Approaches to
modelling
poverty dynamics
Stephen P. Jenkins
(ISER, University of Essex)
2
What’s changed over the last decade
?
“… the latest fashion in poverty research, which
searches after duration and movement ... However
none of the recent work on the dynamics of poverty
gives cause to assume that the structures of poverty
uncovered here [by cross

sectional analysis] would be
any different to those found by dynamic analyses.”
(Mary Daly,
The Gender Division of Welfare. The
Impact of the British and German Welfare States
.
CUP, 2000)
•
Is this view sustainable any more?
3
What’s changed over the last decade
? (ii)
•
Policy giving more emphasis to dynamic perspectives
–
Spread from USA to Europe and elsewhere
–
E.g. UK:
“In the past, analysis … has focused on static, snapshot pictures of where people are at a
particular point in time. Snapshot data can lead people to focus on the symptoms of the
problem rather than addressing the underlying processes which lead people to have or be
denied opportunities. To understand why people’s life chances differ, it is important to
look for the events and experiences which create opportunity and those which create
barriers, and to use this as a focus for policy action.” (HM Treasury, 1999)
•
NB (UK) Income
mobility
mostly linked with
intergenerational movements (‘equality of
opportunity’), and
poverty dynamics
with short

run
movements
4
What’s changed over the last decade
? (iii)
•
Changes in nature and availability of panel data sets,
e.g. …
–
SOEP, BHPS: growing maturity (# waves)
–
SLID, HILDA, SoFIE: new panels
–
ECHP: 1994
–
2001 for EU12+
–
EU

SILC: 2004/5
–
(4

year rotating panel for EU25+4)
–
US PSID: since 1999, biannual with retrospective fill

in (& now less
used)
–
US SIPP: quarterly rotating panel to be replaced by DEWS in 2009
(annual data collection perhaps with admin record linkage)
–
Developing countries: increasing number of panels (see e.g.
JDS
2000)
–
Administrative record data (mainly Nordic countries)
–
UKHLS
5
What’s changed over the last decade
? (iv)
•
Supplementation of official statistics on poverty and
income distribution with information about dynamics
–
UK:
HBAI
includes Low Income Dynamics chapter based
on BHPS;
Opportunity for All
. (# times poor over 4

year
period, ignoring censoring; events and transitions)
–
EU: ECHP

based statistics
–
EU: Laeken indicators
•
Some use of ‘social exclusion’ indicators (in EU), but
continued focus on needs

adjusted HH
income
•
Substantial body of new academic research
–
See later
•
6
Main substantive lessons learnt?
•
Movement out of low income population: turnover
•
Importance of spell repetition
–
Falling (back) into poverty, not only climbing out, and
thence …
–
Persistence: total time spent poor over a period
•
Differential vulnerability of particular groups to
persistent poverty
–
E.g. GB: “Single female pensioners, lone

parent families,
workless households, and people in the social rented sector,
were more likely to experience persistent low income …
than other groups”
(LID 1991
–
2004, Table 8.1)
•
? Past poverty may directly effect Pr(poor),
cet. par.
?
–
Results about duration dependence and state dependence
•
Policy has been most influenced by simpler analyses?
7
The main research questions
These have been, and continue to be, …
•
What are the poverty experiences?
–
Length of poverty spells; spell repetition; time poor over a
period, and …
–
How these differ for different groups
•
What are the determinants of observed outcomes, and
the roles of:
–
Observed characteristics (may be time

varying, and/or
environmental)
–
Unobserved characteristics
–
Duration dependence and state dependence
Multivariate regression models useful for addressing both
8
Multivariate modelling approaches
0.
[Bane

Ellwood trigger event
–
transition cross

tabs]
1.
chronic poverty (averaged income) models
2.
hazard regression models
3.
binary dependent variable dynamic random effects
panel models
4.
Markovian transition models
5.
covariance structure models of
income
6.
dynamic microsimulation models of
component
processes
•
All 6 developed in other contexts, and now applied to
income/poverty
–
appropriate?
•
Income: multiple income sources; multiple people
–
Dynamics: changes in income sources; changing household composition
9
Bane

Ellwood trigger event
–
transition cross

tabs
•
Not multivariate, but arguably informative about the
proximate drivers of transitions
•
B

E (1986), Jenkins (2000), Jenkins & Rigg (2001):
mutually

exclusive hierarchical classification of
demographic and income source events
•
Jenkins & Rigg (2001), Jenkins & Schluter (2003),
Valletta (2006), DWP (annual): non

mutually

exclusive classifications
•
Key results (US, UK, Canada, Germany)
–
Demographic events more relevant to entries than exits
–
Labour market events very important, but (a) not just HH
head’s, and (b) mixture of changes in employment and
earnings
10
Chronic poverty (averaged income) models
•
Chronic poverty: longitudinally

averaged income
below the poverty line
(Rodgers & Rodgers, 1993)
–
Transitory variations and measurement errors smoothed
out, so get a view of ‘permanent’ income level
–
Can people smooth in practice? Differences in borrowing
capacities by income?
–
Over what period to average? (And balanced panel issues?)
•
Examples:
–
Jalan & Ravallion (1997); Hill & Jenkins (2001)
–
Cross

national differences in prevalence and in correlates
(HH characteristics, events): Kuchler & Goebel (2003);
Valletta (2006)
11
(Discrete time) Hazard regression models
•
Most commonly

used approach
•
Single spell models of exit and of re

entry
–
e.g. Oxley et al. (2000), Finnie & Sweetman (2003), Fouarge
& Layte (2005), Jenkins & Rigg (2001), … and others
•
Multi

state multiple

transition models with unobserved
heterogeneity (mixture hazard models)
–
e.g. Stevens (1999), Devicienti (2001), Jenkins & Rigg
(2001), Hansen & Wahlberg (2005), Biewen (2006), Fertig &
Tamm (2007)
f
(
e
id
) =
g
(
d
) +
X
id
+
i
f
(
r
id
) =
g
(
d
) +
X
id
+
i
Exit hazard:
Re

entry hazard:
Bivariate distribution of unobserved effects
i
,
i
,
approximated
by finite number of mass points & associated probabilities
f
(.): logit, probit
or cloglog link
d
: elapsed duration
12
Hazard regression models (2)
•
Mixture models non

trivial to estimate and derive
predictions from (but some ‘technology diffusion’)
•
Hard to find more than small number of mass points
•
Initial conditions issue also arises, but no example yet
where able to fit model satisfactorily with it
•
Identification issues generally with relatively short
panels e.g. duration dependence versus frailty
(J & R
2001)
•
Provides estimates of covariate effects, duration
dependence (
state dependence), and can derive
predicted/simulated time in poverty over a period
given entry
13
Binary dependent variable dynamic random
effects (DRE) panel models
Developed esp. in unemployment dynamics literature:
inter alia
Heckman (1981), Arulampalam et al.
(2001), Stewart (2007)
Poverty applications include: Biewen (2004), Hansen et
al. (2006), Poggi (2007)
Pr(
y
it
= 1
y
i,t
–
1
, … ,
z
i
,
c
i
) =
(
z
it
+
y
i,t
–
1
+
c
i
)
•
y
it
= 1 if
i
is poor at
t
, 0 otherwise (
y
i
0
: initial value)
•
z
i
: vector of exogenous variables
•
c
i
: unobserved individual effect
•
State dependence summarized by
14
DRE models (2)
•
‘Initial conditions’ is main statistical issue addressed
to date: correlation between
y
it
–
1
and
c
i
–
Heckman (1981): approximate the distribution of initial
value conditional on
z
, c
; integrate out jointly with other
periods (non

trivial, but see Stewart 2006)
–
Wooldridge (2005):
model the distribution of the
unobserved effect
c
conditional on the initial value
y
i
0
and
exogenous variables
z
(can use standard software)
•
Reduce potential correlations between unobservable
individual effects and error using time

averaged
z
as
well
(Chamberlain

Mundlak idea)
•
Emphasis on estimates of APEs (via
) and
•
No predictions of poverty experience (but one could)
•
Attrition not usually addressed
15
Markovian transition models
•
Model entry and exit probabilities using endogenous
switching model (e.g. Cappellari & Jenkins, 2004)
y*
it
= [(
y
it
–
1
)
1
+ (1
–
y
it
–
1
)
2
]
z
it
–
1
+ (
i
+
it
)
plus equations for endogenous selections estimated
jointly
•
Simplified dynamics (relative to hazard models),
but
•
Can account for multiple ‘endogenous selection’
effects (e.g. panel attrition, non

response, initial
conditions) by modelling jointly with main process
•
Covariate effects vary with last year’s poverty status
(no state dependence if
1
2
; cf.
0
)
•
Can derive spell duration predictions easily
16
Markovian transition models (2)
•
Maximum Simulated Likelihood estimation rather
than integrating out as in DRE (but ‘technology
diffusion’)
•
Transition parameters identified by changes between
one wave and the next (as for DRE models), but
variance of random effect in the main transition
equation not identified (cf. DRE). Do we need it?
•
(C & J 2004) Endogenous selections non

ignorable
but ‘neglecting to control for endogeneity of initial
poverty status is more problematic than neglecting to
control for endogeneity of retention’
17
Covariance structure models of income
•
Models of the longitudinal covariance structure of
income
, from which results about poverty dynamics
are derived
•
Men’s earnings: Lillard and Willis (1978), …, Meghir
& Pistaferri (2004) [references to ‘poverty’!]
•
Household income and poverty dynamics: Duncan
(1983), Duncan and Rodgers (1991), Stevens (1995),
Devicienti (2001), Biewen (2005)
log(
I
it
) =
Z
i
+
X
it
+
u
it
u
it
=
t
i
+
t
it
it
=
it
–
1
+
it
+
i
t
–
1
cov(
u
it
,
u
js
) = …
Permanent + Transitory
ARMA(1,1)
Example
18
Covariance structure models (2)
•
Estimates provide information about the roles of
permanent and transitory shocks to income (but
simple interpretation complicated when year

specific
weights used)
•
Many labour market and demographic events not well
characterised by model’s characterisation of income
shocks?
•
Same process applies to rich and poor alike (cf.
previous models)
•
Attrition and other endogeneous selections usually
ignored
19
Covariance structure models (3)
•
With (log)normality, the model can be used to predict
poverty transition probabilities, and thence poverty
sequences over a period, but simulations relatively
difficult (some ‘technology diffusion’)
•
‘Beauty contest’: covariance structure versus mixture
hazard models: Stevens (1999); Devicienti (2001):
both models produce fairly similar predictions, but
“for the population as a whole the variance

components models seemed to perform worse in
terms of its ability to replicate the poverty patterns
emerging from the data”
20
Dynamic microsimulation models
•
Aim
at
‘structural’
model
of
underlying
dynamic
processes
which
determine
earnings,
and
the
earnings
associated
with
their
process
outcomes
.
From
these,
income
and
poverty
status
are
derived
•
Aassve,
Burgess,
Dickson
&
Propper
(
2005
)
re
GB
–
5 simultaneous hazards estimated jointly:
birth, union
formation, union dissolution, employment and non

employment
–
Poverty status assigned stochastically depending on mean
Pr(poor) in each 5

outcome combination of states
•
Burgess
and
Propper
(CEPR,
1998
)
model
poverty
dynamics
amongst
a
sample
of
American
women
aged
20

35
years
from
the
National
Longitudinal
Survey
of
Youth
(NLSY)
:
…
21
Dynamic microsimulation models (ii)
•
3 life

course dimensions considered: marriage, fertility,
work.
–
State in each year summarised by an {
m
,
k
,
l
}
combination.
m
: married or not;
k
: has kids or not;
l
:
working or not. Each state has an associated distribution
of earnings
a)
hazard
model
of
Pr(marital
partnership
formation)
b)
hazard model of Pr(marital partnership dissolution)
c)
bivariate probit of probability of having a child and probability of
working
d)
earnings functions per state (conditional on selection into state)
e)
earnings function for a spouse
f)
Income = mixture model (sum of probabilities of being in a state
earnings associated with state), and hence
g)
poverty status
22
Dynamic microsimulation models (iii)
•
All dynamics arise via the dynamics of the
component processes
–
E.g. no state dependence of poverty per se
•
Derive predictions for poverty by simulation of the
underlying processes (not of income per se)
•
“We argue that this indirect approach to modelling
poverty is the right way to bring economic tools to
bear on the issue” (Aassve et al. 2005)
•
Endogeneous selections; identification; robustness
generally; ?
•
Very complicated and time

consuming. Is the pay

off
from this more ‘structural’ approach worthwhile?
23
Evaluating (empirical) modelling approaches
Trade

offs between 3 general criteria (Jenkins 2000)
1.
Fit the past and provide predictions /simulations
–
‘Goodness of fit’ and other specification issues
–
Appropriate focus: estimating parameters versus drawing
out relevant implications of estimates
2.
Be ‘structural’
–
Descriptive associations versus connections with
underlying dynamic processes in labour and other
markets, household formation and dissolution, etc.
3.
Be practical
–
Useful results in reasonable time (‘DWP versus RAE’)
–
‘technology diffusion’ helps
•
More specific issues
–
an assortment discussed now
24
1(a) ‘Discretisation’ on LHS
•
Is ‘poverty’ really a distinct discrete state?
–
So, use models with income as the depvar? But …
•
Poverty line an arbitrary cut

off?
–
Sensitivity analysis using different low income cut

offs
doesn’t quite address the point
•
A way of introducing non

linearities?
–
Stevens (1999): reference to non

linearities (rich versus
poor) in context of hazard models of poverty
–
Stewart & Swaffield (1999) characterise low pay probit in
terms of a general linear model of earnings
•
‘Fuzzy poverty’ approaches have not proved hugely
fruitful IMHO, especially when for dynamics
25
1(b) ‘Discretisation’ on RHS
•
State dependence: is it plausible that past
poverty
(0/1
variable) has a distinct causal effect?
–
Stories explaining SD in incomes mostly refer to labour
market SD e.g. in unemployment
–
More plausible that any effects of past income might be
more graduated?
–
Cf. Cappellari & Jenkins (2004) variation on Markovian
model with multiple categories on RHS (poor; 4 non

poor
categories)
–
C & J finding: “results about the importance of GSD were
not driven by neglect of heterogeneity among the non

poor”
26
2. Measurement error & misclassification
•
Long

standing view that income data are error

ridden
& perhaps more at bottom than at top
–
Move £0.50 above line treated the same as £50 move above
–
Ad hoc adjustments e.g. require a transition to require
>10% change above/below line
–
Chronic poverty approach smoothes out transitory error
–
Covariate structure approach puts measurement error into
transitory component
–
Are measurement errors ‘classical’? Most unlikely!
•
systematically associated with other factors, asymmetrically
distributed, correlated over time?
•
PSID validation study data: errors negatively correlated with true
level of earnings
27
2. Measurement error & misclassification (ii)
•
Glaring gap in knowledge about measurement error
properties of HH income (and lack of suitable
validation sources?)
•
Few clear cut theoretical results about impacts of
measurement error (classical or not) in non

linear
models
–
Several articles explore error

ridden continuous RHS vble
–
Hausman et al. (1998): misclassification in LHS vble leads
to error in logit/probit (cf. ‘errors in eqn’ case)
–
Gustafson and Le (2002
): dichotomisation of cts RHS vble
can sometimes
reduce errors

in

variables bias
28
2. Measurement error & misclassification (iii)
•
Latent class models as a means to correct for
measurement error in poverty dynamics?
•
Breen & Moisio (JEI 2004): latent mover

stayer
Markov model of transition table
–
“because the state of poverty is poorly measured, much of
what appears to be change is, in fact, error in classifying
respondents” … “mobility in poverty transition tables is
over

estimated by between 25 and 50 percent if
measurement error is ignored”
•
Identification assumptions (see their article)
•
Is poverty status really a latent class?
–
More fruitful to look at income and error process and relate
to actual income poverty line?
29
3. Explanatory variable specification
•
RHS vbles in most multivariate regressions models
are expressed in levels (e.g. # workers, household
size) not as events (cf. B

E approach)
–
why not?
–
Might improve Fit? And make more ‘structural’?
–
Leads to problems of simultaneity and endogeneity (see
below)?
–
NB Stevens (1999) reported insignificant event effects if
levels also included (but issue of empty cells?)
–
If events relevant, what dating is appropriate: simultaneous,
one year lag, two year lag, or all of above …?
30
3. Explanatory variable specification (ii)
•
Time

varying RHS variables raise problems for
simulations of poverty spells (need to specify time
paths of these … unless endogenised)
•
NB implausible to fix many levels variables too when
doing simulations
•
Should any individual

level covariates be used as
RHS variables when modelling poverty?
–
Cf. age of HH head versus age of person
–
Poverty is defined in terms of HH income
31
3. Explanatory variable specification (iii)
•
The strict exogeneity assumption in DRE models:
•
‘Feedback effects’: If
y
t
–
1
affects
z
,
then, in the
equation for
y
t
, a correlation is induced between
z
and
error term, and hence bias in parameter estimates
•
Similar problem arises in Markov and hazard models
•
Biewen (2004): extensive discussion, and estimation
of a DRE model with feedback on employment status,
whether lives alone (and comparison with pooled
panel probit model etc.). Stat. sig. effects found
•
General problem? Are feedback effects plausible?
Pr(
y
it
= 1
y
i,t
–
1
, … ,
z
i
,
c
i
) =
(
z
it
+
y
i,t
–
1
+
c
i
)
32
4(a) Unit of analysis issues
•
What units should be used as the obs in the
regressions?
–
All individuals (adults & kids)? as in descriptive statistics
–
Adults only? As only they generate the income
–
Children only (if studying child poverty)?
•
Fertig and Tamm (2007)
•
Problem of defining/modelling a poverty spell: consider a child
born into a HH where the adults have been poor already for 2 years.
What is the elapsed poverty duration that is relevant to the
modelling?
33
4(b) Unit of analysis issues
•
Breakdown of the i.i.d. assumption in e.g. hazard
model context (but also applies in other approaches):
–
Mixture models for control for correlations between spells
for the same individual (individual random effect)
•
Or should it really be interpreted as a household effect given
definition of poverty?
–
But often there are repeated observations from the same
household at a point in time (since poverty defined in terms
of the income of the HH to which someone belongs)
–
? Generalize mixture model to incorporate a household

specific random effect in addition to individual one (as with
firm and worker individual effects)?
•
But how to do this consistently, given that households split/fuse?
–
? Treat each set of individuals who ever lived together during
panel as a ‘cluster’ and use sandwich estimator of SEs
•
Cappellari & Jenkins (2004), Biewen (2005)
34
4(c) Unit of analysis issues
•
Potential mismatch between timing of incomes
received and household composition
–
the importance
of the income reference period definition:
–
At year
t
interview, usually ask about the incomes over past
year of those people present in the HH at date of interview
–
If people have left the household between
t
–
1 and
t,
then
the year
t
interview does not pick up the incomes of the
leavers
–
A ‘current’ income definition reduces mismatch
–
Mismatch complications also exemplified by ECHP:
collected data at
t
about incomes over calendar year prior to
interview: income reference period overlaps with year
t
–
1
interview
35
5(a). Discrete panel issues
Discrete panel observations but underlying poverty
spells in continuous time
•
? Over

estimation of state dependence if poverty in
consecutive waves represents continuation of the
same poverty spell?
–
See discussion in DRE models of unemployment by
Arulapalam et al. (2000), Stewart (2007)
36
5(b). Discrete panel issues
Discrete panel observations (grouped duration data) but
underlying poverty spells in continuous time
•
Single spell model of poverty spell length; sequence
OPPPOOP over 7 year panel
–
# years at risk of exit for poverty spell #1 = 3 or 4? [Most
analysts use 4] Issue: when does censoring occur?
•
Multi

state multi

transition models: sequence OPPPOOP
over 7 year panel
–
Poverty spell 1’s length = 3, followed by 2 year’s non

poverty
… only logically consistent definition (as for discrete model)
•
But no natural ‘zero’ date of entry (assumed that
beginning of interval coincides with beginning of spell)
•
Longer ref income period
more likely miss short spells
37
6. Endogenous selections
•
Initial conditions, panel attrition, employment, item
non

response
•
Only the first of these given much explicit attention in
most applications to date
–
By contrast most studies of attrition regarding outcome in
levels not transitions (
JHR
special issue 1998)
•
Absorbing versus non

absorbing attrition
•
Problems of finding plausible instruments
•
Biewen (2005): uses inverse probability weights (for
initial selection and retention)
–
What is population represented when pool spells?
–
Assumes ignorability of attrition
38
7. Short panels …
•
… are here to stay, and so need methods appropriate
for them
–
rotating panels such as SIPP / DEWS, EU

SILC
–
young panels such as HILDA, SoFIE, UKHLS
–
ECHP (especially given way income defined)
•
Raise issues about extent to which one can identify
aspects of dynamics reliably
–
covariance structures; random effects variance; duration
dependence separately, etc.
•
Greater role for DRE and Markovian models?
•
Greater role for administrative panels? (Unlikely for
HH income, at least in UK?)
39
Envoi: which model?
•
Tensions between the goals of
–
Fitting and predicting
–
Structural versus descriptive
–
Practicality
in development and application of models
•
Plus a range of other issues, as mentioned
•
No obvious winner
•
Role of economic theory for empirical modelling of
poverty?
•
Income versus expenditure versus multiple
indicators?
•
Frequency of measurement (annual vs. more often)
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