Income Mobility in the United States and Germany: A Comparison of Two Classes of Mobility Measures using the GSOEP, PSID, and CPS

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1 Vierteljahrshefte zur Wirtschaftsforschug 70. Jahrgag, Heft 1/2001, S Icome Mobility i the Uited States ad Germay: A Compariso of Two Classes of Mobility Measures usig the GSOEP, PSID, ad CPS By Adrew J. Houteville* Summary The Uited States is ofte cosidered to be more freewheelig ad mobile tha Germay; however, previous cross-atioal studies of icome mobility fid the opposite is true. This paper ivestigates these surprisig results ad fids that they are cofirmed whe icome mobility is measured by chages i the positios of idividuals i the icome distributio members of former West Germa households are more icome mobile tha Americas. However, whe icome mobility is measured by absolute movemets i icome, Americas are foud to be more icome mobile tha members of former West Germa households. 1. Itroductio Burkhauser ad Poupore (1997) compared icome mobility i the Uited States ad former West Germay over the six-year period from 1983 through They were surprised to fid that post-govermet icome mobility over the period was greater i Germay. Burkhauser, Butler ad Houteville (1999) exteded this aalysis ito the 1990s ad foud that equivalized post-govermet icome mobility decreased for members of former West Germa households but remaied higher tha post-govermet icome mobility i the Uited States. 1 These results ru couter to the covetioal belief that America society is more free-wheelig tha Germa society. Worker credetials ad joit uio-maagemet-govermet bargaiig processes play a large role i the Germa labor market. The Germa govermet is more actively ivolved i dampeig the busiess cycle tha the Uited States govermet, ad the Germa social welfare system is larger (higher taxes ad more social welfare expeditures per capita) tha its Uited States couterpart. These factors might lead oe to expect less icome mobility i Germay tha i the Uited States. Usig similar techiques, Aaberge et al. (1997) compared Swede, Norway, Demark, ad the Uited States from 1986 through 1990 ad were also surprised to fid that the Uited States had less post-govermet icome mobility tha Swede ad Norway. Oly Demark had less post-govermet icome mobility. They expected the more extesive Scadiavia social welfare systems to dampe icome mobility. The purpose of this paper is to shed light o these surprisig fidigs. The ext sectio of this paper discusses the two classes of mobility measures. This is followed by discussios of the data, sample restrictios, results, ad cocludig remarks. 2. Two Classes of Mobility Measures Fields ad Ok (1996) made the distictio betwee two classes of icome mobility measures o-positioal ad positioal measures. 2 No-positioal icome mobility occurs whe the icomes of idividuals chage over time. A simple way to measure o-positioal icome mobility is to calculate the mea absolute value of chages i the atural log of icome from time t to time s, 1 l( yi, t) - l( yi, s), i=1 where y i, t is the icome of idividual i i time t ad is the umber of idividuals. Positioal icome mobility occurs whe the positios of idividuals i the icome distributio chage over time. A simple way to measure positioal movemets is to calculate the mea absolute value of chages i deciles of the icome distributio from time t to time s, 1 dec ( yi, t) - dec ( yi, s). i=1 Burkhauser ad Poupore (1997) use a more complex positioal measure of icome mobility, the Shorrocks measure, which cosiders icome mobility at poits withi the period time t to time s. For example, the Shorrocks measure cosiders icome fluctuatios i all the years i the period 1983 to 1988, rather tha just the differece betwee icome i 1983 ad icome i Icome mobility occurs whe the positios of idividuals i aual icome distributios differ from their positios i the distributio of period icome. The Shorrocks measure is s I yi, t t = 1 1, s t = 1 a I ( y t i, t ) where t = 1, 2,, s, I( ) is a icome iequality idex, such as geeralized etropy idices or the Gii coeffi- * School of Idustrial ad Labor Relatios, Corell Uiversity 1 The phrase members of former West Germa households is used because i the years after reuificatio Burkhauser, Butler ad Houteville (1999) tracked oly those idividuals associated with households that were formed i former West Germay. This sample restrictio is discussed below. 2 Fields, Leary ad Ok (1998) use these measures to compare icome mobility i the 1970s ad 1980s i the Uited States. 59

2 ciet, ad a t is the ratio of mea icome i time t to mea period icome. 3 The latter portio of this formula is the ratio of the iequality of period icome to the weighted sum of icome iequality i the icremets of time i the period. If icome is perfectly immobile, the the Shorrocks measure equals zero. For example, if idividuals receive the same icome from year to year, the weighted sum aual icome iequality equals the iequality of period icome. I the results below, the icome iequality is captured by a geeralized etropy idex kow as the Theil(1) coefficiet, 1 y i l yi, i =1 µ y µ y where µ y is mea icome. 4 Positioal mobility is depedet upo the dispersio of the icome distributio, which makes cross-atioal comparisos problematic. If the populatios of two coutries exhibit idetical chages i icome (o-positioal mobility), the populatio with the arrower distributio will exhibit more positioal mobility. 3. Data To compare o-positioal ad positioal icome mobility i the Uited States ad Germay, it is ecessary to follow idividuals over time. The Pael Study of Icome Dyamics (PSID) ad the Germa Socio-Ecoomic Pael (GSOEP) cotai such iformatio. The PSID bega i 1968 with approximately 4,800 America households (about 18,000 idividuals). The GSOEP bega i 1984 with approximately 5,600 households (about 17,500 idividuals) i former West Germay. These households have grow ad childre have split off to form their ow households. Drawig from these growig datasets, the PSID- GSOEP Equivalet File cotais a ubalaced pael of 40,041 idividuals i the Uited States for the period ad a ubalaced pael of 29,219 idividuals from the origial 1984 West Germa households for the period , 6 The PSID-GSOEP Equivalet File cotais the comparable icome ad household iformatio eeded to evaluate icome mobility i the two atios. The aalysis below focuses o equalized household post-govermet icome i the year prior to the survey. For Germas, household post-govermet icome is the sum of household labor earigs, iterest icome, divideds, retal icome, the imputed retal value of oweroccupied housig, private ad public trasfers, ad social security pesios, mius total household taxes. Labor earigs iclude earigs from all sources of employmet (primary, secodary, ad self-employmet), plus ay bouses ad profit-sharig icome. Public trasfers iclude housig allowaces, child beefits, subsistece ad special circumstace assistace, govermet studet assistace, materity beefits, uemploymet beefits, uemploymet assistace, ad uemploymet subsistece allowaces. The tax burde icludes icome taxes ad payroll taxes. For Americas, household post-govermet icome is the sum of household labor earigs, iterest icome, divideds, retal icome, the imputed retal value of ower-occupied housig, public trasfers, ad Social Security pesios, mius total household taxes. Labor earigs iclude earigs from all employmet (icludig both the asset ad labor portios of self-employmet earigs), bouses, overtime, ad commissios. Public trasfers iclude AFDC/TANF paymets, SSI paymets, uemploymet compesatio, Workers Compesatio, ad the face value of food stamps. Taxes iclude payroll taxes plus federal ad state icome taxes, which are estimated usig PSID variables ad the Natioal Bureau of Ecoomic Research (NBER) TAXSIM Model. 7 I survey year 1993 (icome year 1992), the PSID switched from paper ad pecil surveys to computer-assisted iterview surveys ad also reduced efforts to clea the data. These chages make it difficult to compare icome mobility before ad after these chages. Computerassisted iterviews may capture sources of icome that were ot captured previously ad that are subject to more year-to-year fluctuatios. I additio, chages i the cleaig process may also icrease year-to-year movemets i icome. The results from the PSID are compared to results usig the March Demographic Supplemet of the Curret Populatio Survey (CPS) of the Uited States. This survey focuses o sources of household icome, govermet program participatio, ad a variety of demographic characteristics. Iformatio is collected from approximately 50,000 households (about 150,000 idividuals). I the March CPS of ay give year, approximately half of the households beig surveyed were surveyed the prior 3 Period icome represets permaet icome. See Maasoumi ad Zadvakili (1986) for a more complete discussio of the Shorrocks measure ad differet specificatios of permaet icome. 4 Previous work has show that cross-atioal comparisos of icome mobility usig the Shorrocks measure are ot dramatically differet whe alterative measures of icome iequality are used. 5 The PSID-GSOEP Equivalet Data File is a compilatio of the efforts of researchers ad staff affiliated with Corell Uiversity ad the Germa Istitute for Ecoomic Research (DIW). 6 These paels are ubalaced i the sese that a idividual is ot required to have iformatio i all the years. 7 For more iformatio about the TAXSIM estimates, see Butrica ad Burkhauser (1997). Estimates of iequality ad mobility usig the icome tax liability reported by the PSID are very similar to the results below. As was expected whe usig the PSID figures, iequality was slightly higher (due to itemizatio), but mobility was virtually uchaged, suggestig that idividuals retaied their relative positios i the distributio regardless of which tax measure was used. 60

3 March, while the remaiig households beig surveyed are eligible to be surveyed the followig March. This feature makes it possible to measure year-to-year icome mobility. Tax estimates for CPS respodets are ot available; therefore, equivalized pre-govermet icome is used whe comparig results from the CPS ad PSID. I the PSID, household pre-govermet icome is household post-govermet icome, as defied above, igorig household taxes ad public trasfers. I the CPS, it is the sum of household icome from wages ad salaries, farmig, self-employmet, ret, iterest, divideds, ad private trasfers. I all the results below, the uit of aalysis is the idividual. A idividual is give a equal share of his or her household s equivalized post-govermet icome. 8 This approach approximates a idividual s access to household resources. 4. Sample Restrictios The multi-year ature of the Shorrocks mobility measure requires persos to be i the data over the etire period of the specific aalysis. Cosecutive six-year periods are used. All samples are restricted to those idividuals who have complete iformatio over a give six-year period. 9 All samples are restricted to workigage idividuals (aged 25 through 59) with positive equivalized post-govermet icome over a give sixyear period. 10 To isure cotiuity, this restrictio is applied to all mobility idices, eve though some of the idices do ot require icome iformatio for all years i a period. I order to elimiate potetial outliers, i each six-year period, idividuals are raked accordig to the variace i their icome profiles ad the top 1 percet 11,12 are dropped. The Germa sample is restricted to idividuals i households that derive from the GSOEP s origial 1984 samplig of households i former West Germay. Keep i mid that this sample icludes (1) o-germa citizes, (2) idividuals i households that have split off the origial 1984 sample households, ad (3) idividuals who have sice become a part of these households, which icludes residets of former East Germay. I additio, after reuificatio some members of these households moved to former East Germay. The phrase members of former West Germa households is used to describe the Germa sample used i the aalysis below. This aalysis is ot a aalysis of just Germa citizes or just idividuals livig i the wester states of Germay. Comparig results from the PSID ad CPS is complicated by chages over the years i the way icome is topcoded i the CPS. Whe comparig the CPS ad PSID, idividuals above the 90 th percetile of the aual icome distributio are give the icome value at the 90 th percetile. This mitigates the ifluece of top-codig by restrictig mobility i the upper tail. 5. Results Table 1 cotais estimates of the positioal ad opositioal equivalized post-govermet icome mobility of workig age Americas ad members of former West Germa households for cosecutive six-year periods begiig i 1979 for Americas ad 1983 for members of former West Germa households. The first two colums of Table 1 provide estimates of mea absolute value of decile chages (positioal mobility) for the two populatios. I the first six-year period i which both groups ca be compared, 1983 through 1988, members of former West Germa households were more mobile, movig a average of 1.64 deciles withi their equivalized post-govermet icome distributio. I the same period, Americas averaged 1.53 deciles withi their distributio. As ca be see i the third ad fourth colums of Table 1, this fidig is cofirmed by the other positioal mobility measure, the Shorrocks measure. Over this period, 18.4 percet of the equivalized post-govermet icome of members of former West Germa households was trasitory, as compared to 15.3 percet for Americas. The opposite holds true whe mobility is ot a fuctio 8 The Uited States Detailed Equivalece Scale is used to adjust household icome for ecoomies of household size. It is also assumed that idividuals share equivalized household icome equally. All dollars ad deutsche marks are i 1992 figures. Adjustig for exchage rates is ot ecessary, because the mobility measures are homogeeous of degree zero. 9 This choice of sample criteria allows as may idividuals as possible for each calculatio. While each period s sample cotais a somewhat differet set of people, the sample restrictios are the same ad hece are comparable. A alterative is to draw a sample for the etire pael (which would require idividuals to be i the sample for the etire legth of the pael) ad the subdivide the data ito periods. While this would produce a more cosistet sample over time, the sample would be very restrictive. Results usig this more restrictive sample criteria yield similar mobility patters across coutries ad over time. 10 Positive icome values for each idividual are ecessary because atural logarithms are used. 11 See Burkhauser, Butler ad Houteville (1999) for more complete discussio of this restrictio. 12 Both surveys oversampled certai sub-populatios. Roughly two-fifths of the origial PSID households were itetioally draw from low-icome eighborhoods. About oe-fourth of the origial GSOEP households were itetioally draw from the populatio of o-germa guest-workers. Both surveys provide sample weights to adjust for these oversamples. The results below use these oversamples i cojuctio with the idividual sample weights (specifically, the idividual sample weight of the last year of the period). Results derived without usig the idividual sample weights ad results derived from the primary samples are available upo request. The results are similar to the results below. 61

4 Table 1 Estimates of Positioal ad No-Positioal Equivalized Post-Govermet Icome Mobility ad Equivalized Post-Govermet Icome Iequality for Workig-Age Americas ad Members of Former West Germa Households for Cosecutive Six-Year Periods from 1979 ad 1996 a,b Positioal Mobility No-Positioal Mobility Theil(1) Measure of Iequality Mea Absolute Value of Mea Absolute Value of Shorrocks Mobility Measure Chages i Icome Decile Chages i Log-Icome for the First Year of the Period Six-Year Period Americas Members of Members of Members of Members of Former West Former West Former West Former West Americas Americas Americas Germa Germa Germa Germa Households Households Households Households c c c c c Source: Author s calculatios usig the PSID-GSOEP Equivalet Files, a The Germa sample is restricted to idividuals i households that derive from the GSOEP s origial 1984 samplig of households i former West Germay. This sample icludes (1) o-germa citizes, (2) idividuals i households that have split off from the origial 1984 sample households, ad (3) idividuals who have sice become members of these households, which icludes residets of former East Germay. I additio, after reuificatio some of these households moved to former East Germay. This aalysis should ot be see as a aalysis of solely Germa citizes or solely people i the wester states of Germay. b The US detailed equivalece scale is used i all calculatios. c I survey year 1993 (icome year 1992) the PSID switched to computer-assisted iterviews system. 62

5 Table 2 Estimates of Positioal ad No-Positioal Equivalized Pre-Govermet Icome Mobility ad Equivalized Pre-Govermet Icome Iequality for Workig-Age Americas for Cosecutive Two-Year Periods from 1979 ad 1998 usig the Pael Study of Icome Dyamics (PSID) ad the Curret Populatio Survey (CPS) a Positioal Mobility No-Positioal Mobility Theil(1) Measure of Iequality Mea Absolute Value of Mea Absolute Value of Shorrocks Mobility Measure Chages i Icome Decile Chages i Log-Icome for the First Year of the Period Two-Year Period PSID CPS PSID CPS PSID CPS PSID CPS b c c c b,c c Source: Author s calculatios usig the PSID-GSOEP Equivalet Files, , ad the March Curret Populatio Survey, a The US detailed equivalece scale is used i all calculatios. b I the CPS, it is ot possible to match idividuals from 1985 to 1986 ad 1995 to1996. c I survey year 1993 (icome year 1992) the PSID switched to computer-assisted iterviews system. 63

6 of the icome distributio. I the period 1983 through 1988, o-positioal movemets i the equivalized postgovermet icome of Americas were larger tha those of members of former West Germa households. As ca be see i the fifth ad sixth colums of Table 1, the log equivalized post-govermet icome of Americas moved a average of 0.406, as compared to for members of former West Germa households. These results show that i the period 1983 through 1988 members of former West Germa households experieced smaller movemets i equivalized post-govermet icome tha Americas. Yet i the same period members of former West Germa households experieced larger positioal chages tha Americas. This suggests that the distributio of equivalized post-govermet icome is arrower amog members of former West Germa households tha it is amog Americas. As ca be see i the eighth ad ith colums of Table 1, this is the case. I the first year of the period (1983), the Theil(1) coefficiet of members of former West Germa households (0.099) is smaller tha that of Americas (0.157). Usig several measures of mobility, Schluter (1998) examied the equivalized post-govermet icome mobility i Germay, Britai, ad the Uited States. Whe usig positioal measures he foud greater mobility i Germay, which was due to more positioal movemet i the lower portio of the icome distributio. He also compared o-positioal movemets i the three coutries by drawig the distributio of chages i log equivalized post-govermet icome via kerel desities estimatio ad foud that chages i the Uited States were larger tha those i Germay. As ca be see i the other six-year periods preseted i Table 1, these patters exist util the period 1988 through 1993, whe Americas registered uusually large icreases i all three mobility measures ad members of former West Germa households experieced slight declies i all three measures. Americas moved a average of 1.66 deciles, as compared to 1.59 for members of former of West Germa households. Accordig to the Shorrocks measure, 17.8 percet of the equivalized postgovermet icome of Americas was trasitory, as compared to 16.5 percet for members of former West Germa households. As for positioal movemets, log equivalized post-govermet icome of workig-age Americas moved a average of 0.451, as compared to for workig- age members of former West Germa households. I the remaiig periods, oly oce did ay of the measures register more mobility for workig-age members of former West Germa households mea absolute value of decile movemets i 1989 through The chage i the relatioship betwee the two populatios coicides with the PSID s itroductio of computerassisted iterviewer surveys i icome year 1992 (survey year 1993) ad a chage i the process used to clea icome data. I order to ivestigate chages i icome mobility ad iequality amog Americas i the 1990s, Table 2 duplicates the structure of Table 1 but with results from the CPS ad PSID. However, Table 2 cotais results usig equivalized pre-govermet icome ad cosecutive two-year itervals. As ca be see i Table 2, the equivalized pre-govermet icome mobility of workig-age Americas was i geeral higher whe usig the CPS, but the iequality of equivalized pre-govermet icome was higher whe usig the PSID. The results from both datasets ad all three measures of mobility show a icrease i positioal ad o-positioal mobility i the 1990s. However, the chages i mobility whe usig the PSID were much more dramatic. I (the first iterval to iclude data from PSID computer-assisted iterviews), the PSID results show a very large icrease i positioal ad opositioal mobility, while the CPS results show slight decreases i positioal mobility ad a slight icrease i opositioal mobility. Keep i mid that the PSID icome data for survey years 1994,1995,1996, ad 1997 are from early release files. The PSID staff is workig o cleaig these files. The release of ew icome files is slated for September Coclusios The results from two differet classes of icome mobility measures cofirms that, util the 1990s, positioal icome mobility was higher amog members of former West Germa households tha amog Americas, which is couter to covetioal beliefs about the two coutries. However, i lie with covetioal beliefs, o-positioal icome mobility was higher amog Americas tha amog former West Germa households. I the 1990s, icome mobility amog Americas appears to icrease whe usig either the CPS or PSID; however, more work is eeded to isure the validity of this fidig. 64

7 Refereces Aaberge, Rolf, Aders Björklud, Markus Jätti, Mårte Palme, Peder J. Pederse, Nia Smith, ad Tom Weemo Icome Iequality ad Icome Mobility i the Scadiavia Coutries Compared to the Uited States, mimeo, August. Turku, Filad: Åbo Akademi Uiversity. Burkhauser, Richard V., J.S. Butler, ad Adrew J. Houteville Iequality Reaches Germay: A Cross-Natioal Compariso of Permaet Iequality i the Uited States ad Germay i the 1990s, mimeo, Corell Uiversity. Burkhauser, Richard V. ad Barbara A. Butrica Estimatig Federal Icome Tax Burdes for Pael Study Icome of Dyamics (PSID) Families Usig the Natioal Bureau of Ecoomic Research TAXSIM Model. Agig Studies Program Series Paper No. 12, Ceter for Policy Research, The Maxwell School. Syracuse, NY: Syracuse Uiversity, December. Burkhauser, Richard V. ad Joh G. Poupore A Cross-Natioal Compariso of Permaet Iequality i the Uited States ad Germay, Review of Ecoomics ad Statistics, 79(1) (February): Fields, Gary, S. Jesse B. Leary, ad Efe A. Ok Icome Movemet i the Uited States i the Seveties ad Eighties, Workig Paper, Corell Uiversity. Fields, Gary, S. ad Efe A. Ok The Meaig ad the Measuremet of Icome Mobility, Joural of Ecoomic Theory, 71: Maasoumi, Esfadiar ad Sourushe Zadvakili A Class of Geeralized Measures of Mobility with Applicatios, Ecoomics Letters, 22: Schluter, Christia Icome Dyamics i Germay, the USA ad the UK Evidece from Pael Data, Paper preseted at GSOEP98 Coferece. 65

CHAPTER 2 PRICING OF BONDS

CHAPTER 2 PRICING OF BONDS CHAPTER SUARY This chapter will focus o the time value of moey ad how to calculate the price of a bod. Whe pricig a bod it is ecessary to estimate the expected cash flows ad