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1 Dikuionpapierreihe Working Paper Serie Sc i e n c e a n d e a c h i n g: Tw o -d i m e n i o n a l i g n a l l i n g in he academic job marke Andrea Schneider Nr./ No. 95 Augu 2009 Deparmen of Economic Fächergruppe Volkwirchaflehre

2 Auoren / Auhor Andrea Schneider Helmu Schmid Univeriä Hamburg / Helmu Schmid Univeriy Hamburg Iniu für Finanzwienchaf / Iniue of Public Finance Holenhofweg Hamburg Germany Redakion / Edior Helmu Schmid Univeriä Hamburg / Helmu Schmid Univeriy Hamburg Fächergruppe Volkwirchaflehre / Deparmen of Economic Eine elekroniche Verion de Dikuionpapier i auf folgender Inerneeie zu finden/ An elecronic verion of he paper may be downloaded from he homepage: hp://fgvwl.hu-hh.de/wp-vwl Koordinaor / Coordinaor Kai Hielcher

3 Helmu Schmid Univeriä Hamburg / Helmu Schmid Univeriy Hamburg Fächergruppe Volkwirchaflehre / Deparmen of Economic Dikuionpapier Nr. 95 Working Paper No. 95 SCIENCE AND TEACHING: TWO-DIMENSIONAL SIGNALLING IN THE ACADEMIC JOB MARKET ANDREA SCHNEIDER Zuammenfaung / Abrac Po-doc ignal heir abiliy o do cience and eaching o ge a enure giving univeriie he poibiliy of eparaing highly alened agen from he low alened one. However eparaing ha mean ignalling effor for he highly alened become even more imporan in a wo-dimenional ignalling cae. Thi arac noice o ime conrain. Under weak condiion eparaing equilibria do no exi if ime conrain are binding. The exiing equilibria are more coly bu wihou addiional informaion compared o he onedimenional cae. Conidering hi, he efficiency of he curren wo-dimenional academic job marke ignalling can be improved by wiching o a one-dimenional one. JEL-Klaifikaion / JEL-Claificaion: I23, D82, J41 Schlagwore / Keyword: Muli-dimenional ignalling, Academic job marke, Teaching and Reearch

4 1 Inroducion No laer han he 19h cenury he German know he concep of he uniy of reearch and eaching. Thi idea of Wilhelm von Humbold ha mainly influenced epecially he German higher educaion yem and i ill preen oday. On he oher hand po-doc and profeor ofen rail again he double burden of uch a yem. Thee conflicing argumenaion in mind economi udy he opimal deign of he univeriy yem (e.g. Del Rey 2001, De Fraja and Valbonei 2008 or Gauier and Wauhy 2007) a well a heir opimal labour conrac behaviour (Walckier 2008). In line wih he econd par of lieraure he preen paper analye he poibiliy of eparaing highly producive agen from he low-producive one in a model where po-doc can ignal heir abiliy o do cience and eaching o ge a enure. Argumening in line wih a job marke inalling model i i neceary o menion he work of Michael Spence. Spence a he faher of ignalling model how educaion can be an efficien ignal o correc aymmeric informaion in he job marke. I due o him ha we know abou he exience of ignalling equilibria (Spence 1973; Spence 1974). 1 In conra o Spence who mainly deal wih he exience of equilibria Cho and Krep (1987) rank equilibria. They implemen an inuive crierion o eliminae equilibria ha are buil on unplauible ou-of-equilibrium belief. Thi ronger equilibrium concep i finally he baic equilibrium concep of he preen paper. Up o here all concep work in a one-dimenional world. Thu, agen end a one-dimenional ignal. Since fuure profeor produce a wo-dimenional oupu coniing of cience and eaching a muli-dimenional e up i needed. Unforunaely, paper on muli-dimenional ignalling are rare. One of he fir i by Roche and Quinzii (1985). Thi paper analye in a formal way he difference beween he one- and muli-dimenional ignalling e up. Auming a eparable co rucure hey give neceary condiion for he exience of a eparaing equilbrium. In he ame kind of model Enger (1987) focue on pareo-dominan eparaing equilibria. Armrong and Roche (1999) implify condiion ha are neceary o enure a eparaing equilibrium by auming a dicree ype diribuion. Thi alo i an aumpion of my model. A curren paper by Kim (2007) i of inere a well becaue i analye ime binding conrain in a wo-dimenional job marke ignalling 1 While Spence fir paper focue on he general exience of ignalling equilibria he econd paper highligh he differen marke form. 2

5 model. The aim of hi paper i o analye eparaing equilibria in a wo-dimenional ignalling model ha decribe he academic job marke. Po-doc ha differ in heir abiliy o do reearch and eaching can ignal boh alen o ge a enure. A one reul eparaing equilibria of he wo-dimenional cae can vanih wih ime binding conrain. Thi alway happen if eaching (cience) produciviy of he highly alened i higher han he cience (eaching) produciviy of he low-alened. Neverhele, implying he concep of parial eparaing equilibria i can be hown ha under weak condiion here i a lea one parial eparaing equilibrium. More preciely, agen ha are highly producive in boh oupu end he ame ignal like he ype ha i high-alened wih repec o he oupu ha i more prefered by he univeriie. Wha i mporan for policiy implicaion i ha he ignalling effor in he parial eparaing equilibrium - alhough i i maller han in he wodimenional eparaing equilibrium - i higher han in he one-dimenional eparaing equilibrium. Thi i of inere if ignalling only ha an effec on co bu no on produciviy a i i he cae in Spence (1973) and alo in he preen model. Thu, if ime conrain are binding in he academic job marke i could be more efficien o le po-doc only ignal on he oupu ha i more prefered by he univeriie. Under ime binding conrain univeriie can only diinguih highly producive from low-producive ype in one dimenion ju like in he one-dimenional cae. Having hi in mind here i no argumen for he wo-dimenional ignalling proce ha i currenly oberved in realiy. I ju implie addiional co. Only weak condiion concerning he ranking of he produciviy parameer are neceary o make a eparaing equilibrium under ime binding conrain impoible in he wo-dimenional cae. Thu, agen ha are highly-alened in boh oupu can no be idenified by univeriie. The remaining paper i rucured a follow: Secion 2 e he baic model. The exience of equilibria i analyed in ecion 3. While ecion 3.1 focue on he one-dimenional cae ha goe in line wih Spence (1973) ecion 3.2 exend he analyi o he wo-dimenional cae. In hi par I alo diinguih beween a iuaion where ime conrain are no binding reuling in he unique eparaing equilibrium i mo efficien for he univeriie and a iuaion where ime conrain are binding which may lead o he vanihing of he eparaing equilibrium. In he econd cae he exience of parial eparaing equilibria where ome ype of agen can be eparaed while oher play he ame ragey i analyed. Secion 4 conclude. 3

6 2 The model Aume a compeiive academic job marke wih a uni ma of academic. Each univeriy graduae produce cience and eaching which require pecific unobervable abiliie. 2 Scieni a well a oher labourer are no idenical bu vary in heir abiliie. There are four ype ij {HH, HL, LH, LL} of fuure profeor. 3 While i denoe reearch produciviy j decribe he eaching produciviy. Boh produciviie can be high (H) or low (L). Fuure profeor can ignal boh abiliie: Science ij and eaching ij, i, j {L, H}. A in Spence (1973) ignal do no have any influence on produciviy. Agen ue he ignal o influence he univeriie belief on heir abiliie. Thu, he pre-enure reearch and eaching oupu funcion a a ignal for po-enure produciviie. However, here i a ime binding conrain ij + ij = l. Signalling effor can no be higher han he available ime and herefore i limied. I aume he agen ij co funcion depending on hi ype i: c ij ( ij, ij ) = ij θ i + ij, (1) θj where θi and θj, i, j{l, H}, are he produciviie of cience and eaching repecively. Clearly, k > θk L, k {, } hold. For impliciy I alo aume k 1, k {, }. Implicily I aume ha he reearch (eaching) produciviy i independen of he abiliy o each (reearch). The fracion of ype ij agen in he populaion i denoed by α ij. The diribuion of he ype i common knowledge. Univeriie compee on propecive profeor. However, hey face aymmeric informaion and can only form belief on he agen abiliie via ignal. The profi of a univeriy i π((θ i, θ j ), w) = θi + θj w, where w i he wage paid o he agen. The compeiion of he academic job marke implie ha univeriie make a profi of zero and herefore wage are given by produciviie. Thu, he equilibrium wage offered by he univeriie i w where E i he expecaion operaor. w E[α ij (θ i + θ j)] (2) 2 In he remaining paper reearch, cience and publihing are ynonymouly ued. 3 Thi noaion follow Walckier (2008). 4

7 Alhough pre-enure publihing and eaching do no influence he produciviy univeriie can condiion wage offer on he pre-enure cience and eaching oupu. The opimal deciion of a propecive profeor of ype ij i max U ij = E[w ij ( ij ij, ij θi + ij )]. (3) θj ubjec o ij + ij l. In ecion 3 I will analye equilibria of hi ignalling model. 3 Signalling in he academic job marke Fir I focu on ignalling equilibria when univeriie are only inereed in cience (ecion 3.1). Thi analyi goe in line wih he ignalling model of Spence (1973). Aferward in ecion 3.2 I analye a wo-dimenional ignalling model where agen ignal on cience and eaching. In boh cae he main queion i if here are eparaing equilibria where ignalling can help o olve inefficien reul caued by aymmeric informaion. Therefore, pooling equilibria are only analyed in he margin. Under incomplee informaion here i need for a definiion of a perfec Bayeian equilibrium. Definiion 1 Perfec Bayeian Equilibrium (PBE): A PBE i a e ha coni of a ignal ( ij, ij ) for each ype of agen ij {HH, HL, LH, LL} and a wage offer w ij ( ij, ij) ued by he univeriie. For each ignal ( ij, ij) he univeriie make zero profi given he belief µ(ij ( ij, ij )) abou which ype could have en ( ij, ij ). Each ype ij maximie hi uiliy by chooing ( ij, ij) given he wage offer w ij of he univeriy. The univeriy belief mu be conien wih Baye rule and wih he agen raegy: µ(ij ( ij, ij )) = α ij P ij α ij Therefore, one can diinguih beween a eparaing equlibrium and a pooling equilibrium. In he fir cae all ype end differen ignal, i.e. ( ij, ij) ( i j, i,j ) if ij i j. In he econd cae he ignal i idenical for 5.

8 all ype, i.e. ( ij, ij), i, j {H, L}. In conra o a model e up wih wo differen ype of agen ha i normally ued, in he preen model here i alo he poibiliy for an equilibrium in which ome bu no all agen end he ame ignal. Such a perfec Bayeian equilibrium will be called a parial eparaing equilibrium. 3.1 One-dimenional ignalling Le u aume for he momen univeriie are only inereed in cience and no in eaching. In hi cae here i no value of eaching and herefore no agen end a eaching ignal. Thu, ype HH and HL can be inerpreed a one ype denoed by H. The ame apllie o LH and LL. Thi low produciviy ype i denoed by L. 4 Then he fracion of he high produciviy ype i α H α HH + α HL and he fracion of agen wih low produciviy i α L α LH + α LL. Under complee informaion he high produciviy ype would earn a wage of while he ype wih low produciviy ge θ L < θ H. Since pre-enure publihing only implie a co effec bu no effec on produciviy boh ype do no publih anyhing under complee informaion. Under incomplee informaion one can diinguih beween a pooling and a eparaing euilibrium. However, he parial eparaing equilibrium i irrelevan in he cae of wo differen ype of agen. Propoiion 1 Given a wo ype ignalling game where fuure profeor can have high or low produciviy of publihing ( or θ L ) and he univeriie wage offer w() depending on he reearch ignal here i he unique eparaing equilibrium H = θ L(θ H θ L), L = 0 w( H) = θ H, w( L) = θ L µ(h H) = 1, µ(l < H) = 1. 4 Clearly, in hi wo ype cae he co and wage rucure aifie he well known Spence-Mirrlee ingle croing propery condiion, i.e. he wo-ype w i indifference curve wih i {H, L} have only one poin of inerecion. 6

9 The deailed proof of propoiion 1 can be found in appendix A page 17. The moivaion of he reul i a follow: In a epearing equilibrium here i no incenive for he ype wih low produciviy o inve in publihing becaue hi ha ju a co effec bu no impac on produciviy. Therefore, an agen wih high produciviy mu publih exacly he amoun ha enure ype L doe no mimic him. However, i i poible ha he ime conrain i binding, i.e. H > l. Then he agen wih he high produciviy can no publih enough o preven mimicing of he low-producive ype. In addiion here i alo a unique pooling equilibrium where nobody ignal. 5 Thi i a andard reul whenever ignal do no have an effec on produciviy. In hi cae nobody ha an incenive o inve in ignaling playing = 0. Noe, if he ime conrain i binding, only he pooling equilibrium peri. However, hi paper focue on efficien eparaing equilibria. Of coure, all reul peri if univeriie are olely inereed in eaching. In hi cae ju replace by in he previou analyi and redefine α H α HH + α LH and α L α HL + α LL repecively. 3.2 Two-dimenional ignalling A higher load of eaching (and alo adminiraive work) reduce publicaion oupu ince ime o do reearch can no be ued o each (Michell and Rebne 1995). Alhough eaching can enhance reearch (Becker and Kennedy 2005) here i no general evidence ha good reearcher are alo good eacher. In conra economi prefer doing reeach o eaching (Allgood and Walad 2005). Since reul of he inerdependency of cience and eaching i unclear I do no make any addiional aumpion on he diribuion of he four ype of agen. 6 Neverhele noe, if boh alen are ubiue (complemen) α HL and α LH are high (mal) while α HH and α LL are mall (high). 7 5 For he explici noaion of he pooling PBE and for he proof of i exience ee appendix A page Alhough here i no clear evidence ha reearch and eaching are complemen on he individual perpecive level boh ac complemenary on he univeriy level. For a mea-analyi on hi opic ee Haie and Marh (1996). 7 Golieb and Keih (1997) find in heir udy ha he connecion beween reearch and eaching i no ju ubiuive or complemenary bu more complex. In deail hey how ha reearch can poiively affec reearch bu aribue of eaching negaively impac 7

10 In ubecion 3.1 we have already een ha he ime conrain can have an imporan influence on he exience of PBE. In he one-dimenional cae ime conrain can lead o a iuaion where only he pooling equilibrium exi. Now, under wo-dimenional ignalling I how ha he eparaing equilibrium i even more likely deroyed by ime conrain. However, wih wo dimenion here i he poibiliy of parial eparaing equilibria. Fir, I analye he eparaing equilbrium in he wo-dimenional cae. Then I how ha under ome condiion (more preciely, if aumpion 1 hold) ime conrain make a eparaing equilibrium impoible. Neverhele, if agen end a wo-dimenional ignal here i alway a lea one parial eparaing equilibrium. In hi equilibrium ype HH end he ame ignal like he ype ha i highly alened wih repec o he oupu ha i more prefered by he univeriie. Time conrain no binding Propoiion 2 If agen ignal cience and eaching abiliy via ( ij, ij ), univeriie offer wage w( ij, ij ) and he ime conrain i no binding, i.e. ij + ij l, here i a eparaing equilibrium ij = { θ L (θ H θ L ), i = H 0, i = L and ij = { θ L (θ H θ L ), w( ij, ij) = θ i + θ j, i, j {H, L} j = H 0, j = L µ(i, j = H k ij θ k L(θ k H θ k L)) = 1 and µ(i, j = L k ij < θ k L(θ k H θ k L)) = 1 where k {, }. The deailed proof of propoiion 2 i given in appendix B page 19. The baic idea i o derive condiion under which ype ij ha no incenive o mimic ype i j for all i, i, j, j {H, L}. Alhough hee condiion are fulfiled by a coninuum of ignal combinaion ( ij, ij ) here i only a unique ignal for each ype ha maximie uiliy. Caued by addiive lineariy of co and produciviie he ignal in he wo-dimenional PBE equal in each of he wo componen he ignal ariing in he one-dimenional cae. To illurae he deciion figure 1 how he incenive compaibiliy conrain of he reearch. 8

11 differen ype of agen. 8 (a) HL (b) LH LH 2 1 HL HL HL LH LH (c) HH HH HH HH Figure 1: (a) Incenive compaibiliy conrain ha preven ype HL from mimicing LL and vice vera, (b) Incenive compaibiliy conrain ha preven ype LH from mimicing LL and vice vera, (c) Incenive compaibiliy conrain ha preven ype HH from mimicing HL or LH and vice vera The grey riangle in par (a) of he figure how all combinaion ha preven HL from mimicing LL and vice vera. The co minimal combinaion ha fulfil hee incenive compaibiliy condiion i ( HL, HL ). Analogouly, par (b) of he figure give he incenive compaibiliy conrain ha 8 The figure refer o he parameer eing θ L = 2, θ H = 3, θ L = 3 and θ H = 4. 9

12 preven LH from mimicing LL and vice vera. Here, ( LH, LH ) i opimal raegy for ype LH. The grey riangle in par (c) coni of all raegie ha preven HH from mimicing LH and HL and vice vera. The opimal raegy of ype HH i hen ( HH, HH ) which i in boh componen equal o he eparaing raegy of he high-alened ype in he one-dimenional cae. The ame argumenaion a in he one-dimenional cae lead o a pooling PBE where nobody ignal, i.e. all agen raegy i ( = 0, = 0). 9 There i alo he poibiliy for parial eparaing PBE in he preen cae. However, univeriie are inereed in he real ype of he agen. So, he mo efficien iuaion i he eparaing one. I pay more aenion o he parial eparaing PBE in he nex ubecion where ime conrain play a crucial role. Time conrain binding Now, I ry o anwer he queion: Wha happen if ime conrain are binding, i.e. if ype HH can no play hi raegy of he eparaing equilibrium of propoiion 2. More formally, HH + HH > l hold. For impliciy I aume ha k (θk H θk L ) l, k {, }, hold. Thi guranee ha he equilibria of he one-dimenional cae exi. If hi i no fulfiled only he pooling equilibrium remain. A a key mechanim of a eparaing equilibrium he highly alened agen eparae himelf by ignalling o much ha here i no incenive of he lowalened agen o mimic him. Thi i poible becaue of he difference in co. However, if here are no only one bu wo ignal he ignalling effor increae 10 and may become oo high o be realied in he ime given. Before dicuing he main reul of hi ecion I make an aumpion abou he ranking of he produciviy parameer ha i crucial for he remaining analyi. Aumpion 1 The ranking of he produciviy parameer fulfil θ H θ L 9 For he deailed proof ee appendix B page In he preen model he ignalling effor in he wo-dimenional cae i exacly he um of he wo one-dimenional ignalling model where he agen ignal on eaching or cience. However, hi reul i driven by he addiive rucure of produciviy and co. 10

13 and θ H θ L. By definion k > θk L, k {, } alway hold. So, for boh aciviie he highly alened agen i more producive han he agen wih low produciviy. However, nohing i known of he ranking of he produciviy parameer comparing boh aciviie. Aumpion 1 require ha agen ha are highly producive doing one aciviy are more producive han agen doing he oher aciviy wih low alen. Or, he oher way round, aumpion 1 i violaed if he univeriie benefi from one oupu i o high ha producing hi oupu by a low-producive agen i beer han producing he oher oupu by a high-producive agen. Propoiion 3 If agen ignal heir abiliie o do cience ( ij ) and each( ij ), univeriie offer wage w( ij, ij ), he ime conrain i binding, i.e. if in propoiion 2 HH + HH > l, and aumpion 1 hold, here i no eparaing equilibrium. If aumpion 1 doe no hold he eparaing equilibrium from propoiion 2 i deroyed bu here i again he poibiliy of eparaing he four ype in equilibrium. HH HH HH HH Figure 2: Incenive compaibiliy conrain for ype HH when aumpion 1 hold. 11

14 For an illuraion of he iuaion where aumpion 1 hold ee figure The figure decribe he incenive compaibily conrain of ype HH. All raegie in he ligh-grey riangle preven HH from mimicing LH and vice vera. The dark-grey riangle coni of all --combinaion ha preven HH from mimicing HL and vice vera. The black riangle herefore give all raegie ha fulfil boh condiion. The raegy ( HH, HH ) i he equilibrium raegy. The key idea here i a follow: Becaue of he pure co effec of ignalling HH realie a co minimal combinaion ha i angen o he black riangle a i lower bound. The lower bound of he ligh-grey riangle ha a lope of ( /θ L ). The lower bound of he dark-grey riangle ha a lope of ( /θ H ). Since he lope of HH co funcion i (θ H /θ H ) and herefore mee he condiion ( /θ L ) < (θ H /θ H ) < (θ L /θ H ) raegy ( HH, HH ) become he co minimal raegy ha fulfil boh incenive compaibiliy conrain. However, if ( HH, HH ) i he euqilibrium raegy of ype HH and ime conrain are binding here i no raegy ha lie ouh-we of ( HH, HH ) - which i neceary o mee he ime conrain - and i locaed in he black riangle - which i neceary o fulfil he incenive compaibiliy conrain of ype HH. So, if aumpion 1 hold here i no pearaing PBE. HH HH 1 HH 2 _ l 1 _ l HH Figure 3: Incenive compaibiliy conrain for ype HH when aumpion 1 i no fulfiled. 11 The figure refer o parameer eing θ L = 2, θ H = θ L = 3 and θ H = 4. 12

15 Figure 3 how a iuaion in which aumpion 1 doe no hold. 12 The grey area decribe all raegie of HH ha fulfil boh incenive compaibiliy conrain. Conrary o figure 2 a decreae in he available ime from l 1 o l 2 hif he eparaing PBE from HH 1 o HH 2. Thu here i ill he poibiliy of eparaing he differen ype of agen. Propoiion 4 If agen ignal heir abiliie o do cience ( ij ) and each ( ij ), univeriie offer a wage w( ij, ij ) equal o he expeced produciviy here are wo parial eparaing equilibria. If θ H θ H θ L hold here i a parial PBE where raegie of he propecive profeor are: wih C1 LH,HH ( LL, LL) = (0, 0), ( HL, HL) = (θ L(θ H θ L), 0) and ( (LH,HH), (LH,HH)) = (0, θ LC1 (LH,HH) ) α HH α LH +α HH (1 α LH α LH +α HH ) + θ H θ L. If θ L θ L θ H hold here i a parial eparaing PBE where raegie of he propecive profeor are: ( LL, LL) = (0, 0), ( LH, LH) = (0, θ L(θ H θ L)) and wih C1 (HL,HH) = θ H θ L + ( (HL,HH), (HL,HH)) = (θ LC1 (HL,HH), 0) α HH α HL +α HH (1 α HL α HL +α HH ). In caue of clear arrangemen propoiion 4 only denoe raegie of he propecive profeor. 13 The wage eing of he univeriie i for he eparaed ype equal o he wage eing of propoiion 2. The pooled ype are paid by average produciviie. Thu in he fir parial eparaing PBE α i i w (LH,HH) = LH α LH +α HH + α HH α LH +α HH + θ H and in he econd parial eparaing equilibrium i i w (HL,HH) = + α HL α HL +α HH + α HH α HL +α HH. 12 The figure refere o he parameer eing θ L = 1, θ H = 2, θ L = 3 and θ H = Propoiion 4 only decribe wo parial eparaing equilibria. There i alo he poibiliy of oher parial eparaing equilibria, e.g. of ((LL, LH), HL, HH). Neverhele, univeriie ry o idenify he highly producive agen. Thu he parial eparaing PBE of propoiion 4 are he one of inere. 13

16 The deailed proof can be found in he appendix C page 26. In he fir parial eparaing PBE univeriie can diinguih beween LL, HL and (LH, HH), i.e. hey can no eparae ype LH from HH. In he econd parial eparaing PBE univeriie can eparae LL from LH and (HL, HH) bu no ype HL and HH. The key arrangemen of he proof of he fir parial eparaing PBE (and analogouly of he econd one) i a follow: Type LL doe no ignal becaue of he pure co effec. Type HL playe hi raegy from he one-dimenional cae o preven LL from mimicing. Then he incenive compaibiliy conrain of (LH, HH) no o mimic LL or HL and vice vera are calculaed. Thi reul in he equilibrium raegy for (LH, HH). (a) HH (LH,HH) 2 1 (b) HH LH c HH 2 HH c LH HH HH c LH c HH Figure 4: Incenive compaibiliy conrain for (LH, HH) in he fir parial eparaing PBE (a) when θ H θ H θ L hold and (b) if hi condiion i no fulfiled 14

17 To illurae he neceary condiion of he exience of he fir parial eparaing PBE (LL, HL, (LH, HH)), i.e. o illurae he neceiy of θ H θ H θ L, look a figure 4.14 In par (a) of figure 4 i i θ H θ H θ L and boh minimal co funcion of he pooled ype, i.e. c LH and c HH, are angen o he black array ha coni of all raegie which mee he incenive compaibiliy conrain a poin (LH, HH). 15 Thi --combinaion i he raegy LH and HH play in he fir parial eparaing equilibrium. In par (b) i i θ H < θ H θ L.16 Thu, he co funcion of HH, i.e. c HH, run oo fla. The minimal co funcion of ype HH i angen o he black area where he incenive compaibiliy conrain are fulfiled a poin HH. Since he minimal co funcion of ype LH i angen o he black array a poin LH here i no pooling equilibrium raegy for boh ype and o no parial eparaing PBE. A a fir reul one can ee ha boh parial eparaing PBE can only co-exi if θ L = θ L θ H hold. One example for uch a iuaion i he ymmeric cae, where low (high) produciviy of cience equal low (high) produciviy of eaching, i.e. = θ H and θ L = θ L. Thu, univeriie do no have a clear preference for he one or he oher oupu. Auming ha he highly producive agen are he criical one and herefore normaliing he produciviie of he low-alened o one, i.e. = θ L = 1, he fir parial eparaing PBE only exi if eaching produciviy of he highly alened i higher han hi reearch produciviy. Analogouly, if he conrary appraiemen hold he econd parial eparaing PBE appear. In general an angen ha i good in eaching and cience poole wih he ype ha i highly-alened in he oupu ha i more prefered by he univeriie. Thi renghen he argumen of Becker (1975) and (1979) ha he profeor reearch and eaching oupu poiively reac on an increae in pecuniary reurn. Secondly, i i clear ha wihou ime conrain alway a lea one of he parial PBE exi. However, in hi cae hey are le inereing becaue he eparaing PBE i more efficien. 14 Clearly, an analogou argumenaion hold for condiion θ L θ L θ H and he econd parial eparaing PBE. 15 Par (a) of he figure refer o parameer value = θ L = 1, θ H = 2 and θ H = 3. More preciely, opimal raegie hould be labeled ( (LH,HH), (LH,HH)). However, caued by clarificaion I label he raegy wih he ype. 16 Par (b) of figure 4 refer o = 1, θ H = θ L = 2 and θ H = 3. 15

18 Thirdly, propoiion 4 how ha if he ime conrain i oo rong here i even no poibiliy for a parial eparaing equilibrium bu only for he pooling one. Thu, in boh parial eparaing equilibria he ime conrain i relaxed compared o he eparaing cae bu no removed. More preciely, he ime invemen of ype HH in he fir parial eparaing equilibrium i C1 (LH,HH) = α HH α LH +α HH ( θ L ) + θ L (θ H θ L ). Thi i clearly higher han he invemen in he one-dimenional cae, i.e. (θ H θ L ).17 So, ime conrain can ill be binding. They are weakend o he wo-dimenional eparaing equilibrium where ime inpu i (θ H θ L ) + θ L (θ H θ L ) if and only if α HH /(α LH + α HH ) < /θ L. Thi i alway fulfiled if θ L θ L and herefore epecially in he cae where low produciviie are normalied o one. By he ame argumenaion ime conrain of he econd parial PBE i weaker han in he wo-dimenional eparaing PBE if and only if α HH /(α HL + α HH ) < /θ L hold. A ufficien condiion for hi purpoe i θ L. 4 Concluion The oupu of po-doc and profeor coni, beide he adminiraive one ha i no menioned here, of cience and eaching. In general univeriie are inereed in boh oupu and aign a enure conrac only o hoe po-doc ha are highly alened in boh aciviie. However, ince alen i a privae informaion a job marke ignalling model la Spence arie. Podoc ignal heir abiliy of cience and eaching o ge a enure. A Spence (1973) ha hown in he one-dimenional cae ignalling can alo in he wo-dimenional cae eparae highly alened and low alened agen. So i olve he inefficiency problem of aymmeric informaion. Unforunaely, he highly producive agen need a ignalling effor o eparae hemelve from he low-producive ype and hi effor increae in he wo-dimenional cae. Conidering hi, ime conrain arac noice. If ime conrain are binding and he cience (eaching) produciviy of he high-alened i higher han he eaching (cience) produciviy of he ype wih low alen a eparaing equilibrium can no exi in he wo-dimenional 17 Acually, I can no be ure ha hi one-dimenional equilibrium implie he ronger ime conrain, i.e. ha (θ H θ L ) > θ H (θ H θ L ) hold. Neverhele, hi i rue if he high-producive agen are of mo inere and low produciviie are normalied o one. 16

19 cae. The required aumpion i quie weak a i ju ay ha univeriie hould no prefer one oupu over he oher regardle weher he fir i creaed by a high- or low-producive peron. In addiion I how ha even if he eparaing equilibrium i deroyed by ime conrain here i alway a lea one parial eparaing equilibrium where ome ype can be eparaed while oher pool on he ame raegy. More preciely, if he univeriy prefer cience o eaching a parial eparaing equilibrium exi where univeriie can eparae ype wih high or low reearch produciviy. However, hey do no know if an agen wih high reearch produciviy i alo highly alened in eaching. Thi i he ame reul a in he one-dimenional cae. Regreably, he ignalling effor ha only implie a pure co effec i higher in he wo-dimenional parial eparaing equilibrium han in he one-dimenional eparaing one. Correponding o real life, he wo-dimenional ignalling yem ha i currenly ued in academic admiion procee i inefficien if ime conrain are binding. In uch a iuaion univeriie can no idenify boh alen of he po-doc bu only one. The idenifiable alen i he one hey value more. Then univeriie can eae requiremen on po-doc and can le hem - wihou looing informaion - ju ignal on cience or eaching. Appendix Par A: One-dimenional cae Proof of propoiion 1: Separaing equilibrium: Since pre-enure publihing implie co bu ha no effec on produciviy here i no incenive for a L-ype o inve in publihing in a eperaing equilibrium. Therefore, i i L = 0. In addiion any equilibrium mu aify wo incenive compaibiliy condiion: On he one hand ype H mu no have an incenive o mimic he L-ype, i.e. w( H ) c H ( H ) w( L ) c H ( L ) θ H H θ H L. (4) 17

20 On he oher hand he L-ype mu no have an incenive o mimic he H-ype, i.e. w( L ) c L ( L ) w( H ) c L ( H ) L θ H H. (5) Taking ino accoun ha he equilibrium raegy of he L-ype i o publih nohing, i.e. L = 0, inequaion (4) reul in H (θ H θ L ). Analogouly, olving inequaion (5) by H I ge H (θ H θ L ). Boh incenive compaibiliy condiion ogeher imply ha (θ H θ L ) H (θ H θ L ) i a neceary condiion of a eparaing equilibrium. Since he univeriie never pay a wage higher han only he lower bound of he inerval, i.e. H = θ L (θ H θ L ), maximie uiliy of ype H. However, if H > l hold he eparaing equilibrium vanihe. Having he opimal deciion of he agen in mind univeriie belief ha hey focu on an agen of ype H whenever H and ha hey focu on an agen of ype L whenever < H. Pooling equilibrium: The pooling equilbrium in he one-dimenional cae i = H = L = 0 w( ) = α H θ H + α L θ L µ(h α H (θ L(θ H θ L))) = α H, µ(l α H θ L(θ H θ L)) = α L µ(l > α H (θ L(θ H θ L))) = 1 if he ime conrain i no binding, i.e. i l, i {H, L}. The argumenaion i a follow: In every pooling equilibrium agen end idenical ignal, i.e. H = L =. Since univeriie canno diinguih beween boh ype hey e a unique wage ha equal average valuaion of he univeriie, i.e. w() = α H θ H + α L θ L. (6) In a pooling equilibrium boh ype mu no ge lower uiliy han wihou ignaling geing θ L, i.e. θ L w() c H () θ L α H θ H + α L θ L θ H 18 (7)

21 and w() c L () α H + α L. (8) Wih > θ L only condiion (8) become criical. I implie ha in every pooling equilibrium α H + α L ) ( αh (1 α L ) } {{ } =α H α H (θ H ) (9) mu hold. However, ince publihing only implie a co effec boh ype prefer he ignal H = L = = 0. Thi i a pooling perfec Bayeian equilibrium and in addiion alway aifie he ime conrain l. Par B: Two-dimenional cae wihou ime conrain Proof of propoiion 2: In a eparaing PBE univeriie pay an agen ij a wage equal o hi produciviy. Thu, w( ij, ij) = θi + θj hold. Thi direcly give ( LL, LL ) = (0, 0) a equilibrium ignal of ype LL. In a nex ep, ignal of ype HL and LH mu mee he incenive compaibiliy conrain o ha boh ype have no incenive o mimic LL and vice vera. Thi auomaically preven HH from mimicing LL. Type HL doe no mimic LL if w( LL, LL) c HL ( LL, LL) w( HL, HL ) c HL ( HL, HL ) + + HL 1 HL + 1 HL HL θ L 19

22 hold. Analogouly, LL doe no mimic HL whenever w( LL, LL) c LL ( LL, LL) w( HL, HL ) c LL ( HL, HL ) + + HL 1 HL + 1 HL HL θ L hold. Therefore he incenive compaibiliy conrain ha preven HL from mimicing LL and vice vera i 1 θ H HL + 1 HL 1 HL + 1 HL. A ignal ha maximie uiliy of ype HL mu lie on he lower bound which one can rewrie a HL = (θ H ) θ L HL. Type HL will now chooe he ignal ha fulfil hi condiion and minimie co. Since co are (aking he la equaion ino accoun) c HL, HL = HL θ H + HL θ L = θ L (θ H θ L ) θ H = θ L (θ H θ L ) θ H θ L θ H θ L + (1 θ L HL + 1 HL θ H ) 1 θ L } {{ } >0 he minimal co combinaion i HL = 0 and herefore HL = θ L (θ H θ L ). Type HL raegy in he eparaing PBE i ( HL, HL ). In he ame way ype LH doe no mimic ype LL if HL w( LL, LL) c LH ( LL, LL) w( LH, LH ) c LH ( LH, LH ) + + LH 1 LH + 1 LH 20 LH θ H

23 hold. Type LL doe no mimic ype LH if w( LL, LL) c LL ( LL, LL) w( LH, LH ) c LL ( LH, LH ) + + LH 1 LH + 1 LH LH θ L i fulfiled. Taking boh condiion ogeher ype LH ha no incenive o mimic ype LL and vice vera if 1 θ L LH + 1 LH 1 LH + 1 LH hold. Again LH chooe a ignal on he lower bound given by he econd par of he condiion. Thu i i LH = (θ H ) θ L LH. Thi in mind co of ype HL are given by c LH ( LH, LH ) = LH θ L + LH θ H = θ L (θ H θ L ) θ H = (1 θ L θ H ) 1 θ L } {{ } >0 + 1 LH θ L LH θ H LH + θ L (θ H θ L ). To minimie co and herefore maximie uiliy given he wage +θ H ype LH play LH = 0 and LH = θ L (θ H θ L ) in equilbrium. Wih ( HL, HL ) and ( LH, LH ) ype HL ha no incenive o mimic ype LH and vice vera caue w( LH, LH) c HL ( LH, LH) w( HL, HL) c HL ( HL, HL) + θ L (θ H θ L ) θ H + θ L (θ H θ L ) 0 ( ) 2 21

24 and w( HL, HL) c LH ( HL, HL) w( LH, LH) c LH ( LH, LH) + θ L (θ H θ L ) θ L + θ L (θ H θ L ) 0 ( ) 2 are alway fulfiled. In a la ep one ha o make ure ha HH doe neiher mimic HL nor LH and vice vera. Type HH doe no mimic HL whenever w( HL, HL) c HH ( HL, HL) w( HH, HH ) c HH ( HH, HH ) + θ L (θ H θ L ) θ H + HH HH HH + θ H HH (θ H ) + (θ H ) hold. Analogouly, ype HL ha no incenive o mimic HH if w( HH, HH ) c HL ( HH, HH ) w( HL, HL) c HL ( HL, HL) + HH HH θ H + θ L (θ H θ L ) HH + θ H HH (θ H ) + (θ H ) i fulfiled. Boh condiion ogeher are he incenive compaibiliy condiion ha preven HH from mimicing HL and vice vera. Becaue of he pure co effec of ignalling he lower bound of he econd condiion, i.e. HH + θ H HH = (θ H ) + (θ H ) HH = (θ H ) + (θ H ) θ H HH (10) i a necaary condiion for a eparaing PBE. However addiionally, ype 22

25 HH doe no have an incenive o mimic ype LH and vice vera. Therefore, and w( LH, LH) c HH ( LH, LH) w( HH, HH ) c HH ( HH, HH ) + θ L (θ H θ L ) θ H + HH HH θ H HH + HH (θ H ) + (θ H ) w( HH, HH ) c LH ( HH, HH ) w( LH, LH) c LH ( LH, LH) + HH HH θ L + θ L (θ H θ L ) θ H HH + HH (θ H ) + (θ H ) mu hold. Boh condion ogeher are he incenive compaibiliy conrain ha preven HH from mimicing LH and vice vera. Caue of he pure co effec of ignalling he lower bound of he econd condiion, i.e. HH + HH = (θ H ) + (θ H ) HH = θ L(θ H θ L) + (θ H θ L )θ L θ L θ H θ L HH (11) i a neceary condiion for a PBE. In a eparaing PBE ype HH neiher mimic HL nor LH. Thu, condiion (10) and (11) mu hold. Boh linear funcion decribe he lower bound of he area ha fulfil boh incenive compaibiliy conrain. Becaue of he pure co effec of ignalling he opimal raegy i elemen of hi lower bound. To make ure ha he opimal aregy i unique he lope of hi lower bound mu be unequal o he lope of he co funcion of HH. 18 The co funcion of ype HH i c HH ( HH, HH ) = ( HH / )+( HH/ ). So, he lope of hi funcion in a - -area i ( /θ H ). A he lope of equaion (10) in uch an area i (θ L /θ H ) and he lope of equaion (11) i ( /θ L ) here i a unique opimal raegy 18 If hi condiion i no fulfiled he minimal co combinaion would be angen o he area ha fullfiile he incenive compaibiliy conrain on a whole ecion repreened by a par of he linear funcion (10) or (11) and no o a unique poin. 23

26 of HH ha i given by he poin of inerecion of he linear combinaion (10) and (11). Calculaing hi poin of inerecion lead o (θ H ) + (θ H ) θ H HH = (θ H ) + (θ H θ L )θ L θ L θ L HH θ H(θ H ) θ L(θ H ) = θ H θ H θ L θ L HH (θ H θ L)(θ H ) = θ H θ H θ L θ L HH HH = (θ H ). Inering hi in equaion (10) give he fir par of he equilibrium ignal = (θ H θ L ). The pooling PBE in he wo-dimenional cae: The pooling PBE in he wo dimeniona cae i (, ) ( ij, ij) = (0, 0) i, j {H, L} w(, ) = ij α ij (θ i + θ j) ( µ ij (, ) = ( I (α HH +α HL )(θ H )), J (α HH +α LH )(θ H ) )) = α ij where I = 1 if i = H and 0 oherwie and J = 1 if j = H and 0 oherwie. The proof of hi reul i a follow: Univeriie wage eing eeing he pooled ignal (, ) i w(, ) = ij α ij (θ i + θ j). Since each agen ij can alway ge he lowe wage θ L + θ L uiliy wih 24

27 he pooled ignal mu be higher han hi reward, i.e. θ L + θ L w(, ) c ij (, ) θ L + θ L ij θ i θ i θ i + θ j + θ j + θ j α ij (θ i + θ j) θ i θ j (α LL + α LH 1)θ L + (α HH + α HL )θ H + (α LL + α HL 1)θ L + (α HH + α LH )θ H (α HH + α HL )θ L + (α HH + α HL )θ H (α HH + α LH )θ L + (α HH + α LH )θ H (α HH + α HL )(θ H θ L) + (α HH + α LH )(θ H θ L) (α HH + α HL )( )θ j + (α HH + α LH )( )θ j θ j. θi Thi i ju a linear equaion in. Clearly ype LL i he rericing ype. Thu every linear combinaion of (, ) for which θ L + θ L (α HH + α HL )(θ H θ L) + (α HH + α LH )(θ H θ L) hold mee he incenive compaibiliy conrain. However, he pure co effec of ignalling make (, ) = (0, 0) he unique pooling PBE. The incenive condiion ha preven agen from breaking ou of he pooling PBE are illuraed in figure 5. I refer o he ymmeric cae wih = θ H = 2, θ L = θ L = 1 and α ij = 1 i, j {H, L}. The grey area decribe all combinaio ha preven LL - and herefore alo he oher ype - 4 from breaking ou of he pooling PBE. However, only (, ) = (0, 0) implie minimum co and herefore i PBE. 25

28 2 Type HH Type LH 1 Type HL Type LL 1 2 Figure 5: Incenive compaibiliy conrain of ype LL in a pooling PBE of wo dimenion Par C: Two-dimenional cae wih ime conrain Proof of propoiion 4: The equence of he proof of he parial eparaing PBE (LL, HL, (LH, HH)) i a follow: Fir of all I find he opimal raegy for HL ha preven him from mimicing LL. Secondly I give he incenive compaibiliy conrain ha preven LL from mimicing (LH, HH) and vice vera. Thirdly, I give he incenive compaibiliy conrain ha preven HL from mimicing (LH, HH) and vice vera. Sep wo and hree ogeher reul in an opimal raegy for (LH, HH). In a PBE where LL i eparaed he ha no icenive o ignal. Thu, ( LL, LL ) = (0, 0). Then refering o he fir ep HL ignal ( HL, HL ) = ( (θ H θ L ), 0) o preven LL from mimicing him. Thi raegy direcly reul from he eparaing PBE. 26

29 To make ure ha in a econd ep LL doe no mimic (LH, HH) w LL c LL ( LL, LL) w (LH,HH) c LL ( (LH,HH), (LH,HH)) + α LH θ α HH L + + α LH + α HH α LH + α HH (LH,HH) θ L + (LH,HH) θ L (LH,HH) α HH (LH,HH) θ L α LH (1 ) +. α LH + α HH α LH + α } {{ HH } C1 (LH,HH) mu hold. Analogouly, LH and herefore (LH, HH) doe no mimic LL if w LL c LH ( LL, LL) w (LH,HH) c LH ( (LH,HH),LH,HH ) + α LH θ α HH L + + α LH + α HH α LH + α HH (LH,HH) θ L + (LH,HH) θ H (LH,HH) α HH (LH,HH) θ H α LH (12) (1 ) +. α LH + α HH α LH + α } {{ HH } =C1 (LH,HH) i fulfiled. Since ignal can no be negaive a neceary condiion for he exience of he parial eparaing PBE i C1 (LH,HH) > 0. I will come o hi laer on. To preven HL from mimicing (LH, HH) (hird ep) he following condiion mu hold: w HL c HL ( HL, HL) w (LH,HH) c HL ( (LH,HH), (LH,HH) ) θ H + θ L θ L (θ H θ L ) θ H (LH,HH) θ H + (LH,HH) θ L α LH θ α HH L + + α LH + α HH α LH + α HH (LH,HH) θ H 27 (LH,HH) θ L

30 α HH α LH (1 ) + (1 + ) + (θ L )2 α LH + α HH α LH + α HH } {{ } C2 (LH,HH) Analogouly, o preven HH and herefore (LH, HH) from mimicing HL w HL c HH ( HL, HL) w (LH,HH) c HH ( (LH,HH), (LH,HH) ) θ H + θ L θ L (θ H θ L ) θ H LH,HH θ H α HH + (LH,HH) θ H α LH θ α HH L + + α LH + α HH α LH + α HH (LH,HH) θ H α LH (LH,HH) θ H (1 ) + (1 + ) + (θ L )2 α LH + α HH α LH + α HH } {{ } =C2 (LH,HH) (13) mu hold. A neceary condiion for he exience of he parial eparaing PBE i again ha C2 (LH,HH) > 0 i fulfiled. Thi condiion i even ronger han C1 (LH,HH) from above becaue C2 (LH,HH) C1 (LH,HH) = θ H + 2θ L (θ L )2 θ H = (θ H )2 + 2θ H θ L (θ L )2 θ H = (θ H θ L )2 θ H hold. Alhough C2 (LH,HH) < C1 (LH,HH) i fulfiled one can no direcly ee if equaion (12) or equaion (13) i he ronger condiion becaue of he differen LHS. If you compare boh condiion you find ha he relaionhip depend on he exac parameer value. However, I how ha he opimal - co minimal - behavior for ype LH and HH i he ame regardle wheher equaion (12) or equaion (13) i he ronger condiion. Thu aume ha equaion (12) i ronger han equaion (13) hen < 0 28

31 (LH,HH) = θ L C1 (LH,HH) θ L θ L (LH,HH) hold. Thi in mind co of LH are (LH,HH) θ L + (LH,HH) θ H = 1 θ L (1 θ L ) } {{ } >0 (LH,HH) + θ L C1 (LH,HH). Since co increae in (LH,HH) he opimal raegy of LH i (LH,HH) = 0. Analogouly, co of HH are (LH,HH) θ H + (LH,HH) θ H = ( 1 θ H θ L θ L θ H ) + θ L C1 (LH,HH). 1 If θ L 0 hold he opimal raegy i o maximie (LH,HH). However, hen he parial eparaing PBE i deroyed. Type LH and HH θ H do no play he ame raegy. Therefore 1 θ H θ L θ L θ H 0 mu hold o enure he decribed PBE. If equaion (12) i he ronger condiion one θ L θ H θ H θ L become a neceary condiion of he parial eparaing PBE. Now aume ha inead of equaion (12) equaion (13) i he ronger condiion hen (LH,HH) = C2 (LH,HH) θ L θ (LH,HH) hold and co of ype H LH are (LH,HH) θ L + (LH,HH) θ H = ( 1 θ L θ H θ H ) (LH,HH) + θ L C2 (LH,HH) = ( θ H θ H θ L θ L ) (LH,HH) + θ L C2 θ L θ H } {{ } (LH,HH). >0 Again i i opimal for ype LH o play (LH,HH) = 0. Analogouly, co of ype HH are (LH,HH) θ H + (LH,HH) θ H = 1 (1 θ L ) (LH,HH) + θ L C2 (LH,HH). A co increae in (LH,HH) ype HH e (LH,HH) = 0. Summariing, under boh aumpion (LH,HH) = 0 i an opimal raegy for boh pooling ype. Thi reduce condiion (12) o (LH,HH) = C1 LH,HH 29

32 and condiion (13) o (LH,HH) = θ L C2 (LH,HH). Wih C1 (LH,HH) > C2 (LH,HH) from he above condiion (12) become he crucial condiion for he exience of he parial eparaing PBE. The equilibrium raegy of (LH, HH) i ( (LH,HH), (LH,HH) ) = (0, θ L C1 (LH,HH)). A neceary condiion for he exience of he equilibrium i θ L θ H > θ H θ L. Finally, he proof of he econd parial PBE, i.e. of (LL, LH, (HL, HH)) i analogou and i herefore no pecified here. Reference Allgood, Sam and Wiliam B. Walad (2005). View of eaching and reearch in economic and oher dicipline. American Economic Review Paper and Proceeding 95 (2), Armrong, Mark and Jean-Charle Roche (1999). Muli-dimenional creening: A uer guide. European Economic Review 43, Becker, William E. (1975). The univeriy profeor a a uiliy maximizer and producer of learning, reearch, and income. Journal of Human Reource 10, Becker, William E. (1979). Profeorial behavior given a ochaic reward rucure. The American Economic Review 69 (5), Becker, William E. and Peer E. Kennedy (2005). Doe eaching enhance reearch in economic? American Economic Review Paper and Proceeding 95 (2), Cho, In-Koo and David M. Krep (1987). Signaling game and able equilibria. The Quarerly Journal of Economic 102 (2), De Fraja, Gianni and Paola Valbonei (2008). The deign of he univeriy yem. CEPR Dicuion Paper no Del Rey, Elena (2001). Teaching veru reearch: A model of ae univeriy compeiion. Journal of Urban Economic 49, Enger, Maxim (1987). Signalling wih many ignal. Economerica 55 (3),

33 Gauier, Axel and Xavier Wauhy (2007). Teaching veru reearch: The role of inernal financing rule in muli-deparmen univeriie. European Economic Review 51, Golieb, Eher E. and Bruce Keih (1997). The academic reearcheaching nexu in eigh advanced-indurialized counrie. Higher Educaion 34, Haie, John and H. W. Marh (1996). The relaionhip beween reearch and eaching: A mea-analyi. Review of Educaional Reearch 66 (4), Kim, Jeong-Yoo (2007). Mulidimenional ignaling in he labor marke. Mancheer School 75 (1), Michell, John E. and Dougla S. Rebne (1995). Nonlinear effec of eaching and conuling on academic reearch produciviy. Socio-Economic Planning Science 29 (1), Roche, Jean-Charle and Marine Qunizii (1985). Mulidimenional ignalling. Journal of Mahemaical Economic 14, Spence, Michael (1973). Job mark ignalling. The Quarerly Journal of Economic 87 (3), Spence, Michael (1974). Compeiive and opimal repone o ignal: An analyi of efficiency and diribuion. Jounral of Economic Theory 7, Walckier, Alexi (2008). Muli-dimenional conrac wih ak-pecific produciviy: An applicaion o univeriie. Inernaional Tax and Public Finance 15,

34

35 DISKUSSIONSPAPIERE DER FÄCHERGRUPPE VOLKSWIRTSCHAFTSLEHRE DISCUSSION PAPERS IN ECONOMICS Die komplee Lie der Dikuionpapiere i auf der Inerneeie veröffenlich / for full li of paper ee: hp://fgvwl.hu-hh.de/wp-vwl Schneider, Andrea. Science and eaching: Two-dimenional ignalling in he academic job marke, Augu Krue, Jörn. Da Governance-Dilemma der demokraichen Wirchafpoliik, Augu Hackmann, Johanne. Ungereimheien der radiionell in Deuchland vorherrchenden Rechferigunganäze für da Ehegaenpliing, Mai Schneider, Andrea; Klau W. Zimmermann. Mehr zu den poliichen Segnungen von Föderalimu, April Beckmann, Klau; Schneider, Andrea. The ineracion of publicaion and appoinmen - New evidence on academic economi in Germany, März Beckmann, Klau; Schneider, Andrea. MeinProf.de und die Qualiä der Lehre, Februar Berlemann, Michael; Hielcher, Kai. Meauring Effecive Moneary Policy Conervaim, February Horgo, Daniel. The Elaiciy of Subiuion and he Secor Bia of Inernaional Ouourcing: Solving he Puzzle, February Rundhagen, Bianca; Zimmermann, Klau W.. Buchanan-Kooperaion und Inernaionale Öffenliche Güer, Januar Thoma, Tobia. Queionable Luxury Taxe: Reul from a Maing Game, Sepember Dluhoch, Barbara; Zimmermann, Klau W.. Adolph Wagner und ein Geez : einige päe Anmerkungen, Augu Zimmermann, Klau W.; Horgo, Daniel. Inere group and economic performance: ome new evidence, Augu Beckmann, Klau; Gerri, Caren. Armubekämpfung durch Redukion von Korrupion: eine Rolle für Unernehmen?, Juli Beckmann, Klau; Engelmann, Denni. Seuerwebewerb und Finanzverfaung, Juli Thoma, Tobia. Fragwürdige Luxueuern: Saureben und demonraive Konumverhalen in der Gechiche ökonomichen Denken, Mai Krue, Jörn. Hochchulen und langfriige Poliik. Ein ordnungpoliicher Eay zu zwei Reformuopien, Mai Krue, Jörn. Mobile Terminaion Carrier Selecion, April Dewener, Ralf; Haucap, Juu. Webewerb al Aufgabe und Problem auf Medienmärken: Falludien au Sich der Theorie zweieiiger Märke, April Krue, Jörn. Pareien-Monopol und Dezenraliierung de demokraichen Saae, März Beckmann, Klau; Gake, Suan. Sau preference and opimal correcive axe: a noe, February Krue, Jörn. Inerne-Überla, Nezneuraliä und Service-Qualiä, Januar Dewener, Ralf. Nezneuraliä, Dezember Beckmann, Klau; Gerri, Caren. Making ene of corrupion: Hobbeian jungle, bribery a an aucion, and DUP aciviie, December Krue, Jörn. Crowding-Ou bei Überla im Inerne, November Beckmann, Klau. Why do perol price flucuae o much?, November Beckmann, Klau. Wa will Du armer Teufel geben? - Bemerkungen zum Glück in der Ökonomik, November 2007.

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