Overview of Chapter IV:
Statistical Tools and Estimation
Methods for Poverty Measures
John Gibson
Department of Economics
University of Canterbury
New Zealand
Overall Aim of the Chapter

Attempt to describe tools that are simple


Interaction between data and method


Extensions of methods that many statistics offices
may already use
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
Structure
4.0
4.1
4.2
4.3
Introduction
Cross-cutting issues
Types of surveys
Assessing individual welfare and
poverty from household data
4.4 Poverty dynamics from longitudinal
surveys
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
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
1.
2.
3.
4.
Why consumption expenditure is the
preferred welfare indicator
Need for consistency of survey methods
Correction methods to restore consistency
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 incomepoverty 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
2
Consumption
to income
ratio in a
cross-section
1.5
1
0.5
1
2
3
4
Income Quintile
5
Practical problems with current
income as a welfare measure

Requires longer reference period to capture seasonal
incomes

Recall errors more likely


More diverse income sources than types of
consumption

Income surveys need a wider range of questions



Seasonal variation in consumption less than in income
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


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


Poverty line too detailed (155 items) for subsequent surveys to re-price
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



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


(Lanjouw/Lanjouw)
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


From initial survey estimate:
Pi = f(expenditure on items with unchanged recall period)



(Deaton/Tarozzi)
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


Replication techniques



Variance estimator of a linear approximation
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


1.
2.
3.
4.
5.
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)
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





Deaton reports good performance of UVs in updating regional
poverty lines in India but…


Reflect quality differences chosen by households
Reporting errors in E and/or Q
Only available for purchasing households
Capeau & Dercon (Ethiopia) and Gibson and Rozelle (PNG) find that
UV’s overstate prices and cause rural poverty rates to be overestimated 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)
30
30
25
22
Food poverty line
calculated from:
23.8
Market prices
Unit values
Price opinions
20
15
8.9
10
5.9
6.8
5
0
2.4
Headcount
Poverty gap
3.8
2.8
Poverty severity
4.2.1 Problems with HIES/HBS:
short reference periods overstate annual
poverty

Short reference periods because
of difficulty of recalling or
recording consumption




Density
Poverty
Line
Includes many transitory shocks
that are subsequently reversed
OK if just want mean budget
shares or mean spending level
Annual
reference
period
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

Monthly
reference
period
Weekly/monthly poverty rates
less useful because dominated
by transitory fluctuations
0
z
Welfare indicator
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)
Overstatement when extrapolate from
1
2
month mths
Mean
0.1%
annual
expenditure
Annual
headcount
poverty
Annual
poverty
gap index
0.1%
6
mths
0.1%
53.1% 32.2% 15.0%
150%
77.8% 19.4%
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 ( xa )  12  132  r  V ( xm)


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
4.2.2 Correcting overstated annual
poverty from short-reference periods

Annual expenditures extrapolated from household
expenditures observed in one (staggered) month
xa  12  xm


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
xi , A  xit  x m 12  132  r  12  x m



Va  144 Vm

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
4.2.2 Correcting overstated poverty when
annualizing from short periods: example

Correction method
Overstatement when extrapolate from
does good job of
Correct
1
2
approximating the
ed
month mths
poverty estimates from
Mean
12 month diaries in
0.1% 0.1% 0.1%
annual
HIES from urban China


Using just single revisit
to estimate r̅
Further economise by
just revisiting subsamples to get r̅

Added 10% to cost of
a cross-sectional
survey in PNG
expenditure
Annual
headcount
poverty
Annual
poverty
gap index
53.1% 32.2% 0.1%
150%
77.8% 5.0%
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


Consumption and poverty from core incompatiable
with estimates from detailed module


Potentially get the high frequency and large sample for
monitoring and broad topic coverage for modelling
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 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:



φ≤1 θ≤1
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
Spending on
adult goods
Reference household
(2 adults)
Larger household
(2-adult, 1-child)
x
0
A
x0
x1
Total expenditure
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 adultequivalent 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 boygirl 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

1.
2.
3.
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
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


Weaknesses:



focuses attention on headcount
‘sometimes poor’ too broad if many vs few survey waves
Components




Simple cross-tabulation with two-wave panel
chronic poor have mean welfare over time below the poverty
line
Ci  P( yi , yi , , yi )
Transient are residual component T  P  C
“always poor” are subset of chronically poor
Numerical example to show the two approaches may
give different shares of chronic/transient poverty
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


Less evidence on effect on poverty
measurement


May be OK to just study stayers?
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 19941995 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%
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?


Whose diet sets the CBN food basket and what if final
poverty rate differs from the starting group?


Ravallion/Lokshin (Russia) and Simler et al (Mozambique) use WARP
to test and adjust
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