Approaches to modelling poverty dynamics

1
Approaches to modelling poverty dynamics

• Stephen P. Jenkins
• (ISER, University of Essex)

2
Whats 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
Whats 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 peoples 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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Whats 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 19942001 for EU12
• EU-SILC 2004/5 (4-year rotating panel for
  EU254)
• 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
Whats 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 19912004, 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 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

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Multivariate modelling approaches

• 0. Bane-Ellwood trigger event transition
  cross-tabs
• chronic poverty (averaged income) models
• hazard regression models
• binary dependent variable dynamic random effects
  panel models
• Markovian transition models
• covariance structure models of income
• 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-exclus
  ive 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 heads, 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(.) logit, probit or cloglog link d
elapsed duration
Exit hazard Re-entry hazard
f(rid) g(d) ??Xid ?i
Bivariate distribution of unobserved effects ?i,
?i , approximated by finite number of mass points
associated probabilities
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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,t1, , zi, ci) ??(zit? ?
  yi,t1 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 yit1 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)
• yit (yit1)?1? (1yit1)?2?zit1 (?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 years 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
• Mens 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 ??t?i ?t?it
• ?it ??it1 ??it ???it1
• ? cov(uit, ujs)

Example
Permanent Transitory
ARMA(1,1)
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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 models 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
• hazard model of Pr(marital partnership formation)
• hazard model of Pr(marital partnership
  dissolution)
• bivariate probit of probability of having a child
  and probability of working
• earnings functions per state (conditional on
  selection into state)
• earnings function for a spouse
• Income mixture model (sum of probabilities of
  being in a state ? earnings associated with
  state), and hence
• 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 approaches

• Trade-offs between 3 general criteria (Jenkins
  2000)
• 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
• Be structural
• Descriptive associations versus connections with
  underlying dynamic processes in labour and other
  markets, household formation and dissolution,
  etc.
• 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 doesnt 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 gt10 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 yt1 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,t1, , zi, ci) ??(zit? ?
yi,t1 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 t1 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 t1 interview

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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)

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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 1s length 3, followed by 2
  years 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)