NOT FOR CITATION WITHOUT AUTHORS PERMISSION Socal Coheson and the Dynamcs of Income n Four Countres Mles Corak, Wen-Hao Chen, Abdellatf Demant, and Denns Batten Famly and Labour Studes Statstcs Canada 24 th Floor, R.H. Coats Buldng Ottawa K1A 0T6 Paper Prepared for the Ffth Internatonal German Soco-Economc Panel Conference Berln, Germany July 3 and 4, 2002 * Mles Corak s Drector of the Famly and Labour Studes Dvson at Statstcs Canada and s also afflated wth Carleton Unversty as an adjunct professor of economcs and wth the Insttute for the Study of Labor (IZA) as a Research Fellow. Wen-Hao Chen s Research Economst wth the Famly and Labour Studes Dvson and a Doctoral canddate at Mchgan State Unversty. Abdellatf Demnat and Denns Batten are wth the Socal Surveys Methods Dvson at Statstcs Canada. The responsblty for the content of ths paper rests solely wth the authors and n partcular should not be attrbuted to Statstcs Canada. Comments may be sent to mles.corak@statcan.ca.
Abstract Longtudnal data from the Unted Kngdom, Germany, the Unted States and Canada are used to offer a comparatve analyss of the dynamcs of household ncome durng the 1990s, wth partcular attenton to both low- and hgh- ncome dynamcs. The analyss begns by offerng a broad descrptve overvew of the major characterstcs and events (demographc versus labour market) that determne levels and changes n adjusted household ncomes. Ths overvew s meant to offer a broad pcture of the state of household ncome n each country and the challenges faced by the welfare state. The paper then employs dscrete tme hazard methods to model the dynamcs of entry to and ext from both low-ncome and hgh-ncome. Both observed and unobserved heterogenety are recognzed but tradtonal methods based upon fxed ponts of support are extended to analyse mxtures of dstrbutons. These latent classes are nterpreted as the bass for dentfyng potentally excluded groups that rase challenges for the degree of socal coheson.
SOCIAL COHESION AND THE DYNAMICS OF INCOME IN FOUR COUNTRIES 1. Introducton The mportance of vewng the labour market from a dynamc perspectve s now accepted wsdom n both polcy and academc crcles. The avalablty of longtudnal data and the approprate analyss of t has helped to create a clearer pcture of North Amercan and European labour markets that relates drectly to polcy concerns. The most obvous example s the fuller understandng that has developed about the nature of low-ncome. Bane and Ellwood (1986) usng longtudnal data from the US are often cted as one example of a partcularly cogent portrat of the low-ncome populaton and the dynamc processes that determne entry nto and ext from poverty. The gradual avalablty of smlar data n other countres has spawned a wde lterature on ths topc, only the most recent examples beng Bradbury, Jenkns and Mcklewrght (2001), Jenkns (2000) and Stevens (1999). Whle ssues dealng wth low-ncome reman pressng concerns n many countres, broader but perhaps less well defned concerns have also recently come to the foreground. In part, these relate to the mpact of ncreasng ntegraton of product and labour markets durng the 1990s that have at once wdened the scope of the market n determnng famly ncomes and rased concerns about the role of the welfare state. The extent to whch natonal governments can ntervene to alter labour market outcomes s sometmes also related to the degree of socal coheson, and fears are often expressed that nequalty n labour market outcomes erodes ths mportant prerequste for collectve acton. In an analytcal sense t s not clear what exactly socal coheson means or what ts relatonshp s to other frequently used
2 concepts lke socal captal, and socal excluson. Implct n some dscussons s a reference to an underlyng sense of communty n a socety as well as the degree of support gven to collectve projects lke the welfare state as a scheme for socal nsurance. Ths dscusson s most developed n the European context and s reflected n the development of a host of ndcators by the European Unon as well as a set of specfc targets to reduce socal excluson (D Ambroso et al 2002, Stewart 2002). Income nequalty s certanly one mportant aspect of what s nherently a multdmensonal concept, and more unequal socetes are sometmes thought to be less cohesve. It s not, however, mmedately clear why ths should be the case wthout there beng at the same tme a clear understandng of the underlyng ncome dynamcs that determne the cross-sectonal ncome dstrbuton and the degree of nequalty. It s easy to magne that the welfare state wll have more broad based support f the ncome dstrbuton s very flud wth all ndvduals, regardless of ther current stuaton, facng smlar rsks of both enterng and extng low-ncome. In contrast, f the ncome dstrbuton s very rgd wth lttle movement nto or out of lowncome as well as nto or out of hgh-ncome then for the same level of cross-sectonal nequalty t mght be reasonable to suggest that a unversal scheme of socal nsurance wll not have as wde support. Ths mght be all the more so f the process determnng ncome dynamcs s very dfferent at the two extremes: f the rch perceve themselves as not really facng a rsk of lowncome but also of beng fundamentally dfferent from those who do. The objectve of our research s to nform these types of polcy concerns by buldng upon the lterature examnng the dynamcs of low-ncome to also study hgh-ncome dynamcs. We do ths n a comparatve way by focusng on North Amerca and two European countres n order llustrate the way n whch the underlyng determnants of market ncome dynamcs
3 condton the nature and scope of the tax-transfer system. We use longtudnal data from Canada, the Unted States, Germany and the Unted Kngdom and focus on developments durng the 1990s. The analyss begns by frst descrbng the statc characterstcs of the ncome dstrbuton n these countres durng the 1990s. An overvew of market ncomes durng ths perod reveals that the degree of nequalty s broadly smlar over tme and across place. But ths smlarty n market ncomes dsappears when taxes and transfers are taken nto account. Inequalty based upon net ncomes vares a good deal across the four countres. Ths forms the backdrop for our analyss: s t possble that the extent to whch governments alter market outcomes s determned n part by the nature of the underlyng dynamcs of market ncomes? There are two broad parts to our analyss: (1) an extensve descrptve overvew of market ncomes n the four countres; (2) an econometrc analyss of the determnants of low and hgh ncome spell dynamcs. The analyss s structured to answer the followng questons: (a) How s ncome earned? (b) What elements are most varable? (c) What s the extent of movement at the two extremes of the dstrbuton? (d) What are the causes of these movements? (e) Do these causes suggest there are fundamentally dfferent sub-populatons facng rsks of enterng and leavng both hgh and low ncome? The descrptve overvew follows Jenkns (2000) and examnes the major characterstcs and events that determne levels and changes n adjusted household ncomes, payng attenton to movements nto and out of low ncome but also hgh ncome. The econometrc analyss of these movements extends the dscrete tme hazard models n the manner of Stevens (1999) and
4 Heckman and Snger (1984). Both observed and unobserved heterogenety are controlled for wth the ntenton of nformng dscussons about the fundamental dfferences between groups at the two poles of the ncome dstrbuton. The analyss s based upon mxtures of dstrbutons and allows the nfluence of unobservables to be reflected not only n the number of fxed ponts of support but also dfferent parameter estmates across these ponts. The analyss uses data from the Cross-Natonal Equvalent Fles of the Brtsh Household Panel Survey (for the UK), the German Soco-Economc Panel (for Germany), the Panel Study of Income Dynamcs (for the US), and the Survey of Labour and Income Dynamcs (for Canada). Wth the excepton of the Canadan data these are all relatvely long panels that permt n the least an assessment of ncome dynamcs for the 1990s. All of these data are dscussed n much more detal n the followng secton. A descrptve overvew of ncome dynamcs s offered n sectons 3 and 4, whle the econometrc methodoology s descrbed n secton 5 along wth the results. 2. Data Sources and a Descrptve Overvew The data come from the Cross-Natonal Equvalent Fles (CNEF). The CNEF brngs together multple waves of longtudnal data from Canada, Unted States, Great Brtan, and Germany. Varables across the surveys have been defned n a smlar manner n order to encourage crossnatonal research. Burkhauser et al (2000) offer a detaled descrpton of the CNEF. The current panels avalable n CNEF nclude the Canadan Survey of Income and Labour Dynamc (SLID, 1993 to1999), the Unted States Panel Survey of Income Dynamcs (PSID, 1980 to 1997), the Brtsh Household Panel Survey (BHPS, 1991 to 1999), and the German Soco-Economc Panel (GSOEP, 1984 to 2000). A key advantage of the CNEF s that t provdes relable estmates of
5 annual ncome varables that are not drectly avalable on the orgnal data sets. It ncludes preand post-government household ncome, estmates of annual labour ncome, assets, prvate and publc transfers, and taxes pad at household level. The avalablty of nformaton on each household ncome source allows a full pcture to be developed of the relatve roles of market, famly, and state n determnng ncome levels (OECD, 2001). The other beneft of the CNEF s that t uses the most mature of a number of longtudnal surveys across the OECD countres and therefore provdes relatvely long panels of nformaton. The SLID s the one excepton. Ths s a result of ts rotatng sample desgn. SLID conssts of two overlappng samples, each of whch s followed for only sx years wth the last of three years of the older panel overlappng wth the frst three years of the newer panel. 1 Economc well-beng for each household member depends on the total household ncome level as well as household composton. We use both market and post-tax post-transfer defntons of ncome, but emphasze the former. 2 The sharng unt s the household (persons lvng n the same household whether or not they are related to each other by blood or marrage). The annual household adjusted ncome s defned as the rato of total household ncome to the square root of famly sze. Ths can be regarded as an estmate of potental ncome for each household member under the assumpton of equal sharng. One advantage of usng annual 1 SLID has the advantage of offerng a much larger sample sze, n the neghbourhood of about 30,000 ndvduals. The sample szes from the other countres vary from about 4,000 for the BHPS to about 8,000 for the PSID. In future work we ntend to supplement the SLID nformaton by also usng the Longtudnal Admnstratve Data (LAD) from tax fles. The LAD s a 10 percent sample of Canadan tax flers followed as ndvduals over tme and matched nto famly untes on an annual bass. It offeres demographc, ncome and other taxaton data for ndvduals as well as ther famles for 1982 to 1998. 2 For the CNEF we do not use the post-government varable due to the nconsstent defnton across natons. Instead, we defne our own Total household net ncome varable equal to the sum of household labour ncome, asset ncome, mputed rent, prvate and publc transfers, socal securty pensons, prvate retrement pensons, and total household taxes for all countres.
6 ncome rather than ncome at the tme of ntervew s that t avods temporarly hgh or low ncome and more accurately reflects the annual economc well-beng of ndvduals. There s no one defnton of low-ncome n the four countres we are examnng, the US beng the only one wth an offcal poverty lne. Our analyss uses relatve measures of low and hgh ncome based upon the ncome dstrbuton n each country n a gven year snce socal coheson s tself an nherently relatve concept. Indvduals are defned as beng n low ncome f ther household adjusted ncome falls below 50% of the natonal medan n the frst year of the analyss; they are defned as beng n hgh ncome f ther household adjusted ncome s above 150% of the natonal medan. 3 Though n large measure the CNEF data are based upon consstent defntons across all four countres, there are stll some dfferences that should be kept n mnd. Households are not defned n exactly the same way n most of CNEF countres, nor are household heads. We modfy some of the varables n order to use concepts that are as consstent as possble across all of the data. A summary table outlnng these and other dfferences between the country data sets s appended as Appendx Table 1. The samples are meant to be representatve of all ndvduals n the populaton ncludng chldren and non-workng people. Data from 1990s are drawn from CNEF for each country. Tables 1a and 1b show summary statstcs of the household adjusted market ncome dstrbuton and ncome after-taxes and transfers durng the 1990s. The data are adjusted for nflaton and expressed n each country s own 1997 currency. Wth respect to market ncome summarzed n Table 1a, real medan ncome grew only modestly durng the 1990s n all four countres. The degree of nequalty s ndcated by the Gn 3 In actual fact we preclude small transtory fluctuatons n ncome from causng movements across these thresholds by requrng the ncome change to be 10 per cent beyond the hgh or low ncome threshold.
7 coeffcents and ratos between the 90 th and 10 th percentles, as well as the 90 th and 50 th for the upper part of the ncome dstrbuton and 10 th and 50 th for the lower part. The Gn coeffcents range between 0.42 and 0.44 n Canada and the UK, are slghtly hgher n Germany (0.44 to 0.47) and a bt hgher stll n the US (0.45 to 0.49). [ There are a number of peculartes n the 90-10 ratos. In the US there s a sharp rse between 1993 and 1994 reflectng both a drop n the 10-50 rato n 1994 and a rse n the 90-50 rato n 1995. Ths may be due to qualty problems n these data. The 90-10 ratos n Germany are much hgher than all the other countres rangng from 55 to 64 between 1992 and 1994, but over 100 n 1995 and reachng 200 n 1999. If we exclude those ndvduals over 60 years of age ths rato falls to the neghbourhood of 14 or 15. As such the very hgh rato seems to be related to the market stuaton of those over 60 years of age, but we are not clear why ths should have changed over the perod. Once taxes and transfers are nclude the anomaly dsappears and ths also leads us to beleve that the hgh market ncome ratos have to do wth the absence of any market ncome among the elderly and the operaton of the penson system n Germany. ] Smlarly low-ncome rates are about 25 to 27% n Canada and the US, and a lttle hgher n the two remanng countres, though they fall slghtly n the UK after about 1994 and rse n Germany. Hgh ncome rates are roughly 30% or a lttle less n all of the countres wth a tendency to rse wth tme. Generally nequalty n market ncomes does not vary dramatcally across the countres. Perhaps on the bass of the Gn coeffcents Canada s relatonshp wth the US s roughly smlar to that between the UK and Germany. The pcture s dfferent wth respect to net ncome, as llustrated n Table 1b. The Gn Coeffcents are sgnfcantly lower n Canada, the UK and Germany, but less so n the US. The Gn s about 0.3 n Canada, a bt hgher n the UK and a bt lower n Germany. In the US t s 0.36 to 0.41 [ though the hgher fgures after 1993 may agan reflect a data ssue.] Ths same
8 general pattern holds for the 90-10 rato, whch are always below 4.0 n Germany, but never below 5.0 n the US. Canada s closer to the German standard than the UK. The pattern also holds for low-ncome rates though the dfferences are more stark. Low-ncome rates are for the most part about 10% n Germany, about 11 to 13% n Canada, hgher n the UK (though fallng sgnfcantly n the later part of the decade), and hgher stll n the US where t approaches 20%. Comparng these rates to those n Table 1a suggests that the tax-transfer systems reduce lowncome rates by more than 10 percentage ponts n Canada and the UK, but that Germany and the US stand out. The tax-transfer system reduces low ncome rates by as much as 20 percentage ponts n Germany, but n contrast only n the order of 5 to 6 percentage ponts n the US. The pattern s smlar but more muted wth respect to hgh ncome rates: four to fve percentage pont reductons n most countres, but up to eght n Germany. [ Cauton s stll very much n order n makng these cross-natonal comparsons as the treatment of taxes may dffer, ths s partcularly the case n the Unted States where the reportng and assgnment of taxes s done dfferently, beng based upon a smulaton model. Ths s one reason for the focus on market ncomes n much of what follows.] At a very broad level the man message from ths nformaton s that market ncomes are not drastcally dfferent between the countres wth Canada standng roughly n the same relaton to the US as the UK does to Germany. Germany s the only country to experence growng lowncome rates yet t does sgnfcantly more redstrbuton than any of the other countres. The US does the least to redstrbute ncomes and reduce low-ncome. Ths message s stll approprate when a dynamc vew s taken of the data. Tables 2a and 2b offer a pcture of the ncdence of low and hgh ncome usng a number of dfferent defntons n order to capture developments over a sx year perod. Ths nformaton reveals the degree to whch the rsk of experencng
9 low or hgh ncome s equally shared across the entre populaton, or n another sense the degree to whch there s a potental empathy for the plght of low-ncome ndvduals. The focus n Table 2a s on market ncomes. 4 The ncdence of at least one year of lowncome s very hgh across the four countres. About 40% of ndvduals have touched lowncome at least once, the Canadan and UK rates beng only slghtly lower than the US and German. However, ths rsk s much lower when longer term measures of the ncdence of lowncome are used: low ncome n all sx years, and low ncome based on the average ncome over sx years (referred to as permanent ncome n the tables). In both these cases the US has lower rates than the other countres but Canada s not too dfferent. The ncdence of low-ncome usng permanent ncome s about one-ffth n North Amerca but about one-quarter n Europe. A consderable fracton of the populaton faces the rsk of experencng at least a transtory bout of low-ncome; a somewhat smaller though stll sgnfcant fracton faces the chance of a long-term spell or seres of spells. These data begn to develop the suggeston that there are dfferent subgroups n the populatons of these countres. On the one hand when the focus s on ncdence there s the potental for a great deal of empathy wth low-ncome ndvduals because a sgnfcant fracton of the populaton faces ths rsk; on the other hand when the focus s on severty the degree of empathy s lkely to be much less and depend very much on the determnants of long spells and the extent to whch other groups feel they face the same stuaton. The chances of attanng hgh-ncome are greater: n North Amerca 50 to 55% of the populaton had at least one year n hgh ncome; n Europe about 45%. The ncdence of hgh 4 The results n Tables 2 and also n Tables 3 are based on persons who were present n the surveys for all years between 1993 and 1998 (1991-1997 for US).
10 ncome based on longer term measures s about the same across all countres: 14% for hgh ncome n each of sx years, and not qute 30% for permanent ncome. Table 2b offers smlar nformaton but on the bass of after tax after transfer ncome. The ncdence of at least one spell of low-ncome over sx years vares consderably more under ths defnton than t does under market ncome. In Germany the rsk falls by more than half: from 43% to less than 20%. The tax-transfer system also sgnfcantly reduces the rsk n Canada and the UK, by 15 and 12 percentage ponts respectvely, but only by 7 percentage ponts n the US. The longer-term measures of low ncome are much reduced n all the countres but most sgnfcantly n Canada and Germany. Wth respect to hgh ncome, Canada, the UK and Germany all dsplay very smlar patterns about 37 to 38 % experence hgh ncome at least once, about 9% n all sx years and about 7 to 8% on the bass of permanent ncome. The US s the clear outler wth the tax-transfer system dong lttle to alter market outcomes. Tables 3a and b dsplay the average annual transton rates over these same years across the ncome dstrbuton. Indvduals are classfed nto ncome groups accordng to the sze of ther adjusted ncome relatve to fxed year 1 medan ncome. The top panel n Table 3a shows the annual outflow rates from year t-1 ncome group to year t ncome group for market ncome; the bottom panel the nflow rates. Overall there s consderable movement throughout the ncome dstrbuton wth nflow and outflow rates rangng from 20 to as hgh as 40% n some cases. However, those n the two tals of dstrbuton are lkely to stay n the same ncome group over tme. For nstance, n Canada over four-ffths of those n the lowest and hghest ncome categores (less than 50% of year 1 medan ncome and greater than 1.5 of year 1 medan ncomes) reman n the same category n the followng year. The low-ncome ext rate s about 20% n North Amerca and but 15% n Europe. Only n Canada are outflow rates greater than
11 nflow rates, but only slghtly so. Generally market dynamcs mply a constant or growng proporton of low-ncome ndvduals. The outflow rate s only slghtly greater than the nflow rate n the UK, but more notceably so n the other countres. Ths s partcularly the case n Germany. On an average annual bass 18% of the low ncome populatons entered ths state durng the past year, but only 14% left. Ths leads to the growng stock of low ncome ndvduals llustrated n Table 1a. Table 3b offers the same nformaton on an after-tax, aftertransfer bass, and llustrates n Germany a reversal of magntudes wth outflow rates greater than nflow rates. In a sense the German welfare state has to work overtme. Market forces are generatng net nflows that are reversed by the tax-transfer system. In Canada the welfare state has been gvng some breathng room by market forces. The challenges to the Canadan welfare state seem to come more from hgh ncome dynamcs. The hgh ncome populaton s clearly growng, most substantally n Canada: less than 17% of hgh-ncome ndvduals fall out of hgh-ncome but 19% move n each year. No other country dsplays such a dfference between outflow and nflow rates, though there s a tendency for the nflow rates to be greater than the outflow rates. Table 3a also dsplays a movng up trend for the upper mddle ncome groups. For those just above the low ncome threshold (0.5 to 0.75 of the medan) the nflow from and outflow to low-ncome are roughly the same and there s a tendency for the outflow upward to be slghtly greater than the nflow from above. Ths pattern, however, s much more notceable for the movements to and from the other categores (0.75 to 1.5): nflows from below domnate outflows downward, and outflows upward domnate nflows down. In other words, the mddle groups are dong better n terms of earnngs, whle the lower mddle and low-ncome group reman roughly
12 the same. In all countres there has been a tendency for the mddle ncome groups to progress upwards whle the lowest and hghest groups show much less moblty. 3. The sources of Income and ther Varablty We explore the dynamcs of ncome n more detal by examnng the varablty of each of eght consttuent components of total annual ncome followng Jenkns (2000). The nformaton n Table 4 sets the stage for ths dscusson by offerng sx year averages of total ncome and the components by the ndvdual s 1993 household type. The sum of the shares of each ncome component n total household ncome s 100%. 5 (Taxes are consdered an ncome source wth negatve contrbuton.) Overall, head s labour earnngs account for the largest share of household ncome component, rangng from 42% n UK to 73% n the US. The lower UK fndngs could result from dfferences concernng the defnton of a household head. Secondary labour earnngs n a household are also mportant, and they account for about a quarter of total household ncome on average. The mportance of ncome sources other than labour earnngs vares across dfferent household types and also across natons. Generally, dsadvantaged groups rely on market sources of ncome to much greater extent n the US. In Canada as well as n Brtan, more than 20% of ncome n lone parent households come from publc transfers. Ths s 15% n Germany but only 7% n the US. In both the US and Germany about 70% of the ncome of Lone Parent famles s derved from the Head s labour earnngs, n Canada and notably n the UK ths s lower. Smlarly, 30 to 40% of ncome n elderly households n most of the countres comes from socal securty penson, but the fgure s almost 70% n Germany. Elderly households n many countres also rely heavly on assets and transfers from non-household members. In 5 The shares do qute sum to 100% n the US and UK due to nconsstent nformaton on ndvdual labour earnngs n both country s data.
13 Canada and the US about 50% of ncome n senor households comes from assets or prvate transfers. 6 Two parent households wth chldren receve slghtly over 7% of ther ncome from publc transfers n Canada, the UK, and Germany, but less than 2% n the US. The publc transfer system also plays lttle role n supportng sngle US households. To explore longtudnal varablty n ncomes, two methods followed by Jenkns (2000) are used n Table 5. The frst deals wth the longtudnal varablty of Personal Equvalent Income, net ncome, household sze, and the equvalence scale. Ths can be characterzed usng the coeffcents of varaton (CV) for these varables. The CV s the spread of the dstrbuton relatve to ts mean and s calculated longtudnally over sx year perods for each person as follows: CV n x = σ, (2) n x where n σ x and n x are the standard devaton and mean respectvely for varable x over sx-year observatons for person n. The second method nvestgates the contrbuton of each ncome component to the total varablty of household net ncome. Here, we use the varance as a measure of total varablty, and the so-called β coeffcent. As suggested by Shorrocks (1982), let k Y denote the ncome of ndvdual from source k, and let total net ncome Y = k Y k. Then, for each ndvdual, the varance of total net ncome over 6 years perod s: σ 2 Y = k σ 2 k + j k k ρ σ σ jk j k (3) 6 Notce that the shares of each ncome components are not qute comparable across natons. For example, one mght wonder why Canada has a lower tax burden (24.7%) then the US (28.7%). One possble reason s that payroll taxes are not ncluded n Canadan data but are n the US data. Besdes, the dfferent defntons of head, household, and ncome components would possbly alter the actual shares and makes cross-country comparson more dffcult.
14 where ρ jk s the correlaton coeffcent between ncome component component, the contrbuton to net ncome becomes: j Y and k Y. For each σ 2 ky k 2 = Cov( Y, Y ) = σ + ρ σ σ (4) k j k jk j k It s also useful to standardze the varablty measure. We defne varablty contrbuted by component k, and the sum of these s equaled to 1. s * s k as the proporton of total 2 K 2 σ ky Cov( Y, Y) σ ) =, σ s * 2 k ( ) = 1 Var( Y ) σ. (5) * k ( = 2 Y As ndcated n equaton (5), the measure of k * s k s the same as the slope coeffcent from a sxobservaton regresson of the gven ncome component on total net ncome for each person. The frst and second rows of Table 5 provde nformaton of longtudnal varablty for household adjusted ncome as well as for household net ncome as measured by the CV. For each country the longtudnal varablty n household adjusted and net ncome s larger for sngle as well as for lone parent households, whle s relatvely stable for couples and elderly households. Across countres ncome s most varable n the US and least varable n Germany. In the US lone parent famles have partcularly volatle ncomes wth CVs of about 0.40, much hgher than any other groups n any other countres. Lone parents n the UK face a roughly smlar stuaton but have much more stable ncomes n Canada and Germany. (It should also be noted that n the US they make up over 17% of all persons, but less than half that n the other countres.) The mddle rows of Table 5 provde the β coeffcents for each ncome component. The patterns are consstent wth those shown by ncome share n Table 4. On average, head s labour ncome contrbutes the largest proporton (0.32 to 0.58) to longtudnal varablty n household net ncome. However, t s worth notng that although the secondary labour earnngs (spouse and others) account for about 30% of ncome share, they contrbute a sgnfcant proporton (0.25 to
15 0.35) of longtudnal varaton n net ncome, wth Germany beng at the upper extreme. Ths ndcates that changes n secondary labour earnngs also play an mportant role n determnng ncome transtons. Ths s especally the case for couples and chldren. In the households wth an elderly head, the changes n asset and prvate transfer are the major source of longtudnal varaton n household net ncome (except Germany). Asset and prvate transfers together make up at least 41 to 77% of longtudnal varaton n net ncome among the four countres. However, n Germany, 59% of ncome changes n elderly households are due to the changes of ncome from socal securty pensons, and only 21% are due to the changes n assets and prvate transfers. The hgh contrbuton of socal securty penson to longtudnal ncome varaton along wth ts hgh ncome share mples that the ncome transtons for German senors are greatly dependent on ther government penson and welfare status. For lone parent famles changes n other famly labour earnngs represent an mportant source of rsk, consstent wth the fact that household dssoluton and formaton are the major causes of both enterng and leavng lowncome among ths group. Ths s partcularly so n Germany, where 40% of the varablty n ncome for ths group s accounted for by other famly labour earnngs. (The longtudnal varablty of demographc events are located at the bottom rows of the table. Households wth sngle and lone parent appear to have relatvely greater longtudnal varatons n both household sze and equvalence scales.) Publc transfers are also an mportant dmenson of the varablty of ncome for ths group. In Canada, the contrbuton of publc transfers to longtudnal ncome varablty (0.11) s a lot smaller than ts share (0.21). Ths mght ndcate that the transfer system contrbutes to bufferng household ncome from changes due to other more volatle components. Ths s also the case n Germany and less so n the UK.
16 In sum ncomes are most volatle n the US and least volatle n Germany, but n all countres the major source of varaton over 50% s due to the heads labour earnngs. The excepton to ths s elderly households where market rsks are reflected n asset ncome and prvate transfers (wth the excepton of Germany), and lone parent households where demographc events are mportant. 4. The Extent of Movement at the Two Extremes of the Income Dstrbuton and ther Causes How do these average patterns n the varablty of ncome translate nto dynamcs nto and out of low and hgh ncome, and what are the underlyng causes? We approach ths queston n ths secton by offerng emprcal hazard rates of the assocated transtons and provde an overvew of ext and re-entry rates for both low and hgh ncome. In addton, ncome transtons and ther concdent events are examned to assess the mportance of the roles of market condtons, famly, and the state. Data s transformed nto a person-year format where one person has potentally multple records, each correspondng to a year n a partcular state. The sample covers every person wth non-left censored spells. For the tme beng f one person has more than one spell, both spells are ncluded and treated ndependently. To avod potental measurement errors, small ncome changes between ncome cutoffs are not consdered as a transton. 7 Fgures n the followng tables are based on unweghted statstcs, however persons who have zero crosssectonal weghts are not ncluded. Table 6 shows Kaplan-Meer estmates of low ncome ext and re-entry rates. We assume that all persons start a spell that wll last for at least one year. As a result, there s no transton rate for the frst year. In all of the countres more than one-thrd of people (36 to 47%) are able to 7 Persons whose post-transton earnngs rse (fall) by not more than 10% above (below) low ncome lne are not consdered as an ext (re-entry). A smlar defnton s used for hgh ncome transtons.
17 leave low ncome after one year, but the ext rate s lower n North Amerca than Europe. The ext rates then fall further as the tme spent n low ncome ncreases and reach about 0.2 at the ffth year of low ncome, the UK beng the excepton experencng a rse n the ext rate between the fourth and ffth years. In the UK and Germany less than one-ffth of low-ncome spells are stll n progress by the ffth year, but almost one-quarter n Canada and almost one-thrd n the US. Low-ncome spells last longer n North Amerca. The bottom panel of Table 6 shows the low ncome re-entry rates for low-ncome persons who start a non-low ncome spell. In the US, as many as 25% of people fall back nto low ncome after one year, whle the fgures are only 10 to 15% n the other three countres. In the longer term, almost one-half of those leavng low ncome n the US wll have experenced another spell wthn fve years, compared to about 30% n Canada and the UK and only 25% n Germany. The chance of fallng back nto low ncome drop sharply as survval tme n non-low ncome ncreases. The re-entry rates at the end of the ffth year drop to 6% n Canada, below 5% n UK and Germany, and to about 10% n the US. Combnng both ext- and re-entry rates gves a more comprehensve vew of the low ncome dynamcs. Persstent low-ncome s more acute n the US and s the result of both lower ext rates and hgher re-entry rates. In the UK a great percentage (94%) of those enterng lowncome are able to escape wthn eght years. However, as hgh as 41% fall back durng the subsequent eght years. Germany has both the hghest ext rates and lowest re-entry rates after fve years. Although a larger fracton of the German populaton reman n low ncome after eght years than n the UK (12% versus 6%), the rate of re-entry s much lower (71% of ndvduals who left low-ncome stll have not fallen back n after eght years versus 59% n the UK). In fact
18 the German re-entry rate after eght years s comparable to that after fve years n Canada and after only two years n the US. There s much more persstence n hgh ncome. The ext and re-entry rates for hgh ncome transtons are presented n Table 7. For each country about 45 to 50% of ndvduals reman n hgh ncome by the ffth year after a start of a spell, Canada and Germany beng at the upper end of ths range. Except for the US ths s more than double the low-ncome ext rate for each country. The US s unque n that t appears to combne a hgh degree of persstence for both low and hgh ncome, there beng much more varaton n low-ncome persstence across the countres than n hgh-ncome persstence. The re-entry rates back nto hgh ncome after a spell has ended are about the same as the low-ncome re-entry rates n North Amerca, but hgher n Europe. In Canada and Germany only slghtly more than 30% of spells moved back nto hghncome after fve years, but n the UK about 40% and n the US about 50%. In order to assess, n a descrptve way, the underlyng causes of these transtons we assgn each person who experences an ncome transton to one of 15 mutually exclusve groups. (Left-censored spells are excluded). The approach follows Jenkns (2000) and s summarzed n Fgure 1. For each spell we frst determne f there was a change n famly structure, and refer to stuatons n whch there s a change n household head concurrent wth the transton as a demographc event. The type of demographc event s then determned. On the other hand, f there s no change n famly structure (same head, same sze) the transton s classfed as an ncome event, and categorzed accordng to whch ncome source changed the most durng the transton. If the famly head remaned the same but the sze changed two possbltes are allowed. The transton s consdered an ncome event f the percentage change n household net
19 ncome s proportonately greater than the percentage change n equvalence scale. Otherwse, t s a demographc event. Tables 8 and 9 dsplay low ncome spell endng and begnnng types respectvely by person s household type. The strong majorty of low ncome spells end because of an ncome event but there s consderable varablty across the countres. In Germany these events account for almost 85% of all spell endngs, n the US and UK the comparable fgure s 75%, but n Canada t s 65%. In the US and UK ncome events account for roughly the same fracton of spell begnnngs as they do endngs, but n Canada and Germany demographc events play a more promnent role n determnng the start of low-ncome spells, though the majorty contnue to be caused by ncome events. In Canada about 56% of spells start because of an ncome event (versus 66% that end for ths reason), and n Germany the comparable fgure s 66% (versus 84% for spell endngs). The rsk of low-ncome s n the frst nstance an ncome event, but t s much more lkely to be demographc n Canada and Germany than n the other two countres. Amongst ncome events, changes n labour earnngs (especally heads ) are the leadng causes of transtons across non-elderly/lone parent households n all countres. Changes n socal securty pensons are the most common event assocated wth low ncome endngs for households wth an elderly head n Canada and Germany (35 and 53% respectvely). However, senors n the UK are lkely to rely on publc benefts (32%), whle older households n the US are lkely dependng on assets/prvate transfer (30%) to escape low ncome. In Europe publc benefts provde greater help for lone parent households to get out of low ncome; ths s less lkely to be the case n the North Amerca. For example, nearly 23% of all low ncome endngs n UK are concdent wth an ncrease n publc transfer. On the contrary, most lone parent households (over 40%) n the US rely on labour ncome to escape low ncome.
20 Turnng to demographc events, a greater percentage of lone parents n Canada (33%) and n the UK (25%) left low ncome because of marrage or partnershp, whle the proportons are only 17% n the US and 12% n Germany. Undoubtedly, separaton and dvorce are the major reason for begnnng a low ncome spell for current lone parents n all countres but ths s more so n North Amerca. In Canada, 47% of low ncome spells for lone parents begn because of separaton or dvorce, n the US 35%, but n the UK and Germany only 24 and 28% respectvely. Tables 10 and 11 show the events concdent wth hgh ncome transtons. Income events are the major reason for hgh ncome transtons. The labour ncome of the secondary earner s as mportant as head s labour ncome n determnng hgh ncome endngs and begnnngs. Hgh ncome spells are even more lkely to begn because of ncome events: 87% of such spells n Germany do so, 84% n the US and 70 to 76% n Canada and the UK. Double earners n a household are an mportant factor n attanng hgh ncome, but ths s less lkely to be the case n the US. Changes n the head s labour earnngs are stll the leadng event assocated wth hgh ncome spells begnnng or endng n the US (for non-senor couples). Hgh payng jobs propel US famles nto hgh ncome. Income events other than those assocated wth the labour market have a smaller mpact on hgh ncome transtons across most of the household types for all countres. In households wth elderly heads, changes n asset/prvate transfers play an mportant role n determnng hgh ncome transtons. For example, as much as 50% of all hgh ncome spell begnnngs n the US are because of an ncrease n ths category. Compared to ncome events, the number of demographc events concdent wth hgh ncome transtons are lower. (In fact many of these calculatons are based on less than 30 observatons.) In general, a newly establshed famly as well as a rse n needs are the leadng
21 reasons for the endng of hgh ncome spells. Notce that newly establshed famly refers to people who leave a household to start a new one, whle a needs rse refers to the same household wth addtonal people jonng. 5. The Exstence of Dfferent Sub-Populatons Our econometrc analyss of these transtons s desgned to uncover the extent to whch these overall patterns reflect the exstence of fundamentally dfferent subpopulatons. To ths end we generalze the approach used n Huff-Stevens (1999) by castng the econometrc analyss n terms of mxtures of dstrbutons. That s, we extend the treatment of unobservables n the economcs lterature from an assessment of fxed ponts of support to a mxture of dstrbutons wth not only the constant but all of the coeffcent values varyng across the subpopulatons. The objectve of the exercse s to establsh the degree to whch the model determnng the transton process characterzes the entre populaton or f there are dfferent models for dfferent subpopulatons. Ths s done condtonal on a set of co-varates. That s to say, condtonal on a set of ndvdual crcumstances are there stll underlyng dfferences n the processes determnng these transtons and n what manner s the populaton sub-dvded across these processes? If the model determnng transtons nto and out of low and hgh ncome s fundamentally dfferent across a number of dfferent sub-groups t may be that some groups see themselves as dfferent than others n terms of the rsks to ther ncome status. Ths would suggest a less cohesve populaton and the presence of excluded groups. Ths s the nterpretaton we gve to the presence of unobservables, or as we term them latent classes, n the estmaton of the hazard rates determnng low and hgh ncome dynamcs.
22 The nfluence of latent classes wll depend upon the explanatory varables ncluded n the model. In the estmatons that follow we actually offer two sets of estmates based on two dfferent sets of explanatory varables. The frst set ncludes (n addton to elapsed duraton and year effects) ndcators for age, famly structure, and gender. All other nfluences are consdered latent. That s to say the dfferences across famly structures outlned n the prevous tables are taken nto account. As the dscusson surroundng Table 5 suggests, volatlty n ncomes vares by famly structure. We control for ths and examne ncome dynamcs net of famly nfluences. Hgh ncome transtons are domnated to a greater degree by ncome events than low-ncome transtons. So t s certanly possble that hgh ncome ndvduals may see themselves as dfferent from others on the bass of demographc decsons, partcularly wth respect to ssues surroundng separaton, dvorce and chld bearng. Ths has certanly been part of the debate over the role of publc transfers n the US. Even so ncome events are the major reason for transtons for all groups and as such our analyss takes ths focus and should be consdered as an assessment of the role of market forces net of demographc crcumstances. 8 Further, the sharp dstncton between these two types of causes may not be totally approprate. To some extent demographc events are endogenous and could be the result of ncome events. The second set ncludes all of these varables wth the addton of educaton and an ndcator for belongng to what at least n Europe are consdered to be a potentally excluded group. Ths latter varable vares across the countres. In the US t s an ndcator of race (whether the ndvdual s black or not); n Canada t s a vsble mnorty ndcator; n the UK an ndcator of race; and n Germany three separate ndcators of whether the ndvdual s a guest worker, East German, or an 8 Also the prevous analyss has uncovered very dfferent approaches to the support of the elderly and chldren. We also net out these nfluences by controllng for age.
23 Immgrant (after 1984). 9 We are nterested n determnng the extent to whch the results change by addng a choce varable mportant n the ncome determnaton (educaton), and drect ndctors of characterstcs often consdered to be the bass of socal excluson. If the results are not senstve to these choces ths may suggest that excluson may be a more dffcult ssue to address than by the standard polcy decsons drected to human captal choces and dscrmnaton. a. Econometrc Method Let t y, = 1... n be the outcome for ndvdual at tme t, t = 1... T, where y = 1 f t t the th ndvdual makes a transton at tme t and y = 0 otherwse. We assume that the condtonal probablty of success at tme t s modeled as a logstc dstrbuton wth t p = log t( x β ) where logt ( a) = exp( a) /(1 + exp( a)), t t x s a 1 p vector of ndependent varables and β s p 1 vector of parameters. We are nterested n makng nferences about β. If each ndvdual s observed T tmes untl a transton or rght censorng occurs the lkelhood functon for ndvdual under-ndependence s T = L f t= 1 t, where t t t t 1 y t y = (1 p ) ( p n f ) case of a Bernoull dstrbuton wth t p as parameter. The estmaton of β can be made by standard statstcal packages and obtaned teratvely usng Newton-Raphson or Fsher scorng method. The estmator βˆ s the soluton of an estmatng equaton of the form t t t U ( β ) = u ( β ), where u ( β ) = ( y t p ) x n the case of ndependent Bernoull 9 The models for the UK do not nclude an ndcator for educaton. In the other countres ths s controlled for by creatng ndcator varables for less than and more than 12 years of educaton.
24 dstrbutons. When nterest s n two events or more the above formulaton contnues to hold. For example when consderng smultaneously the condtonal probablty of extng low ncome and the probablty of re-enterng low ncome, t 0 1 t-1 0 1 λ λ 1 q 1 q all that s needed s to redefne the vector of ndependent varables. Let t z be the new vector of t t t ndependent varables of order ( 1 2 p) wth z = x,0) for extng low ncome and z = (0, x ) T T T for re-enterng low ncome, where 0 s ( 1 p) vector 0 s. Let β = β, β ) be the new vector ( t ( 1 2 of parameters of order ( 2 p 1). Each probablty can be wrtten n term of t z and β, t t t λ = log t ( x β 1 + 0β 2 ) = p and q = log t(0β 1 + x β 2 ) = p. t t t We seek to dentfy ndependent varables that predct the probablty of a transton. However, condtonal on ths choce the probablty of a transton may also be nfluenced by a latent class and as dscussed above ths s also an mportant part of the story we wsh to address. An unobservable dscrete varable ndcates the latent class of the th ndvdual. The varable s assumed to take G dstnct values, each of whch corresponds to a dstnct transton probablty. The condtonal probablty of success gven that an ndvdual s n group g can be modeled, as t t s tradtonally done, wth common slopes as p = logt( α + x β ), where α g represents the g effect of latent group g. The dentfcaton of the latent class effect s statstcally equvalent to g
25 determnng whether α g dffers across latent groups. Mxture of dstrbutons framework,whch covers ths specal case, s used when the data can be vewed as arsng from two or more populatons mxed n varyng proportons. Each observed y s drawn from a super-populaton P whch s a mxture of a fnte number, say G, of populatons P,..., P n some proportons 1 G g π 1,...,π G, wth π = 1 and π 0, g = 1,..., G. Gven the data, and a known form of the g g dstrbutons, we wsh to estmate the model parameters and the mxng dstrbuton. Mxture of dstrbutons can be handled by usng the Expectaton Maxmzaton (EM) algorthm (Dempster, Lard, and Rubn 1977). The maxmzaton can be mplemented usng standard software. Ths can be acheved by essentally creatng G copes of the data and then usng the condtonal probabltes as weghts. The calculaton of the weghts and the estmaton of the parameters are repeated untl convergence. Defne the latent groups membershp ndcator varables as z = 1 f g P g and z = 0 f P. The EM algorthm s appled to the mxture of dstrbutons by g g treatng the varable z g as mssng data. The log-lkelhood for the complete data s gven by l c = zg (logπ g + log fg ), where ( 1 T f g = fg y,..., y β, g). Usng some ntal value for g (m) φ ' = ( β ', π '), say φ, the E step requres the calculaton of the pseudo complete log-lkelhood ( m) ( m) based on the ncomplete data Q( φ, φ ) = E( lc y, φ ). That s, each ndcator varable z g s replaced by ts expectatonτ g, condtonal on (m) ( m) ( m) ( m) ( m) ( y, φ ),where τ = π f ( β ) / π f ( β ). g g g j j ( m+1) (m) The M step ntent s to choose the value of φ, say φ, that maxmzes Q( φ, φ ) subject to j j g π g = 1. To accomplsh the maxmzaton step for each EM teraton, t suffuses to solve the
26 followng estmatng equaton τ g log f g / β, and get the subsequent estmate of g π g as follow, π g = τ / τ. A convergence crtera s ( m ) ( m+ 1) max φ φ < ε based on g g g the parameters because the lkelhood s may be flat n some drectons. One lmtaton wth the analyss of non-gaussan longtudnal data s the lack of a rch class of models such as the multvarate Normal for the jont dstrbuton of y = y,..., y )'. ( 1 T The generalzed estmatng equatons (GEE) proposed by Lang and Zeger (1986) allows regresson modelng of longtudnal data by specfyng only the mean and the covarance of the outcome varables. The GEE approach covers ndependent dstrbutons and can be ftted usng a number of statstcal software. These software now provde a large varety of common structures for the correlaton matrx. In ths approach, we assume that the margnal expectaton of t y, t E ( =, s modeled as before by g ( p ) = x β, where g (.) s a known lnk functon such as t t y ) p the logt functon and the estmatng equaton for β s also as before t U ( ) = u ( β ) β wth 1 1 T u ( β ) = ( p / β )' V ( y p ) where p = ( p,..., p )' and V s the workng covarance matrx of y. Note that for the EM algorthm, the condtonal expectaton of the latent class ndcators requre full specfcaton of the dstrbuton but the β parameter can be obtaned usng the GEE approach. Longtudnal surveys lead to dependent observatons wthn and between ndvduals. The latter s a result of complex samplng desgn. Under panel survey data, parameters can be estmated by solvng the correspondng desgn-consstent estmatng equatons, U ( β ) = d u ( β ), where d s are the desgn weghts. These are avalable for the SLID but not for the other surveys. [As a result we estmate two sets of results for the SLID, one