Approaches to modelling poverty dynamics

Stephen P. Jenkins

(ISER, University of Essex)

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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?

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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

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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

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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

•

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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?

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The main research questionsThese 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

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Multivariate modelling approaches0. [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

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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

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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)

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(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(eid) = g(d) + Xid + i

f(rid) = g(d) + Xid + 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 linkd: elapsed duration

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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

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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(yit= 1| yi,t–1, … , zi, ci) = (zit + yi,t–1 + ci)

• yit = 1 if i is poor at t, 0 otherwise (yi0: initial value)

• zi: vector of exogenous variables

• ci: unobserved individual effect

• State dependence summarized by

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DRE models (2)• ‘Initial conditions’ is main statistical issue addressed to

date: correlation between yit–1 and ci

– 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 yi0 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

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Markovian transition models• Model entry and exit probabilities using endogenous

switching model (e.g. Cappellari & Jenkins, 2004)

y*it = [(yit–1)1 + (1–yit–1)2]zit–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

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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’

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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(Iit) = Zi + Xit + uit

uit = ti + tit

it = it–1 + it + it–1

cov(uit, ujs) = …

Permanent + Transitory

ARMA(1,1)

Example

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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

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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”

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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) : …

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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

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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?

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Evaluating (empirical) modelling approachesTrade-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

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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

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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”

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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

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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

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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?

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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 …?

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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

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3. Explanatory variable specification (iii)• The strict exogeneity assumption in DRE models:

• ‘Feedback effects’: If yt–1 affects z, then, in the equation for yt, 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(yit= 1| yi,t–1, … , zi, ci) = (zit + yi,t–1 + ci)

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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?

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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)

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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

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5(a). Discrete panel issuesDiscrete 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)

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5(b). Discrete panel issuesDiscrete 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

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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

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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?)

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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)