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

John GibsonDepartment of EconomicsUniversity of Canterbury

New Zealand

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

Structure4.0 Introduction4.1 Cross-cutting issues4.2 Types of surveys4.3 Assessing individual welfare

and poverty from household data4.4 Poverty dynamics from

longitudinal surveys

4.0Introduction 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

4.1Cross-cutting issuesCovers issues that a statistical agency may face

that are somewhat independent of the particular type of household survey used

1. Why consumption expenditure is the preferred welfare indicator

2. Need for consistency of survey methods3. Correction methods to restore consistency4. Variance estimators for complex samples

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

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)

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

0.5

1

1.5

2

1 2 3 4 5Income Quintile

Consumptionto incomeratio in across-section

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

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

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…

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

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

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

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

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

1. Income and expenditure (or budget) surveys

2. Correcting overstated annual poverty from short-reference HIES/HBS

3. LSMS surveys4. Core and module designs5. DHS (and MICS)

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

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

Aggregate food poverty rates from different food price data(PNG experiment – currently not in Ch. 4)

22

30

23.8

5.98.9

6.8

2.4 3.8 2.8

0

5

10

15

20

25

30

Headcount Poverty gap Poverty severity

Market pricesUnit valuesPrice opinions

Food poverty line calculated from:

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

Welfare indicator

Density Poverty Line

Annual reference period

Monthly reference period

0 z

4.2.1 Problems with HIES/HBS: example of overstated poverty when annualizing from short periods

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)

1 month

2 mths

6 mths

Mean annual expenditure

0.1% 0.1% 0.1%

Annual headcount poverty

53.1

%

32.2

%

15.0

%Annual poverty gap index

150% 77.8

%

19.4

%

Overstatement when extrapolate from

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’

σt standard 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

r ̅ 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

)(13212)( xVrxV ma

4.2.2 Correcting overstated annual poverty from short-reference periods Annual expenditures extrapolated from household

expenditures observed in one (staggered) month

Implicitly assumes r ̅= 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-x ̅m) to annual value with factor based on empirical estimates of r ̅

E.g. if r ̅ = 0.5 scaling factor on deviations from monthly average is 8.8 (=78), rather than 12

Intuitively, many shocks causing (xit-x ̅m) are subsequently reversed so have less impact with this method

mama VVxx 14412

xxx mmitAi rx 1213212,

4.2.2 Correcting overstated poverty when annualizing from short periods: example

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 r ̅

Further economise by just revisiting sub-samples to get r ̅

Added 10% to cost of a cross-sectional survey in PNG

1 month

2 mths

Corrected

Mean annual expenditure

0.1% 0.1% 0.1%

Annual headcount poverty

53.1

%

32.2

%

0.1%

Annual poverty gap index

150% 77.8

%

5.0%

Overstatement when extrapolate from

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?

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

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

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?

4.3.1 Equivalence scales Convert households of different size and composition

into number of equivalent adults Ne = (A +φC )θ φ ≤ 1 θ ≤ 1

φ is adult equivalence of a child θ is 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 φ and 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

Varying φ and θ as sensitivity analysis may be best approach

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)

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

xA0

x0 x1 Total expenditure

Reference household (2 adults)

Larger household (2-adult, 1-child)

Spending onadult goods

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)

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

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

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

1. Methods of measuring chronic and transient poverty

2. Attrition bias in longitudinal survey data3. Reliability ratio approach to measurement

error in longitudinal survey data

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

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

T P C ( , , , )i i i iC P y y y

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

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?

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

Y1995

Y1996

r=0.42

r=0.51

r=0.29

2-step correlation: 0.42×0.51 = 0.221-step = 0.29Reliability 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%

Conclusions Yet to be done!

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