Overview of Chapter IV: Statistical Tools and Estimation Methods for Poverty Measures

1. Overview of Chapter IV:Statistical Tools and Estimation Methods for Poverty Measures John Gibson Department of Economics University of Canterbury New Zealand

2. Overall Aim of the Chapter • Attempt to describe tools that are simple • Extensions of methods that many statistics offices may already use • Interaction between data and method • Highlight improvements in data collection that may assist the further development of some of the estimation methods described • Possible additions/deletions to the chapter and recommendations in yellow

3. Structure 4.0 Introduction 4.1 Cross-cutting issues 4.2 Types of surveys 4.3 Assessing individual welfare and poverty from household data 4.4 Poverty dynamics from longitudinal surveys

4. 4.0 Introduction • Justify priority given to quantitative, monetary indicators • Generalisable • Potentially consistent • Able to be predicted/simulated • Ease of budgeting interventions if poverty measured in a money metric • Note that poverty-focused surveys include both quantitative and qualitative non-monetary indicators • Desirability of link between case study/qualitative evidence and quantitative survey evidence • Box 1: Poverty and Water in PNG

5. 4.1 Cross-cutting issues Covers issues that a statistical agency may face that are somewhat independent of the particular type of household survey used • Why consumption expenditure is the preferred welfare indicator • Need for consistency of survey methods • Correction methods to restore consistency • Variance estimators for complex samples

6. 4.1.1 Reasons for favouring consumption as welfare indicator • Most popular • 52/88 countries in Ravallion (2001) • Could drop this, given Chapter 2? • Reasons why consumption expenditure is increasing used • CONCEPTUAL • Consumption is a better measure of both current and long-term welfare • PRACTICAL • It is more difficult for surveys to accurately measure income

7. Conceptual problems with current income as a welfare measure • Current income has larger transitory component than current consumption • Consumption is a function of permanent income rather than current income • Households save and dis-save and use informal support networks to smooth consumption over time • Less inequality in current consumption than in current income • Profile of income-poor is less likely to identify the characteristics of the long-term poor • U.S. income-poor have home ownership rate of 30% versus only 15% for consumption-poor (60% for all HH) • Food budget share for income poor is 24% versus 32% for the consumption poor (NB: 19% for all households)

8. Expect different trends in income-poverty and consumption-poverty • Income-poor dis-save to maintain their consumption • With fixed poverty line and economic growth, get a rising consumption to income ratio for the poor • U.S. consumption poverty rate fell 2.5% per year (1961-89), income poverty rate fell by only 1.1% per year

9. Practical problems with current income as a welfare measure • Requires longer reference period to capture seasonal incomes • Recall errors more likely • Seasonal variation in consumption less than in income • More diverse income sources than types of consumption • Income surveys need a wider range of questions • Splitting household and business expenses for informal sector • assets data to get income flows, especially for livestock • Income is more sensitive • Understated due to tax concerns and when some income is from illicit activities

10. 4.1.2 Consistency of survey methods and poverty comparisons • Highlight sensitivity of consumption and poverty estimates to changes in survey methods • Selected experimental results • Diary rather than recall raised reported food expenditure by 46% in Latvia • Detailed recall list (100 items) rather than same items in broader categories (n=24) raised reported consumption by 31% in El Salvador • Reported spending fell by 2.9% for each day added to the recall period in Ghana • Recall error levels off at 20% after two weeks

11. 4.1.2 Practical evidence on the effect of survey non-comparability • India’s NSS traditionally had 30-day recall for all items • Switched to • 7-day recall for food, • 30-day for fuel and rent etc, • 365 day recall for infrequent purchases • changes increase measured consumption of the poor • Less forgetting of food in 7-days than 30 days • Mean and variance of spending on infrequent items fell • Replaces zero monthly spending on infrequent items with low annual spending for the poor • Changes in survey method reduce measured poverty by 175 million!! • Scale attracted several experts who devised adjustment methods to restore comparability • But what about smaller, less significant countries…

12. Box 2: Incomparable Survey Designs and Poverty Monitoring in Cambodia • Non-comparable surveys in 1993 (detailed recall ≈ 450 items), 1997 (33 items) and 1999 (36 items) • 1993: very detailed survey to calculate CPI weights but CPI price surveys only ever collected in capital city • Poverty line too detailed (155 items) for subsequent surveys to re-price • Short-recall surveys affected by other topics included in the rotating modules • 1997: detailed health spending questions in social sector module gave higher expenditure than in the consumption module, consumption estimates were arbitrarily raised by up to 14% • Apparent fall in headcount from 39% to 36% reversed absent this • 1999: attempt to reconcile consumption at household level with detailed income module for a random half-sample • Headcount poverty rate fell from 64% round 1 to 36% in round 2 • No robust poverty trend for 1990s from these irreconcilable date

13. 4.1.3 Correction methods for restoring comparability to poverty estimates • Change in commodity detail (Lanjouw/Lanjouw) • Restrict food poverty line to items that are consistently measured in the two surveys • Estimate Engel curve to get non-food allowance in each survey • Normally only do it for baseline survey and inflate the non-food allowance • Potential contradiction between treatment in Ch. 3 and 4 • Poverty comparisions are restricted to the headcount index at the upper poverty line • Distinction between the food share for lower (‘austere’) and upper poverty line is not clearly set out in any of the draft chapters – talk generically of Engel methods

14. 4.1.3 Correction methods for restoring comparability to poverty estimates • Change in recall period (Deaton/Tarozzi) • From initial survey estimate: Pi = f(expenditure on items with unchanged recall period) • E.g. fuel and rent in India’s NSS • Use regression or non-parametric estimation • Assuming that this relationship holds, use distribution of expenditures on the items with unchanged recall period in the new survey to predict poverty

15. 4.1.4 Variance estimators for complex sample designs • Most household surveys have samples that are clustered, stratified and perhaps weighted • Standard software gives incorrect inferences from these samples • Standard error of headcount poverty rate in Ghana 45% higher once clustering and stratification taken account of, compared with wrongly assuming Simple Random Sampling • Variance Estimators • Taylor series linearization • Variance estimator of a linear approximation • Replication techniques • Repeated sub-samples from the data • Estimates computed from each and variance calculated from deviation of the replicate estimates from the whole sample estimate • List some software that has these estimators

16. 4.2 Types of Surveys • Discusses the types of surveys a statistical agency can use to measure and analyse poverty • Most surveys have multiple objectives and some design features that reflect other purposes may not be desirable for poverty measurement • Income and expenditure (or budget) surveys • Correcting overstated annual poverty from short-reference HIES/HBS • LSMS surveys • Core and module designs • DHS (and MICS)

17. 4.2.1 HIES and HBS • Primary objective is to provide expenditure weights for a CPI • Appropriate design for a CPI objective is different than for a poverty-focused survey • Include few other topics because of burden on respondents of recalling/reporting detailed consumption • Many do not collect the local prices needed for CBN food poverty line or spatial price index • Short reference periods may not measure long-run welfare • Even for consumption, which is unlikely to be fully smoothed

18. 4.2.1 Problems with HIES/HBS: lack of local prices • Urban prices often collected for a CPI inapplicable in rural areas • Gap between IFLS and BPS estimates of poverty rise in Indonesia • Food expenditures (E) and quantities (Q) often available from HIES or HBS so unit values (E/Q) used as ‘prices’ Problems • Reflect quality differences chosen by households • Reporting errors in E and/or Q • Only available for purchasing households • Deaton reports good performance of UVs in updating regional poverty lines in India but… • Capeau & Dercon (Ethiopia) and Gibson and Rozelle (PNG) find that UV’s overstate prices and cause rural poverty rates to be over-estimated by more than 20% • Recommend: more effort on collecting local prices

19. Aggregate food poverty rates from different food price data(PNG experiment – currently not in Ch. 4) Food poverty line calculated from:

20. Poverty Line Annual reference period Monthly reference period 0 z 4.2.1 Problems with HIES/HBS:short reference periods overstate annual poverty • Short reference periods because of difficulty of recalling or recording consumption • Includes many transitory shocks that are subsequently reversed • OK if just want mean budget shares or mean spending level • Causes higher poverty estimates if poverty line below the mode • Affects surveys that annualise from short reference periods and those that both collect and report on short periods • Weekly/monthly poverty rates less useful because dominated by transitory fluctuations

21. 4.2.1 Problems with HIES/HBS: example of overstated poverty when annualizing from short periods Overstatement when extrapolate from • Respondents in HIES in urban China keep expenditure diary for full 12 month period • Benchmark to compare with extrapolation from short reference periods • 1 month (x12 for each household) with sample spread evenly over the year • 2 months (so x6 for each household) collected six months apart • 6 months (collect every 2nd month of data on each household)

22. 4.2.2 Correcting overstated annual poverty from short-reference periods • True variance of households’ annual expenditures: • rt,t’ correlation between same households’ expenditures in t & t’ • σtstandard deviation across households in month t • If dispersion across households does not vary from month to month… • V(xm) is variance of monthly expenditures across all i households and t months in the year • r̅ is the average correlation between the same household’s expenditures in all pairs of months in the year • May get reliable estimate of r̅ without 12 months of data

23. 4.2.2 Correcting overstated annual poverty from short-reference periods • Annual expenditures extrapolated from household expenditures observed in one (staggered) month • Implicitly assumes r̅ = 1 (no instability in the monthly ranking of households)  overstates the variance, inequality and poverty • Instead, scale each household’s deviation from monthly average, (xit-x̅m) to annual value with factor based on empirical estimates of r̅ • E.g. if r̅ = 0.5 scaling factor on deviations from monthly average is 8.8 (=78), rather than 12 • Intuitively, many shocks causing (xit-x̅m) are subsequently reversed so have less impact with this method

24. 4.2.2 Correcting overstated poverty when annualizing from short periods: example Overstatement when extrapolate from • Correction method does good job of approximating the poverty estimates from 12 month diaries in HIES from urban China • Using just single revisit to estimate r̅ • Further economise by just revisiting sub-samples to get r̅ • Added 10% to cost of a cross-sectional survey in PNG

25. 4.2.3 LSMS Surveys • Full coverage in Grosh and Glewwe and Deaton and Grosh so only two aspects discussed • Bounded recall to prevent telescoping • Consistent with the literature but unaware of any evaluation • Only used in some LSMS • Annual recall of consumption, even for frequent purchases • Months purchased × times per month × usual purchase per time • If accurate overcomes problem of short reference periods exaggerating annual poverty • Limited evidence that estimates similar to previous month recall but both collected in same interview so not independent • More experiments needed on this • Box 3: modeling to help long-run poverty alleviation • Better examples available?

26. 4.2.4 Core-Module Surveys • Simple core survey fielded frequently and rotating modules tacked on • Potentially get the high frequency and large sample for monitoring and broad topic coverage for modelling • Consumption and poverty from core incompatiable with estimates from detailed module • SUSENAS core has mean-reverting error and no simple correction factor to give core-to-module consistency • Contents of rotating module can affect the core • Interviewers, respondents and analysts may try to reconcile or adjust core estimates based on what is reported in a detailed module • Lose core-to-core consistency

27. 4.2.5 DHS (and MICS) • Standardised questionnaires that aid cross-country and temporal comparisons • Available for almost all developing countries, often for two points in time • No income or consumption data • Information on dwelling facilities and asset ownership to form a “wealth index” that has been used for poverty and distributional analysis • Principal components or factor analysis used • Some evidence this index is a reasonable proxy for consumption • no evidence on validity of “poverty” estimates

28. 4.3 Assessing individual welfare and poverty from household data • how should adjustments be made for differences in household size and composition when inferring individual welfare and poverty status from household data? • are there reliable methods of observing whether some types of individuals within households, such as women or the elderly, are differentially poor?

29. 4.3.1 Equivalence scales • Convert households of different size and composition into number of equivalent adults • Ne = (A +φC )θφ≤ 1 θ≤ 1 • φis adult equivalence of a child • θis elasticity of cost with respect to HH scale • while φ=θ= 1 is most common choice in developing countries, many use different values (chap 2?) • Empirical data alone cannot identify φand θ • Same demand function can be derived from two (or more) cost functions that embody different scale economies and costs of children • Two common identifying assumptions used: • Engel: food share is a welfare measure across household types • Rothbarth: expenditure on adult goods is a valid welfare measure • Varyingφand θas sensitivity analysis may be best approach

30. 4.3.2 Rothbarth method • Valid method of estimating φ, the adult equivalence of a child • Cannot be used to estimate scale economies, θ • Depends on a set of goods that children do not consume • Children only exert income effects on these goods • Formal test for valid adult goods based on “outlay equivalent ratios” • Show effect of a demographic group on demand, from budget share equation • Also used in a method for detecting differential poverty within the household (4.3.6)

31. 4.3.2 Rothbarth method • Require outlay x1 to restore adult goods spending to former level • (x1-x0) is cost of the child and (x1-x0)/(x0/2) is the adult equivalence Spending on adult goods Reference household (2 adults) Larger household (2-adult, 1-child) x0 x1 Total expenditure

32. 4.3.3/4 Engel method not recommended • No theoretical justification for using food share to measure either cost of children or economies of scale • If parents perfectly compensated for cost of a child, family food share would still rise • Food is larger share of child’s consumption than parent’s • Rise in the food share indicates need for extra compensation under logic of Engel method  over-compensates • Larger household with same per capita expenditure as a smaller one • Economies of scale make larger household better off • Better off households have lower food shares according to Engel method • Per capita spending on food must fall (given constant PCX) • When poor people become better off, dollar value of spending on food is unlikely to fall, especially when under-nourished • Sensitive to variation in survey design that affect measured food shares (seems to give large scale economies with recall surveys)

33. 4.3.5 Adjusting poverty statistics if adult equivalents are units • Standard FGT formula uses N and Q • Total population and number of poor • Overstates monetary value of poverty gap if poverty defined in adult-equivalent terms • Use adult equivalent numbers rather than population • Adjustment formula from Milanovic

34. 4.3.6 Differential poverty within the household (intra-household allocation) • Describe Deaton’s method of detecting boy-girl bias • Is reduction in spending on adult goods larger when the child is a boy rather than a girl? • Generally hasn’t worked as expected • Finer disaggregation of adult goods when statistics agencies form consumption recall lists may help • Harder to study unequal allocations between adults • May reflect preferences, whereas children only had income effects • Emerging methods could be aided by surveys that use diaries for each adult and also record if purchases are for own consumption or consumption of others

35. 4.4 Poverty dynamics from longitudinal surveys • Increased emphasis • Very demanding surveys • Sampling frame of individuals or households rather than dwellings • Must be prepared to track split-offs and reformed households, plus movers • Methods of measuring chronic and transient poverty • Attrition bias in longitudinal survey data • Reliability ratio approach to measurement error in longitudinal survey data

36. Separating Poverty into Chronic and Transient Components • Motivation • Transient poverty reduces sharpness of poverty profiles • Transient share likely to vary over time and space so distorts comparisons of long-run poverty • Different policies needed • smoothing vs raising average consumption/income • Methods • Spells • Components • Don’t necessarily give same result

37. 4.4.1 Spells vs Components decomposition • Spells • HHs below poverty line each period • Remaining poor are transient • Simple cross-tabulation with two-wave panel • Weaknesses: • focuses attention on headcount • ‘sometimes poor’ too broad if many vs few survey waves • Components • chronic poor have mean welfare over time below the poverty line • Transient are residual component • “always poor” are subset of chronically poor • Numerical example to show the two approaches may give different shares of chronic/transient poverty

38. 4.4.2 Attrition bias in longitudinal survey data • Wide variation in attrition in LSMS longitudinal surveys (from 16-69% attrite) • Regression relationships seem unaffected • May be OK to just study stayers? • Less evidence on effect on poverty measurement • UK evidence suggests a bias • Example and value of tracking out-of-village movers in IFLS

39. 4.4.3 Measurement error in longitudinal survey data • Poverty dynamics overstated due to measurement error • Describe simple “reliability index” method for detecting measurement error • Some statistical agencies familiar with this for static variables, from test-retest or post-enumeration surveys • Correlation between two error-ridden reports on same variable can indicate data reliability, if measurement errors are uncorrelated • Tool does not work for dynamic variables because imperfect correlation expected because the variable ‘moves’ • Requires extending panels from typical two waves to at least three waves • Reliability index for longitudinal data could be more widely calculated to temper conclusions about poverty dynamics • Is this redundant, given more sophisticated correction method described in Ch. 6?

40. Example of imperfect reliability: RLMS urban household income • Measurement error attentuates correlation coefficients • in proportion to squared reliability index • 1-step correlation between expenditure in 1994 and 1996 is once-attentuated • 2-step correlation from product of correlations between 1994-1995 and 1995-1996 is twice attentuated • If expenditure generated from a first order-autoregressive model, should be the same whether going directly or via 1995 expenditure Y1994 r=0.42 Y1995 r=0.29 r=0.51 Y1996 2-step correlation: 0.42×0.51 = 0.22 1-step = 0.29 Reliability index=(0.22/0.29)=0.86  Standard deviation of observed household expenditure in RLMS has true component of 86% and error component of 14%

41. Conclusions • Yet to be done!

42. Omissions • How many food poverty line baskets? • Are regional taste and availability variations respected? • Do different baskets mean different living standards? • Ravallion/Lokshin (Russia) and Simler et al (Mozambique) use WARP to test and adjust • Whose diet sets the CBN food basket and what if final poverty rate differs from the starting group? • Pritchett et al. have an iterative procedure • Even if single basket, how many regions/sectors should the basket be priced in? • How to know if poverty line should vary by region, by sector, or both • Relationship between spatial price deflator and regional values of poverty line