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Nov 16, 2013 (3 years and 10 months ago)

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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)