On he join p oduc ion o
esea ch and aining∗
An ónio F ei as†and Inés Macho-S adle ‡
Uni e si a Au ònoma de Ba celona
Feb ua y 9, 2011
Abs ac
Uni e si ies and esea ch ins i u ions ha e he esponsibili y o p oduce science
and o p o ide aining o new gene a ions o esea che s. In his pape , we p o-
pose a model o analyze he de e minan s o a senio scien is ’s decisions abou
alloca ing ime be ween hese asks. The esul s o his decision depend upon he
cha ac e is ics o he esea ch p ojec , he senio scien is ’s conce n o aining and
he expec ed inna e abili y o he junio scien is in ol ed. We analyze he ole ha
a egula o can play in de ining bo h he alue o scien i ic p ojec s and he u u e
popula ion o independen scien is s.
Keywo ds: Alloca ion o ime be ween asks; esea ch and aining; senio and
junio scien is s
∗We a e g a e ul o Da id Pé ez-Cas illo, Pau Oli ella and Ped o Rey-Biel o hei insigh ul com-
men s. We would also like o hank he pa icipan s in he p esen a ions a Jo nadas de Economía
Indus ial (Mad id, 2010), Uni e si a Au ònoma de Ba celona, Uni e sidade do Po o and Uni e si a
Ro i a i Vi gili. We would like o hank ECO2009-7616, Consolide -Ingenio-CSD2006-16, 2009SGR-169,
and Fundação Ciência e Tecnologia (G an SFRH/BD/40182/2007) o inancial suppo . Inés Macho-
S adle is a esea ch ellow o MOVE (Ma ke s, O ganiza ions and Vo es in Economics) and Ba celona
Economics.
†Depa men o Economics. Uni e si a Au onoma de Ba celona. E-mail: an[email p o ec ed]
‡Co esponding au ho . Depa men o Economics. Uni e si a Au onoma de Ba celona. Fac CCEE
Edi ici B. 08193 Bella e a (Ba celona). Spain. Phone: 34 93 5811812. Fax: 34 93 5813767. E-mail:
ines.mac[email p o ec ed]
1
1 In oduc ion
I is widely accep ed ha uni e si ies and esea ch ins i u ions ha e he esponsibili y
o p oduce science. Howe e , he e is ano he ask o g ea impo ance o ou socie y’s
ad ancemen o knowledge: aining he new gene a ions o esea che s. In his pape , we
conside senio scien is s o be in ol ed bo h in doing esea ch and in p o iding aining
o junio scien is s, as in a sys em o app en iceship. Unde s anding he alloca ion o ime
among he wo ac i i ies is o g ea in e es because he aining o junio esea che s needs
o be pe o med by he people who know how o do esea ch, and his is c ucial in assu ing
a high-quali y esea ch wo k o ce o he u u e. Howe e , he e a e oices ha poin ou
ha ou esea ch ins i u ions may be ailing in his dimension, meaning ha he e is a
sho age o ime de o ed o aining scien is s able o pe o m ou s anding independen
esea ch in he u u e.1In his pape , we p opose a model o add ess his p oblem,
o discuss he alloca ion o ime be ween esea ch and aining he nex gene a ion o
esea che s and o discuss he p oblems ha may a ise.
Ou mo i a ion comes om wo ac s. On he one hand, i is a documen ed ac ha
he mos p ominen candida es who a ain an independen esea ch s a us a e PhDs and
pos doc o al esea che s who, h i e h ough mo e expe ience and skills in science, ei he
in academics o in indus y (Cech and Bond, 2004). The li e a u e on highe educa ion,
human esou ce managemen and men o ing ex ensi ely ecognizes he effec s o aining
by senio s affin he compe ence, p oduc i i y, ca ee de elopmen and independen skills
o young p o essionals, bo h in indus y and academia. The s uden -supe iso ela ion-
ship is he mos c i ical issue affec ing he quali y o he PhD aining (which affec s bo h
e en ual job placemen and success in ob aining a deg ee). In his p ocess, i is na u al
ha doc o al s uden s hold expec a ions wi h espec o he ole o hei supe iso s. The
mos impo an expec a ions a e guidance in he ea ly days o ob aining a PhD, knowl-
edge abou he a ea hey a e wo king in, and mos impo an ly in ol emen wi h hei
wo k (Pole e al., 1997).2On a pos doc o al le el, Vogel (1999) epo s he expe ience
1Ob iously, an al e na i e o aining one’s own esea che s is o a ac esea che s ained elsewe e.
While his is an in e es ing idea, we choose o igno e his opic in his pape .
2Mu ay (2004) illus a es his issue on a s udy on academic scien is s wo king o he indus y in
he biosciences. The au ho iden i ies one o he sou ces o social capi al o be he scien is ’s labo a o y
2
o a p incipal in es iga o (PI) supe ising pos docs in an in e na ionally app aised lab.3
She s a es ha he PI’s key o p oducing success ul and high-quali y junio scien is s is
o p o ide hem wi h o iginal ideas and o ien a ion, o encou age s ong pa icipa ion in
he p ojec s, and o lis en o hem o assess hei skills, mo i a ions and ambi ions.
On he o he hand, aining p oblems pe sis on a global scale. S uden doc o al a i-
ion emains a common p oblem in PhD aining, and his is es ima ed a app oxima ely
50% on he U.S. (Lo i s, 2001). In a case s udy abou o me s uden s who spen a leas
wo yea s in a PhD p og am Golde (2000) iden i ies a lack o suppo and guidance om
supe iso sasoneo hecauseso a i ion.Theau ho isalsoable oiden i ycha ac e -
is ics o good supe ision: he amoun o ime spen , he quali y o in e ac ions be ween
s uden and supe iso , and an in e es in he s uden ’s wo k a e impo an o gua an ee
aining success. Accessibili y seems o be an impo an issue as well.4T aining p oblems
also occu a he pos doc o al le el. Puljak (2006) epo s ha he mos common com-
plain in pos doc o al aining is i onically, a he lack o pos doc o al aining. Pos docs
join a esea ch lab and, sho ly he ea e , many ealize ha hey a e on hei own. I
has also been iden i ied ha some ad iso s end o ake o e he design o expe imen s,
making pos docs eel like hey a e o e educa ed echnicians.5
We s udy his issue by building a mul i ask model ha examines he incen i es o a
senio scien is o p o ide aining o a junio scien is . The senio scien is chooses he
ime o alloca e o he own esea ch and he ime o ain o he junio scien is unde
he supe ision. We hen e alua e he impac o ime alloca ion on he le el o esea ch
ne wo k, which includes his o me Ph.D. ad iso , pos -doc o al men o , g adua e s uden colleagues and
his own g adua e s uden , esiden , and ellow ad isees.
3A PI is a head esea che and au ho who supe ises doc o al s uden s, concei es ideas and conduc s
p ojec s ha may include collabo a ing wi h esea ch assis an s (A mb us e , 2008).
4I seems ha he e can be a misma ch in he pe cep ions o he supe iso and o doc o al s uden s
wi h espec o accessibili y. In a s udy on he p o isions o PhD aining in biomedical esea ch PhD
p og ams, i ually all supe iso s epo ed mee ing equen ly wi h hei s uden s, whe eas 1/4 o he
s uden s epo ed p oblems in accessing hei supe iso (F ame and Allen, 2002).
5Ne ad and Ce ny (1999) also su ey he pe spec i e on pos doc o al employmen in he U.S. and
epo ha he e exis s a gene alized discon en on behal o pos doc o al esea che s. The leng h o
pos doc o al appoin men s has inc eased and hese appoin men s a e inc easingly being seen as ‘holding
base’, a he han being an impo an s ep in a young esea che ’s ca ee .
3
and he inal skills o he junio scien is s as a esea che . The junio scien is is no an
ac i e playe in ou model (he does no make any decisions), bu has a p oduc i e ole
in he p ojec (he con ibu es o i s inal alue). In addi ion, we assume ha he junio
scien is ’s inal capabili ies a e no only affec ed by he aining ecei ed om he senio
scien is bu a e also affec ed by his inna e abili y. On his espec , we abs ac om
in o ma ion ea u es: senio and junio scien is s ha e he same in o ma ion abou he
junio scien is inna e abili y.6
No su p isingly, when we analyze he senio scien is ’s alloca ion o ime be ween
esea ch and aining, we ind ha when she has mo e ime a ailable his esul s in mo e
ime alloca ed o bo h asks. Also, we show ha when he e is an inc ease in he inna e
abili y o he junio scien is , an inc ease in he impo ance ha aining has on he senio
scien is ’s u ili y unc ion, o a dec ease in he p oduc i i y o he senio scien is in he
p ojec hen he e is a endency o inc ease he ime alloca ed o aining. We also discuss
he inal capabili y o he junio scien is and he inal alue o he scien i icp ojec in
diffe en scena ios. Mos in e es ingly, we show ha igno ance abou he ue inna e
abili y o he junio scien is may lead o mo e aining o less able junio scien is s,
while he e is a endency owa d an unde -in es men in aining o he mos alen ed
ones.
As a obus ness check, we conside wo ex ensions. Fi s , we conside he case whe e
he senio scien is can also spend ime selec ing a be e junio scien is . Second we
examine he case whe e he senio scien is chooses he o al amoun o ime she will
wo k (and alloca e o esea ch and aining), ha is, he o al amoun o ime spen on
bo h asks.
We also discuss possible policy ins umen s o a egula o who is conce ned wi h
maximizing he alue o p ojec s and a aining highly quali ied scien is s in a desi ed p o-
po ion. We highligh ha he implemen a ion o aining p og ams in ea lie educa ion
6This does no mean ha he junio scien is ’s inna e abili y is public in o ma ion. I is ex-an e
unknown by bo h pa icipan s. E en hough a s uden is selec ed o pa icipa e in a g adua e p og amme
o in a lab acco ding o a GRE sco e, and o he in e nal admission c i e ia o a depa men , signi ican
unce ain y emains in p edic ing i a s uden has he po en ial o become a success ul independen
esea che (Lo i s, 2005).
4
and oughe selec ion p ocesses o a ac high-abili y junio scien is s o esea ch unde
supe ision, as well as a ac i e aining condi ions, can be effec i e measu es o a ain
i .
Following he wo k by Holms om and Milg om (1991), whe e he au ho s p opose
a p incipal-agen model whe e he p incipal wan s he agen o pe o m mul iple asks,
se e al pape s ha e conside ed he incen i es o scien is s o pe o m diffe en asks. Fo
example, Lace e a and Zi ulia (2008), in a con ex o co po a e science wi h a g ea deal
o compe i ion, p opose a model o explain he op imal choice o an effo o do applied
esea ch and an effo o do basic esea ch. They analyze he s eng h o incen i es in he
effo alloca ion decision o he scien is and he effec s o diffe en le els o compe i ion. In
Banal-Es añol and Macho-S adle ’s wo k (2010), he au ho s p esen a model o incen i es
o a esea che who can choose o ei he alloca e ime be ween unde aking a new esea ch
idea o de eloping an exis ing one ha will deli e immedia e comme cial bene i s. In he
same b anch o he li e a u e, Walckie s (2008) a gues abou whe he i is mo e a ac i e
o a uni e si y o p oduce bo h esea ch and eaching. The au ho conduc s his analysis
in a con ac ual se ing be ween he uni e si y (p incipal) and he academic/scien is
(agen ) and s udies he incen i es o uni e si y scien is s o pe o m ei he one o he
asks o bo h o hem. In con as o Walckie s (2008), whe e he agen does eaching a
he unde g adua e le el, we conside aining a he g adua e le el which implies ha he e
a e complemen a i ies among he wo asks. Walckie s (2008) uses an ad e se selec ion
amewo k, whe e esea che s diffe on hei p e e ence o bo h asks7and he shows ha
i can be op imal o p oduce esea ch and eaching in he same ins i u ion (bundling he
wo asks).
This pape is o ganized as ollows. Sec ion 2 desc ibes he model and analyzes he
equilib ium alloca ion o ime o he wo asks: esea ch and aining. I also p o ides
he compa a i e s a ics o he equilib ium effo s wi h espec o he pa ame e s o he
model. In Sec ion 3, we e alua e and d aw he pa e ns ha he p ojec ’s expec ed alue
and he junio scien is ’s inal capabili y ollow. We also p esen he ex-pos abili y o he
junio scien is and he ole o impe ec in o ma ion in he dis o ions wi h espec o
7In ou model, we could also discuss he esea che p e e ences, bu his is no he main aspec o he
analysis.
5

he ull in o ma ion and efficien ou comes. In Sec ion 4 we pe o m a obus ness check
by conside ing wo possibili ies. Fi s , we conside ha he senio scien is can choose
he o al amoun o ime o exe in bo h asks. Second, we conside he incen i es o
a senio scien is o spend ime in p e ious ac i i ies ha allow he o know mo e abou
he inna e abili y o he junio scien is . In Sec ion 5 we discuss some policy ins umen s
ha may change he ime alloca ion. In Sec ion 6 we conclude. All p oo s a e emi ed
in he Appendix.
2BasicModel
We conside a senio scien is who is in cha ge o a esea ch p ojec and alloca es he ime
be ween esea ch and he aining o a junio scien is unde he supe ision. We deno e
he esea ch effo by and he aining (guidance o educa ion) effo by and assume
ha he senio scien is has limi ed ime  o alloca e o hese asks. Fo mally, he senio
scien is ’s ime cons ain is w i en as:
+=
In Sec ion 4.1, we s udy how he a ailable ime  ha he senio scien is wo ks is de e -
mined. Fo now, we assume ha 0is exogenously gi en.
In ou model, he junio scien is does no make any decisions. He is endowed wi h an
inna e abili y ˆ,ex-an e unknown by all he playe s. We assume ha he e is a popula ion
o junio scien is s wi h diffe en inna e abili ies. The inna e abili y o he junio scien is
who wo ks wi h he senio akes a alue in he in e al [¯],wi h¯, and he expec ed
inna e abili y is ()8
The senio scien is ’s ec o o effo s affec s wo ou comes: he quali y ( he alue) o
he esea ch p ojec and he inal capabili y o he junio she is aining.
The inal capabili y o he junio scien is depends on his inna e abili y and on he
senio scien is ’s educa ional effo . Ou iew is ha educa ion p o ided by he senio is
8In ou model, he e is always symme ic in o ma ion abou he junio scien is ’s inna e abili y. Unde
comple e in o ma ion senio and junio know ha his inna e abili y is ˆ;unde igno ance hey expec i
o be ()
6
a necessa y inpu o de elop he junio ’s scien i ic capabili y. The junio scien is ’s inal
capabili y, deno ed by , is a unc ion o his ue inna e abili y ˆ∈[¯]and he aining
he ecei es , and i is de ined as ollows:
=ˆ(1)
Wi hou aining, e en he mos gi ed junio scien is will no be able o acqui e he
capabili y o wo k on he esea ch p ojec in a p o i ableway(andmaybe una esea ch
p ojec in he u u e).
The p ojec ’s alue depends on he di ec esea ch effo exe ed by he senio scien is
and on he junio scien is ’s inal capabili ies. The scien i ic alue o he senio ’s p ojec
is gi en by:
=+(2)
whe e is he p oduc i i y o he senio ’s esea ch ime ,andcap u es he syne gies
o wo king oge he wi h a junio scien is o capabili y . In his sense, senio and junio
scien is s p o ide complemen a y inpu s o he esea ch p ojec . Resea che s may ha e
diffe en p ojec s de ined by ( )and we will discuss his u he on. The le el may
ep esen he publica ions ob ained, pa en s achie ed o o he esul s o he disco e ies.
No e ha by ollowing his unc ional o m, no alue will be p oduced om he p ojec i
he senio scien is does no p o ide any esea ch effo .
We assume ha he senio scien is ’s u ili y unc ion combines he p ojec ’s alue and
he junio ’s inal capabili y. Fo mally,
( )=+
The p ojec ’s alue is included in he senio ’s p e e ences because i is a e i iable ou come
ha de e mines he senio scien is ’s payoff. I is also a p oxy o he usual a gumen o
pee ecogni ion and he “puzzle joy” (S ephan and Le in, 1992). The junio scien is ’s
inal capabili y en e s he senio ’s u ili y in a p opo ion , which ep esen s he ela i e
app ecia ion o he aining ou come. We may also in e p e his second e m o he
senio ’s u ili y as a conce n wi h epu a ion associa ed o ha ing a ne wo k and disciples
who excel in he p o ession.9
9Ou model aims o encompass he ac ha bo h senio and junio scien is s bene i om he ain-
7
Gi en he pa ame e s (   )and he ex-an e expec a ion abou he junio scien-
is ’s inna e abili y wi h ∈{ˆ ()}, he senio scien is chooses he op imal alloca ion
o ime be ween and  ha maximizes he ex-an e (expec ed) alue o he u ili y:10


{++}
 +=
∈[0]
∈[0]
F om he solu ion o his p oblem we ob ain he esul ha ollows.
Lemma 1 Gi en (   )and he inna e abili y o he junio scien is  wi h ∈
{ˆ ()} he senio scien is ’s alloca ion o ime among he asks o esea ch and aining
is:
a) When and  
−
∗
=0and ∗
=
b) When  
+
∗
=and ∗
=0
c) O he wise,
∗
=
2+−
2 and ∗
=
2−−
2
ing ela ionship. Fo he senio scien is , aining inc eases isibili y and epu a ion when he young
p o essional is a p oduc i e membe . The e o e, she ea ns mo e espec om he o ganiza ion by de-
eloping he ainee (K am, 1983). This model also includes he aine ’s inne sa is ac ion in passing
along knowledge (Le inson e al., 1978). Fo he junio scien is , he bene i s include lea ning echnical
aspec s o he p o ession, de eloping w i ing and c i ical skills, de ining ca ee pe spec i es, pe o ming
esea ch collabo a ions (K am, 1983) and ecei ing an impo an push owa d building ne wo ks (K am
and Isabella, 1985).
10No e ha is a linea unc ion o  ha allows us o use a simpli ica ion whe e we w i e he ex-an e
alue o he p ojec as a unc ion o ,∈{ˆ ()}. This allows us o conside a he same ime he
cases whe e he in o ma ion abou he junio scien is ’s inna e abili y is pe ec o impe ec .
8
The senio scien is ’s alloca ion o ime o he in e io solu ion depic ed in Lemma 1
µ∗
=
2+−
2 
∗
=
2−−
2 ¶
depends on all he ele an pa ame e s. I shows he de ia ion om he hal -hal dis ib-
u ion o ime as a unc ion o he senio scien is ’s effec i eness in he esea ch p ocess
(), he complemen a i y among he senio ’s and junio scien is ’s pa icipa ion (), he
expec ed inna e abili y o he junio () and he senio ’s conce n abou he junio ’s ain-
ing (). Lemma 1 also shows ha when he junio has a low expec ed abili y he does
no ecei e any aining. I also shows ha when he senio scien is ’s conce n abou
he junio ’s aining is high as compa ed o he ime a ailable and he complemen a i y
() hen he possibili y exis s ha she decides ,only o pe o m aining. No e o
example, ha i =0(and 6=
)i.e., he e is no effec o he junio scien is owa d
he esul o he esea ch p ojec , hen ime will only be alloca ed o aining.
Co olla y 2 Fo he combina ion o pa ame e s sa is ying ∈[(−)(+)]
( egion c) in Lemma 1), he s a ic compa a i e o he effo s is p esen ed in Table 1:
    
∗
+− − iff +−
∗
−+ + iff + +
Table 1
As expec ed, he senio scien is ’s esea ch effo ( esp., aining effo ) inc eases ( esp.,
dec eases) when inc eases, dec eases o dec eases. Bo h effo s go in diffe en
di ec ions when inc eases, and he di ec ion o he change depends on he sign o −
In addi ion, bo h effo s inc ease wi h he ime  he senio scien is has o wo k.
The effec o in equilib ium is in acco dance wi h s ylized ac s. In a 5 1
2yea
longi udinal in es iga ion wi h 233 PhD s uden s (Paglis, G een, and Baue , 2006, which
was an ex ension o a simila s udy by G een and Baue , 1995), he effec s o supe iso y
men o ing o ad iso s on PhD s uden s in he applied sciences we e analyzed. The esul s
show ha supe iso y men o ing inc eases he p oduc i i y and he sel -efficacy o PhD
s uden s. Mos impo an ly, a posi i e ela ionship be ween s uden po en ial (abili y,
9
he dis o ion inc eases p opo iona ely. The effec o a highe p io ()o e he junio
scien is ’s abili y is a highe slope o he "igno ance" ex-pos cu e, which means ha
he dis o ion inc eases o lowe alues o ˆand will dec ease o highe alues. Mo e
accu a e aining is p o ided o he popula ion o junio scien is s wi h mo e po en ial.
â
q
)(aE




aE )(
Case



Igno ance
Full in o




aE )(



Figu e 4: ∗(ˆ)and (ˆ ()) when  ≥
Fo   , as illus a ed in Figu e 5, he dis o ion and he effec s o a highe ()
a e e y simila .
As in he case wi h he alue o he p ojec , he sign o he dis o ion may be aligned
o no aligned wi h social in e es . We will discuss his aspec in Sec ion 5. No e also ha
i he in e al [¯]is smalle o i , o a gi en in e al he expec ed inna e abili y o he
junio scien is , ()ishighe , heni maybe hecase ha mo eeduca ionisp o ided
unde igno ance and he dis o ion is no oo big.
4Ex ensions
Le us conside wo na u al ques ions ha may come o mind ha we p esen he e in
wo independen ex ensions. In he i s one, we allow o he senio scien is o choose
he amoun o ime ha she will wo k. In o he wo ds, is no exogenous bu he choice.
In he second ex ension we assume ha he ime a ailable is exogenously gi en, bu we
16

â
q*
)(aE
)
Case



Igno ance
Full in o




aE )(







aE
)(
aE



)(






Figu e 5: ∗(ˆ)and (ˆ ()) when   
allow he senio scien is o ha e access o a be e pool o junio scien is s a he cos o
some o he ime.
Bo h ex ensions can be iewed as a sequen ial decision p oblem whe e, once ei he he
ime alloca ed o wo k o he abili y o he junio scien is is de e mined, he analysis o
he p e ious sec ions ells us he esul in e ms o esea ch and aining. Hence, i is
use ul o use he op imal alloca ion o ime as a unc ion o and  o w i e he u ili y o
he senio in e ms o hese a iables. Using Lemma 1 we see ha :
a) When and  
−
∗( )=
b) When  
+
∗()=
c) O he wise,
∗( )=( +)2−()2
4 +µ
2−−
2¶
4.1 To al Time Wo ked
Un il now we ha e conside ed ha he ime  he senio scien is wo ks is ixed. Le
us now conside ha , as in he line o mo e adi ional mo al haza d models, he senio
17
scien is may decide he o al amoun o ime shewillde o e owo k( he o aleffo ).
To de e mine his o al wo king ime , he senio scien is maximizes he expec ed u ili y
ne o hecos o hewo king ime. Wewillassume ha hecos o wo king imeis
high enough. Mo e p ecisely, we assume ≥
2.16 Hence, he senio sol es

n∗( )−
22o
F om his p oblem, we ob ain he ollowing esul :17
Lemma 3 The senio scien is ’s o al ime as a unc ion o he pa ame e s is
a) When − ≥0and ≥
− 
∗=

b) When − ≥0and 
2≤
− o −  0and 2
−
∗=+
2−
c) When −  0and 
2≤2
−
∗=

Lemma 3 is depic ed in Figu e 6 in he space ( (−)).
F om Lemma 3 we conclude ha , as expec ed, he ime he senio scien is wo ks ∗
is a non-dec easing unc ion o     and is dec easing in  The compa a i e s a ics
16I he cos is smalle ha 2 he op imal ime goes o in ini e. In his case i would be na u al
o include a maximum ime limi  We will commen on his assump ion la e , bu we will concen a e
on he case whe e is high o he sake o simplici y.
17No e ha o − ≥0we ha e 
2≤
− and o −  0we ha e 
22
−Hence, he
egions o Lemma 3 a e well de ined.
18

a
c
c


*


ac
a


2
*
c
a


*


a
a
c




a
a
c2
Figu e 6: Op imal ∗in he space ( (−))
a e summa ized in Table 3.
    
∗=
+00−0
∗=+
2− +++−+
∗=
0+0−+
Table 3
Gi en he op imal ∗we compu e he ime alloca ed o each ask. As expec ed, he
ime alloca ed o bo h asks is dec easing in ( ha now plays a ole simila o a dec ease
in in he p e ious sec ions). Effo is non-inc easing and is non-dec easing in
he conce n o aining,  Mo e p ecisely, o ∗=
 he op imal alloca ion o ime is
¡=

=0
¢and esea ch inc eases wi h bu no hing is affec ed by o  A he
o he ex eme, o ∗=
 he op imal alloca ion o ime is ¡=0
=
¢Fo he
case ∗=+
2− he ime alloca ed o bo h asks dese es some a en ion, and we pe o m
compa a i e s a ics gi en in Co olla y 4.
Co olla y 4 When ∗=+
2− , egion b) in Lemma 3, we ha e ha he alloca ion o ime
19
o he asks is
∗
=1
2µ+
2− +−
 ¶
∗
=1
2µ+
2− −−
 ¶
and he compa a i e s a ics a e p esen ed in Table 4:
   
∗
(   ) + +iff

+iff

2
(2+)

+iff

2³(+)12
(−)12−1´
∗
(   )+iff
 + + +
Table 4
Fo comple eness le us ema k ha in a e sion o he model whe e is no cons ained
om below, and he e is a maximum amoun o ime  ha he senio scien is has
a ailable, he esul s will be simila , excep o low cos s ¡≤
2¢and/o small
enough ³|−|
 ´. In hese cases, he senio chooses o wo k o all he a ailable ime
and she alloca es all he ime ei he o esea ch () o o aining ()
(excep i = case whe e she is indiffe en ). Changes in o in do no affec he
o al ime alloca ed o wo k and only disc e e changes may affec o which ask his ime
is alloca ed. In hese cases, only changes o he ime a ailable o hese ac i i ies may
ha e an effec on he senio scien is ’s beha io .
4.2 WhenExpec edAbili yandTimeA eRela ed
In Sec ion 2 we analyzed he decisions o a senio scien is ha is ( andomly) ma ched
wi h a junio scien is o inna e abili y  Howe e , one may wonde abou wha happens
i he junio ’s expec ed inna e abili y depends on some p e ious ac i i y ha he senio
pe o ms and ha consumes ime. This may co espond o a selec ion p ocess ha ies
o iden i y a be e popula ion o junio scien is s, an ad e ising o in es men p ocedu e
ha aims o a ac a junio scien is wi h a highe expec ed inna e abili y, o an un-
de g adua e sys em ha p o ides be e skills and be e in o ma ion abou he junio s’
20
abili ies. He e, we model he ela ionship be ween he ime in es ed in inc easing he
inna e abili y o he junio she wo ks wi h and he emaining ime a ailable o esea ch
and aining.
Le us assume ha is he maximum amoun o ime a ailable o he h ee asks and
 he inna e abili y o he junio scien is i no effo is made o imp o e i . Le us deno e
by (−)wi h 0 he imp o emen o he inna e abili y o he junio scien is ha
he senio can ob ain by using an amoun o ime (−) o imp o e he quali y o he
junio wi h whom she wo ks, in such a way ha she will ha e  o alloca e o he asks o
esea ch and o ma ion. Hence, he abili y o he junio scien is wi h whom he senio
will wo k wi h is =+(−)
In his case, he senio scien is chooses ( )by maximizing he u ili y unc ion,
aking in o accoun he cons ain s =+(−). To simpli y p esen a ion and
o a oid cumbe some calcula ions o diffe en egions o pa ame e s, we jus p esen an
example whe e we assume ha he senio has no app ecia ion o he junio scien is ’s inal
capabili y (=0) and ha he complemen a i y effec is 1 (=1).Thisimplies ha we
will be in Region  ≥( ha , in his case, is educed o ≥0)Unde his pa ame e
combina ion, as a unc ion o  he senio ’s alloca ion o ime depends on whe he ≥

(and he ime will be alloca ed o esea ch and o ma ion) o ≤
 (and she will only
do esea ch).
Lemma 5 Assuming =0,=1and he ela ion be ween ime and abili y gi en as
=+(−), he senio scien is ’s decision on he op imal inna e abili y and on he
op imal amoun o ime spen in p e ious ac i i ies is:
a) When ( +)2−12 ≥0
∗= ++p( +)2−12
6and ∗=5( +)−p( +)2−12
6
b) When ( +)2−12  0
∗=and ∗=
Lemma 5 illus a es ha in p ojec s whe e he p oduc i i y o he senio scien is ’s
di ec esea ch () is low enough, he senio is willing o spend ime in selec ion ac i i ies
21

ha allow o wo k wi h a junio scien is o highe expec ed inna e abili y. This inding
is because being a less p oduc i e scien is , he senio will wan o inc ease he p ospec s
o wo king wi h a mo e alen ed junio scien is . When is high enough, hen she will
choose no o spend any ime in ac i i ies o e ie e mo e in o ma ion abou he junio ’s
inna e abili y, lea ing i a le el . This way, she chooses o alloca e all o he ime
esou ces o aining and esea ch only. No e also ha o a gi en combina ion o he
o he pa ame e s ()when o a e small i is mo e o en he case ha he senio ’s
op imal decision is no spend ime in imp o ing he inna e abili y o he junio (while his
does no mean ha she will no alloca e some ime o o ma ion).
5Wel a eAnalysis
We would like o conside he e a si ua ion wi h a social planne who is conce ned abou
he le el o esea ch ha he senio scien is achie es and he inal capaci y o he junio ,
ha he in e p e s as a measu e o he po en ial o he nex gene a ion o esea che s. We
conside i s ha his social planne has he wel a e unc ion:
=((ˆ ())) + ((ˆ ()))
whe e can be in e p e ed as he socie y’s ela i e conce n abou he capabili y o he
nex gene a ion o esea che s.
I coincides wi h  hen he decision o he senio and he aims o he socie y concu .
I and do no coincide, he social planne may be emp ed o in e ene. To discuss
his possibili y, we ake as a s a ing poin ou basic model p esen ed in Sec ion 2, whe e
we assume ha he e is no mo al haza d p oblem, jus a decision abou he alloca ion
o ime. An al e na i e way o looking a he compa a i e s a ic in Table 1 (and he
discussion a e i ) is o conside how socie y may induce changes in some pa ame e s o
affec he senio scien is ’s alloca ion o ime o esea ch and o ma ion. Fo his pu pose,
he social planne mus affec he senio ’s u ili y =++possibly using
( )and as ins umen s.18
18Ob iously, he social planne can also change he ime a ailable o hese asks ( o example, by
educing he senio ’s in ol emen in o he ime-consuming asks, such as adminis a i e ones).
22
I he ou come o esea ch and he ou come o aining a e e i iable, he egula o
can manipula e he decision o he senio scien is by changing he awa eness abou hese
wo a iables. The planne can inc ease he senio scien is ’s u ili y om he p ojec ’s
alue ( ha is, inc easing and in he same p opo ion o , equi alen ly dec easing )
o o inc ease he senio ’s payoffas a unc ion o he quali y o he junio she men o s
(inc easing ) ia hede ini ion o a success ul ca ee o he alloca ion o esea ch unds
ha weigh his aspec o he academic ca ee . No e ha inc easing bo h pe cep ions is
useless when he aim is o change he alloca ion o o al ime, because o al ime is ixed.
Also, i only publica ions (and o he measu es o he senio scien is p ojec esul s) a e
e i iable, he social planne can only encou age mo e ime o esea ch ( h ough enu e
ack ules, oppo uni ies o a el and access o esea ch unds, o pee es eem, which
in ou model co esponds o dec ease )bu he canno inc ease i abo e he na u al
inclina ion o he senio scien is . Only by discou aging esea ch can he ime alloca ed
o aining be inc eased.
The social planne can change he junio scien is ’s inna e quali y ( o example,
by ha ing an a ac i e and selec i e p og am o ellowships) ha allows he a ac ion
o be e s uden s. Indeed, se e al Eu opean expe ins i u ions (e.g., EURAB, ESF)
ha e gi en p io i y o he aining o scien is s and de eloped ac ions so ha pos doc o al
esea che s ascend o PIs in ecen yea s. These ac ions in ol e p o iding access o special
g an s, as well as p omo ing ee and secu e mobili y.
When o al ime is ixed, hese ins umen s ha e a posi i e effec on one ask bu
anega i eeffec on he o he . Bo h effo s only inc ease simul aneously by inducing a
highe , as al eady men ioned. I a mo al haza d si ua ion exis s, and he senio scien is
decides how much ime o wo k, he p e ious discussion o he ins umen s o use holds
pa ially. In his case, incen i izing he esul s o bo h esea ch and aining may be
op imal because hese ins umen s affec no only ime alloca ion bu also how much ime
he senio decides o wo k. As shown in Co olla y 4, i he cos o he effo o he quali y
o he junio is high enough, hen inc eases in ( )which co espond o a highe u ili y
associa ed o he alue o he esea ch p ojec , o inc eases in induce mo e esea ch
and mo e aining (because hey induce mo e incen i es o wo k). I junio s a e gi ed
enough, bo h ins umen s (inc easing he u ili y he senio scien is ecei es om esea ch
23
o om aining) ha e posi i e effec s on he senio scien is ’s dedica ion o bo h asks.
In a socie y whe e he popula ion o junio s is o low expec ed abili y, he ins umen s
ha e posi i e effec s on one ask and nega i e on he o he and encou aging one ac i i y
c owds ou he effo on he o he one. This emphasizes he impo ance o a ac ing a
good popula ion o junio scien is s. This commen connec s wi h he analysis conduc ed
in Sec ion 4.2 whe e Lemma 5 d aws a en ion o he possibili y ha he popula ion o
junio s can be linked o he ime alloca ed o selec hem. No e howe e , ha measu es
ha inc ease ∗will dec eases ∗. This may lead o an inc ease in he senio ’s dedica ion
o a ask bu may igge a dec ease in he ime alloca e o he o he ask unless he cos
o ob aining be e pools o junio scien is s,  dec eases.
Ano he poin o iew is o conside ha he social planne is no jus conce ned abou
he expec ed le el o esea ch and aining. His conce n may be o each high enough
ou comes in bo h asks. In o he wo ds, i can be he case ha he social planne is only
in e es ed in excellence and in achie ing he highes inno a ion le el (p ojec quali y) and
he highes le el o ex-pos capabili y.19 Imagine a social planne conside s esea ch o be
aluable only i ≥and wan s junio scien is s o be endowed wi h a minimum inal
capabili y ≥ o be conside ed good independen esea che s. In his amewo k, he
social planne ca es abou ˜
,
˜
=≥((ˆ ())) + ≥((ˆ ()))
whe e he minimum equi emen s ()a e gi en by he social planne a le el o exigency.
We use now he esul s p esen ed in Sec ion 3.1 based on he model whe e ime 
is gi en. To ha e p ojec s and young esea che s abo e he cu offs()wi h high
p obabili y (o a high p opo ion) he social planne may use he a ailable ins umen s
 ,. We ha e seen in Figu es 5 and 6 ha he le el o inal capabili y unde igno ance,
(ˆ ()), inc eases wi h he senio scien is ’s p io s wi h espec o he inna e abili y
o he junio .
To help he discussion along, in Figu e 7 (using he in o ma ion con eyed in Table 2)
19The eason may be ha he socie y may no conside esul s below a minimum equi emen on bo h
ou comes as an achie emen : he socie y may alue only "good enough" disco e ies o be pa en ed o o
imp o e knowledge, and only "capable enough" junio scien is s may be conside ed good esea che s.
24
we ep esen in he space ( ) he expec ed alue o he p ojec in equilib ium, as well
as he iso-p ojec alue cu es and he iso- inal capabili y cu es o he junio scien is ,
keeping cons an o he pa ame e s ( he do ed lines). This igu e shows ha a highe
o al amoun o ime always induces a highe expec ed p ojec alue as well as a highe
junio scien is capabili y. Howe e , inc easing only does no ha e he same effec . I he
social planne wan s p ojec alues o ha e a leas alue 0and he junio capabili y 0
hen i has, on one hand, o p ocu e a highe o al ime a ailable o he senio scien is ,
and on he o he hand induce as much as possible a selec ed junio scien is wi h enough
po en ial.
Fo he social planne , he senio scien is ’s p io s is a possible ins umen o ob ain
a supe io ou come in he aining componen because a highe p io induces mo e ime
alloca ed o aining. Besides he quan i y effec , which is he ac ha mo e o he
popula ion eaches an independen esea ch s a us (a ains abo e ), he e is a quali y
effec on junio esea che s since hey a e be e p epa ed. Analyzing he e, we con-
clude ha he p ojec alue unde igno ance inc eases wi h he senio scien is ’s p io s,
bu only un il a ce ain poin . Fo e y high alues o he expec ed abili y he equilib ium
alue o he p ojec s a s o dec ease. Hence, when ixing he le el o ()bo h effec s
mus be aken in o accoun . Inc easing he expec ed abili y o he junio s popula ion,
(), can be pe o med by implemen ing o inc easing subsidies o a oughe selec ion o
scien is s eligible o pe o m esea ch unde supe ision.20 Implemen ing good p og ams
in ea lie educa ion can also cause his shi . Also, offe ing mo e a ac i e condi ions
in p og ams o PhD and pos docs may a ac be e candida es o he ask, who a e
o he wise d awn o mo e a ac i e ca ee s in o he sec o s. These condi ions mean no
only be e s ipends, bu also be e lab equipmen accessible o junio scien is s. Im-
plemen ing such measu es will shi he popula ion o highe le els o inna e abili y, i s
o de s ochas ically domina ing he ini ial popula ion dis ibu ion o e en an inc ease in
20One can assume ha he senio scein is o i he depa men a e in a be e posi ion o assess he
abili y o a junio scien is , bu i also seems easonable o hink ha highe esou ces alloca ed o
he selec ion p ocesses may help. Any selec ion p ocess would include he pas educa ion o he junio
scein is , as well as conside ing he uni e si y o o igin and in i ing he junio s o an in e iew. I hese
esou ces a e no a ailable, hei own s uden s may be less isky ha ou side s.
25
wi h espec o he i s egion:

½µ−−
¶¾
  ≥
≤ +−p( +)2−4
2
The lag angian is L=³−−
´+(−)+(+−√(+)2−4
2−).TheFOC
is −
+−=0
The e a e wo possible cases o he lag angian mul iplie s:
1) 0=0=is a candida e.
2) 00.Thisholdswhen=+−√(+)2−4
2⇔ =which is a
pa icula case o 1). Hence =is again a candida e.
Fo malizing he p oblem wi h espec o he second egion, he FOC is:
−
−+=0
One possible case exis s o he lag ange mul iplie :
1) =00.In hiscase,=++√(+)2−4
2is a candida e.
Since he u ili y unc ion is dec easing in ,=is a candida e o he op imal
abili y.
Case b)  ≤and ( +)2−4  0
The egion o wo k wi h is ≤≤ +, since he unc ion always has posi i e
alues in his case. Since he u ili y unc ion o he senio is dec easing in ,=is a
candida e o he op imal abili y.
Case c)    and ( +)2−4 ≥0
This is a pa icula case o case 1.a), whe e we only conside he second egion, hence
=++√(+)2−4
2is a candida e o he op imal abili y.
We now summa ize he candida es o s ep 1:
=i  ≤
= ++p( +)2−4
2i    and ( +)2−4 ≥0
S ep 2: 2−( +)+ ≤0
32

The u ili y unc ion o be conside ed in his case is ∗( )=(+)2
4
Following hesamelogicasins ep1,weha e2subcases osol e hisp oblem:2.a)
when  ≥and ( +)2−4 ≥0; 2.b) when  ≤and ( +)2−4 ≥0.
The o he wo subcases a e impossible, since ( +)2−4  0means he unc ion
always has posi i e alues. Hence, in his s ep we ake as gi en ha ( +)2−4 ≥0
Case a)  ≥
The e is one egion o  o wo k wi h: ≤≤++2
√(+)2−4
2.Themaximiza-
ion p oblem is:

 (1
4µ(−−
)+¶2)
  ≥and ≤ ++p( +)2−4
2
The FOC is:
1
2µ(−−
)+¶µ(−3−
)−¶+−=0
The e a e 4 possible cases o he lag ange mul iplie s:
1) 0=0.Lookinga heFOC,i mus be ha (−3−
)−0, ha is,
∈(+−√(+)2−12
6++√(+)2−12
6),whichis hecasewhen=.
2) =00In his case, =++2
√(+)2−4
2is a candida e i ∈(+−√(+)2−12
6
++2
√(+)2−12
6).Wecheck ha indeedbelongs o his in e al. This holds
only i ( +)2−12 ≥0
3) =0=0=+±2
√(+)2−12
6a e candida es, p o ided ( +)2−12 ≥
0
4) 0,0. This holds when =+−√(+)2−4
2⇔ =. Hence =
is a candida e again.
The u ili y unc ion is dec easing om un il +−√(+)2−12
6inc easing om
hen on un il ++√(+)2−12
6, and dec easing onwa ds. Hence, when ( +)2−
12 ≥0=++√(+)2−12
6is candida e o he op imal abili y and when ( +
)2−12  0=.
Case b)  ≤
33
The e is one egion o  o wo k wi h:+−√(+)2−4
2≤≤++√(+)2−4
2.
TheFOCis hesameasincasea),hence hepossiblecases o helag angeanmul iplie s
a e:
1) 0=0.=+−√(+)2−4
2andi mus be ha ∈(+−√(+)2−12
6
++√(+)2−12
6).Since+−√(+)2−4
2+−√(+)2−12
6, indeed i is a
candida e.
2) =00.=++√(+)2−4
2andi mus be ha ∈(+−√(+)2−12
6
++√(+)2−12
6). I is s aigh o wa d o check ha indeed belongs o his
in e al, so i is a candida e, p o ided ha ( +)2−12 ≥0
3) =0=0In his case, =+±√(+)2−12
6p o ided ha (+)2−12 ≥
0
4) 0,0.In hiscase,=+
6, which happens when ( +)2−12 =0,a
pa icula case o 3).
Analyzing all he candida es and he beha io o he u ili y unc ion, =++√(+)2−12
6
is a candida e o he op imal abili y when (+)2−12 ≥0and =+−√(+)2−4
2
when ( +)2−12  0
We now summa ize all candida es o case 2:
= ++p( +)2−12
6i ( +)2−12 ≥0
=i  ≥and ( +)2−12  0
= +−p( +)2−4
2i    and ( +)2−12  0
As unc ion o he pa ame e s, we e alua e and compa e he u ili y o he solu ions
a ained in s ep 1 and s ep 2. The inal solu ions o ∗and ∗(a ained ecu si ely) a e:
( +)2−12 ≥0∗=++√(+)2−12
6∗=5(+)−√(+)2−12
6
( +)2−12  0∗= ∗=
34
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