income shortfall of the poorest among the poor.

• It does so by squaring the income shortfall of each poor person so those who are further away from the poverty line carry more weight.

• (Unlike P1, P2 does not have direct monetary interpretation. However, it can be compared over time for a given country or across countries at a given point in time.)

• A reduction in P2 means standards of living have improved for the poorest among the poor.

What does 𝛂 measure what value corresponds to each FGT index?

alpha measures a policy maker’s aversion to poverty or inequality among the poor.

• alpha =0 corresponds to Head Count Ratio (P0)

• alpha=1 corresponds to the Poverty Gap (P1)

• alpha=2 corresponds to Severity of Poverty (P2)

1.D. Desirable Properties of a Poverty Index

What is the Monotonicity Axiom?

• What FGT Poverty Indices satisfy it?

Other things being equal, a reduction in the income of a poor person should increase the poverty measure.

• Violated by P0 but satisfied by P1 and P2.

1.D. Desirable Properties of a Poverty Index

What is the Transfer Axiom?

• What FGT Poverty Indices satisfy it?

A transfer of income from a poor person to another poor person who is better off (i.e., closer to the poverty line) must increase the poverty measure.

• P0 and P1 violate this axiom but P2 satisfies it

1.D. Desirable Properties of a Poverty Index

What is the Transfer Sensitivity Axiom?

• What FGT Poverty Indices satisfy it?

A transfer of income from a poor person to another better off poor person should increase the poverty measure at a decreasing rate the closer the donor is to the poverty line.

• Only alpha>2 can satisfy this axiom.

1.D Desirable Properties of Poverty Indices

What is the Additive Decomposition Axiom?

• What should the overall poverty in a given country be equal to?

Palpha is additively decomposable across population groups with population shares as weights:

• j indexes population sub-groups, nj/n is the population share of sub-group j, and palphaj is a poverty measure in subgroup j.

• The overall poverty in a given country should be equal to the weighted average of sub-group poverty levels where the weights are population shares of sub-groups.

1. Desirable Properties of Poverty Indices

What is the Sub-Group Consistency Axiom?

• what other axiom is it derived from?

Total poverty should increase if poverty in a given sub-group increases even if poverty in other sub-groups remains unchanged. (This axiom assumes no cross-group migration of people)

• Derived from the additive decomposition axiom

1.E. Poverty Profile

What is a poverty profile?

• A poverty profile disaggregates national poverty indices into poverty measures for subgroups of a population.

• Typically decomposes the national poverty based on characteristics of the household head.

• (In doing so, a poverty profile allows us to answer the following questions: Where do the poor people live? What are their main sources of income? Do they have access to public services?)

1.E. Poverty Profile

What is the axiom that is the basis for constructing a poverty profile?

What does the poverty profile compare and what does it help us answer?

• The Additive Decomposition Axiom is the basis for constructing a poverty profile.

• A poverty profile compares the population share of a particular sub-group of households with their share in (or contribution to) aggregate poverty.

• This approach reveals the distribution of the burden of poverty across groups of households.

• In doing so, a poverty profile helps characterize poverty and design well-targeted anti-poverty programs.

1.E. Poverty Profile

How does it help us see who may be overrepresented in poverty?

By comparing nj/n with the contribution of sub-group j to the national poverty Palpha, it is possible to compare a particular group in the total population (nj/n) with its contribution to (share in) national poverty.

• This way we can determine whether a particular group of people are overrepresented in poverty.

Given this poverty profile:
1. Female headed households account for what percent of the households?

2. What is the HCR for female and male head households?

3. How do you calculate the national HCR?

4. How do you calculate the contribution of female headed households to the national HCR?

5. What does this contribution show?

1. Female headed households account for 25% of the population while male headed households account for 75%.

2. 0.45 and 0.55

3. 0.75(0.45) + 0.25(0.55) = 0.475

4. [0.25(0.55)/0.475] = 0.29

5. This shows that overrepresentation of people who live in female headed households in poverty (29%) as compared to their population share (25%).

(This type of evidence is consistent with the female disadvantage in many developing countries in terms of access to education, healthcare, and finance.)

1.F. The Multidimensional Poverty Index (MPI)

• What is the MPI and its 3 dimensions and 10 indicators?

• Instead of focusing on money and consumption to determine poverty, what two qualities does it attempt to measure?

• MPI has 3 dimensions: Education, Health, and Living Standards. Each dimension carries equal (1/3) weight in constructing MPI.

• The MPI has 10 indicators in total: 2 for education, 2 for health, and 6 for living standards.

• Instead of focusing on money/consumption, we should focus on Capabilities and Functionings

Functionings: refer to being the person you want to be or doing what you want to do in life.

Capabilities: indicate the freedom to achieve functionings (Health and education, for instance, enable a person to achieve what other members of society are capable of achieving).

2. Measuring Inequality

What does inequality capture?

What does inequality affect?

• Inequality captures the distribution of income and other measures of welfare in society.

• The extent of inequality reflects the quality of institutions that determine the distribution of income and investment opportunities: it reflects the risk of exclusion, marginalization, and discrimination.

• Inequality is believed to affect economic growth as well as
  the effectiveness of growth in reducing poverty

2. Measuring Inequality - The GINI Coefficient

• Defined on the basis of what?

• What is the GINI coefficient?

• What does it not pick up?

• It is defined on the basis of an underlying Lorenz Curve - a line that maps the cumulative income share of people at different percentiles ranked by per capita income.

• The GINI coefficient varies from 0 (perfect income equality) to 1 (complete inequality).

• It does not pick up underlying differences in the level and distribution of income for countries with similar GINI coefficients.

How do you calculate the GINI coefficient?

GINI = A/(A+B) = 2A

2. Measuring Inequality - The Theil Index

What is it?

How is it calculated and what is the range?

What makes it unique?

• a widely used index of inequality which has the advantage of additive decomposition.

• Xi is individual income, xbar is mean income, and N is population.

• The Theil Index ranges from 0, where everyone has the same income, to ln(N) where one person gets all the income.

• An interesting feature of the index is that it can be decomposed into within and between group inequality.

2. Measuring Inquality - The Theil Index

How does decomposition work?

• What is each variable?

• What does the first term measure?

• What does the second term measure?

• xj is income from source j and alpha j is its share in the total income; Tj is the Theil index for a particular income source j. Xbar is overall/national mean income and xbarj is mean income in sector j.

• The first term is a weighted average index based on sector-specific Theil indices → within sector inequality.

• The second term captures inequality across sectors → between inequality. If average income is equal across sectors, the second term = 0.

3. Vulnerability

What does it refer to?

What does it capture?
What does it affect?

• Refers to the risk of becoming poor or falling deeper into poverty in the future.

• It captures the degree of insecurity of ones well-being.

• Vulnerability affects households’ resource allocation and choice of economic activities (I.e., Households may opt for less profitable but more secure economic activities instead of more productive but high risk activities).

• In doing so, vulnerability may lead to low average income (high poverty) in the absence of insurance mechanisms.