Overview of Chapter IV:

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Nov 16, 2013 (3 years and 8 months ago)

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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


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

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

4.0

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.
Why consumption expenditure is the
preferred welfare indicator

2.
Need for consistency of survey methods

3.
Correction methods to restore consistency

4.
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
5
Income Quintile
Consumption
to income
ratio in a
cross-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:

P
i

= 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 surveys

4.
Core and module designs

5.
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
5.9
8.9
6.8
2.4
3.8
2.8
0
5
10
15
20
25
30
Headcount
Poverty gap
Poverty severity
Market prices
Unit values
Price 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
2
nd

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:





r
t,t’


correlation between same households’ expenditures in
t

&
t’



σ
t

standard deviation across households in month
t


If dispersion across households does not vary from month to
month…




V
(
x
m
) 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
r
̅
without
12
months of data



)
(
132
12
)
(
x
V
r
x
V
m
a



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, (
x
it
-
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 (
x
it
-
x
̅
m
) are subsequently
reversed so have less impact with this method

m
a
m
a
V
V
x
x




144
12


x
x
x
m
m
it
A
i
r
x






12
132
12
,
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

Correct
ed

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


N
e

= (
A

+
φ
C
)
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 x
1
to restore adult goods spending to former level


(x
1
-
x
0
) is cost of the child and (x
1
-
x
0
)/(x
0
/
2
) is the adult equivalence

x
A
0
x
0

x
1

Total expenditure

Reference household

(2 adults)

Larger household

(
2
-
adult,
1
-
child)

Spending on

adult 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 data

3.
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 i
C 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

Y
1994

Y
1995

Y
1996

r=
0.42

r=0.51

r=
0.29

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?


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