Contents
1 Introduction 1
2 Institu tional Ba ckgrou nd and Data 3
3 Econometric Model 5
4 Estimation Results 8
5 Summary an d C onclu sion 14
6 Figures 28
Pri vat e and Publ i c Sect or Wage St ructures i n
Germany
C hrist ian Dustmann
and
Ar thu r van Soest
March 1995
Abstrac t
Thi s paper an al yzes wage struc tu re s in th e pub li c and the private
sector for Germany. The data contai ns a rich set of vari able s on
par-ents'ch aracteristi csthatweuseasin struments. Weexten dth eempi ri cal
l iteratureinthi sel dbyen doge niz in ged ucationl evelandhoursworke d,
andbyusi ngl ifecycl ewagedi e re nti alsi nth estructuralse lec ti onequ
a-tion. Weshowthat these extenti ons si gni cantly improve thestand ard
mo del . Moreover, th ey l ead to consi derably di e re nt parame ter
esti-mate s. Wecompu te cond iti on al an d uncond iti on al wagepredi ctionsfor
thevariousspeci cations u singmo de l si mul ati on s. We ndthat,on
av-erage, potential wages in th e private sec tor excee d th ose i n the p ubl ic
sector. Thoseactual lyworkin ginthep ubl icsector,wou lddosomewhat
better i n the p ri vate sector, whi le th ose working i n the pri vate sector
wou ld earn mu ch l essi nthepu bl icsector.
3
Wearegr at efultoRichardDisne yandananonymousCent ERr efere eforuse fulcomme nts. Re search
of t he se cond author is mad e p oss ible by a fellowship of the Net herlands Royal Ac ademy of Arts and
Scienc es(KNAW).
y
Unive rsityColle ge ,Gowe rStre et,Lond on,WC1E 6BT,UK.
z
1 Int roductio n
In allind ustria lized co untriesa nd many developingcou ntries the sta te has an imp o rtant
role as employer. In 198 0, to tal public s ector employment accrued to an average o f 24 .2
p ercent o f n on{a gricultural employment foroecd - cou ntries . Public sector employment
may occur at dierent levels, like the central government,state and locala uthorities a nd
na ncial andn onna ncialpublic enterprises. Ma nyservicessupp liedby the publicsecto r
areno to nly essentia l,buta ls omono p o lized. Asacons equence,employmentconditio nso f
publicemployeesare notregulatedby marketforces,butratherdeterminedbypoliticians
or p o litically imp o rtantinterest g roups(including that ofpu blicemployeesthemselves). 1
Wag esan dworkingco nditionsinthepub licsecto rdierg enerallyfromthos eintheprivate
sector. D eviceswhichrela tewa gesto productivity a reoftenmiss ing . 2
Moreover,ifpublic
sector employment is substa ntial, wage and emp loyment co nditions o f th e public secto r
maya lsoaectco nditionsinthep rivatesector. 3
Inrecentyea rs,pub licsectoremployment
conditio ns andthe ecien cy of the publicsecto rversu sth epriva tesector has becomea n
importantp o licyissue. Asaconsequence,eco nomistshaveb ecomeincrea sin glyinterested
in a nalyzing co nditions in p ublic an d private s ectors . One main research interest is the
wag estructu rein both sectors .
Relyingo nthe ass umptionthat inequilibrium someone witha givenvectoro f hu ma n
capitalchara cteris ticssho uldreceivethesa mewag einbothsectors,s omestud iescompare
estimated co ecients o f wag e regressions a nd pred icted wa ges fo r the two secto rs. 4
But
as a con sequence of dierences in occup atio ns a nd requirements, secto r cho ice may no t
b e rando m. This leads to a selectio n problem in estima ting wage equa tio ns. The more
recent literatureusua lly takes a cco unt of this by es timating s witching regression models.
Such an a nalysis hasb een p erformedforva rio uscou ntries . Van der Gaa g a nd Vijverberg
(19 88) analyze pub lic- priva te s ector employment fo r Ivory Co ast. Their OLS estima tes
arecons iderablydi erentfromestima tesacco unting forselectio nbias. Similarmo d elsa re,
for example, estimated fo r the US (Belma n and Heywo od, 19 89), Peru (Stelcner et al.,
19 89),Italy (Brun ello and Rizzi,19 93 ), a nd the Netherlands (Theeuweset a l.,19 85, va n
Ophem, 19 93 , a nd Ha rtog and Oos terbeek, 199 3). Pedersen et a l. (199 0) a nalyze public
{ priva te sector ea rning s in Den ma rk using panel da ta . Zweimu ller and Winter-Ebmer
(19 94) a nalyze wage structures for Aus tria . Gind ling (19 91 ) a nd Terrell (1 993 ) provide
1
Whe therornotthede cisionofth ep olicymakerr epre se ntsinthisconte xtt heinte res tofthemedian
vot erisanopenis sueinthelit eratur e(se e,for instanc e,Downs(1957) andRe der( 1975)).
2
In many indus trializ ed countries , public se ctor wages are bargaine d b e twee n public se ctor unions
andthegove rnme nt. SeeHolmlund(1993)andDe Fraja (1993) for the or eticalmo dels. Thebargaining
outcome b etwe en public se ctor unions and e mp loye rs is often inuenc ed by agree me nts in the private
se ctor. Forinstance ,JacobsonandOhlsson(1994)analyzethelong-runre lationshipb etwee ngover nme nt
wage sandprivates ec torwages inSwede nan d ndt hatt heprivate sec toristhewagele ade r.
3
Jacobse n(1992)provide ssomeevidenc eforthishypot hesis.
evidencefo r Co sta Ricaa nd Haiti, res p ectively.
Thesestud iesad dres sthefollowingquestions: Firstly,wha tdeterminestheselectio nin
the private and thepu blicsector. Seco ndly, whatare the dieren ces in the pay structure
b etween the two s ectors. And thirdly,wha t a re the conditional a nd unconditio nal wag es
dierentials b etweenthe two s ectors. Co nclusions va ry cons iderably a cro ss the cou ntries
ana lyzed . One may conclud e from this tha t wag e structures , incentives and selectio n
mechanismsbetween pub licandprivate sector diera crosscountries,whichisreas onable
in viewofthe diverg entinstitutio nal settings forprivate andpublicsector occupa tio nsin
dierent countries .
However, sometimes conclusions di er also b etween s tudies for the same country. A
reaso n for this is tha t results are very sensitive to model a ssumptio ns. We sh ow in this
paperthats omea ssumptionsfrequentlyma deinthislitera tureareques tio nableandtha t
small cha nges in the specicationof th e model may lea dto dierent conclus io ns. At the
sa me time, we provide a rs t a nalysis o f pay structures in the p ublic a nd the private
sector for Germany. We use data from the German So cio Econo mic Panel. The data
provide ba ckgrou nd info rma tio n on p arents' socia l a nd eco nomic sta tus. This equips us
witharichs etofinstrumentsandenablesustoallowfo rendo geneityofso meoftheus ual
regressors in wag ea nd choice equations.
A crucial question in th is typ e of models is identication. Non-p arametric
identica-tio no fstructural selectionand wa geequ atio nsrequiresexclusionres trictio nso nvariables
in both equations. Ma ny studies use di erent educa tion measuresin the wa geequations
and in the selectio n equation, and/ or u se ag e in one equation and potentia l exp erience
in the other. Fo r in stance, Belman and Heywo od (1 98 9) us e co ntinuous mea sures of
ed-ucationin the wa ge reg ression a nd degrees in the selectio n equ ation. Van d er G aag a nd
Vijverb erg(19 88)and Stelcner eta l. (198 9)goexa ctlythe o pp o siteway. Identicationis
intheseca sesobta inedbyimposingdi erentrestrictio nso nthewaythesameinfo rma tio n
enters s election andwa geequa tio ns.
Educa tion isacrucialvariableinalltheses tudies,noto nly foridentica tion ,but a lso
as a determina ntof secto ral cho ice. Nearly allstudies nd that a high level of ed uca tio n
in creas essignica ntlythe p robab ilityof working inthepu blicsecto r. We argue,h owever,
thatth etreatmentofeducatio ninallth es es tudiesispro blematic. Sincemos toccupations
arenotequallyavaila bleinb oth s ectors , o neshouldexpectthathumancapitalinthe two
sectorsisnot readilytrans fera bleand specic o ccupationsinb o thsecto rsrequires p ecic
typeso f educa tion . Itistherefo relikelytha tindividua lsmeetthesecto rd ecis io ntogether
with part of their edu ca tio nal cho ice. In other words, an individua l w ho wa nts some
occupa tio nin the public sector, may cho o se the n ecessary edu ca tio n simultaneous ly. We
therefo re endo genize education. We n d that exog en eity o f this variable in the selectio n
equa tio nisstro nglyrejected. Thischang estheconclus io nsa b outthee ecto feducatio no n
bias o f the educatio nal coecients.
Follow ing Ha rtog a nd Oos terbeek (19 93), we include ho urs worked a s a reg ress or in
the wag e equation. However, we allow ho urs of work to b e endog eno us. Aga in, we nd
that exog en eity is s trong ly rejected.
Ina llstudiesus ings witchingregress io ns,thes tru ctura lselectio nequationisestimated
with the c urre nt predicted wa ge dierential as additio nal regresso r. The und erlying
as-sumption isth at individuals may chang esectors at any p o intin time. However, we have
arg ued alrea dy that the decision to join a sector is o ften not eas ily reversible. It then
sho uld b eseen a s a lo ng- termeddecision, bas ed on a compa riso nof expected lifetime
in-comes . Weconstruct alife cyclewage dierentiala nd allow th esectoralcho iceto depend
on both the current and the life cycle wa ge d i erentia l. Our empirica l res ults do no t
una mbig uous ly indica tew hichof the two meas ures to choose.
Fin ally,we co mpa reco ndition al and unconditio nalwag edi erentia ls b etweensectors,
using simulations. We show that predictions dier b etween models w hichd o and do no t
takesectorselectio nintoaccount. Theg eneralco nclus ion sab o utdi erencesinconditio nal
andunconditio nal wagedierentials,a pp earto b era therro bustw ithrespectto theother
specica tio n as sumptio ns.
The pa p er is structured as fo llows. In the next sectio n we give a sho rt overview o n
the public a nd the private sector in Germany and d iscuss the data . Section 3 describes
the econometric model. The results are discussed in section 4. Sectio n 5 gives some
conclus io ns.
2 Institutional Ba ckg round and Da ta
Public an d Private Sector in Ger many
Thep ublicsectorinGermanyd istinguishesb etweentwotyp esofemployees : civils erva nts
proper (B eamt e) and blue a nd white collar public secto r employees . Civil s erva nts are
usua llya pp ointed forlifetimeaftera ninitialpro bationp eriod. Theirrightsa reregulated
by law, and they a re exclud ed from collective ba rg ainin g. Civil serva nts include tho se
atta ched to the essentia lfunctions o f the sta te (defense,p o lice force, law and order) a nd
account for ab o ut 41% of all sta te employees. Other sta te employees have a less special
rela tion shipw iththe state. Theirworking contractsmay wellb etemp o rary. T heir rig hts
are regulated by nego tiated a greements between u nio ns and employers , a s in the private
sector. They have the right to neg otiate wa ges. Still, alth ough civil s erva nts a re no t
allowed to g et a ctively involved in wag e neg otia tio ns, civil s erva nts ' wag e increa ses are
stro ngly linked to the results of wage negotiations o f o th er public secto r employees. The
public s ector workers at the federal, sta te and local level (see Brandes et al, 19 90). We
sha ll not dis ting uish the twoca teg ories of p ublic secto r employeesin the empiricalwork.
Co mpa redwiththeprivatesector,entra ncetothepublicsecto rismoreformalizeda nd
bas ed on educational certi ca tes (seeBrinkmann, 197 6). In the public secto r,employees
receivespecialtraining not onlyfor the occupa tio na ss uch,bu tfor ea chdi erentpos tin
theirca reergroup . As aco nsequenceof thiss ubstantialamou nt ofjob-s p eciceducation,
stro ng ties develo p between employee a nd employer a nd entrance into the public secto r
fromp riva tesecto roccu pationsisdicult. Mo reover,ag eregulationsrestrictentranceto
civil servant occup atio ns (seeBrandes et al,1 988 ). Blos sfeld and Becker(1 989 ) describ e
the va rio us res trictio ns on cha nges b etween secto rs. They conclude tha t institutio nal
constra ints h inder ch anges b etween secto rs in both directions considerably, particu larly
with increasing seniority. This isconrmedby the lownumbers o ftra nsition s: in eacho f
theyears19 84till19 87,lessthano nepercento fa llemployeeschang eds ector. Thepublic
sector in Germa ny expan ded rapidly in the 6 0's and 70's. T he expa nsion was ma inly
in duced by a n extens io n of the welfare sta te and the co rresponding expa nsion o f socia l,
educa tio nal an d medical services . Between the 1 950 an d 19 92 the nu mb er o f employees
in the publics ector increas ed from 2.2 Mio to more th an 4.95 Mio . 5
The share of public
sector employees o n the total number o f salary earners increa sed from 12 .5 p ercent in
19 65 to 18 p ercent in 19 80 a nd sta bilized since then a t ab o ut 20 p ercent. In 1 98 5, 82 .9
p ercent o f all publicsector emp loyeeswereemployed full- time.
The socia lsecurity systemforcivil s erva nts is s lightly dierentfrom tha t a pplying to
other public s ectors employees. Compared with public secto r employees, p riva te secto r
employeesa resimila rlysecuredinca seof illn ess . However,incaseo finva lidity,d ea tha nd
seniority, p ublic secto r emp loyees are subs tantia lly b etter protected than priva te secto r
employees. For instance, w hile pensio ns of civil servants a mo unt to ab o ut 80 percent o f
theirlatestnetinco me,a ndpens io nsofo therpublicemployeeseventoa b o ut105p ercent,
private s ector employees who havepa id their contrib utio ns to the pens io ns cheme for 45
years ,o nly receive a b o ut72 p ercent o f their latestn et income(see Kra use, 198 1).
Data a nd Va riab les
The empirical an alysis is ba sed on da ta from the German So cio-Eco nomic Panel, w hich
in cludes ab o ut 6 00 0 househo lds. 450 0 of thes e have househo ld heads with G erman
na-tio nality, 15 00 with fo reign nationa lity. This s tu dy is restricted to the rs t sub sample.
We comb ine information from the rs t (19 84 ) an d third (1 986 ) wave of the panel. 6
We
5
Allnumb e rsre fertoWe st Ge rmanyonly.
6
Wec ons truc tmostvariablesfromt hers twavewhichprovidesinformationab outactu allab ormarke t
experienc e, allowing u s to distingu ish b etwe en c ohort an d exp e rie nce e ec ts in the selec tion equation.
restrict the a nalys is to male in divid uals who a re in dependent emp loyment a t the time
of the interview. Table A1 in the appendix des crib esthe variables used for the ana lysis.
After exclud ing a ll individua ls with missing va lues in releva nt variables (see table A2),
thes ample usedforthe presentanalysisreducesto 14 28o bservations,with 972 employed
in the priva te secto rand 45 6 inthe public s ector.
Summary s tatis tics are g iven in ta ble A3 . The rst two columns give means and, if
app ro pria te,sta ndarderrorsforthepooledsampleo fprivateandpublicsectoremp loyees.
Theotherco lumnsrefertoth esub sampleso fprivateandpub licemployees. Theed uca tio n
level variable is o rdered, with values 0 to 5. It is constructed from deta iled info rma tio n
about ed uca tio nal ba ckgro und. From ta ble A3, it is clear that public sector employees
haveastro ngereducationa lba ckgroun dtha npriva tesectoremployees,onaverag e. Public
sector employees a re s omew hat o lder a nd slig htly mo re experien ced tha n private secto r
employees. Private s ector emp loyees work, on averag e, 8 h ours per month mo re tha n
publics ector employees, wh ereas their ho urly earn ing sare lower.
A number of fa mily backg round variables are used. T hes e re ect the labor ma rket
sta tus of the father when the child was a ged 15 , whether the mother participated in
the labor market or not, a ge o f fath er and mo ther when the in divid ual was born, a nd
educa tio n level o f fa ther a nd mo ther. We nd, for example, that fathers o f tho se in the
public s ector more o ften worked in the public sector than fa thers of th ose in the private
sector.
3 Econometric Model
Wepresentthemainfeaturesoftheempiricalmodel. D eta ilsareprovid edintheap p endix.
Forea chind ividu al,weexpla inthechoiceb etweenp ublica ndprivate secto rworkandthe
hou rlywa gera teinthe chos ensector. In previous research ,an importa ntvariablefor the
sector cho ice has beenthe individual's education level. As sa id ab ove, this islikely to b e
endog eno us. Wea ddanequa tio ntoexplainthisvariable,inwh icheducationlevelsofb o th
parentsare the main explanato ry variables. Following Ha rtog and Oos terbeek (19 93),we
allow th e wag e ra te to dep end upon hours wo rked. Since hours worked , a ccord ing to
la b o r supp ly theory, may dep end upon the wage ra te, we a llowfo r endog eneity o f hou rs
worked,a ndad d anho ursequ atio n. T hemodelthuscon sis tsofveequations ,explaining
Education Level
Educationlevelsarecodedfro m0to5,ina scendingorder(seesection3 ). Ana ppropriate
mo delis an orderedprobit specicatio n(Madda la , 198 3,cha pter 2): 7 E 3 =X E E +u E ; E =j if m j01 <E 3 m j fo r(j =0 ;:::;5); (1 )
whereE denotestheeduca tio nallevelatta ined,andE 3
isala tentva ria ble. Thevecto r
of explana tory variablesX
E
contains information co ncerning the parents (s ee estima tio n
resultsinnextsectionfordetails ). Assumptionsontheerro rtermu
E
areg ivenbelow. The
b o undariessatisfy 01 =m 0 1 <m 0 <:::<m 4 <m 5 =1. Bymeans o f normalization, we ass ume m 0 =0 :5 and m 4 =4:5; m 1 ;m 2 and m 3 a rep arameters to be es timated. Wage Ra tes
Potential before tax ea rning s per ho ur worked are modeled fo r the p rivate and public
sector sepa ra tely:
lnW j =X W j +D E Ej + Hj lnH +u j ; j =0 ;1; (2 )
where j = 0and j =1 den ote the public and private s ector, res p ectively. The vecto r
DE co nta insvedummy va ria bles forthe vehighest educa tion levels. H denoteshou rs
worked per fo ur weeks. E xo genous variables such a s ag ea nd experience a reincluded in
X
W
. Propertieso f the erro rterms u
0
and u
1
are g ivenb elow .
Selection
Wemodelth ebinarych oiceb etweenprivatesecto r(S =0 )andpub lics ectorwo rk(S =1).
The structura lfo rm ofthis equationis g iven by
S 3 =X S S +DE E + c 1 c l nW + l 1 l l nW +u S ; (3 ) where S = ( 0 : S 3 <0 1 : S 3 0: X S
is a vecto r o f expla nato ry va riab les, in cluding, for exa mp le, the fa th er's
occupa-tio nal grou p. 1
c
ln W a nd 1
l
l nW are the current a nd life cycle log wage di erentials
b etween p otentia l public a nd private secto r wag e rates. 8
As argued above, the secto r
cho ice decis io n is not easily reversible. T his implies tha t individuals may no tba se th eir
cho ice on the current wa ge dierential, but o n the discounted lifetime wag e di erentia l:
thedieren cebetweenthedis co unted(n etpresent)va lueo fpas t,currenta ndfuture
earn-in gs over the who le working life. We have a pproximated the life cycle wage dierential
by an avera geo f wage predictions at vario uss tages of the life cycle (seea pp endix).
Hours worked
We add a s tructura l fo rmequa tio nfor h ours wo rked:
l nH =X H H + S S+ W l nW +u H : (4 )
Here W is th e befo re tax wag era te in the chos en s ector, i.e. W
0
if S = 0 an d W
1 if
S =1. The secto r dummy S itself is includ ed to reectinstitutio nal di erences b etween
the two types of jobs.
Dis tribution of Error Terms
The vecto r of erro r terms u = (u
E ;u S ;u 0 ;u 1 ;u H ) 0
is assu med to be in depen dent o f a ll
explana toryvariablesinX
E ,X S ,X W andX H , 9
andmulti-variatenormalwithmea nzero
and covariance matrix 6. By means of normalization, 6(2;2) = Var (u
S
) is set equalto
one. Fo r practica l purp o ses , u
H
is as sumed to be ind epend ent o f the other error terms.
Endo geneity o f ho urs worked thus only comes ab o ut throug h the systema tic part of the
hou rs equa tio n. 6(3 ;4 ) = Cov(u
0 ;u
1
) is no t identied. The other elements of 6 (fo ur
variancesa nd ve cova ria nces)can b eestima ted.
Identi ca tion
For mo del identication, we need various exclus ion restrictions . In the wage equ atio ns,
weexcludeallp arenta lch aracteristics,thusas sumingthatcorrela tio nb etweenabilitya nd
obs ervedparentalcha racteristics onlycomesaboutthroug h selectio na nd educationlevel.
Intheselectionequation,weexclud eeducationlevelsoftheparentstoidentifyend ogeneity
of education, but wedo reta inth epa rents'o ccupationa l g roupva ria bles. To identify the
impa ct o f th ewag edierential,we excludea ctual exp erience. Only tho se overidentifying
restrictionswereimpos edwh ichwerenot rejectedbythe data. Anexceptio nisthe hou rs
of workequation, whichwe co nsid er a s auxiliary onlya nd do not give it much emphasis.
8
Tob epre cise,weuse dthesys tematicpartofth elogwagedi ere ntialsonly. Seeapp e ndixforde tails.
9
Estimatio n
The model is estima ted by maximum likelihood. T he hourly wa ge ra te and ho urs o f
work are obs erved fo r allindividuals in the sample. The likelihoo d co ntributio n of each
in dividual ca n b e written as the bivariate density of wa ge rate (in the o bserved secto r)
and ho urs of work,timesthe conditional proba bility o f the observededucatio n level a nd
sector ch oice, givenwag erate and hours of wo rk. S ee a pp endixfo r details .
4 Estimation Results
Weconsideravarietyofd i erentspeci ca tio ns. Dierencesb etweenmo delsmainlyrelate
todierentzerorestriction son6ando ncoecientsofexp lan atoryvariables ,theinclus io n
ofthecurrentor th elife cyclewa gedi erentia linthe selectionequation. Table1presents
themodelswehaveestimated andtheir likelihoodva lues. Likelihoodra tio testsba sedo n
this tab le lea d to the fo llowing co nclusions .
[Table 1 about h ere]
Firs t, exo geneity o f education level (Cov(u
E ;u 0 ) = Cov(u E ;u 1 ) = Cov(u E ;u S ) = 0 ) is s trong ly rejected. 10
E xo geneity o f education level is a maintain ed as sumptio n in the
majority o f the empirical literature (see sectio n 1). Second , exo geneity of ho urs wo rked
(
W =
S
=0)isa lso stro nglyrejected,sug gesting that allowing forendo geneity o fhou rs
worked is a signica nt improvement compared to , fo r example, Ha rtog and Oos terbeek
(19 93). Third, we nd that neither the current no r the life cycle wa ge dierential are
signicant in th e s election equation. The 'reduced form' model in which wa ge
dieren-tia ls are no tincluded is not rejected a gainst models with one or b o th wage dierentials.
Moreover, once th e wa ge di erentia ls are included,the educational dummies do not a dd
anythin g. 11
Fina lly,wend thattheselectivityproblemisalways pres ent: the hypothesis
that selectio n is exog enous in the wa ge equations (
c = l = Cov(u 0 ;u S ) = C ov(u 1 ;u S )
= 0 ) is stro ngly rejected , no matter whether we allow for en dogeneity o f ed uca tio n a nd
hou rs worked or not. We exa mine these ndings in more detail b elow . Wefocus the
dis-cussionofthepara meterestima teso nthemos tg en era lmo del(model1). Fo rthe selectio n
equa tio nan d the wag eequations , wea lso present some altern ative estimates.
Hours Worked and Educa tion
Tab le 2 reports the results o f the education and the hours equation in model 1 . In the
equa tio n expla in ing the individua ls' education level, b oth the fa ther's and the mother's
10
Unle ss s tatedothe rwis e,weuseasignic ancelevelof5p er ce nt( two-tailedte st) .
11
educa tio nhaveasig ni ca ntp o sitiveeect,with th atof thefather b eing mo reimportant.
Theoccupa tio nal ca teg oryofthefath erisa lso imp o rtant: ifthefatherwas acivilservant,
this has a strong ly imroves education (no fa ther o r father is blue co llar worker is the
reference g roup). Age is introduced as a p o lyno mial of order ve to a ccount for coho rt
eects in a exible way. Figure 1 sh ows th e probab ility of a high educa tio n level a s a
functio n of age (other variables a re s et equ al to th eir sample mea ns). It a pp ears tha t
educa tio nal a chievement is relatively low for those w ho received their education during
the second wo rld wa r.
[Table 2 about h ere]
From the hours equation, it appea rs th at hours worked for pay is neg atively related
to log wag es . T his is a typical income eect. Hours worked fo r pay are lower in the
public than in the private sector. An explana tio n is that pa id overtime is less commo n
in th e public than in the p rivate secto r. Over the life cycle, hours wo rked increase with
ag euntil a b ou t ag e 38 ,and decreas e after tha t. Hous e owners tend to wo rk mo re hou rs
than renters, which prob ably reects a nancia l co nstraint. T he numb er of children is
p o sitively related to ho urs wo rked. T his may b e rela ted to the fact that in hous eho lds
with (many) child ren, the wife is mo re likely to withdraw from the lab o r force if the
husba nd has a compara tive a dvantag e in the market sector. The hu sband then wo rks
moreto co mpens ate fo rthe in co me lo ss(seeBecker,19 81 , cha pter 2 ). Unexp ectedly, the
amount of interes t income has a positive a nd sig nica nt eect on ho urs wo rked, while a
dummy indica ting that interes t inco me is received has a nega tive impa ct. The la tter is
signicantat th e 10 p ercent level on ly.
Sectoral Choice
In table 3, we present the res ults for the selectio n equa tio n in the mo st general mo del
(mo del 1,column 1) an d in two alterna tive sp ecications . Column 2is the reduced form
mo del without wag e di erentia ls in the selection equation, but a llowing fo r end ogeneity
(mo del 4 in table 1) of education a nd ho urs worked. Co lumn 3 refers to the p ro totyp e
mo delinwhicheducation andho urs workeda reexogeno us(model1 2). The fa ther'styp e
of occu pation sub stantia lly inu ences the secto r decision o f the o s pring . T hose who se
father wa s a civil servant have a sign icantly higher pro bability to have a public secto r
job than thos e who se father had a blue-collar p riva te secto r job (the reference g roup).
Tho sew hosefather wa sself-employedo rhad awhite-collar jobinthe private secto rhave
an intermediate p o sition in this res p ect.
[Table 3 about h ere]
In all mo d els presented, we inclu de education as a series of dummy variables. In
the g eneral model, education level plays no ro le fo r sector choice. In the reduced form
reect the wa ge e ect. In the rst two models , the co rrelation coecient b etweenerro rs
in education equa tio n and selection equation is s ig nicant. Exo geneity o f education is
rejected ,indica ting that educa tion al cho ices and secto rcho icesare made s imu ltan eo usly,
as suspected in the discussion in section 1 . If we do n ot a llow fo r en dogeneity (mo del
12 ),education leveldummiesa rejointlysig ni ca ntat the 5p ercentlevel. Th epara meter
estimatesinmodel12 strong lydierfromthos einmodel4. Thep o sitiverela tionb etween
educa tio nlevela ndselectio nintothep ublics ectorismuchs tronger. Thisremainstheca se
if the wa ge di erentia ls a re in cluded, and seems completely due to setting Cov(u
E ;u
S )
to zero. The p os itive eect o f edu ca tio n found in other emp irica l s tu dies mig ht thus b e
due to uno bserved factors, correla ted with both education level a nd selectio n, instead o f
to education levelits elf.
This result questions the conclusions draw n in o ther stu dies about the eect o f
edu-cation on secto ral choice. Mo reover, it s uggests tha t many estimates of wa ge equations
mig ht a lso b e bia sed,s inceco rrectio nfor selectivity is often identied throug h the u seo f
dierent s p ecications of the educational va ria bles ins election a nd wa geequa tio ns.
We now turn to the wa ge dierential. All stud ies u se the curre nt predicted wa ge
dierential as a dditiona l regress or. To a llow for the possibility tha t secto ral choice may
b e a lo ng-termed decision, we include b o th the current a nd the expected lifetime wa ge
dierential. In model 1, b o th wag e dierentials have the exp ected p o sitive s ig n, but are
in sig ni ca nt. If one of the wag e di erentia ls is removed fromthe equa tio n, the other
re-mainsp os itiveandins ig nicant(models2and3inta ble1). Thecurrentwag edierential
has a somewhat la rger t-va luetha n the life cycle one. Our rather crude way of
approxi-matin gthe lifecyclewag edierential,igno ring ,fo rexample,di erencesinunemployment
ris ks , o r benet o rp ension rig hts ,cou ldexpla inthis .
Anotherexpla nationco uldb ethe lack ofidentifyingres trictio nso nthes election
equa-tio n. If, for example, we imp o se tha t education level enters linearly in th e selectio n
equa tio no rexcludeage,b o thwa gedierentialsb ecomesignicant. Weconcludetha to ur
ndingsinthisres p ecta reno trobustwithresp ecttothechos enspecicatio n. Ourresults
sug gest tha t the cho ice of identifying res trictio nsis crucia la nd could expla in di erences
b etweentheva rio usstudiesintheliterature. Fo rexample,Hartoga ndOosterb eek(1 993 )
nd a p os itive a nd stro ngly signicant impa ct of the current wa ge dierential. They
in-clude years of scho o ling a nd general educa tion inthe selectio n equa tion ,versu s dummies
for education levels a tta in ed in the wa ge equa tio ns, thu s adding a ddition al identifying
constra ints. Van Ophem (199 3), als o u sing Dutch da ta, nds a n insignica nt impact o f
thewag edi erentia l. Hisidentifyingres trictio nsa remuchweaker: o nlytenureisexcluded
fromthe selectio n equation.
In gure 2 ,wehavesketchedthe estimatedpro babilityof workin ginthe publicsecto r
as a function o f age and education level for model 1. T he pub lic sector prob ability is
highest for the two lowest educa tio n levels and fo r the highest level. 12
The public secto r
proba bilitygra duallyincreaseswithagefortheyoung ercoho rts,butdro psstrong lyforthe
oldestcoho rt. Aswesha ll seebelow,this ca nnotbe exp lained fro mthe wage di erentia l.
Itisproba blyacoho rte ect. Notethatthos einth eoldestage cohortsta rtedtheircareer
justa fter the seco nd world war.
Wage Equations
Estimatio n results forp ublic and p rivate s ector wa geequa tio ns a reg iven inta bles 4 a nd
5. Ag ain, we present three specications: the genera l mo del (model 1), the model in
which edu ca tio n level a nd hours worked are exogeno us (model 9), and the OLS results
(mo del 1 2). In model1 , exog eneity of educa tio n in the wage equa tio n is rejected for the
private sector, but not for the public sector. Both correla tio n coecients a re nega tive.
An explana tio n for this might be incomplete measurement o f the educa tio n level. A
mea surementerro ron edu ca tion levelco mbinedwith the p o sitiveimpa ctof educationo n
wag esmay explainb o ththenega tivecorrelatio n andthe downward b ias ofthe estimated
impa ct ofeducation in models9a nd 1 2,forthe s amereaso nsas inasimplelinea rmodel.
[Tables 4, 5 about here]
In models 1 a nd 9 , we nd that the correlation b etween errors in selectio n a nd wa ge
equa tio nisinsignicantfo rtheprivates ector,but p os itivea nds tro nglysignicantfo rthe
publicsector. 13
Thisreinforcesthep o sitiveselectio neectofthewagedierential. Along
thelinesofRoy(19 51),itindicatestha t themeanwa geoftho sew hohavechos ento work
inthep ublicsectorislarg ertha ntheexpectedpublicsecto rwageofa narbitraryindividual
withthes ameo bservedchara cteristics. Wereturnto thisinthenextsubsectio n. Pos itive
selectio ninto the public s ector, bu t no s election into th e priva te s ector, is als o fo undby
van Op hem (19 93 ) and Hartog and Oo sterb eek (1 993 ). Van der Ga ag and Vijverberg
(19 88)nd a p o sitive s election into both s ectors .
The e ect o f lo g hours worked o n the ho urly wa ge ra te is sig ni ca ntly nega tive fo r
b o th s ectors, with elasticity b elow o ne. It increa ses w hen endog eneity o f ho urs wo rked
is ign ored. L ike Hartog and Oosterb eek (1 993 ) we nd that the e ect is stro nger in the
public tha n in the private secto r. An explana tio n could be meas urement erro rs in hou rs
worked,s incewa gera tesa recomputeda stheratioofmonthly earningsandho ursworked.
For a ll s p ecications and b oth secto rs,the wa ge in creas es mo noto nically with ed uca tio n
level. In the g eneral model, the impact of education level is strong er tha n in the models
which d ono t allow for endo geneity of education.
We have included a quadra tic function of both age and actua l experience. Inclu ding
ag etermsa partfromexperien cetermslea dstoasignicantimprovementofthelikelih o od.
tothec onc lus ionthatthep robabilityofpublic sec toremploymentin cre as eswith ed ucationlevel.
13
Thesame res ult s were found with othe r mo de lsallowing for the se c orre lations ( mo de ls 2 - 8) and
Thea gevariablesmayreectboth co horta ndlifecyclee ects. Surprisingly, ageplaysno
role in the pub lics ector, but is s ig nicant in the private secto r. D i erences b etween the
three models are quite small in this respect. In gure 3, we have sketched the expected
wag eratesinb o thsectorsas afunctio no feducationlevelan da ge. Exp erienceisreplaced
by itsbest lin ea r predictio n,g ivena geand education level. Other variables a res etequal
to their samplemeans. P ublic secto r wa ges increas ew itha ge,w hile p riva te sector wag es
showamucha tterpattern. Fo ryo ung workers,theprivatesectorpaysmuchb ettertha n
the public s ector. Fo r the oldest ag egrou p, the d i erence is neg ligible.
Wage Dierentials
We cons ider unco ndition al an d cond itional wa ge prediction s a cco rd ing to the estimated
mo dels. The unco nditiona l (pu blic or private sector) wa ge predictio n is dened a s the
(averag e) predicted value o f the (public or priva te) wag e ra tefor an a rbitra ry individual
in thepopulation. The conditio nalwag eprediction isthe weighted p o pula tio naverag e o f
thewa gepredictionsof allin dividualsinthe sa mple,wherethe weightsarethe estimated
sector prob abilities (s ee, e.g., Heckman, 19 90, for a dis cus sio n o f various d enitio ns).
To take acco unt of th e fu ll structure of the erro r terms , we have computed the wa ge
predictions u sing a simula tio n of the complete model. See a pp endix for details . The
results fora ll models inta ble 1 are rep o rted in table6 .
[Table 6 about h ere]
The rs t three column s refer to wages in the private secto r, the last th ree columns
to wag es in the pub lic sector. The rs t a nd fourth columns present predicted log wag es
in th e two secto rs for a n average in dividual (uncondition al). Acco rding to all models,
the p rivate secto r p ays better than the p ublic sector, on averag e. For the private secto r
wag e,a llmo delsyieldsimilar prediction s. For th epu blics ectorwa gehowever,di erences
b etween the models are much la rger. In pa rticular, the models in which selectivity is
nottaken intoa ccount(models1 0-1 2,C ov(u
S ;u 0 )=Cov(u S ;u 1
) =0 )yieldhigherpublic
sector wag epred ictio ns tha n the oth er models, with dierencesof more tha n 20 p ercent.
The o therco lumnsreferto con dit ional wage predictions. C olumn2refersto wa gesin
the private secto r of an individual wh o ha s ch osen to work in the priva te secto r. These
predictions are similar for all mo d els. All models a re able to reproduce the avera ge log
wag e rate in the p rivate secto r rather well. Simila rly, colu mn 6 refers to pub lic secto r
wag es of public sector workers . Aga in, a ll models rep ro duce the averag e log wage in the
public sector reaso nably well. T he mos t interesting predictions are those in co lumns 3
and 5, which have no observed sa mp le equivalent. Column 3 refers to the wages tha t
public sector workers could have received when they wo uld have wo rked in the private
sector. Co lumn 5presentsp o tential public s ector wa ges o f private secto rworkers . These
of p rivate sector wo rkers in the model not a llowing for endo geneity of education levelo r
hou rs wo rked (model 9) are a b o ut 9 percent lower (co lumn 2). Surpris ing ly, the mo st
general model a nd the mo st restrictive models (models 11 and 1 2) lead to very simila r
predictions of p otentia l public s ector wag es. This is, however, n ot th e ca sefo r p o tential
private sector wa ges o f public secto r workers (co lu mn 5). Here mo d els 1 a nd 9 yield
simila r results, w hile the o utco mes of the most res trictive modelsexceed tho se o f mo del
1 by more tha n 35 percent.
A common observation of allmo delsis that pred icted un con ditional wag es a rehigher
inthe priva tethaninth epublicsecto r: a naverageindividua lfaceshig herwag epros p ects
inthe priva tethaninthe publicsecto r(columns1and4). Thos ewhos electedthemselves
into the private sector (columns 2 an d 5 ) are those w ith lower potentia l wa ges in b o th
sectors. T hisisdu eto b othobs ervedan duno bservedchara cteris tics: fromg ures2a nd3
forexample, we con clude that a geis neg atively correla ted with selection into the private
sector, but p o sitively with wages in both secto rs. Acco rdin gly, those who work in the
publics ector d o better inboth sectors thanth e average individual. 14
Now consider th e conditional wag e dierentials. T hose in th e private secto r would
b e much wors e o in the public secto r (co lumns 2 and 5). According to mo del 1 , the
dierence would b e about 3 0 percent, on avera ge. T he dierence is mu ch smaller in
mo delstha t do not a llow fo r selectivity (in mo d el 12 ,ab o ut 6 p ercent). T heendo genous
selectio n implies that tho se in the public secto r are those with, on avera ge, the smaller
wag e dierential between the two s ectors . Thus s election works in the 'right' direction.
This result is stable a cross specicatio ns. For thos e wh o actually work in the public
sector, the averag e wage dierentialinmodel 1is les stha n 7 p ercent(columns 3and 6).
For mo dels 7 and 9 , th is wag edierential has the opposite s ig n. If wag es werethe only
criterio n fo r sector choice, then the results fo r model 1 indica te that the ch oice o f many
public secto r wo rkers is n ot rational. However, choo sing the public sector is no t purely
bas ed on wage con siderations . For exa mple, job security, entitlements to unemployment
b enets,pensio nrights,and many othernon- mo neta ry jobch aracteristics play aro le. In
section 2,wehavediscu ssedso med i erencesinb eneta nd pens ion entitlementsb etween
the sectors that may comp ensa te the wag e dis advanta ge from choosing a pu blic secto r
occupa tio n.
[Table 7 about h ere]
Wa gea dvantag esb etweensecto rsareoftenfo undtova rya cro sseducatio nalca tegories
or a gegroup s. Van d erGa aga nd Vijverb erg (1 98 2),for ins tance,nd tha t unconditio nal
expected wag es in the priva te s ector a re hig h for tho se with low educa tio n, but low
for those with hig h education. Harto g a nd Oo sterb eek (199 3) nd tha t pub lic secto r
occupa tio ns have hig her wa ge pro sp ects for all educationa l g roups , while van Ophem
(19 93) reports tha t the un co nditiona l wa ge adva nta ge of the public sector diminis hes
14
withincrea singag e. Ta ble7presentsconditio nalandunconditio nallogwa gesfordi erent
educa tio nal an d ag egroup sfor model 1. The results s p eak for themselves.
Ta bles6 a nd 7 are ba sed upon the point estimates. In table 8,we present 9 0 p ercent
condence intervalsfo r the wag e di erentia ls , taking accounto f the errors in the para
m-eter es timates (s ee a pp endix). The lefth and panel shows that the averag e unconditio nal
public sector wag es are sig nica ntly (at the two-s ided 1 0 p ercent level) lower tha n
aver-ag eunconditio nal private s ector wages for all education and ag egro ups. Dierences are
diminis hing w ith ag e, and lowes t fo r the lowest educa tion al g ro ups. The latter co nrms
wha t we sawin g ure 3fo r a representativein divid ual.
[Table 8 about h ere]
Themidd leandrighthan dpanelinta ble8referto conditio naldi erentia ls. Fo ralla ge
and education catego ries, we nd that thos e in the p rivate sector would b e signica ntly
worse o in the public sector, o n averag e. According to th e rightha nd pa nel, tho se with
lowed uca tio nlevelwhochos ethepublicsectordo signica ntlyb etterinthe publicsector.
For public secto rwo rkers in the oldest age gro up, the dierentialis insig ni ca nt. For a ll
othergrou ps,theavera gewa gedierentialissignica ntlyn eg ative,i.e. intermsofcurrent
wag es , p eop le would be b etter o in the private tha n in the public s ector. The avera ge
acros s a ll gro ups, is s ig nicantly negative a lso . T hesize o f the conditio nal dierentialis
mo dest fo r public secto r workers co mpa red to private secto r workers. The precision o f
the estimated con ditiona l di erentials is larger for priva te sector than for public secto r
workers. 15
5 Summary and Conclusion
In this paper we ana lyze pu blic - priva te sector choice a nd wag e stru ctures in b o th
sec-tors for G ermany. We estimate g en era lized s witching regression models , exten ding the
sta ndard modelin this eld invarious directio ns.
Weuse info rma tion o ned uca tio nandoccupa tio nal statuso f thepa rentsa sadditio nal
in struments. We thus avoid ad hocexclusion res trictio nsand are able to allow fo r
endo-geneity ofedu ca tion . Wendthat theco mmon co nclus ion that hig herlevelso fed uca tio n
in creas e th e p robability of cho o sing a public s ector jo b, is o nly va lid if we ass ume tha t
educa tio n is exo genous inthe selection equation. Allow ing for endog eneity imp roves the
mo delsign icantly,and implies thatthe eecton the sector cho icedro ps to zero interms
of size a nd signica nce level. Th e positive correlatio n b etween educa tio n and choice is
so lely driven by uno bservedch aracteristics that a ectbothin the sa me d irection.
15
Notethat we can only consider t heave rage die re ntial and notthein dividual variation in the
dif-fere ntials. For example ,we cannotpr edict thefr ac tion ofwor ke rs for whomthe di ere ntialispos itive,
To ta keaccountof thefa ct tha ts ectora lchoicesare lo ng- termedd ecis io ns,weuse the
current a s well as an imp uted life cycle wag edierential in the selectio n equa tio n. Bo th
haveth erightsig n,butsignica ncelevelsarelow. T heres ultsslig htlyfavo rtheuse o fthe
current wage dierential, which may be due to the ro ugh way in whichwecons tru ct the
life cycle wa ge d i erentia l. Further research on this bas ed o nthe use of panelda ta is o n
our ag enda . Bo thwag e dierentials becomesignicant, however,if we inclu deed uca tio n
as alevelva ria bleintheselection equation, instea dofus ing dummies . Thusthep recis io n
of the estima tes o f th e wag e dierential coecients depends strong ly on the identifying
restrictions, which may wellexpla in di erent resultsin the literature.
Notallow ingfo rend ogeneityoftheeducationa llevelres ultsinasu bstantia ldow nwa rd
biasin theestima tedimpactof educa tion levelon the private sectorwa ge. Fo rall
educa-tio nal group s,wen d tha t u nco nditiona l wag es a reinitially hig her inth e private sector,
but th is adva nta ge levels o ut with a ge. Unconditio nal public s ector wages are lower fo r
alledu ca tio nal and age catego ries than un co nditiona l priva tes ector wages.
On averag e, co nditiona l wag es o f pub lic sector employees a re so mewha t hig her in
the p rivate secto r th an in the public s ector. Co nsidering sepa ra te a ge a nd ed uca tio n
gro ups,we nd that onlytho sein the pub licsector with lowes teducation level a redo ing
signicantly b etter inthe pu blic sector. The co nditiona l wag edi erentialis insignicant
forthe oldestag eg roup; other ag ea nd educa tio n gro upswould do s ig nicantlybetter in
thepriva tesector. Thismayb eexplainedbyothermonetaryor non -mo netary di erences
b etweenpu blic andpriva tesecto r occupa tio nsinG ermany,not explicitly includedin o ur
ana lysis.
Our analysis sug gests that di erences in the results o f the many stu dies o n pu
blic-private sector choice and pay stru ctures may partly b e explain ed by di erentidentifying
as sumptio ns. Relaxin g the a ssumptio n of exog eneity of crucial variables like education,
may con siderab ly cha nge some of the co nclus ion s. On the other ha nd, the results o n
conditio nala ndunco ndition alwag edierentialsarefou ndtoberema rkablesta blethroug h
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Mo del of Pu bli c-Pri vate S ector Wage Di e re nti als in Peru: 1985-1986," Jou rnal of
Hum an Resou rces,24,545-559.
Ter re ll, K.(1993): \Pu bl ic - Pri vate WageDierential s i nHaiti ," Jour nalof Development
Econo mics,42,293- 314.
Thee uwes, J., Koopmans, C., vanOpstal,R . and H.van Reijn(1985): \Esti mati onof
Hu manCap italAccumul ati onParametersfortheNetherl ands,"EuropeanEcono mic
Review,29, 233-257.
Van Op hem (1993): \A Mo di ed Switchi ng R egressi on Mo del for Earni ngs Dierential s b e
Van de r Gaag , J. and W. Vij verb erg (1988): \ASwi tch ing R egre ssi on Mo del for Wage
Determin ants in th ePubl ic an d Private Se ctors of a Devel op in g Country," Review
of Economicsand Statistics,70,244- 252.
Z weim
ulle r,J.and R. Winter -Eb mer(1994): \Gende r Wage Dierential si nPri vateand
Tabl e 1: Mo del sp ec ica ti ons and Li keli hoo ds
Mo de l NoRe str ic tions Sp ec ic ation Log Likeliho o d
1 0 | -1679.08 2 1 Wl =0 -1679.34 3 1 Wc =0 -1680.62 4 2 Wl = Wc =0 -1680.63 5 5 E =0 -1680.04 6 7 E =0, Wl = Wc =0 -1697.17 7 3 6(1;2)=6(1;3)=6(1;4)=0 -1688.14 8 2 S = E =0 -1729.62 9 5 6(1;2)=6( 1;3)=6(1;4)=0, S = E =0 -1738.42 10 2 6( 2;3)=6(2;4)=0 -1683.26 11 7 6(1;2)=6( 1;3)=6(1;4)=0, S = E =0, 6(2;3)=6( 2;4)=0 -1743.56 12 9 6(1;2)=6( 1;3)=6(1;4)=0, S = E =0, 6(2;3)=6(2;4)=0, Wl = Wc =0 -1744.61
Table 2: Education Level and Hours Worked, Model 1
---Education Level log Hours worked
Variable estimate t-value Variable estimate t-value
---constant ed 9.0608 0.71 constant 5.2657 101.17 EDLEV_F 0.4212 9.15 M 0.0003 0.03 EDLEV_M 0.2210 3.97 HEAD 0.0315 1.80 AGE/10 -15.8435 -0.92 DINTINC -0.0292 -1.67 (AGE/10)**2 10.4728 1.18 LINTINC+1 0.0063 2.11 (AGE/10)**3 -3.0001 -1.36 HOWN 0.0192 2.13 (AGE/10)**4 0.3885 1.46 CHILD 0.0062 0.75 (AGE/10)**5 -0.0187 -1.49 AGE/10 0.0467 1.54 AGE_F_BIRTH 0.0135 1.56 (AGE/10)**2 -0.0061 -1.68 AGE_M_BIRTH -0.0026 -0.25 PUBLIC -0.0461 -5.11 <2_PARENTS -0.1956 -1.36 LHEARN -0.0880 -5.13
F_SELF 0.3409 2.73 sigma hours 0.1223 76.21
F_CIVIL 0.8536 5.85 F_WHITE 0.5613 4.56 M_EMPL -0.0718 -0.87 sigma edl 1.3177 41.13 bound 2 2.9358 52.33 bound 3 3.7846 72.48 bound 4 4.1131 92.95
---Table 3: Selection equation
---model 1 model 4 model 12
Variables parameter t-value parameter t-value parameter t-value
---constant pp 2.1047 0.13 2.2335 0.13 6.7201 0.44 AGE/10 -7.4239 -0.33 -9.1658 -0.41 -14.9415 -0.70 (AGE/10)**2 6.8308 0.58 7.3072 0.61 9.8622 0.86 (AGE/10)**3 -2.3831 -0.77 -2.4004 -0.78 -2.9507 -0.98 (AGE/10)**4 0.3639 0.94 0.3550 0.91 0.4131 1.09 (AGE/10)**5 -0.0205 -1.07 -0.0195 -1.03 -0.0220 -1.18 F_SELF 0.2545 2.42 0.2590 2.44 0.1233 1.14 F_CIVIL 0.5667 4.23 0.5841 4.33 0.4047 3.29 F_WHITE 0.2615 2.30 0.2337 2.05 0.0546 0.50 ED_LEVEL ED_LEVEL1 0.2102 0.29 -0.3882 -1.97 0.0714 0.52 ED_LEVEL2 0.0595 0.08 -0.2111 -0.73 0.5670 3.74 ED_LEVEL3 -0.2383 -0.28 -0.6218 -1.87 0.2305 1.12 ED_LEVEL4 0.4555 0.35 -0.7544 -2.08 0.1656 0.81 ED_LEVEL5 -0.1916 -0.21 0.0142 0.03 1.0952 6.01
wage diff curr 3.5508 1.24 0.0000 ---- 0.0000
----wage diff lifec 3.2579 0.82 0.0000 ---- 0.0000
----rho ed pp 0.3219 3.41 0.3121 3.11 0.0000
----
---Table 4: Log Private Sector Wage Rate
---model 1 model 9 model 12
Variables parameter t-value parameter t-value parameter t-value
---const wpriv 3.0837 5.93 4.1821 13.92 4.1204 13.85 ED_LEVEL1 0.2218 5.09 0.1515 4.30 0.1537 4.43 ED_LEVEL2 0.4087 6.47 0.2759 6.18 0.2953 7.71 ED_LEVEL3 0.5148 7.31 0.3858 7.36 0.3960 7.75 ED_LEVEL4 0.6887 8.93 0.5581 9.32 0.5691 9.64 ED_LEVEL5 0.8041 8.82 0.5998 7.99 0.6432 13.22 M 0.0981 4.69 0.1012 4.86 0.0778 2.88 SIZE 0.0351 2.40 0.0361 2.44 0.0304 1.63 EXP/10 0.1699 3.16 0.1806 3.27 0.1807 3.31 (EXP/10)^2 -0.0441 -3.61 -0.0471 -3.88 -0.0469 -3.91 AGE/10 0.3605 3.73 0.3730 3.98 0.4120 4.69 (AGE/10)^2 -0.0341 -3.12 -0.0364 -3.52 -0.0404 -4.14 LHWMONTH -0.2912 -2.90 -0.4974 -9.20 -0.4943 -9.10 sigma w 0.2689 51.97 0.2678 26.61 0.2645 68.39 rho w pp -0.0290 -0.09 -0.2222 -0.82 0.0000 ---rho w ed -0.3064 -2.33 0.0000 ---- 0.0000 ---
---Table 5: Log Public Sector Wage Rate
---model1 model 9 model 12
Variables parameter t-value parameter t-value parameter t-value
---const wpub 4.4153 8.29 5.2295 12.22 5.5145 12.97 ED_LEVEL1 0.1276 2.09 0.0706 1.48 0.0617 1.37 ED_LEVEL2 0.3573 4.45 0.2773 5.29 0.1877 3.94 ED_LEVEL3 0.4460 4.23 0.3522 4.44 0.3007 4.06 ED_LEVEL4 0.4901 3.91 0.3711 4.42 0.3485 4.56 ED_LEVEL5 0.8149 7.33 0.6852 11.30 0.5187 10.56 M 0.0837 3.30 0.0841 3.31 0.1319 4.61 SIZE 0.0324 1.74 0.0308 1.66 0.0496 2.12 EXP/10 0.2702 4.50 0.2810 4.57 0.2362 4.25 (EXP/10)^2 -0.0681 -4.89 -0.0721 -5.06 -0.0587 -4.79 AGE/10 0.0994 0.71 0.0947 0.67 0.0727 0.57 (AGE/10)^2 0.0070 0.43 0.0081 0.48 0.0056 0.39 LHWMONTH -0.5441 -6.30 -0.6951 -11.14 -0.6711 -10.70 sigma w 0.2837 15.72 0.2924 16.11 0.2191 36.68 rho w pp 0.6963 8.74 0.8042 14.10 0.0000 ----rho w ed -0.1326 -1.28 0.0000 ---- 0.0000 ----
---Table 6: simulated unconditional and conditional wages; sample means
---model log wage private sector log wage public sector
---all private public all private public
---1 2.971 2.927 3.052 2.664 2.487 2.986 2 2.993 2.938 3.128 2.673 2.532 3.018 3 2.991 2.945 3.086 2.684 2.522 3.024 4 3.003 2.927 3.142 2.674 2.450 2.991 5 2.989 2.935 3.113 2.671 2.523 3.014 6 3.035 2.955 3.233 2.707 2.579 3.023 7 2.942 2.927 2.977 2.641 2.481 2.996 8 2.992 2.952 3.078 2.670 2.513 3.009 9 2.944 2.936 2.961 2.634 2.485 2.986 10 2.989 2.940 3.084 2.914 2.864 3.012 11 2.974 2.935 3.047 2.898 2.857 2.976 12 2.973 2.939 3.058 2.900 2.871 2.972
---Note: Definition of models: see table 1.
all: all workers (unconditional);
Table 7: simulated unconditional and conditional wages,
by education level (ED_LEVEL) and AGE; model 1
---log wage private sector log wage public sector
---all private public all private public
---ED_LEVEL=1 2.694 2.683 2.724 2.455 2.335 2.801 ED_LEVEL=2 2.891 2.881 2.918 2.558 2.436 2.867 ED_LEVEL=3 3.044 3.021 3.069 2.765 2.562 2.985 ED_LEVEL>=4 3.297 3.244 3.349 2.998 2.759 3.233 AGE<30 2.743 2.715 2.831 2.363 2.249 2.728 29<AGE<40 3.055 3.022 3.120 2.668 2.516 2.971 39<AGE<50 3.094 3.059 3.155 2.790 2.619 3.088 AGE>49 2.915 2.915 3.015 2.821 2.614 3.035
---Table 8: 90 percent confidence intervals unconditional and conditional
wage differentials; model 1.
---[(public sector wage rate/private sector wage rate)-1]100%
---all workers private sector public sector
---ED_LEVEL=1 -22.2 -19.3 -30.0 -26.6 0.6 9.9 ED_LEVEL=2 -28.3 -26.8 -35.6 -34.1 -6.1 -2.5 ED_LEVEL=3 -25.3 -22.6 -37.4 -34.6 -8.9 -4.9 ED_LEVEL=4 -26.1 -23.3 -39.8 -37.1 -10.9 -6.4 AGE<30 -32.9 -30.4 -38.4 -36.0 -12.4 -7.4 29<AGE -31.5 -28.9 -39.5 -37.0 -13.8 -9.5 39<AGE -25.7 -24.0 -34.8 -32.9 -7.2 -3.7 AGE>49 -15.7 -12.9 -28.7 -25.6 -0.0 4.5 all -26.3 -25.3 -35.4 -34.4 -6.3 -4.3
---Appendix: Data descriptio n
Table A1: Explanation of Variables
---Variable
---AGE Age of Individual
EXP a) Actual Labor Market Experience of Individual
ED_LEVEL0 Dummy; 1 if basic or intermediate schooling (Haupt/Realschule)
ED_LEVEL1 Dummy; 1 if basic schooling and apprenticeship
ED_LEVEL2 Dummy; 1 if intermediate schooling and apprenticeship
ED_LEVEL3 Dummy; 1 if high school (Gymnasium, Fachhochschule)/high school and apprenticeship
ED_LEVEL4 Dummy; 1 if engineering school or higher specific school
ED_LEVEL5 Dummy; 1 if university
ED_LEVEL Ordered variable on education, calculated from information about degree
TEARN Total Monthly Gross Earnings
HWMONTH b) Hours worked per month for pay
LHWMONTH Log of Hours worked per month for pay
HEARN Hourly earnings
LHEARN Log of Hourly earnings
INTINC Interest income per month
LINTINC+1 Log(Interest income per month+1)
DINTINC Dummy; 1 if interest income
M Dummy; 1 if married
BLUE Dummy; 1 if blue collar
WHITE Dummy; 1 if white collar
CIVIL Dummy; 1 if civil servant
HOWN Dummy; 1 if individual house owner
HEAD Dummy; 1 if individual head of household
PUBLIC Dummy; 1 if employed in public sector
SIZE Dummy; 1 if town larger than 100 000 inhabitants
CHILD Dummy; 1 if child younger than 16 in household
F_ERW Dummy; 1 if father employed when individual was 15
F_SELF Dummy; 1 if father self employed
F_WHITE Dummy; 1 if father white collar
F_BLUE Dummy; 1 if father blue collar
F_CIVIL Dummy; 1 if father civil servant
M_EMPL Dummy; 1 if mother employed when individual was 15
<2_PARENTS Dummy; 1 if grown up with father or mother only
EDLEV_F Ordered education variable, father (constructed from degree information)
EDLEV_M Ordered education variable, mother (constructed from degree information)
AGE_F_BIRTH Age of father when individual was born
AGE_M_BIRTH Age of mother when individual was born
---a)Construc te dfromabiogr aphicals che me ;aftertheageof 15.
b) Two variables on hours worked are available: normal h our s wor ke d, and actual hours worke d
in cluding overtime. Furthe rmor e, the individual was asked whethe r over time work was paid for. The
var iable on hours worke d use d her e measu res earn ings-eective hours wor ke d and was c on struc ted as
Table A2: Missing Information
---Number Observation: Percent Public:
---Males in dependent employment 1809 29.96
No Missings in: AGE_F_BIRTH, AGE_M_BIRTH 1749 30.36 EDLEV_F, EDLEV_M 1722 30.48 F_ERW, M_EMPL 1564 31.39 ED_LEVEL 1557 31.34 TEARN, HWMONTH 1428 31.93
---Table A3: Descriptive Statistics
---Pooled Private Public
Variable Mean Std Dev Mean Std Dev Mean Std Dev
---PUBLIC 0.319 0 1 AGE 39.711 11.302 38.895 11.426 41.451 10.841 EXP 19.668 11.718 19.387 11.796 20.267 11.541 EDLEV 3.263 2.144 2.902 1.884 4.032 2.443 EDLEV_F 2.210 1.688 2.131 1.652 2.377 1.752 EDLEV_M 1.475 1.171 1.400 1.102 1.635 1.293 SIZE 0.556 0.496 0.549 0.497 0.572 0.495 AGE_F_BIRTH 31.622 7.052 31.513 7.089 31.855 6.974 AGE_M_BIRTH 28.397 5.981 28.344 6.059 28.508 5.815 HWMONTH 167.924 23.956 170.543 24.752 162.342 21.133 TEARN 3366.385 1279.640 3341.042 1310.932 3420.405 1209.868 HEARN 20.294 7.892 19.750 7.640 21.455 8.294 LHEARN 2.945 0.355 2.919 0.353 3.001 0.351 INTINC 193.441 701.630 176.326 650.588 229.925 799.187 DINTINC 0.247 0.235 0.274 HOWN 0.417 0.389 0.476 M 0.764 0.757 0.780 BLUE 0.462 0.584 0.203 WHITE 0.367 0.410 0.276 CIVIL 0.166 0.002 0.517 CHILD 0.455 0.463 0.438 HEAD 0.897 0.871 0.953 F_SELF 0.143 0.134 0.162 F_CIVIL 0.103 0.075 0.164 F_WHITE 0.141 0.134 0.155 M_EMPL 0.412 0.422 0.390 <2_PARENTS 0.069 0.068 0.070 ---NOBS 1428 972 448
---Appendix: Model Specica tion and Likelihood
Model
We address the issue of e ndogenei ty of experie nce by rewri ti ng some of th e equations and by
addi ng an equ ati on expl aini ng experi ence. The equations(1) (ed ucation l evel ), (3) (sele cti on)
and(4) (hours worked )remai n un changed.
Experi en ce: if we al low for endogenei ty of e ducation l evel, i t i s al so n atural to al low for
end ogen eityof e xp eri ence , si nce experien ce wi l l b e negativel y ae cted by edu cati on l evel . We
adda regression equati on toexpl ain exp eri enc e(Exp):
Exp=X Exp E xp +DE E +u Exp : (5)
D E i s the vec tor of e ducational dummie s (see sec ti on 4). X
Exp
c ontain s age and oth er
exogenousvari ab le s. Assu mp ti onsab outu
Exp
determin ewhetherthi sequati onshouldexpl i citl y
b etaken intoac count (see b e low).
Wage Rat es: totakeaccount ofexperien ceexp li ci tl y, we changethen otati onof (2):
l nW j =g W (X W ;E;Exp; j )+ Hj l nH+u j ;j=0;1: (6) X W
now excl ud ese xp eri ence . g
W
i s a given func ti on (for examp le a li near combi nation of
edu cati ondu mmi es,Expand Exp 2
).
Wage di erenti al s i n selec tio n equat ion: i n(3), we i ncl ude b oth the cu rrent and th e
l ifec ycle wagedi erenti al. The re aretwoways to de nethecurrent wage di erenti al:
1 c 1 l nW =g W (X W ;E;Exp; 1 )0g W (X W ;E;Exp; 0 )+( H1 0 H0 )ln 160; (7) 1 c2 l nW =1 c1 lnW +u 1 0u 0 : (8) 1 c1 l nW do e snotd ep en d uponu 1 or u 0
. Iti sth edi eren cebetweenp redi ctedl ogwagesfor
astandardworkin gmonth ,nottakin gaccountof p otential kn owle dge ofu
1 andu 0 . We d enote these l ogwages byl nWP 1 and lnWP 0 . 1 c2
l nW i s preferabl e from an economic poi nt of vi ew, sin ce the i ndi vid ual wil l also take
account of u
1 - u
0
. Assume for the moment that
l
=0 (no li fe cyc le wage di erenti al i n (3)).
Then,i fwe use1
c 2
l nW,wecan wri te the sel ecti on equation (3)in termsof 1
c1 l nW:
S 3
where v S =u S + c (u 1 0u 0
). Thi sshows th at (7) and (8) l ead to observational equi val ent
mo del s, unl esssp e ci c assumptions onthe covari ancesof u
S withu E ,u 1 and u 0 aremade.
For th el ifec ycle wagedi erenti al, agai n, two de ni ti ons can besuggested.
1 L1 l nW =l nNPV(WP 1 )0l n NPV(WP 0 ); (10) 1 L2 ln W =1 L1 l nW +NPV(u 1 0u 0 ); (11) whereNPV(WP 0 )and NPV(WP 1
) arethenetpresentval ue sofpred ic ted wages i nthetwo
sectors,forsomegi ve ndi scountrate . Thepatternofl ogwagesasafuncti onofageandexp eri enc e
i s taken i nto acc ou nt. In fac t, we ap proxi mate NPV by th e average val ue of predi cted wages
at ve equ id istant points of time duri ng an i nd ivi dual 's workin g li fe. Thi s i s a rath er rou gh
approxi mati on. We assu me th at i ndi vid uals d o n ot change sec tor or l ose thei r job, and that
cohort eects do n ot aect wage s. Worki ng with the l i fe cyc le wage di erenti al requ ires an
assumptionab outthe ti mep ersi sten ceoftheerrorterms. Iftheu
1 and u
0
ofone i ndi vid ualare
unc orrel atedovertime,th eyapproxi matel yave rageout,and(10)i sare asonabl eapproximati on.
Ifu
1 and u
0
remai n constant overti me, (11) i s to be used . S inc e, however, NPV(u
1 0u 0 ) wil l b ea li near functi on of u 1 and u 0
, (10)and (11)l ead to observational e quivale nt mo del s, asin
thecaseof thec urrentwagedi e re nti al. We therefore workwi th(10).
Di st ri buti onoferrorterms: Totheassu mp ti onsinsecti on4onu=(u
E ;v S ;u 0 ;u 1 ;u H ) 0 ,
we add theassump ti onthat u
Exp
i sin dependent of uand of al l exoge nousvari ab les.
Likelihoo d Contribu tions
We u se the sele cti on e quati on given i n (9). Th e case wi th the li fe c ycle wage dierential i s
si mi l ar. Consi dersomeone worki ngi nthepub li csec tor(S=1). E,Exp,W
1 (= W) an d H are observed, W 0 ,E 3 and S 3
are notobserved. Denote , forgiven parameter val ues, the 'resid uals'
of(5),(6)and(4)bye E xp ,e W ande H
. Forgi ve nparame ters,the searethereal iz ati on sofu
E xp , u W and u H
. Denote th edensi ty of xcond iti on al ony by f
xjy
. The l i kel i ho o d contri buti on can
b ewri tte nas L= Z R(E ) Z R(S) f E 3 ;E xp;S 3 ;lnW 1 ;lnHjX (E 3 ;Exp;S 3 ;l nW 1 ;l nH)dS 3 dE 3 : (12)
Here R (E) is the regi on of possi bl e valu es of E 3
for th e ob se rved value of E (for gi ven
parame ters m
j
). R(S)i s dene d li ke wise (R(S) =[0;1 )). X contai ns al l exogenous variabl es.
(12)can be rewritteni n termsof resid uals:
L= Z Z q jD et jf u E ;v S ;u 1 ;u H ;u Exp (u E ;v S ;e 1 ;e H ;e Exp )dv S du E : (13)
HereRU(E)andRU(S)aretherangesofthee rrorsu
E an dv
S
correspondi ngR(E)an dR(S).
D et isthe Jacobianterm:
D et=10
H1
W
: (14)
The integral i n(13) can bewri ttenas ade nsitytimesa b ivari ate condi ti onalp robabi l ity:
L= q jD et jf u 1 ;u H ;u E x p (e 1 ;e H ;e Exp ) Z RU(E) Z RU(S) f u E ;v S ju 1 ;u H ;u Ex p (u E ;v S )dv S du E : (15)
The integral i s a bi variate cu mul ati ve n ormal p rob abi l ity (see, e.g., Greene , 1993, p. 76).
Si nce u
E xp
i s i ndepende nt ofthe othere rrors,L can bewritten asfoll ows.
L= q jD etjf u E x p (e Exp )f u1;u H (e 1 ;e H ) Z RU(E) Z RU(S) f u E ;v S ju1;u H (u E ;v S )dv S du E : (16)
The factor rel ated to u
Exp
i sth eon ly factor contai ni ngth eparametersin (5)and contai ns
no other parameters. As a c on se quenc e, (5) can b e i gn ored whi l e e sti mati ng the rest of th e
mo del ;th emo del can be estimatedas i fExpwasexogenous. The i ntuiti on isthat end ogene ity
ofExpi s on ly c au se dbyen doge nei tyof E,and thi si staken i ntoacc ou nt.
Simula tions
Tocomp utethewaged ierential si nsecti on6,wehaveusedthemo deltosimul ateal len doge nous
vari ab les, taki ng exogenous vari able s as gi ven. We h ave treated experien ce as an en doge nous
vari ab le. Forth isp urp ose, we sp e cifyand estimate (5). We use a li near equation, and assu me
normal i tyof u
Exp
. The esti mate drel ati on is
Exp=015:22 0 1:10D E1 03:03D E2 04:40D E3 0 6:61D E4 08:62DE5 + 0:93AGE+0:69M+ u
Exp
(17)
DE1- DE5 are theeducati on l eveldu mmi es(0 excl uded ). Mi s1 if marrie d,0otherwi se. Al l
vari ab lesare si gni cant at the5percent l evel. The esti mate of(u
E xp
) i s 4.22;the R 2
i s0.87.
The si mul ati on now works as fol lows. For each i ndi vi dual , we draw 10 val ues of all e rror
terms from th e esti mated sixvari ate normal distrib ution of error terms. Usin gactu al valu es of
exogenous vari ab le s, we re cursivel y compute E from (1), Exp from (17), and S from (3). For
each sectorsep aratel y,we solve (2)and (5) toc ompu te l nW
0
and l nW
1
. We the n average over
draws p er ind ivi dual and over i nd ivi dual s i n the (su b)p opul ati on. I n thi s way we construct
tab les 6 and 7, b ased on the parameter estimate s. For tab le 8, we re p eated the exerci se 100
