Measuring and Modeling Poverty: An Update

1. Frontiers in Practice: Reducing Poverty Through Better Diagnostics PREM Workshop, World Bank, March 2006 Measuring and Modeling Poverty: An Update Martin Ravallion Development Research Group, DEC World Bank

2. Part 1: Measuring poverty 1.1 What is a “poverty line”? 1.2 Objective poverty lines 1.3 Subjective poverty lines 1.4 Poverty measures revisited 1.5 Robustness tests 1.6 Growth incidence curves 1.7 Measuring the impacts of policies

3. Part 2: Modeling poverty 2.1 Static models 2.2 Poverty mapping 2.3 Dynamics: Repeated cross-sections 2.4 Dynamics: Panel data 2.5 Micro growth models

4. Part 1: Measuring poverty

5. 1.1: What is a “poverty line”? • The welfare ratio: Add up expenditures on all commodities consumed (with imputed values at local market prices) and • Deflate by a poverty line (depending on household size and composition and location/date) • => “real expenditure” or “welfare ratio:” = price vector facing person i = quantities consumed by i But what is z?

6. The poverty line as money-metric welfare For informing anti-poverty policies, a poverty line should be absolute in the space of welfare • This assures that the poverty comparisons are consistent in that two individuals with the same level of welfare are treated the same way. • Welfare consistency in poverty comparisons will be called for as long as: • the objectives of policy are defined in terms of welfare, and • policy choices respect the weak Pareto principle that a welfare gain cannot increase poverty,

7. The poverty line as money-metric welfare The ideal poverty line should then be the minimum cost to a given individual of a reference level of welfare fixed across all individuals: e=expenditure function, giving minimum cost of achieving welfare level wz when facing prices p and with characteristics x Welfare function:

8. Poverty line as the “cost of basic needs” = quantity consumed of good j by i • Poverty line is the cost of a bundle of goods needed to assure a minimum level of welfare

9. How then do we measure “welfare”? Traditional approach in economics: an interpersonally comparable utility function defined on consumptions, with differences in tastes represented by a vector of household characteristics: • Consistent with choices over private goods, i.e., q maximizes w(q, x) at given x. • But interpersonal comparisons of utility are essential, and x also serves this role.

10. Sen’s capability-based approach: an interpretation Welfare depends on the functionings (‘beings and doings’) that a person is able to achieve. • “Poverty” means not having an income sufficient to support specific normative functionings. • Functionings depend on goods consumed and characteristics. Utility depends on functionings. • Thus we can still derive as the reduced form. • Functioning-consistency requires that fixed normative funtionings are reached at the poverty line. • Multiple solutions for the poverty bundle: • Minimum income s.t. all normative functionings are met • Income level at which functionings are met in expectation.

11. Two generic problems Identification problem: how to weight aspects of welfare not revealed by market behavior. • How do family characteristics (such as size and composition) affect individual welfare at given total household consumption? • How to value command over non-market goods (including some publicly supplied goods)? • How to measure the individual welfare effect of relative deprivation, insecurity, social exclusion? Referencing problem: what is reference level of welfare above which one is not poor, i.e., the poverty line in welfare space, which must anchor the money-metric poverty line. Poverty measurement in practice attempts to expand the information base for addressing the identification and referencing problems

12. Absolute vs. relative poverty • Poverty should be absolute in the space of “welfare” but relative in the space of commodities • Welfare depends on relative income: (where m= mean income) • Welfare poverty line: • which gives poverty line as a function of the mean: $1/day

13. Evidence for Malawi Relative deprivation amongst the poor? • Test for perceived welfare effects of relative deprivation using self-assessed welfare and perceived welfare of friends and neighbors (Lokshin and Ravallion) • Subjective welfare addresses the identification problem. • Findings: Relative deprivation is not a concern for most of the sample, although it is for the comparatively well off (upper fifth, esp., in urban areas). => welfarist explanation for the high priority given to absolute poverty in poor countries.

14. 1.2: Objective poverty lines 1. Cost-of-basic-needs method Poverty line = cost of a bundle of goods deemed sufficient for “basic needs”. Food-share version: poverty line = Cost of food-energy requirement Food-share of “poor” 2. Food-energy intake method Find expenditure or income at which food-energy requirements are met on average. • i.e., functioning consistency in expectation, but only one functioning

15. Methods of setting poverty lines matter!

16. Problems to be aware of 1. Defining "basic consumption needs" • Setting food energy requirements (variability; multiple equilibria; activity level). • Setting "basic non-food consumption needs" (behavioral approaches). 2. Consistency in terms of welfare • Is the same standard of living being treated the same way in different sub-groups of the poverty profile? If not, then the profile may be quite deceptive. • Is the definition of welfare consistent with the definition of poverty? If some good is purchased by poor people why should it not be included in the poverty bundle? Key question: how sensitive are the rankings in a poverty profile to these choices?

17. Inconsistent poverty lines? Example 1: “Cost-of-basic-needs method” • The two bundles yield same food-energy intake. • But the "urban" bundle is almost certainly preferable • The standard of living at the urban poverty line is higher than at • the rural line. • This makes the poverty comparison inconsistent, which can • distort policy making based on the poverty profile.

18. Example 2: "Food-energy intake method" Different sub-groups attain food energy requirements at different standards of living, in terms of real consumption expenditures. e.g., "rich" urban areas buy more expensive calories than "poor" rural areas. Do your poverty lines have the same real value to the poor across the poverty profile? Much evidence that they do not!

19. Allowing for differences in relative prices • Ideally we only want to adjust the poverty bundle for differences in relative prices • The problem is how to implement this ideal in practice • The identification problem remains Parametric demand models: If we know the parametric utility function then or we can figure it out from demand behavior then use this to determine the cost of the reference welfare level in each region Numerical methods: • Look at consumption behavior of poorest x% nationally in each region of the country • Cost the consumption bundle of that group in each region • Calculate the poverty rate nationally • Iterate if the answer differs too far from x

20. When non-food prices are missing Step 1: Find the cost at prevailing prices of a single national food consumption bundle that assures that recommended caloric requirements are met at prevailing tastes nationally. This gives the food poverty line. Step 2: Set the non-food allowance, consistent with consumption behavior of those who can either just attain or just afford the food poverty line. Utility-consistency can still be a problem!

21. Testing poverty lines • Well-defined “poverty bundles” by area + • Complete price matrix (commodity x area) • Revealed preference test for utility-consistency (Lokshin and Ravallion) • This assumes homogeneous preferences (given x). • The problem of welfare comparisons across different tastes remains. • A promising clue: subjective welfare data

22. 1.3: The social subjective poverty line The Minimum Income Question (MIQ) "What income do you consider to be absolutely minimal, in that you could not make ends meet with any less?“ • Is this method suitable for developing countries? • Can one estimate z* without the MIQ?

23. Subjective poverty lines for developing countries • Minimum income question is of doubtful relevance to most countries • Subjective poverty lines can be derived using simple qualitative assessments of consumption adequacy. • Consumption adequacy question: “Concerning your family’s food consumption over the past one month, which of the following is true?” Less than adequate ...1 Just adequate .......…. 2 More than adequate.. .3 "Adequate" means no more nor less than what the respondent considers to be the minimum consumption needs of the family.

24. Modeling consumption adequacy Individual needs are a latent variable: Subjective poverty line identified from qualitative data using the model: (Pradhan and Ravallion)

25. Examples for Jamaica and Nepal • Respondents asked whether their food, housing and clothing were adequate for their family’s needs. • The implied poverty lines are robust to alternative methods of dealing with other components of expenditure. • The aggregate poverty rates turn out to accord quite closely with those based on independent “objective” poverty lines. • However, there are notable differences in the geographic and demographic poverty profiles.

26. 1.4: Poverty measures revisited General class of additive (“subgroup consistent”/ ”subgroup decomposable”) measures: Aggregate poverty index • Individual poverty index • non-increasing in y • non-decreasing inz Unidimensional approach: y and z are scalars Multidimensional approach: y and z are vectors

27. “Money-metric welfare” vs. “multidimensional poverty measures” 1. Multidimensional poverty measurement: {Person i is poor iff } 2. Welfare function approach to poverty measurement: {Person i is poor iff } or equivalently: {Person i is poor iff where } • Surely these must be consistent, so why do we need both approaches? • The real issue is how to implement multi-dimensional welfare metrics, whether or not one uses a “multidimensional” poverty measure.

28. FGT measures Headcount index (H): % living in households with income per person below the poverty line. Poverty gap index (PG): mean distance below the poverty line as a proportion of the poverty line Squared poverty gap index (SPG): poverty gaps are weighted by the gaps themselves, so as to reflect inequality amongst the poor (Foster et al., 1984).

29. FGT: multidimensional version (Bourguignon and Chakravarty, 2003) Four groups of parameters: v weights attached to each dimension elasticity of substitution (shape of contours) poverty aversion parameter (concavity) z poverty lines (how can they be constant?

30. Watts measure • Watts index based on the aggregate proportionate poverty gaps of the poor: • This is the only index that satisfies all accepted axioms for poverty measurement including: focus axiom, monotonicity axiom; transfer axiom, transfer-sensitivity and subgroup consistency (Zheng) • Multidimensional Watts index:

31. 1.5: Testing robustness The three poverty curves: 1. The poverty incidence curve = H for each possible poverty line Each point gives the % of the population deemed poor if the point on the horizontal axis is the poverty line. 2. The poverty depth curve = area under poverty incidence curve Each point on this curve gives aggregate poverty gap per capita. 3. The poverty severity curve = area under poverty depth curve Each point gives the squared poverty gap per capita.

32. First-order dominance test If the poverty incidence curve for A is above that for B for all poverty lines up to zmax then there is more poverty in A than B for all poverty measures and all poverty lines up to zmax A B What if the PICs intersect at some point < zmax? e.g., higher rice prices in Indonesia: very poor lose, those near the poverty line gain.

33. Second-order dominance test If the poverty deficit curve for A is above that for B up to zmax then there is more poverty in A for all poverty measures which are strictly decreasing and weakly convex in consumptions of the poor (e.g. PG and SPG; not H). Third-order dominance test If the poverty severity curve for A is above that for distribution B then there is more poverty in A, if one restricts attention to distribution sensitive (strictly convex) measures such as SPG and the Watts index.

34. 1.6: Growth incidence curves • Invert the CDF to obtain the quantile function: • Then calculate growth rates at each percentile to give the growth incidence curve: • Note that if the Lorenz curve does not change then

35. Example 1: China and India in 1990s

36. But looked what happened in China around mid 1990s

37. Example 2: Indonesia in a crisis

38. Measuring the rate of “pro-poor growth” Watts index for the level of poverty implies using the mean growth rate of the poor in measuring the rate of pro-poor economic growth. (Not growth rate in the mean for the poor.) Example: Growth rates for China

39. 1.7: Measuring the poverty impacts of policies and programs Various measures of “targeting performance:” • SHARE: the share of total payments going to those with pre-transfer income y<z (or some fixed %) • Concentration index (CI): the area between the concentration curve and the diagonal (along which everyone receives the same amount). • SHARE normalized by headcount index • Targeting differential (TD) is the difference between the participation rate for the poor and that for the non-poor

40. However, better “targeting” does not imply a higher impact on poverty There can be no guarantee that better targeting by these measures will enhance a programs’ impact on poverty: • Coverage maters: avoiding leakage to non-poor may entail weak coverage of the poor. • Deadweight costs (incentive effects); e.g., income foregone by participants in workfare programs • Political economy: fine targeting can undermine political support for anti-poverty programs

41. Example for China’s Di Bao programImpacts on poverty measured across 35 municipalities Only the targeting differential has any predictive power for poverty impacts!

42. Better to focus directly on the poverty impact, though decompositions help understand that impact For example, the impact of a targeted transfer program on poverty (by any FGT measure) can be decomposed into four components: (1) the budget outlay per capita; (2) the extent of leakage to the non-poor; (3) a vertical equity component; and (4) a horizontal equity component. (Bibi and Duclos, 2005)

43. Part 2: Modeling poverty

44. For all additive measures we can decompose the aggregate measure by sub-groups e.g., “urban” vs “rural”, “large” vs “small” households The poverty profile can be thought of as a simple model of poverty: 2.1: Static models of poverty Prob(y < z)= Sub-group poverty measures (“poverty profile”)

45. We would like to introduce a richer set of covariates (some continuous) to: Account better for the variance in circumstances leading to poverty Disentangle which are the key factors, given their inter-correlation. For example: poverty profile shows that rural incidence > urban incidence, and that poverty is greater for those with least education. But education is lower in rural areas. Is it lack of education or living in rural areas that increases poverty? But this is too simple a model

46. Multivariate poverty profiles Welfare indicator modeled as a function of multiple variables: or Fixed effects, one for each sub-group with a different poverty line

47. Probits for poverty make little sense Probit regression for poverty (normally distributed error): • However: • This is just an inefficient way of estimating the OLS regression parameters. • You do not need a probit/logit when the continuous variable is observed. • You can still estimate poverty impacts: • And under weaker assumptions (e.g., normality of errors is not required)

48. 2.2: Poverty mapping Impute measure of welfare (e.g. comprehensive real consumption) from household survey into census, using estimated static model: Note: • Constrained to using x’s that are available in the census • Can’t have geographic fixed effects • Can’t allow for idiosyncratic local factors • Standard errors can allow for these sources of error

49. 2.3: Studying poverty dynamics using repeated cross-sectional data Decomposing changes in poverty Decomposition 1: Growth versus redistribution Growth component holds relative inequalities (Lorenz curve) constant; redistribution component holds mean constant Change in poverty between two dates = Change in poverty if distribution had not changed + Change in poverty if the mean had not changed + Interaction effects between growth and redistribution

50. Example for Brazil Poverty and inequality measures Very little change in poverty; rising inequality