Parallel Session IARIW 2014

1. IARIW2014 Conference, session 4B‘Poverty Measurement and the Durations of Poverty Spells’Comments on: (1) ‘Chronic and transient poverty in rural Ethiopia: a new decomposition’, byNatalie Quinn(2) ‘How and why the distribution of poverty durations haschanged in the United States since the mid-1980s’ byIrynaKyzyma
Stephen P. Jenkins (LSE)
Email: s.jenkins@lse.ac.uk
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2. Overview
•Two interesting and stimulating papers, each summarising poverty from a longitudinal perspective
•But each takes a totally different approachto the longitudinal features of the data, reflecting different literature streams
Outline
1.General contextual remarks
2.Quinn paper: exegesis and commentary
3.Kyzymapaper: exegesis and commentary
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3. Summarising poverty given a sample of persons over an observation window
Calendar time (windowT = 7 months)
Person
March
April
May
June
July
August
September
A.
B.
C.
D.
E.
F.
G.
H.
I.
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Completed but left censored
Completed (no censoring)
Right censored only
Left and right censored (never poor)
Left and right censored (always poor)
Singlepoverty spell: A, C, E, I
Multiplepoverty spells: B, G, H
Coloured cells: months poor
White cells: months non-poor
Lots of aspects to summarise:
total months, length first spell,
number of spells, etc. etc.
Also: depth of poverty if poor
Types of spell

4. Two non-overlapping literatures
1.Measures of ‘longitudinal’ (intertemporal) poverty
Indices aggregating poverty experience over individuals and over subperiods…
… using a period (window) of fixed and commonlength
(differences across individuals via subgroup decompositions?)
Ignores left-and right-censoring
2.Description of poverty spell length distributions
Individuals’ poverty spell length distributions, accounting for right-censoring, …
… over windows that are not fixed nor common (spells)
(differences across individuals via regression methods)
Ignores aggregation issues: across subperiods(single spell focus is typical); across people (mean or median spell length summaries)
•“This literature [1] works with a time horizon of fixed length and summarizes individuals’ experiences within that window, ignoring whether poverty spells were already in progress at the beginning of the window, or remained in progress at the end of the window. If one wants to derive the shape of the poverty spell distribution in the population (rather than simply the sample), these issues of left-and right-censoring of poverty spell data (which are ubiquitous) need to be accounted for. They are given great attention in the spell-based literature [2] on poverty persistence following Bane and Ellwood (1986) which, on the other hand, ignores longitudinal aggregation issues.”
From: pp. 58–59, Jäntti& Jenkins, ‘Income mobility’, http://ftp.iza.org/dp7730.pdfHandbook of Income Distribution, Volume 2, forthcoming
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5. ‘Chronic and transient poverty in rural Ethiopia: a new decomposition’
Natalie Quinn
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6. 1. Measures of longitudinal poverty
1.Official statistics: EU and the UK
Four-year window; count number of times poor within the window; ‘persistent poverty’ = 3 or 4 years poor out of 4
2.Indices of multi-period poverty
Aggregation across (i) periods and (ii) people
E.g. Bossertet al. (2012), Dutta et al. (2013), Foster (2009), Gradínet al. (2012), Hoy and Zheng (2011), Mendolaet al. (2011), Mendolaand Busetta(2012), Porter and Quinn (2012), etc. etc.
3.Indices of ‘chronic poverty’ (and ‘transitory poverty’)
Aggregate over periods for each person to produce longitudinal measure of well-being (e.g. longitudinal average income)
Identification: compare each person’s measure to poverty line
Aggregate across people
E.g. Rodgers and Rodgers (1993, 2009), Jalanand Ravallion(1998, 2000), Hill and Jenkins (2001), Duclos et al. (2010)
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7. Quinn: contribution
New longitudinal indices developed, building out of Lit. 2but more inspired by Lit. 3, with empirical illustration
•(within each period): how poor you are matters –poor versus poverty gap versus poverty gap-squared as the personal ‘deprivation’ measure
This paper follows most in this area and uses Gap-Squared
•(across periods) aversion to fluctuations over time in deprivation (in limit, spell repetition) versusaversion to ‘chronicity’ (persistence)
This paper is about latter: duration (more times poor is worse) and contiguity (more adjacent spells is worse)
Cf. Bossertet al. and Foster indices: invariant to permutations of the order of the poverty experienced over a period
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8. Quinn: development of index
Axioms:
•Anonymity, subset consistency, population size neutrality (standard)
•Comparisons of constant-wellbeingtrajectories
Trajectories above poverty line don’t count
More deprived (among poor) more aggregate poverty
Less unequal distribution (among poor) more aggregate poverty
[compactness] “Poverty is maximised when all individuals have zero consumption in all periods and minimised when all individuals have poverty-line consumption in all periods; furthermore all levels of poverty between these bounds may be achieved for some profile of equal and constant wellbeings”
Axioms plus normalisation plus gap-squared deprivation general form of aggregate poverty index …
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9. Quinn: index form
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•Index Pis average of squared gap, where ‘gap’ is a measure of each person’s intertemporalprofile
Cf. FGT(2) index in cross-sectional poverty case
•Note ordering of aggregation (over profiles within people and then across people): reflects ‘chronicity’ interest
Which axiom(s) lead to this ordering of aggregation tasks?
•But what form does the thecp(.) function have?

10. Quinn: the individual-level chronicity function, cp(.)
1.Continuity and monotonicity
2.Duration-sensitivity: more periods being poor raises your score
•Ifa particular single-parameter CES (generalised mean) function is used, thenduration-sensitivity satisfied
Sensitivity parameter: larger more duration-sensitive
But ‘time symmetric’; insensitive to contiguity aspects, so …
3.Contiguity-sensitivity: having more contiguous spells raises your score
•Ifa particular parametric weighting of periods is used (choice constrained to satisfy other axioms), thencontiguity-sensitivity satisfied as well
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11. Quinn: the index
•Meets NQ’s desiderata!
•Complicated and ‘non-transparent’ functional form – but these are complicated issues to address!
•Index can be used to decompose Total poverty over Tperiods into sum of Transitory poverty and Chronic poverty (where latter two components have same form as NQ’s index)
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12. Quinn: illustrative application
•Ethiopian Rural Household Survey
•7 waves (‘rounds’): 1994, 1994, 1995, 1999, 2004, 2009
Restricts attention to 1994, 1999, 2004, 2005
Equally-spaced rounds ~ subperiods
•Household per-adult-equivalent consumption per month, assessed relative to a cost-of-basic-needs poverty line
‘standard’ definitions, used before with these data
•Unit of analysis is ‘household’
•Balanced panel present at each of the 4 rounds
Ignores changes in household composition / attrition
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13. Quinn: NQ versus JR
% persons chronically poor, by Peasant Association
• Each J-R percentage greater than corresponding Q percentage
• Less chronic poverty (as % of Total poverty) according to Quinn approach
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0 5 10 15 20 25
All
Debre Berhan Bok
Debre Berhan Kar
Debre Berhan Kor
Debre Berhan Mil
Doma
Gara Godo
Adado
Aze Deboa
Imdibir
Trirufe Ketchema
Korodegaga
Adele Keke
Sirbana Godeti
Shumsha
Yetmen
Dinki
Geblen
Haresaw
Jalan-Ravallion Quinn
Note:
Derived
from NQ
Tables 1
and 2

14. Quinn: NQ versus JR (2)
% persons chronically poor, by Peasant Association
(normalised by All %)
• J-R and Q approaches show similar Peasant Association
profile if one uses normalised percentages!
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0 .5 1 1.5 2 2.5 3
All
Debre Berhan Bok
Debre Berhan Kar
Debre Berhan Kor
Debre Berhan Mil
Doma
Gara Godo
Adado
Aze Deboa
Imdibir
Trirufe Ketchema
Korodegaga
Adele Keke
Sirbana Godeti
Shumsha
Yetmen
Dinki
Geblen
Haresaw
Jalan-Ravallion Quinn
Note:
Derived
from NQ
Tables 1
and 2

15. Quinn: comments (1)
1.Missing literature
E.g. Duclos et al. (JDE2010),Mendolaet al. (JRSSA2011)
Orientation: poor versus rich country literature?
2.‘Sell’ contribution more, up-front
Chronicity = duration + contiguity
3.Clarify target audience and rewrite accordingly
Esp. concerns weight to be given to empirical illustration
4.Necessary as well as Sufficient conditions, a.k.a. less “ad hoc” assumptions to generate specific index form?
More explanation (graphs didn’t help me) or better ‘defence’
5.Empirical illustrations
Compare with more approaches than only J-R (see #1 above)?
Use different data set to distinguish your approach? (BHPS?)
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16. Quinn: comments (2)
6.What happens to index form if you don’t use gap- squared evaluation function (cf. gap or indicator)?
Simplicity increases transparency? EU versus World Bank!
7.Make more of the advantage of having (xit/z) within the index form; and what if (xit/zt) –e.g. relative poverty line?
8.Balanced panel assumption!
Common fixed-length window for assessment means credibility of empirical estimates is less, the larger Tis
–attrition; and “there’s no such thing as a longitudinal household” (you can only consistently track individuals over time)
–general issue? (left-and right-censoring)
9.How would we expect an intertemporalindex to vary with different values of T, other things being equal?
10.Standard errors for estimates shown? Bootstrap?
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17. ‘How and why the distribution of poverty durations has changed in the United States since the mid-1980s’
IrynaKyzyma
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18. Kyzyma: overview
‘Howand why…
1.Methods re ‘how’ and ‘why’
Discrete-time survival analysis to summarise poverty spell lengths for persons beginning a poverty spell
How(overall change): lifetableestimators of survivor/failure function
Why: ‘non-linear Blinder-Oaxaca’ methods used to decompose survivor/failure function into (i) changes in characteristics of entrants to poverty, and (ii) changes in poverty spell length distributions
2.Application to SIPP panels for 1984, 2004, 2008
Monthly obs, from poverty entry to up to 32 months later
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19. Kyzyma: methods (1)
Discrete time survival time analysis of poverty spells:
•Probability of having a spell tmonths long (since entry)
Failure function (CDF): F(t) = Pr(Tt)
•Probability of remaining poor at least tmonths since entry
Survivor function: S(t) = Pr(T> t) = 1–F(t)
•One-number summaries of spell length distribution:
Mean duration: E(T) = alltS(t)
Median duration: ms.t.S(m) = 0.5
•Howhave poverty spell distributions changed between SIPP panels?
Estimate F(t) for each panel, and compare them (changes in whole distributions, or one-number summaries)
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20. Kyzyma: methods (2)
Whyhave poverty spell distributions changed between a pair of SIPP panels from dates aand b?
•Now let Failure functions (CDF) depend on personal characteristics X as well as survival time t
F(t, X) = F(t| X)g(x)dx
•Hence, the change in overall CDF between aand b,F(t):
F(t)= Fb(t)–Fa(t)= F(t| X)ga(x)dx+ Fb(t| X)g(x)dx
1.changes in the conditional distributionsof poverty spell lengths for each group of poor people with characteristics X, F(t| X)
2.changes in the distributions of characteristicsof the people beginning a poverty spell (‘composition of poor’),g(x)
with relative importance of components depending on ‘weights’: base-year versus final-year; {ga(x), Fb(.)} versus {gb(x), Fa(.)}
NB IK has an additional decomposition component relating to changes in population structure –see below
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21. Kyzyma: methods (3)
Q: how to estimate these components?
A: via discrete-time hazard regression modelling used as a type of ‘distribution regression’:
1.Monthly poverty exit hazard rate, h(t, X) , modelled as inverse-logistic function of
–Survival time (duration dependence): duration-month-specific function
–Personal characteristics (researcher’s choice from what available in data!)
–Regression coefficients
2.Derive estimates of ha(t, X), hb(t, X)from each SIPP panel
3.From these, derive estimates of Fa(t, X), Fb(t, X)using standard formulae, and hence estimates of F(t| X)
4.Sample estimates of ga(x), gb(x), and hence g(x)
5.Finally, derive estimates of the 2 change components using numerical integration (over types of people)
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22. Kyzyma: data and definitions
•US Survey of Program Participation (SIPP):
Series of panels starting at different dates
Interviews held every 4 months; retrospective recall enables derivation of monthly sequences on family income
Follow-up for up to 8 rounds (i.e. 32 months)
SIPP ‘1984’: October 1983–July 1986
SIPP ‘2004’: February 2004–January 2008
SIPP ‘2008’: September 2008–December 2010 (GR period!)
•Poverty: poor if family income below poverty line (corresponding to ‘Official’ definitions of income, line)
•Sample(s):adults (aged 18+)
•Selections:
drop all left-censored spells; some spells are right-censored
only first poverty spell per person in panel
–no repeat spells; not total time poor over period since entry
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23. Kyzyma: howhave poverty durations changed?
•Distinct rightward shift in CDF; increase in median duration
•Relatively small change between 2004 panel and 2008 panel (surprising: Great Recession!)
•Bottom chart (Fig. 4.2) shows F(t): F2008(t)–F1984(t) and F2004(t)–F1984(t)
•Relative to 1984 SIPP poverty entrants, CDFs for later panels have fewer at shorter durations, more at longer durations
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24. Kyzyma: why have poverty durations changed?
Changes in conditional CDFs
(Fig 4.7)
Changes in composition of poor
(Fig 4.6)
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•Increase in overall distribution of spell lengths between panels driven almost entirely by changes in conditional CDFs!
•[NB differences in y-axis scale between Figures]

25. Kyzyma: changes in conditional CDFs (detail)
•Importance of component = F(t| X)ga(x)dx
•So, look at F(t| X)in detail:
Counterfactual CDFs predicted from poverty exit hazard regressions for each panel
Changes in regression coefficients (Table 4.3)
Changes in CDFs for particular types of individual (Figures 4.8 and 4.9 containing 6 graphs each)
Hard to summarise all the detail succinctly or (said differently) no one change jumps out at reader, but …
“which socio-economic groups have been affected the most by the Great Recession. Judging from the trends, it is mainly black individuals, single person and single parent families, as well as uneducated people, who became especially likely to have a long spell of poverty in the 2008 panel. In contrast, the patterns of poverty duration for individuals of pre-retirement and retirement age remained almost unchanged during the years of the crisis.” (page 26, emphasis added)
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26. Kyzyma: ‘robustness checks’
1.Decomposition can depend in principle on whether use base-or final-year weights (or vice versa)
Reversing order makes no difference to headline result (phew!)
2.Was there a change in poverty re-entry distributions (for those who started a spell)?
Fig 4.4: change in CDFs for time-between-poverty spells
Yes: between 1984 panel and later panels
No: between 2004 and 2008 panels
–So, Great Recession effect mainly on poverty spell lengths
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27. Kyzyma: comments (1)
More focusand more clarityin order to better ‘sell’ the paper
1.What should we be most interested in?
Distribution of total time poor over a period related to: Pr(first enter Poverty); Pr(exit|entry); Pr(re-entry|exit)
Changes over time in poverty experienced depends on which component?
[related] left-censored spells dropped (this is common, but is also selective –mostly relatively long spells):
–Hard to model, but …
–Has the prevalenceof left-censoring changed over the 3 SIPP panels?
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28. Kyzyma: comments (2)
2.Comparisons of which panels are of greatest substantive interest? Focus on those that enable telling the most compelling ‘story’
E.g. greatest interest in changes associated with Great Recession (2004, 2008 panels)? See SIPP panels in context in the Figure below
Also, long interval between 1984 and later panels (harder to assess changes without controlling for this)
Engage with the US debate on poverty more, including more contextual comparisons with standard cross-sectional focus (and results about groups ‘most affected’)
What are the SIPP cross-sectional poverty rates relative to Official?
If retain 1984 panel, the re-entry results imply that the whole decomposition exercise needs to be applied to time-to-entry spells as well!
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Official US poverty rates, by year (and recession)
Source: US Census
Bureau P-60 Report,
2013

29. Kyzyma: comments (3)
3.Drop the decomposition component relating to changes in ‘population structure’
Formally not ‘wrong’: decomposition formula is an identity
But has no substantive rationale, given focus is on poverty spells for people who start a spell, so only changes in ‘composition of the poor’ are relevant
4.Drop the graphs showing ‘percentage changes’; retain only ‘absolute changes’, as it is the latter that relate to decomposition formulae
5.Consider using more one-number summaries in addition to graphs to summarise decompositions
Decompose changes in mean/median poverty spell duration?
6.SEs (CIs) for decomposition components?
Complicated to do, but potentially useful in telling story
Do regression SEs account for within-family clustering?
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30. Kyzyma: comments (4)
7.(related) Separate regressions for each poverty month spell-month specific regression coefficients, but cell sizes for some person-types must be very small, especially at long durations
Consider pooling months: TVCs but constant coeffs(as in Table 4.3!)
8.Clearer if separate the discussion of decomposition idea from discussion of estimation
Put the hazard regression material second and reduce discussion of well-known stuff (regression model) and increase discussion of less-known stuff (assembling decomposition components)
Better cross-referencing between ‘results’ and ‘formulae’
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31. Kyzyma: comments (5)
9.Clarify how ‘integration over characteristics’ implemented: F(t| X)g(x)dx …but Xis a vector
Is it in fact kFk(t| X)pkfor distinct non-overlapping subgroups k= 1,…,Kdefined by joint distribution of characteristics, with population share pk?
10.More discussion of predictors used in the regressions: race, sex, age group, education level, family type
Why these and not others?
Are they time-varying or measured as at poverty entry?
What about unobservables(cf. frailty survivor function)?
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32. Kyzyma: comments (6)
11.Spells start in different calendar months within each panel –should this be accounted for?
Cf. pooling 2004 and 2008 panels and looking at macro effects directly in terms of spell start month (and perhaps incorporating, say, state-level unemployment rates)?
12.Retrospective recall about income components n between-interview months
Bias in recall?
Seam effects? How were the poverty status sequences created?
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33. Kyzyma: comments (7)
Some other details:
•“period” “month” throughout?
•Equation 3.3 is a formula for the mean duration, not CDF
•Use consistent line patterns across Figures (same lpatternfor each panel)
•Table 4.2 describes composition of the poor in the first spell month? Also, …
Characteristics shown here are apparently more detailed than used in the regressions (cf. Table 4.3)
These are univariatebreakdowns, but isn’t it multivariate breakdowns (combinations of characteristics) that are relevant, and changes in them? Cf. comment 9
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