Economic Modelling 35 (2013) 931–939

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Economic Modelling

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Inequality, growth andmobility: The intertemporal distribution of income inEuropean countries 2003–2007☆

Philippe Van Kerm a,⁎, Maria Noel Pi Alperin a,b

a Centre d'Etudes de Populations, de Pauvreté et de Politiques Socio-Economiques/International Networks for Studies in Technology, Environment, Alternatives, Development, 3 avenue de la Fonte,L-4364 Esch-sur-Alzette, Luxembourgb LAMETA, Université Montpellier I, France

☆ An extended working paper version of this article is avologies and Working Papers series; see Van Kerm and Pi Acarried out in the context of the first “Network for the afunded by the EU Statistical Office and coordinated by CEPcleaning utilities were provided by Alexandra Skew, as parin Europe (ALiCE) project, funded by the UK's Economic apaper benefited from comments by Tony Atkinson, StepNolan, three anonymous referees and participants at theMethods for the Analysis of Incomes and Inequalities (ISEconference in Warsaw, March 25–26 2010.⁎ Corresponding author.

E-mail address: philippe.vankerm@ceps.lu (P. Van Ker

0264-9993/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.econmod.2013.07.001

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 4 July 2013

Keywords:Income mobilityIncome growthInter-temporal inequalityEU-SILC

This paper exploits EU Statistics on Income and Living Conditions longitudinal data 2003–2007 to describethe intertemporal distribution of income in twenty-six European countries prior to the onset of theGreat Recession. We document levels, inequality and progressivity in the distribution of year-on-year in-come gains and losses and examine the relationship of these with inequality and poverty indicators. NewMember States have typically seen individual incomes grow faster than other EU countries. Income gainswere disproportionately pro-poor in all countries. We therefore observe regression to the mean bothamong EU countries and among individuals within countries. However, short-run income mobility doesnot significantly reduce inequality of time-averaged incomes. Potential issues about cross-country compa-rability of the data and the short period under consideration call for caution in interpreting our results,however.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Behind an ‘economic growth’ of x percent hides a diversity of indi-vidual experiences. Some people see their income grow by a lot morethan x percent while othersmay be losing ground despite the economicgrowth. In contrast to some popular feelings, it is not necessarily therichest who are getting even richer (and the poorest poorer), at leastif we look at annual flows of income. It has been well documentedthat there is ‘income mobility’ in modern societies with people movingup and down the income ladder over time, some escaping povertywhileothers are falling into deprivation. Understanding social benefits of eco-nomic growth requires detailed information about the diversity of indi-vidual experiences. This is what this paper provides on the basis of theEuropean Union Statistics on Income and Living Conditions (EU-SILC).Who has gained and by howmuch?Who has lost? How unequally dis-tributed have been gains (and losses) over time? Did they exacerbate

ailable in the Eurostat Method-lperin (2010). The research wasnalysis of EU-SILC” (Net-SILC),S/INSTEAD. Data extraction andt of the Analysis of Life Chancesnd Social Research Council. Thehen Jenkins, Eric Marlier, BrianColloquium on Cross-national

R, Colchester) and the Net-SILC

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ghts reserved.

social inequality or did growth and mobility had an equalizing impact,and by how much? This paper attempts to provide some answers tothese questions, highlighting differences observable across twenty-sixEuropean countries, and between recent and older Member States inparticular, in the period 2003–2007 prior to the onset of the GreatRecession.

Our aim, more generally, is to show how EU-SILC longitudinal datacan add to the cross-sectional picture on poverty and inequality inEurope. We provide a broad-brush picture of what can be learned em-pirically on these issues, pointing out findings but also raising questionsabout the reliability of some estimates given the design of the EU-SILClongitudinal dataset.

It is now widely acknowledged that ‘income mobility’ is a multi-faceted concept (Fields, 2008).We consider several facets of it. We pro-ceed by first documenting the distribution of individual income gainsand losses in each of the twenty-six countries analyzed, emphasizinglevels of (percentage) income growth, but also aspects of inequalityand progressivity (Jenkins and Van Kerm, 2011). We then considerthe impact of these income changes on poverty dynamics and assesshow much individual income fluctuations reduce intertemporal in-equality as compared to inequality of annual income. We find evidenceof regression to the mean both between countries (with poorer coun-tries showing higher average income growth than richer countries)and within countries (with poorer individuals experiencing higher in-come growth than initially richer people in each country). However,short-run income mobility does not significantly reduce inequality intime-averaged incomes within countries. Similarly, in the short timeframeand the countries considered, high levels of poverty do not appear

3 By pooling data, we discard any potential effect of cyclical macroeconomic fluctua-tions in the timewindowconsidered. Note thatwe are covering the period of growth priorto the onset of the Great Recession (Jenkins et al., 2013).

4 There are two exceptions to the summation of incomes over the previous calendaryear: for Ireland, incomes are summed over the 12 months prior to the interview, and

932 P. Van Kerm, M.N. Pi Alperin / Economic Modelling 35 (2013) 931–939

associated with high poverty exit rates.1 Caution is required in inter-preting our results as we find suggestive evidence that divergence indata collection methods across countries is influential; in particular, es-timates from countries using register data to collect income appear todiffer in systematic ways from those relying on surveys.

The paper is organized as follows. Section 2 briefly describes the EU-SILC dataset, the samplewe extracted therefrom, and details the incomeconcept that we look at. Section 3 documents the distribution of incomegains and losses. Section 4 describes poverty exit and entry rates andconsider the impact of short-run incomemobility on inter-temporal in-equality. Section 5 provides a discussion of our results and Section 6concludes the paper.

2. The longitudinal EU-SILC data, sample selection and the incomeconcept

EU-SILC is an instrument aiming at collecting comparable cross-sectional and longitudinal micro-data on income poverty and social ex-clusion. The micro-data on households and individuals available in EU-SILC are expected to be representative of the population living in privatehouseholds in each of the participating countries. It has become the ref-erence source for comparative statistics on income distribution and so-cial exclusion in Europe. This instrument was developed to replace theEuropean Community Household Panel (ECHP), supported and coordi-nated by Eurostat. EU-SILC has a legal basis making its implementationin EUMember States mandatory. The Council and European Parliamentregulation 1177/2003defines the scope of EU-SILC, provides definitions,time reference, data characteristics, sampling rules, sample sizes, etc.

While EU-SILC is based on a common frameworkwith a common setof target variable definitions and rules, it is not a fully harmonizedEuropean-wide survey. Distinct data collection methods are beingused in different countries within the framework provided by the regu-lations. Data sources of various types are being compiled, possibly dif-ferently for cross-sectional and longitudinal data. Target variables onincome, for example, are collected from household surveys in somecountries while they are extracted from administrative sources inother countries. Following pilot surveys in 2003, full-scale EU-SILCdata collection was conducted in 15 countries in 2004, in 25 countriesin 2005, and in 27 countries (EU-27 minus Bulgaria and Romania, plusNorway and Iceland) in 2010. The number is expected to reach around30 countries, including all EU Member States.

The EU-SILC database contains a set of annual cross-section datasetssince 2003 and a distinct set of longitudinal datasets covering overlappingperiods of up to four years. The longitudinal datasets are based on a rotat-ing panel sample. In the rotational design, the longitudinal sample is com-posed of several rotation groups, each of them similar in size and designand representative of the whole population. From one year to the next,one rotation group is dropped and replaced by a new one. The generalrule for EU-SILC is a rotational design based on four replications, whichimplies that repeated, longitudinal observations on individuals are avail-able for up to four years. The longitudinal components of EU-SILC aremore limited in content and in sample size compared to the cross-section components. Details on the structure, content and design of thedataset are fully documented in Eurostat (2009b).2

The analysis conducted in this paper exploits three longitudinaldatasets covering the periods 2003–2004–2005, 2003–2004–2005–2006and 2004–2005–2006–2007. With the rotating design of EU-SILC we areable to analyze income changes from year t − 3 to year t for fourteencountries only with these datasets. Consequently, to provide a broadercoverage of countries, we focus on short-run income variations fromone year to the next. This allows us to cover twenty-six countries: Austria(AT), Belgium (BE), Czech Republic (CZ), Cyprus (CY), Denmark (DK),

1 See Jenkins and Van Kerm (2013) for a detailed analysis of indicators of current andpersistent poverty in EU-SILC.

2 See Wolff et al. (2010) for a more detailed description of EU-SILC.

Estonia (EE), Finland (FI), France (FR), Germany (DE), Greece (EL),Hungary (HU), Italy (IT), Iceland (IS), Ireland (IE), Latvia (LV), Lithuania(LT), Luxembourg (LU), the Netherlands (NL), Norway (NO), Poland(PL), Portugal (PT), the Slovak Republic (SK), Slovenia (SK), Spain(ES), Sweden (SE), and the United Kingdom (UK). (Extended analysisof the longer t − 3 to t term is available in Van Kerm and Pi Alperin(2010).)

Our unit of analysis is primarily a pair of incomes for an individualmeasured at times t − 1 and t (income is defined shortly). Tomaximizesample sizes, we merged all three longitudinal datasets and pooled all(t − 1)-to-t income pairs available. With the rotational design of EU-SILC, each individual respondent can possibly provide up to three(t − 1)-to-t income pairs.3 Resulting sample sizes in each country arereported in Table 1. The table illustrates the substantial variations insample sizes across countries, as well as the uneven distribution of thedata over different time periods as not all countries provide data forall pairs of years.

We follow standardpractice in incomedistribution analysis and focuson variations over time in individualized single-adult equivalent house-hold disposable income for the whole population. All members of ahousehold at time t are assumed to share equally total household in-come, adjusted by equivalence scales. Single-adult equivalent disposableincome is generally considered as the best proxy for a person's contem-poraneous standard of living. Specifically, household disposable incomeis computed as the sum over the calendar year preceding the interviewand for all household members of gross personal incomes (employeecash or near cash income; non-cash employee income; employers' socialinsurance contributions; cash benefits or losses from self-employment;unemployment benefits; old-age benefits; disability benefits andeducation-related allowances) plus gross income components at house-hold level (income from rental of a property or land; family/children re-lated allowances; housing allowances; regular inter-household cashtransfers received; interests, dividends, profit from capital investmentsin unincorporated business; income received by people aged under 16)minus employer's social insurance contributions, interest paid on mort-gage, regular taxes on wealth, regular inter-household cash transferpaid, income tax and social insurance contributions.4 This measureof annual household disposable income is then divided by the numberof single adult equivalents in the household (according to the modified-OECD equivalence scale) to arrive at an individual measure of single-adult equivalent disposable income attributed to all householdmembers.

When trying to interpret results presented in this paper, it will beuseful to bear in mind that a person's single adult equivalent income(towhichwewill refer simply as income)may vary through time for a va-riety of reasons: employment and labor market factors (e.g., tenure, pro-motion, job mobility, unemployment, retirement), but also householddemographic factors (e.g., birth, death of a household member, divorce,“nest leaving”), as well as tax and benefit changes, evolution of returnson investments, of private transfers, etc. Some of these sources of varia-tion are voluntary or at leastwithin the control of individualswhile othersare beyond individuals' control. Some are foreseeable while others arenot; some lead to gradual, limited changes while others take the form oflarge shocks; some are transitory in nature while others are persistent.When considering mobility of income, we look at the combined effectsof these variations. It is beyond the scope of this paper to attempt to iden-tify the sources of income variations in any detail.5

for the United Kingdom, incomes refer to the period around the date of interviewwith in-come totals converted to annual equivalents.

5 Van Kerm and Pi Alperin (2010) summarizes a “direct standardization” analysis ofthese factors.

Table 1Sample sizes: Number of (t − 1)-to-t individual income pairs by country and time period.

03–04 04–05 05–06 06–07 Total

BE (S) 6533 7444 9212 23 189CZ (S) 8904 16 118 25 022DK (R) 2347 4920 7931 15 198DE (S) 21 647 21 647EE (S) 9020 10 177 9487 28 684IE (S) 5868 5630 11 498EL (S) 7948 10 188 9783 27 919ES (S) 20 242 21 251 21 190 62 683FR (S) 18 216 14 765 19 783 52 764IT (S) 38 347 36 669 35 308 110 324CY (S) 7841 7554 15 395LV (S) 6675 6755 13 430LT (S) 7581 8279 15 860LU (S) 7517 7809 8041 8371 31 738HU (S) 12 627 13 659 26 286NL (R) 16 878 16 208 33 086AT (S) 7850 9194 10 961 28 005PL (S) 31 484 29 931 61 415PT (S) 6157 8443 7682 22 282SI (R) 21 104 17 770 38 874SK (S) 10 573 9471 20 044FI (R) 13 356 12 398 11 682 37 436SE (R) 11 346 10 521 9744 31 611UK (S) 14 699 12 256 26 955IS (R) 5213 4826 4615 14 654NO (R) 9664 11 436 9061 7455 37 616

Notes: (R) identifies countries relying on administrative registers for collecting householdand individual income information. (S) refers to countries using survey data. Sample sizesare as used for estimating all measures reported in the core of the paper, namely afterexcluding any observation with missing, negative or extreme income at either time t − 1or time t, or with non-positive base sample weight at time t.

6 See for example Fields and Ok (1996, 1999), D'Agostino and Dardanoni (2009) orSchluter and Van de gaer (2011) for discussions on alternative measures of individual in-come mobility.

933P. Van Kerm, M.N. Pi Alperin / Economic Modelling 35 (2013) 931–939

In practice, we use the variable ‘equivalent income’ as directly pro-vided in the EU-SILC user database (Eurostat, 2009a) deflated to 2005prices using the harmonized index of consumer prices (available fromEurostat). All income changes we look at are therefore in real terms. Anumber of statistics estimated in this paper are sensitive to the presenceof extreme and/or negative data, just likemeasures of inequality for ex-ample. To avoid presenting results driven by extreme data, we haverecorded asmissing any income smaller than 75% of the lowest percen-tile or higher than 125%of the highest percentile of the income series foreach year and each country. The top and bottompercentiles of referencewere estimated for each country and each year from the EU-SILC cross-section datasets. This recoding affected approximately 1% of the data ineach country and year and stabilized estimates substantially comparedto an alternative strategy to keep all incomes unrecoded (see Section 5).

We estimate standard errors for all statistics reported in the paperusing the same bootstrap resampling procedure. All statistics havebeen re-estimated on 250 bootstrap samples drawn from the originalEU-SILC user database. In drawing the bootstrap samples we attemptedto approximate the original survey design as closely as possible withthe information available in the data. This is only an approximationsince identification of stratification variables is not released in the data-base for reasons of confidentiality and information about primary sam-pling units is partial (Goedemé, 2013). Also it was not possible toaccount for variability implied by data imputation and in the computa-tion of sample weights. Our strategy was to sample households with re-placement from each rotation group at the year of entry of the rotationgroup in the survey. This resampling was stratified by NUTS-1 region.To account for the dependence of the sample composition throughtime and within households we then select all members of theresampled households and all subsequent split-off household membersoriginating from the resampled households. Bootstrap sampling wasdone using the repeated half-sample bootstrap algorithm of Saigo et al.(2001). Standard error estimates are based on the standard deviationof estimated indices over the 250 bootstrap replications. For any estima-tion in our pooled sample of income pairs, we use year t base weights.

3. The magnitude and distribution of individual income gains andlosses

A variety of experiences can hide behind an aggregate economicgrowth of x percent. Not everyonehas seen her economic circumstances– income, in the context of this paper – grow by x percent; some havegained, some have lost. We illustrate the magnitude of individual in-come gains and losses in the different EU countries and documentsthe diversity of experiences observed within any given country. Whileconventional analysis of income distributions looks at the dispersionof income levels the focus here is on the distribution of income changesover time.

The building block of the analysis is a measure of individual incomegrowth from one year to another. To facilitate comparisons across coun-trieswith very diverse levels of income,we consider here the percentagegrowth of people's income, that is the value δ(yi1,yi2) in

δ y1i ; y2i

� �¼ 100� y2i

y1i−1

!

where yi1 and yi2 denote the income of person i respectively in an ini-

tial year and in a final year. Two remarks are in order. First, while wewill refer to people's income growth, nothing prevents δ(yi1,yi2) to benegative to reflect the reduction of a person's income. Second, withthis measure of income growth, we are making an assumption thata gain from €100 to €150 is of the same magnitude as a gain from,say, €1000 to €1500 despite the fact that the growth in currencyterms is higher in the second case. This has the effect of giving rela-tively more importance in our analysis to the currency gains of indi-viduals with lower incomes, but this makes comparisons of growthfigures more meaningful, especially when comparing individualswith different income levels, and more importantly in the contextof this paper, when comparing aggregate values for countries withstrikingly different income levels.6

Fig. 1 establishes our point that the distribution of gains and losses isdispersed, with both winners and losers found in all countries, albeit indifferent proportions. Each row on this plot (and on all subsequent fig-ures) refers to a country labeled on the left end of the plot. Themarkerson the horizontal lines give the percentage of individuals observed (i)losing more than 25% of their income from year t − 1 to t, (ii) losingat least some income, and (iii) gaining no more than 25% of income(the complement of the latter, that is, the proportion gaining morethan 25% of income can be read from the distance to the right side ofthe plot; the closer the right-hand dot is to the left of the plot, the great-er is the proportion of “winners”). The number reported on the righthand side is themeanpercentage incomegrowth. Countries are orderedfrom top to bottom by this value. NewMember States labels are shiftedto the right for ease of identification. In order to spot the potential im-pact of differences in data collection strategies on our estimates, coun-tries relying on administrative, register data for collecting incomeinformation in EU-SILC are identified by hollowed symbols, while solidsymbols are used for countries relying on survey data.

While average income growth was positive in all countries, a sub-stantial fraction of the population experienced income losses (morethan 50% in Germany or Hungary). In Hungary or Spain, up to 15% ofpeople experienced losses of more than a quarter of their initial yearincome. On the other hand, between 8% (in Denmark) and 35% (inPoland) of the population had income gains larger than 25% betweentwo consecutive years.

To summarize the distribution of these individual-level percentagegains and losses, we exploit three types of indices. Each index emphasizes

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Percent

Fig. 1. Percentage of population (i) losing more than 25% of income, (ii) losing at leastsome income, and (iii) losing some income or gaining no more than 25% of income.Note: Each horizontal refers to one country. Left-hand dotsmark theproportion of individ-uals losing more than 25% of their initial income from year t − 1 to t in each country. Tri-angles mark the proportion of individuals with income at t smaller than income at t − 1.Right-hand dots mark the proportion of individuals losing income or not gaining morethan 25% of their initial income. Countries are ordered from top to bottom by the valueof the mean percentage income growth reported on the right-hand side of the plot. NewMember States labels are shifted to the right for ease of identification. Register countriesare in hollowed markers.

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0 10 20 30 40 50 60 -10 0 +10

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Fig. 2. Estimates of mean percentage income growth, mean income volatility and equallydistributed equivalent income growth. Note: Dots mark mean percentage income growth(E(δ; Y1, Y2)). Triangles mark mean income volatility (E(|δ|;Y1,Y2)). Squares mark equallydistributed equivalent growth (W2(δ; Y1, Y2)). Countries are ordered from top to bottomby thevalue of themean percentage income growth.Horizontal stripes showbootstrapped1.645-standard-error variability bands. New Member States labels are shifted to the rightfor ease of identification. Register countries are in hollowed markers.

934 P. Van Kerm, M.N. Pi Alperin / Economic Modelling 35 (2013) 931–939

a distinct aspect of this distribution. The first, and simplest, is the meanpercentage income growth formally defined as

E δ;Y1;Y2ð Þ ¼Z

Ωy

δ y1; y2ð ÞdH y1; y2ð Þ

whereΩy is the domain of all possible values for pairs y1 and y2, and H isthe joint, bivariate distribution of incomes in periods 1 and 2. This mea-sure is indicative of the overall magnitude of income growth, but ignoresthe dispersion of individual experiences. Higher values for this measurewill typically be preferred since they are indications of greater incomegains. (Estimates of E(δ; Y1, Y2) are shown in the right-hand side of Fig. 1.)

The secondmeasure is themean absolute value of the percentage in-come growth, to which we will refer as the mean volatility, hereafter:

E δj j;Y1;Y2ð Þ ¼Z

Ωy

δ y1; y2ð Þj jdH y1; y2ð Þ:

This is the Fields–Ok measure of income mobility (Fields and Ok,1999). By treating gains and losses symmetrically, thismeasure is reveal-ing of the degree of income volatility. Greater dispersion in the gains andlosses will translate into a larger value. While this measure is indicativeof the degree of variations in year-to-year incomes – something themean income growth does not tell anything about – it is not obviouslyclear whethermore of this is preferable or not. In particular thismeasuredoes not take into account whether incomes are growing or contracting.

Our third summarymeasure can be seen as a combination of thepre-vious two. It is an equally distributed equivalent mean percentage in-come growth indicator computed as a weighted average of percentagegrowth

Wυ δ;Y1;Y2ð Þ ¼Z

Ωy

ω δ y1; y2ð Þ;υð Þδ y1; y2ð ÞdH y1; y2ð Þ

with

ω δ y1; y2ð Þ;υð Þ ¼ υ 1−G δ y1; y2ð Þð Þð Þυ−1

where G is the empirical cumulative distribution of the individual in-come growth indicators δ(y1, y2). It can be interpreted as a measure ofincome growth “deflated” by the degree of inequality in the incomegrowth distribution. Wυ will be equal to the mean income gain in thehypothetical situation in which everyone has income growing in thesame proportion. Any deviation from this equally distributed gain situ-ation will result in a penalty that will reduce Wυ compared to E(δ; Y1,Y2), provided the inequality aversion tuning parameter υ set to a valuelarger than one, that is, provided we want to penalize inequality in thegains distribution. Wυ can be interpreted as an ‘equally distributedequivalent’ index of percentage income growth, and for example, coun-trieswith high average growthbut very unequal gainswill not appear toperform as well as in terms of E(δ; Y1, Y2). This measure is a variant ofclasses of mobility measure axiomatically justified by Demuynck andVan de gaer (2012). It also leads to ranking countries in a way that isconsistent with the dominance criteria suggested in Fields et al. (2002).

Estimates of these three summary measures are presented in Fig. 2.As in Fig. 1, countries are ordered from top to bottom bymean percent-age income growth (E(δ; Y1, Y2)) and estimates are read off the abscissaof the plot. For each country, mean percentage income growth ismarked on the horizontal line by a dot, mean income volatility ismarked by a triangle and equally distributed equivalent growth ismarked by a square. Bootstrap variability bands are reported as shadedbars behind each point estimate (variability bands around point esti-mates are bootstrap standard errors times +/−1.64).

The prime observation is that countries with highest income growthare all recent EU Member States, namely all three Baltic states, Polandand Slovakia, as well as, to a lesser extent the Czech Republic. Theseare also countries with lower levels of income to start with. By contrast,mean percentage income growth in Cyprus, Slovenia and Hungary hasnot been different from that of most other EU countries. Countrieswith the lowestmeangrowth tend to be those richest in levels. This sug-gests that catching up, or regression to the mean, is taking place acrossEU countries. We return to this observation supra.

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0 10 20 30 40 50 60

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Fig. 3. Estimates of progressivity-adjusted income growth (υ equal to 1 (mean percentageincome growth) and 2). Note: Dots mark estimates of progressivity-adjusted incomegrowth indices with υ = 1 (these are equal to the mean percentage income growthsince P1(δ; Y1, Y2) = E(δ; Y1, Y2)). Triangles mark estimates with υ = 2 (P2(δ; Y1, Y2)).Countries are ordered from top to bottom by the value of the mean percentage incomegrowth. Horizontal stripes show bootstrapped 1.645-standard-error variability bands.NewMember States labels are shifted to the right for ease of identification. Register coun-tries are in hollowed markers.

7 See Van Kerm and Pi Alperin (2010) for estimates with a higher, more extreme, υparameter.

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0 .1 .2 .3 .4 .5 .6 .7 .8

Rate

Fig. 4. Poverty exit, entry rates and cross-section poverty rates. Note: Squaresmark pover-ty entry rates. Dots mark cross-section poverty rates. Triangles mark poverty exit rates.Horizontal stripes show bootstrapped 1.645-standard-error variability bands. NewMem-ber States labels are shifted to the right for ease of identification. Register countries are inhollowed markers.

935P. Van Kerm, M.N. Pi Alperin / Economic Modelling 35 (2013) 931–939

Looking at mean income volatility reveals a different picture. Al-though it tends to be higher in countries with highmean percentage in-comegrowth, it turns out to be almost as high in countries such as Spain,the United Kingdom or Hungary, despite them having lower meangrowth. This suggests that incomes have been particularly volatile,both upward and downward, in these three countries. On the otherhand, income volatility appears smaller in the Netherlands, Sloveniaor most Scandinavian countries. It is disturbing to note that estimatesof income volatility appear in general smaller in EU-SILC ‘register coun-tries’. While sampling variability appears small with the sample sizesavailable in the dataset (bearing in mind that we pool multiple surveyyears), there is indication of potential non-sampling error in the formof bigger measurement error in countries using survey data. We returnto this issue in Section 5.

The ranking of countries changes when income growth is penalizedby the inequality in the gains and losses. If Poland, Lithuania and Slovakiastill exhibit the best performance, the Czech Republic appears to catchup with them almost entirely, thanks to a relatively equal distributionof gains and losses despite their smaller size. Scandinavian countriesalso appear to performbetter than in terms ofmean growth only. By con-trast, four countries appear to perform substantiallyworse than others inthis respect, namely Spain, the United Kingdom, and more surprisingly,Germany andHungary. The situation ofHungarymay appear particularlyperplexing in that it is not in line with observations made for all othernewEUMember States. Note however that some authors have cautionedagainst potential problems in both the German and Hungarian EU-SILCdata. Frick and Krell (2010) identified striking differences in measuresof income mobility estimated from the German EU-SILC data and fromthe German Socio-Economic Panel (SOEP) data (see also Hauser, 2008).Important divergence between EU-SILC and alternative data sourceshas also been reported for Hungary (see Lelkes et al., 2009; Toth andMedgyesi, 2011). In sum, themessage conveyed by the equally distribut-ed equivalent index of income growth is that looking at mean incomegrowth may lead to misleading conclusions if one cares about the distri-bution of gains in addition to their levels.

The equally distributed equivalent incomegrowth index incorporatesthenotion of inequality in gains and losses in the summary assessment ofgrowth. There is however a related concern about the distribution of

gains and losses that is not taken into account by this approach, namelywhether those who start with lower income obtain higher gains. In-equality in gains and losses might after all be desirable if people withlow incomes at the initial period get high income gains and richer peo-ple get lower growth (or suffer the losses). In other words, borrowingconcepts from the taxation literature, it might be desirable if the distri-bution of gains and losses is ‘progressive’. Such a distribution of gainsand losseswould, ceteris paribus, tend to reduce inequality of aggregateincomes and inequality in the second period (to the extent that this isnot entirely offset by reranking among individuals). This issue isdiscussed in Bénabou and Ok (2001) and Jenkins and Van Kerm(2006, 2011). Another summary index is needed to capture the degreeof progressivity of gains and losses. We follow Van Kerm (2009) andJenkins and Van Kerm (2011) and estimate progressivity-adjusted in-come growth indices

Pυ δ; Y1; Y2ð Þ ¼Z

Ωy

ω y1;υð Þδ y1; y2ð ÞdH y1; y2ð Þ

with

ω y1;υð Þ ¼ υ 1−F1 y1ð Þð Þυ−1

where F1 is the empirical cumulative distribution of individual incomeat the initial period. This measure bears much similarity with the Wυ

index. The only, but crucial, difference is that the weight is determinedby a person's rank in the initial period income distribution. Pυ(δ; Y1, Y2)is a weighted average of income gains with weights determined by ini-tial income position. The value of Pυ(δ; Y1, Y2) is therefore dispropor-tionately driven by the income growth of initially poor people andmeasures the degree of regression to the mean in income within coun-tries. It can also be interpreted as a uniformly distributed equivalent in-come growth as if gains and losses were uniformly distributed over allincome ranks in the initial distribution.

Estimates of Pυ(δ; Y1, Y2) for υ equal to 1 and 2 are shown in Fig. 3.7

(The case of υ = 1 is, in fact, themean percentage income growth.) Themain observation is that income growth is clearly progressive within

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0 .1 .2 .3 .4

Fig. 5. Average annual inequality, inequality of aggregated (t − 1) − t income andShorrocks index. Note: Dots mark average level of annual inequality (Gini coefficient). Tri-angles mark the Gini coefficient of multi-period aggregated incomes. Squares mark the rel-ative difference between annual inequality and inequality of aggregated incomes. Countriesare ordered from top to bottom by decreasing level of annual inequality. Horizontal stripesshow bootstrapped 1.645-standard-error variability bands. New Member States labels areshifted to the right for ease of identification. Register countries are in hollowed markers.

936 P. Van Kerm, M.N. Pi Alperin / Economic Modelling 35 (2013) 931–939

countries. Individuals with initially low incomes have higher percent-age income growth than richer individuals in their country. Increasingυ, that is, putting more weight on low income people, leads to higher

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Mean income1.00

Gini-0.54

Perc. growth-0.64

Volatility-0.61

Progressivity-0.63

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Exit rate0.07

Entry rate-0.52

(a) Countries sorted by mean income

Fig. 6.Mean income, inequality and the range of indicators of income mobility. (a) Countries smates for newMember States, dots are used for other countries. Register countries are in holloordering variable (mean income (a) or Gini coefficient (b)).

values for the progressivity-adjusted growth index. This holds in allcountries. However, the degree to which this is the case varies by coun-try. Poland is the country exhibiting the highest level of progressivity.Interestingly, Spain, the United Kingdom and Germany – countriesthat were identified as having the most unequally distributed growth– exhibit a substantially higher degree of progressivity. Conversely,the Czech Republic appears to perform relatively badly with regard tothe degree of progressivity in its income growth. While this is not nec-essarily true in principle, it appears that there is a tension betweenachieving progressivity in income growth and keeping the incomegains relatively equally distributed.

The progressivity analysis concludes our description of the distribu-tion of gains and losses. We now examine the implications of these in-come variations on poverty dynamics and intertemporal inequality.

4. Poverty dynamics and inter-temporal inequality

Results from Section 3 show that percentage income gains are sub-stantially larger for people with low initial income. A consequencethereof is that many people in poverty at a point in time manage to es-cape from it the following year and poverty rates measured at a point intime are not reflecting accurately neither the proportion of people inlong-term poverty, nor the overall proportion of people ever affectedby poverty over several years. Note however that while percentage in-come gains of individuals at the bottom of the distribution may belarge, this is not a guarantee that the corresponding gains ‘in euros’are sufficiently large to lift people above the poverty line. Furthermore,with the typical definition of the poverty line as a fraction of some refer-ence income (mean or median), countries with large average income

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Mean income1.00

Gini1.00

Perc. growth0.59

Volatility0.72

Progressivity0.63

Shorrocks0.01

Exit rate-0.32

Entry rate0.77

(b) Countries sorted by Gini coefficient

orted by mean income. (b) Countries sorted by Gini coefficient. Note: Triangles mark esti-wedmarkers. The numbers in each panel heading is the rank correlation with the country

937P. Van Kerm, M.N. Pi Alperin / Economic Modelling 35 (2013) 931–939

gains will also see their poverty line rise at the same time. So the effectof mobility on poverty dynamics is not unambiguous.

Fig. 4 illustrates this phenomenon: (i) triangles indicate poverty exitrates (the fraction of individuals in poverty at time t − 1 that are notpoor at time t), (ii) squares indicate poverty entry rates (the fractionof individuals not in poverty at time t − 1 that are poor at time t), and(iii) dots indicate the cross-section poverty rates. Countries are orderedfrom top to bottom by decreasing level of poverty entry rate. As is con-ventional, we define a person as poor if her income is below a povertyline set at 60% of her country's median income.8

We observe a great variety in experiences across countries in exitrates which range from approximately 0.25 to 0.50 between t − 1 andt. Surprisingly, poverty exit rates do not appear to be related in any sys-tematic way to our earlier statistics on individual income gains andlosses. Countries with, say, an exit rate above 0.5 do not seem to haveparticularly high measures of progressive income growth. We shouldhowever be careful here when looking at country rankings becausethe poverty exit rates appear to have large standard errors. We noteagain an association between the estimated indices and the incomedata collection method, in particular with regard to the poverty rateand the entry rate.

Differential income gains and regression to the mean in income de-scribed in Section 3 imply that inter-temporal inequality of income isgenerally smaller than annual inequality when several years of incomeflows are aggregated. This section examines how much this is the casewith the short-run averaging over two consecutive annual incomes. Isthere any support for a claim that countries with higher inequality inone year compensate this with higher mobility and, consequently,achieve similar levels of inequality when incomes are aggregated overmultiple years? Fig. 5 provides some answers to this question. Dots onthese plots indicate the average level of annual inequality as estimatedfrom our sample, with inequality measured by the Gini coefficient.9

Countries are ordered from top to bottom by decreasing level of annualinequality, with Portugal and Baltic States at the top andmostly Scandi-navian countries at the bottom. Triangles mark the value of the Gini co-efficient of time-averaged incomes over two consecutive years. Asdemonstrated in, e.g., Shorrocks (1978), to the extent that individual in-come changes depart from a proportional growth in everyone's income– estimates from earlier sections clearly show that this is far from thetruth – inequality of time-averaged income will be lower than averageinequality in the cross-sections. The question of interest is ‘by howmuch?’ According to Fig. 5 the answer seems to be ‘little’: inequality isonly moderately lower if incomes are pooled over two years. Thesquares on each figure give the value of the relative difference between(the average of) annual inequality and inequality of time-averaged in-comes. This difference is frequently used as an index of mobility in itsown right (Shorrocks, 1978). The reduction of inequality observed byaveraging incomes over two years is stronger in Austria, Slovakia,Germany, and Hungary (despite its relatively low degree of progressiv-ity of income growth). It is the lowest in Portugal which cumulates boththe highest annual inequality and the lowest inequality reduction fromaggregating income over time. We do not observe any systematic rela-tionship between the degree of annual inequality and the reduction ofinequality achieved by short-run time-averaging of incomes: there isno support here for a claim that higher mobility ‘compensates’ forhigher inequality among European countries (the case of Portugalbeing the only counter-example).

8 We estimated the value of the poverty line at each year from the EU-SILC cross-sectiondatasets.

9 Our estimatesmay differ from values estimated elsewhere from the EU-SILC databasefor two reasons. First, we report averages over several years of theGini coefficient and, sec-ond, we estimate the indices on our pooled longitudinal sample whereas the dataset ofchoice for estimation of annual inequality would typically be the EU-SILC cross-sectiondata.

5. Discussion

5.1. Mean income, inequality and measures of income mobility

At this stage, we have covered and documented key aspects of thedistribution of gains and losses and their impact on poverty and in-equality.We attempt towrapup this discussion here by relating our sta-tistics to the degree of cross-section inequality andmean income.We dothis informally by inspection of the patterns of the different indices ofmean percentage income growth, mean income volatility, progressivity-adjusted income growth, poverty entry and exit rates, and Shorrocks'index. Fig. 6a and b display estimates of these six indices along withestimates of mean income and Gini inequality indices. To visualizethe association between these indices across countries, estimates areordered from top to bottom by decreasing order of mean income(Fig. 6a) and by decreasing order of Gini coefficient (Fig. 6b). Spearmancorrelation coefficients between each index and the two ordering vari-ables are reported in each panel heading. Dots are used for recent EUMember States and triangles for former EU15Member States or Icelandand Norway.

A birds-eye view on these plots reveals a number of patterns. First,mean percentage income growth is inversely related to the level of in-come, with low income countries experiencing bigger growth thanricher countries. This holds true if we consider progressivity-adjustedmeasures that focus on initially poorer people. This association is how-ever largely driven by new Member States (triangles). Progressivity isalso positively associated to income inequality. Second, income volatili-ty is generally closely related to annual inequality with more unequalcountries having more income volatility. Yet volatility is also related tomean income, with richer countries exhibiting lower income volatility.Third, in spite of the positive relationship between progressivity and in-equality, Shorrocks' index appears unrelated to mean income and in-equality (or, in effect, to any of the other summary measures of thedistribution of gains and losses).

No clear patterns appear to emerge from experiences of single coun-tries or groups of countries, beyond the catching up of new MemberStates. Experiences of new Member States in terms of inequality ingains and losses, progressivity or reduction of long-term inequalityhave been notably heterogeneous on the range of indicators considered.

5.2. Measurement error

Our second element of discussion is about the overall reliability ofour estimates. Like most indices used to summarize the income distri-bution in a cross-section perspective, the measures used in our analysisare sensitive to extreme data (Cowell and Flachaire, 2007; Cowell andSchluter, 1998; Van Kerm, 2007; van Praag et al., 1983). Their relativefrequency in the different country datasets and how we have treatedthem may possibly affect our observations. Additionally, measurementerror – not necessarily in the formof outlying data – poses specific prob-lems in analyses of income dynamics. The reason for this is simple.Imagine a simple ‘classical’ measurement error case in which incomesin our data are recorded with some purely random error. If the error isuncorrelated through time, then this will lead to apparent variationsin income over time thatmight be entirely spurious. This problem is no-toriously difficult to deal with (see, e.g., Bound and Krueger, 1991;Gottschalk andHuynh, 2010), in particular asmeasurement error is typ-ically non-classical and the implications thereof are not unambiguous.10

In the present analysis, our concern is that the degree of measurementerror might differ from country to country according the survey designand thereby biasing our cross-country comparisons. Of obvious concernis the difference between countries using registers to collect income

10 Gottschalk and Huynh (2010), for example, show that combination of non-classicalerror components may offset each other and lead to estimates of somemobility measureswhich are less affected than measures of inequality.

938 P. Van Kerm, M.N. Pi Alperin / Economic Modelling 35 (2013) 931–939

versus those relying on surveys. We have noted clear differences insome of our estimates, with respect to inequality (Fig. 6b), income vol-atility (Fig. 2), progressive income growth (Fig. 3), or poverty rates andpoverty entry rates (Fig. 4). Note for example how Slovenia differs fromthe other new Member States in terms of many of these measures. Ofcourse these differences might also be related to true differences be-tween countries using register data, notably Scandinavian countries,and the survey countries because of their different institutions, welfarestate, etc.

We have run a series of simple robustness checks in order to assesswhether, and how much, measurement error and the treatment of ex-treme data might be driving our observations. The checks consisted inre-estimating all our measures on alternative subsamples. One subsam-ple was composed of all available data with the exclusion of only nega-tive incomes. This first subsample was therefore larger than the one webased all estimates reported so far on. A second subsample was beingmore protective in the treatment of extreme data: we dropped fromour analyses observations of income growth based on an incomeabove the top percentile or beyond the bottom percentile in any of thetwo years. This is a relatively common strategy in incomemobility anal-yses. Considering that self-employment income is typically prone tomeasurement error, in a third subsample we also dropped all observa-tions with income that include some self-employment earnings (orprofits) in any of its components. Of course this reduces our samplesizes substantially (by between 15% and 45%, depending on country)and makes it not representative of the total population, but it allowsus to assess basic robustness of themain conclusions. Finally we consid-ered two subsamples from which we dropped all observations forwhich income is recorded has having been imputed by more than 10%or by more than 25% (or if household inflation factors have beenused). For obvious reasons, imputation introduces measurement errorand is likely to affect income change data. But the direction and magni-tude of the influence will vary with the imputation models used in thedifferent countries. Applying this deletion of imputed data further re-duced our samples to between 30% and 70% of the original sample(but note that for several countries, it was not possible to identify im-puted data reliably from the EU-SILC database and thesewere thereforedropped from this last robustness check).

To save space, we only summarize themain observations and do notreport detailed results here. The first lessonwe can draw from this exer-cise is that elimination of themost extreme data is needed for meaning-ful estimation of the type of measures we have used here. Our measuresare not robust (in a statistical sense) and seem indeed to be driven arbi-trarily large if we do not exclude the largest or smallest observations asin our first subsample. But estimation on the more conservative sub-sample than the one we primarily relied on did not further modify ourestimates in any significant way. Second, removing the influence ofself-employment income had relatively significant impacts, yet not ex-tremely large inmagnitude. In almost all cases, our various indices of in-come growth and mobility were reduced in size. The extent of thisreduction varied in different countries – with countries most stronglyaffected being Greece, Spain and Italy – but reassuringly the broad pat-terns of cross-country differences in the various dimensions consideredremained largely unchanged. Similar observations hold after removingthe imputed data. Finally, the results pointed again to the ‘register’/‘survey’ distinction. Register countries were affected in much smallerways by our redefinition of estimation samples. This suggests that dif-ferences observed in our main analysis between register countries andsurvey countries are likely to be related in a non-negligible way to dif-ferent influences of measurement error, and not just due to ‘real’, sub-stantive differences. Interpretations should therefore be cautious.

6. Conclusion

Analysis of the distribution of gains and losses and their impact onmedium-term inequality is worthy of investigation in its own right,

beyond inspection of annual, cross-section income distributions. Theavailability in EU-SILC of some longitudinal information on income fora broad set of countries is unique for this, and there is particular interestin monitoring the patterns of income dynamics in the most recent EUMember States. This paper has aimed to provide a first, broad-brush pic-ture of what early releases of EU-SILC can reveal on these questions.

While some empirical regularities are identified –such as regressionto the mean within and across countries or the limited inequality-reducing impact ofmobility in the short-run –, no clear picture emergesfrom the analysis, especially when we try to link individual mobility toindicators of poverty dynamics. Understanding the intertemporal distri-bution of income and how different aspects of it relate to each otherremains relatively complex, both conceptually and empirically. The lit-erature on the measurement of income mobility and inequality doesnot provide, to date, clear guidance or a unified framework about howthis issue should be analyzed. The approach adopted in this paper tolook primarily at the distribution of a particular individual incomechange indicator – namely the percentage growth in income – is oneof potentially many other strategies. Empirical difficulties, such as oneposed by measurement error and how it affects different aspects ofthe intertemporal distribution of income, also need to be faced. The im-pact of relying on register or survey sources for income appears non-negligible in this respect; this is of concern given the design of EU-SILC.

Our analysis exploits EU-SILC over the period 2003–2007: it stopsbefore the onset of the ‘Great Recession’. Early analysis of the distribu-tive impact of the crisis suggests that tax and benefit systems have pro-vided households with an effective cushion against adverse economicshocks (Jenkins et al., 2013). Yet, little is still known about the distribu-tion of household-level income variations and who has been mostseverely hit during the crisis and, perhaps more importantly, in theyears of slow growth and high unemployment which followed. Futureresearch on later releases of EU-SILC will help address these issuesfrom a European perspective.

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