Ine cient Unemployment Dynamics under Asymmetric Information

Transcription

1 Ine cien Unemploymen Dynamics under Asymmeric Informaion Veronica Guerrieri Universiy of Chicago January 2007 Absrac In his paper, I sudy he e ciency properies of a compeiive search model wih machspeci c privae informaion on he worker s side. This informaion is necessary o evaluae wheher saring an employmen relaionship is pro able or no. Employmen conracs are designed opimally no only o arac workers bu also o induce hem o reveal heir informaion. I rs show ha in a saic seing he compeiive search equilibrium is consrained e cien. Then, I show ha in a dynamic seing he equilibrium is consrained ine cien whenever he iniial unemploymen rae is di eren from is seady sae level. The crucial di erence beween he saic and he dynamic environmen is ha he worker s ouside opion is exogenously given in he former, while in he laer i is an endogenous objec. Ine ciency arises because he worker s ouside opion a ecs he cos of informaion revelaion, generaing a novel exernaliy. Firms o ering conracs a a given poin in ime do no inernalize heir e ec on he ouside opion of workers hired in previous periods. Finally, I derive a se of axes ha implemens he consrained e cien allocaion. Keywords: maching, search, asymmeric informaion, unemploymen, consrained e ciency, exernaliy JEL Classi caion: D62, D82, D83, J64 1 Inroducion I has long been recognized ha in labor markes rade is cosly and subjec o fricions. Firms need o pos vacancies, workers spend ime searching for jobs, and wages are deermined by For counless discussions and suppor I hank Daron Acemoglu, Mike Golosov, Guido Lorenzoni and, las only for alphabeical order, Iván Werning. I am graeful for very helpful commens from Manuel Amador, Pol Anras, Gadi Barlevy, Olivier Blanchard, VV Chari, Emmanuel Farhi, Francesco Giavazzi, Rober Hall, William Hawkins, Pa Kehoe, Narayana Kocherlakoa, Chrisopher Pissarides, Richard Rogerson, Rober Shimer, Aleh Tsyvinski, Marcelo Veraciero, Randall Wrigh and from seminar paricipans a Chicago GSB, Chicago Fed, Cleveland Fed, Columbia, CREI and Pompeu Fabra, IIES, Universiy of Iowa, Kellogg MEDS, Minnesoa, MIT, Norhwesern, NY Fed, NYU Sern, Rocheser, Sanford, UPenn and NBER Summer Insiue, NAES Summer Meeing.

2 decenralized conracing. This imposes a deparure from he fricionless Walrasian paradigm. A classic quesion arises: o wha exen do decenralized labor markes achieve e ciency? In paricular, do hey reach an e cien level of unemploymen and job creaion? Search heory o ers a naural environmen o represen decenralized markes wih rading fricions. In addressing he e ciency issue, he lieraure has focused on he bargaining side of he model, ha is, on he way in which he worker and he rm spli he surplus of he employmen relaionship. Di eren assumpions on wage deerminaion can drive di eren implicaions in erms of e ciency. On he one hand, he classic Morensen-Pissarides model shows ha random maching combined wih Nash bargaining inroduces a search exernaliy ha generically generae ine ciency. 1 On he oher hand, Shimer (1996) and Moen (1997) show ha e ciency can be resored once an appropriae noion of compeiion is inroduced, ha is, when rms pos wages and workers direc heir search owards he mos aracive ones. This form of compeiion is known as compeiive search. However, he conracing problem of workers and employers is no only abou how o divide he surplus generaed by he mach. A crucial addiional problem is ha he conracing paries ypically have privae informaion necessary o evaluae his surplus. Such informaion is needed o decide wheher saring an employmen relaionship is pro able or no. In his paper, I focus on his informaional problem and on is impac on e ciency. Speci cally, I propose a compeiive search model wih privae informaion on he worker s side. Employmen conracs are designed opimally no only o arac workers, bu also o induce hem o reveal heir informaion. My main resul is ha he dynamic compeiive search equilibrium is generically consrained ine cien. In paricular, he unemploymen rae reacs subopimally o iniial shocks. This implies a poenial role for governmen inervenion in he presence of labor marke ucuaions. I consider an economy where employers and workers are boh risk-neural and ex-ane homogeneous. Employers pos conracs and workers direc heir search owards hem. When a mach is formed, he disuiliy of labor is drawn randomly and observed privaely by he worker. An employmen conrac is an incenive-compaible mechanism ha sais es a paricipaion consrain on he worker s side. The paricipaion consrain can be inerpreed as he resul of lack of commimen. A worker canno be forced o work, he can always qui and join he ranks 1 The convenional model is buil on Diamond (1982), Morensen (1982a, 1982b), Pissarides (1984, 1985) and Morensen and Pissarides (1994). Hosios (1990) shows ha his model is consrained ine cien, excep ha for a speci c bargaining power division. See Pissarides (2000) for an overview. 2

3 of he unemployed. I begin by characerizing he compeiive search equilibrium and showing ha equilibrium conracs ake he simple form of a xed wage and a hiring cu-o. Then, I urn o sudy consrained e ciency. I de ne a social planner who faces he same incenivecompaibiliy and paricipaion consrain of he marke economy. Given hese consrains and he resource consrain, he planner conrols he maching process by deciding how many vacancies o open and how many jobs o creae, and allocaes consumpion o employed and unemployed workers. Boh in he compeiive equilibrium and in he planner problem, I assume ha workers who qui canno be disinguished from oher unemployed workers. In a saic seing, I show ha he compeiive search equilibrium is consrained e cien. By conras, once I urn o he dynamic seing, I show ha he compeiive search equilibrium is generically consrained ine cien. The crucial di erence beween he saic and he dynamic environmens is ha he worker s ouside opion is exogenously given in he former, while in he laer i is endogenously deermined as he coninuaion uiliy of unemployed workers. When he informaional problem is relevan, ha is, he incenive compaibiliy consrain is binding, he workers ouside opion a ecs he cos of informaion revelaion. Firms who pos conracs a ime + 1 a ec he workers ouside opion a ime, bu hey do no ake ino accoun he informaional cos ha hey impose on conracs designed by oher rms a ha ime. This exernaliy is no inernalized by compeiive search and is he source of consrained ine ciency. The social planner akes ino accoun he impac ha he coninuaion uiliy of unemployed workers has on curren conracs, and can improve upon he equilibrium allocaion. The ine ciency resul holds whenever he economy sars a an unemploymen rae level di eren from is seady sae. The direcion of he ine ciency depends on he iniial condiions of he economy. If he iniial unemploymen rae is above he seady sae level, he mass of poenial maches is higher oday han omorrow. Hence, he aggregae cos of informaion revelaion is also higher oday. I follows ha he planner would like o reduce job creaion omorrow, in order o reduce he coninuaion uiliy of unemployed workers oday and achieve higher job creaion oday. The opposie happens when he unemploymen rae sars below he seady sae level. Finally, I show ha he consrained e cien allocaion of resources can be implemened wih a policy ha combines a linear ax/subsidy on hiring wih a non-linear ax/subsidy on job vacancy posing. The ine ciency in my model is driven neiher by he search exernaliy arising in he 3

4 sandard Morensen-Pissarides model, nor by subopimaliy in privae conracing. On he one hand, my model reains he Walrasian spiri of compeiive search o absrac from ine ciencies associaed o ex-pos bargaining. On he oher hand, I allow for general employmen conracs under asymmeric informaion. Presco and Townsend (1984) show ha, in he presence of privae informaion, compeiive markes can decenralize he consrained e cien mechanism. However, in ha paper agens can ener exclusive conracs. In his paper, insead, when workers ener unemploymen hey become anonymous and free o ener a new conracual relaion. This maching environmen is a naural way of sudying dynamic compeiion among conracs, and inroduces a novel exernaliy. Such an exernaliy is akin o he pecuniary exernaliies explored by Arno and Sigliz (1987) and Golosov and Tsyvinski (2006), in models of insurance where side rades are feasible. This paper is relaed o a vas lieraure on search heoreic models of he labor marke, 2 and, in paricular, o models using compeiive search, as Shimer (1996), Moen (1997), Acemoglu and Shimer (1999a). A series of papers highlighs he robusness of he e ciency properies of compeiive search. 3 My paper is also relaed o a growing lieraure on asymmeric informaion in search environmens. In paricular, Shimer and Wrigh (2004) and Moen and Rosen (2005) analyze labor markes where rading fricions inerac wih asymmeric informaion, using compeiive search. However, hey do no focus on e ciency and do no analyze he ransiional dynamics of he equilibrium. Faig and Jerez (2004) propose a heory of commerce, where buyers have privae informaion abou heir willingness o pay for a produc. They de ne a noion of consrained e ciency similar o his paper, bu hey focus on he saic version of he model, hence obaining an e ciency resul. In a similar spiri, Wolinsky (2005) analyzes he e ciency properies of a sequenial procuremen model wih lack of commimen on he buyer s side, and nds ine cien equilibria. However, in his model he ine ciency arises because of conracing resricions. The fac ha he seller s e or is no conracible disors he buyer s search inensiy. In my paper, privae conracs are unresriced and he ine ciency comes only from a general equilibrium e ec. 2 See he survey by Rogerson, Shimer and Wrigh (2005). 3 For example, Acemoglu and Shimer (1999b) show ha compeiive search is e cien even wih ex-ane invesmens, Morensen and Wrigh (2002) generalize resuls on price deerminaion and show how compeiive search achieves e ciency by exploiing all gains from rade. Hawkins (2005) shows ha even when a rm can hire more workers, compeiive search is e cien when rms pos conracs ha are general enough. 4

5 Finally, from a mehodological sandpoin my paper is relaed o he lieraure on mechanism design wih asymmeric informaion, e.g. Mirrlees (1971), Myerson (1981), Myerson and Saerhwaie (1981), La on and Maskin (1980). The paper is organized as follows. In Secion 2, I inroduce he saic version of he economy. I characerize he compeiive search equilibrium and analyze is e ciency properies. In Secion 3, I describe he dynamic environmen and characerize he dynamic compeiive search equilibrium. In Secion 4, I describe he welfare properies of he dynamic model, derive he main ine ciency resul, and show how he consrained e cien allocaion can be implemened. I also explore he alernaive environmen where he unemploymen bene is ransferable. Secion 5 concludes. Finally, he Appendix conains all he proofs ha are no presen in he ex. 2 Saic Economy In his secion, I inroduce he saic version of an economy feauring boh rading fricions and privae informaion on he worker s side. I de ne and characerize he compeiive search equilibrium for his economy and analyze is e ciency properies. In he saic economy I assume, for simpliciy, ha all he workers are iniially unemployed. Environmen. The economy is populaed by a coninuum of measure 1 of workers and a large coninuum of employers. Boh workers and employers are risk-neural and ex-ane homogeneous. Workers can search freely, while employers need o pay an enry cos k o pos a vacancy. When an employer hires a worker, he mach produces y. The value of y is common o all he maches and is given exogenously. However, workers su er a mach-speci c disuiliy from labor. When a mach is formed, is drawn randomly from he cumulaive disribuion funcion F (), wih full suppor on ;, and is observed privaely by he worker. 4 The cumulaive disribuion funcion F () is di ereniable, wih f () denoing he associaed densiy funcion, and sais es he monoone hazard rae condiion, d [F () =f ()] =d > 0. A he beginning of he period, employers can pay k and open a vacancy which eniles hem o pos an employmen conrac. A conrac is a revelaion mechanism, ha is, a map C : 7! [0; 1] R +, specifying for each mached worker who repors ype ~, he hiring 4 The value can also be inerpreed as he cos of e or ha he worker has o exer o make he mach producive, e.g. a privae raining cos. 5

6 probabiliy e( ~ ) 2 [0; 1] and he wage!( ~ ) 2 R +. 5 Wihou loss of generaliy, by invoking he Revelaion Principle, I can resric aenion o he se C of incenive-compaible and individually raional direc revelaion mechanisms. Each worker observes he conracs posed by acive rms, he se C P C, and chooses o search for a speci c conrac C 2 C P. Then, maching akes place and, for each mach, he draw is realized and privaely observed by he worker. He decides wheher o paricipae o he employmen relaionship and which ype ~ o repor. If he worker does no mee an employer or is no hired, he remains unemployed and ges b, a ow of non-ransferable uiliy from leisure. Assume ha y > b + in order o make he problem ineresing. 6 Trading fricions in he labor marke are modeled hrough random maching. 7 Employers and workers know ha heir maching probabiliies depend on he conrac ha hey, respecively, pos and seek. For each conrac C, le v(c) denoe he mass of employers o ering C and u(c) he mass of unemployed workers searching for C. The mass of maches creaed is given by a consan reurns o scale maching funcion m (v(c); u(c)). Le (C) v(c)=u(c) denoe he ighness of he marke for conrac C and de ne he funcion () m (; 1). Then ( (C)) represens he probabiliy ha a worker applying for C nds an employer, and ( (C)) = (C) denoes he probabiliy ha a rm posing C nds a worker. The funcion () : [0; 1) 7! [0; 1] sais es sandard condiions: (i) () min f; 1g, 8 (ii) () is wice di ereniable wih 0 () > 0 and 00 () < 0. 9 Employmen Conracs. The employmen conrac C = fe () ;! ()g 2 mus be incenive compaible and individually raional, ha is, i has o ensure ha he worker reveals ruhfully his ype and chooses o paricipae in he employmen relaionship afer he draw has been realized. Individual raionaliy can be inerpreed as a no-commimen consrain on he worker s side and can be jusi ed by he ypical a will employmen conracs widespread in he Unied Saes. Insead, rms can fully commi o he posed conrac. 5 More generally!( ~ ) could depend no only on he repor ~, bu also on wheher he worker is hired or no. However, due o risk neuraliy his would have no e ec on he resuls. Also, I allow for!( ~ ) > 0 also for workers who are no hired. In equilibrium i will show ha!( ~ ) = 0 whenever he worker of ype ~ is no hired. For simpliciy, I always refer o! (:) as wage. 6 Noice ha if y < b +, hen he equilibrium would be characerized by zero rade for any. 7 Random maching can be hough of as coordinaion fricions, as in Burde, Shi and Wrigh (2001). 8 Wih discree ime, his condiion ensures ha boh () and () = are proper probabiliies. 9 The exponenial funcion sais es his assumpion. One can relax i o include funcions wih one or wo kinks, such as a properly modi ed Cobb Douglas or linear funcions, where he modi ed version of a funcion ^ () is given by () = min f^ () ; ; 1g. See Guerrieri (2005). 6

7 Le v(; ~ ) denoe he uiliy for worker of ype revealing ~, under conrac C, 10 v(; ~ )!( ~ ) e( ~ ) + (1 e( ~ ))b: (1) An employmen conrac is incenive-compaible whenever v (; ) v(; ~ ) for all ; ~ 2 ; (IC) and individually raional whenever v (; ) b for all 2 : (IR) Following a sandard resul in he mechanism design lieraure, 11 I can reduce he dimensionaliy of he consrains. In paricular, condiions IC and IR are equivalen o e (:) being non-increasing ogeher wih he following wo condiions for v(; ): v(; ) = v ; + v ; b: e (y) dy for all 2 ; (IC ) (IR ) This allows me o separae he problem of nding an opimal hiring schedule e (), from he problem of nding a wage schedule! () ha implemens i. From now on I will refer o v(; ) v ; as he informaional ren of a worker of ype, ha is, he addiional uiliy ha such a worker mus receive in order o reveal his own ype. 2.1 Compeiive Search Equilibrium I now de ne he concep of compeiive search equilibrium in his economy. De niion 1 In he saic economy, a symmeric Compeiive Search Equilibrium is a se of incenive-compaible and individually raional conracs C ogeher wih a funcion : C 7! R + [ 1 and an uiliy level U 2 R + saisfying (i) employers pro maximizaion and free-enry: 8C fe () ;! ()g 2, (C) [e () y! ()] df () k 0; (C) subjec o incenive compaibiliy IC and individual raionaliy IR, wih equaliy if C 2C ; 10 In order o simplify he noaion, I drop he dependence of v(; ) on he conrac C. 11 Among ohers, Mirlees (1971), Myerson (1981), Myerson and Saerhwaie (1981), La on and Maskin (1980). 7

8 (ii) workers opimal job applicaion: 8C fe () ;! ()g 2, U (C) [! () e () ( + b)] df () + b; and ( (C)) 1 wih complemenariy slackness, where U is given by U = or U = b if C is empy. max C 0! 0 () e 0 () ( + b) df () + b; C 0 2C In equilibrium, boh rms and workers know he marke ighness associaed wih each conrac, ha is, hey know he ighness funcion for any conrac C 2C, even if no o ered in equilibrium. (C). Noice ha his funcion is de ned Given ha funcion, rms pos conracs ha maximize heir pro s, and free enry drives heir pro s o zero. Moreover, opimal job applicaion ensures ha workers only look for conracs ha maximize heir exane uiliy. In paricular, noice ha rms will never pos conracs ha do no guaranee U o workers, because hey anicipae ha, oherwise, hey would no be able o arac any worker. Generalizing he sandard resul in he search lieraure, 12 he symmeric compeiive search equilibrium is such ha he uiliy of an unemployed worker is maximized subjec o he zero pro condiion for he employer, and he incenive and he paricipaion consrain for he worker. Proposiion 1 If C ; ; U is an equilibrium, hen any pair C ; wih C 2C and = C solves max C; [! () e () ( + b)] df () + b (P1) subjec o e () 2 [0; 1], he incenive consrains IC, he paricipaion consrains IR and he free-enry condiion () [e () y!()] df () = k: (2) Conversely, if a pair C ; solves he program P1, hen here exiss an equilibrium C ; ; U such ha C = C and = C. 12 Shimer (1996), Moen (1997), Acemoglu and Shimer(1999a) analyze a compeiive search equilibirum when informaion is complee. Shimer and Wrigh (2004) de ne a saic compeiive search equilibrium wih bilaeral asymmeric informaion. 8

9 The mass of workers applying for conrac C ha remains unemployed a he end of he period is equal o 1 C e () df () : Noice ha job creaion depends no only on he equilibrium maching probabiliy, hrough C, bu also on he equilibrium hiring decision, once he mach is realized, hrough R e () df (). The analysis of problem P1 can be furher simpli ed, as shown in he nex lemma. Lemma 1 Any funcion [e ()] 2 and which solve Problem P1 solve also s.. and e (:) non-increasing. max e(:); e () [y b] df () + b ~k (P2) () e () (y b) df () k + () e () F () d (3) Furhermore, for any funcion [e ()] 2 and solving problem P2, here exiss a funcion [! ()] 2 such ha he conrac C = [e () ;! ()] 2 and solve problem P1. Free-enry implies ha he enire surplus of he economy accrues o workers. Hence, de faco, rms maximize he ne surplus of he economy, subjec o he consrain ha he ne expeced oupu mus cover boh he ex-ane cos of vacancy creaion, k, and he average expeced informaional rens, () R Equilibrium Characerizaion. e () F () d.13 Problem P2 allows me o characerize he compeiive search equilibrium of he saic economy in a simple way. De ne ^=(1 + ^), where ^ is he Lagrange muliplier aached o consrain (3). Hence, represens a normalized measure of he shadow cos of he informaional rens. The hiring decision can be fully described by a cu-o value ^ such ha e () = ( ^ 1 if 0 if > ^ : (4) 13 From condiion IC, inegraing by pars, i follows ha he average informaion rens per mach are: v(; ) v ; df () = e () F () d: 9

10 Suppose > 0. Then he equilibrium is characerized by an array ^, and saisfying he rs-order condiions 0 ^ and he binding consrain (3). 14 ^ F (^ ) = y b f(^ ; (5) ) y b F () df () = k; (6) f () From equaion (5) i follows ha he hiring cu-o ^ is decreasing in, ha is, as he consrain ges igher he equilibrium is characerized by less hiring. Finally, using incenive compaibiliy, he opimal wage schedule akes he following simple form: 15! () = ( ^ + b if ^ 0 if > ^ : I follows ha he wage is paid only o workers who are e ecively hired and is equal o he disuiliy of he marginal hired worker plus his ouside opion. Hence, he equilibrium conrac reduces o a xed wage and a hiring cu-o and his economy is equivalen o an economy where rms pos a consan wage and workers apply for jobs. Le me now compare he equilibrium allocaion wih a full informaion benchmark. If he employers could observe he shock, hen he equilibrium would be characerized by problem P2 wihou consrain (3). Then, he opimal hiring cu-o would be ^ F I = y b and F I would be deermined by (6) wih = 0. I follows ha, under asymmeric informaion, he equilibrium allocaion could achieve he full informaion benchmark if and only if = 0. However, nex lemma shows ha his is impossible as long as he ex-ane cos k is di eren from zero. Lemma 2 If k > 0, hen he soluion o problem P2 requires > 0. Implemening he full informaion allocaion would require ^ = ^ F I and hired workers would need o be paid he xed wage ^ F I + b. hiring a worker, ha is, y Hence, he revenues of any employer afer! (), would be driven o zero. Given ha employers have o pay ex-ane he cos of opening a vacancy k, his conradics he zero pro condiion. This 14 To derive (4), (5) and (6) one can solve he relaxed version of problem P2 wihou he monooniciy assumpion on e () and hen check ha he opimal e () is in fac monoone. Proposiion 2 will prove ha his problem has a unique soluion, when > 0. Hence, he rs order condiions are necessary and su cien o characerize i. 15 See he second sep of he proof of Lemma 1 in he Appendix, where > 0. 10

11 Lemma highlighs he ension beween ex-ane and ex-pos e ciency, which keeps he economy away from he full informaion allocaion. Ex-pos allocaive disorions are necessary o induce employers o open vacancies ex-ane. From now on, I focus on k > 0 so ha he consrain is binding and he informaional problem ineresing. Hence, he equilibrium is away from he full informaion allocaion and boh he hiring cu-o, ^, and he ighness value,, are lower han in he full informaion benchmark. This implies ha asymmeric informaion reduces job creaion overall, ha is, F (^ ) < F I F (^ F I ). Finally, he following Proposiion esablishes exisence and uniqueness of a Compeiive Search Equilibrium. Proposiion 2 In he saic economy, a Compeiive Search Equilibrium exiss and is unique. 2.2 Consrained E ciency I now de ne he social planner problem. The planner does no observe he ypes of he mached workers and has o induce hem o ruhfully reveal heir mach-speci c disuiliy. Moreover, he is subjec o a paricipaion consrain on he side of he workers, who can decide no o produce and remain unemployed. Given hese consrains and he aggregae resource consrain, he social planner conrols he maching process by deciding how many vacancies o open a he beginning of he period and which jobs o creae, and decides how o allocae non-negaive consumpion o employed and unemployed workers. An allocaion is a pair of funcions fc( ~ ); e( ~ )g ~2 represening he consumpion and he hiring probabiliy for a mached worker who repors ype ~, a ransfer o unemployed workers C U, and a value denoing he ighness of he marke. As in he case of privae conracs, he Revelaion Principle allows me o resric aenion o direc revelaion mechanisms. Le he uiliy for a worker of ype reporing ype ~ be v(; ~ ) = c( ~ ) e( ~ ) + (1 e( ~ )) b + C U : Following he analysis of he previous secion, an allocaion is incenive-compaible when e (:) is non-increasing and v(; ) = v ; + e (y) dy for all 2 : (7) 11

12 Moreover, a worker can always join he anonymous pool of unemployed workers and receive b + C U. Then, he worker s paricipaion consrain akes he form: v(; ) b + C U for all 2 : (8) Finally, he resource consrain for he saic economy ensures ha aggregae consumpion is covered by aggregae ne producion, ha is,! () c()df () + 1 () e () df () C U () y e () df () k; (9) Moreover, consumpion mus be non-negaive, ha is, C U 0 and c() 0 for all. I can now de ne a consrained e cien allocaion. Given ha all he workers are iniially unemployed, social welfare coincides wih he ex-ane value of being unemployed. De niion 2 A consrained e cien allocaion maximizes he workers ex-ane uiliy! () [c() e () ] df () + 1 () e () df () C U + b (10) subjec o feasibiliy, ha is, (i) he incenive-compaibiliy consrain (7) ogeher wih he monooniciy of e (:), (ii) he paricipaion consrain (8), and (iii) he resource consrain (9) ogeher wih non-negaive consumpion. Afer subsiuing he resource consrain ino he objecive (10), he planner problem can be rewrien as subjec o C U 0 and max e(:); e () [y b] df () + b k (P3) e () y b F () df () 1 f () () CU + k: (11) () The only di erence wih he marke equilibrium is ha he planner can poenially ransfer resources o he unemployed workers hrough C U. However, nex proposiion saes ha such a ransfer is no desirable and ha he compeiive search equilibrium is consrained e cien. 16 Proposiion 3 In he saic economy, a Compeiive Search Equilibrium is consrained e - cien. 16 The proof is sraighforward. Noice ha C U does no appear in he objecive funcion of problem P3, so ha he social planner can choose he value ha relaxes he mos consrain (11), ha is, C U = 0 and he problem becomes exacly he same of problem P2. 12

13 2.3 Money Burning I propose now a simple exercise o capure he mechanism ha will lead o dynamic ine ciency. Suppose ha b can be desroyed, wha I refer o as money burning. I now show how money burning can generae a Pareo improvemen. 17 Proposiion 4 Consider a family of economies paramerized by (k; y; F ()). There exiss an open se of parameers such ha he compeiive search equilibrium allocaion can be Pareo improved by reducing b. Noice ha b represens he worker s ouside opion, which is exogenous in he saic seing. The proof in he Appendix shows ha reducing b generaes a Pareo improvemen whenever 1 F (^ ) < 0. This expression represens he e ec of he workers ouside opion on welfare. There is a direc posiive e ec coming from he fac ha, as he ouside opion is higher, workers who end up unemployed are beer o. This is capured by 1 F (^ ), which represens he ex-ane probabiliy of being unemployed a he end of he period. However, here is a negaive indirec e ec coming from he ighness of he informaional consrain, represened by. As he ouside opion increases, he shadow cos of revealing informaion is higher, since workers have a higher opporuniy cos of remaining in he employmen relaionship. When 1 F (^ ) < he indirec e ec dominaes and a Pareo improvemen can be achieved by reducing b. In he dynamic economy he worker s ouside opion will be an endogenous objec. Hence, his resul suggess a source of dynamic consrained ine ciency, as I will explore below. 3 Dynamic economy In his secion, I generalize he economy o a dynamic seing. Environmen. Consider an economy wih in nie horizon and discree ime. Boh workers and employers have linear preferences and discoun facor. The search and producion echnologies are naural generalizaions of he saic seing. Each mach lass unil separaion, which happens according o a Poisson process wih parameer s, while y and denoe now 17 In Guerrieri (2005) I show ha his resul holds also for funcions () wih wo poins of nondi ereniabiliy, which cover also he common Cobb-Douglas speci caion. 13

14 he expeced value of oupu and disuiliy a he momen of he mach. 18 A he beginning of each period, workers can be eiher employed or unemployed and employers can be eiher acive or inacive. Inacive employers can open a vacancy a a cos k which eniles hem o pos an employmen conrac. A conrac posed a ime is a revelaion mechanism, ha is, a map C : 7! [0; 1] R +, specifying for each mached worker a ime who repors ype ~, he hiring probabiliy e ( ~ ) 2 [0; 1] and he expeced value of wages! ( ~ ) 2 R Invoking he Revelaion Principle, wihou loss of generaliy, I can again resric aenion o incenive-compaible and individually raional direc revelaion mechanisms C for each ime. 20 Noice ha conracs canno be condiioned on he pas employmen hisory, given ha I assume ha unemployed workers are anonymous. Le C P C be he se of conracs posed by acive rms. Each unemployed worker observes C P and applies for a conrac C 2 C P. As in he saic environmen, each conrac C is associaed o a speci c so ha employers and workers know ha heir maching probabiliies will depend on he conrac ha hey, respecively, pos and seek. Afer workers sar o search for a speci c conrac, maching akes place and, for each mach, he draw is realized and is privae informaion of he worker. A worker who is mached a ime chooses a repor ~ and wheher o paricipae or no o he employmen relaionship. If he walks away or he is no mached, he eners an anonymous pool of unemployed workers, ges a non-ransferable uiliy from leisure b, and searches for a job nex period. If he worker is hired, he mach is producive unil separaion. Employmen Conracs and Bellman Values. De ne v (; ~ ) he expeced uiliy of a worker of ype, mached a ime, and reporing ype ~. For analyical convenience i is useful o spli v (; ~ ) in hree componens as follows v (; ~ ) = [! ( ~ ) e ( ~ )] + e ( ~ )V + [1 e ( ~ )]U : (12) Firs, he worker receives he wages ne of disuiliy, denoed by! ( ~ ) e ( ~ ), second, if hired, he ges he coninuaion value V, re ecing he opion of being separaed and becoming unemployed in he fuure, hird, if no hired, he ges he coninuaion value U of remaining 18 Le he insananeous oupu and disuiliy be ~y and ~, which are boh consan for he duraion of he mach. Then, y = ~y(1 (1 s)) 1 and = ~ (1 (1 s)) The wage pro le over he life of he relaionship is irrelevan for he analysis, given ha preferences are linear, ypes are xed over ime wihin a mach, and here is no commimen problem afer he mach is implemened. 20 The se C is ime-varying because he ouside opion for unemployed workers is poenially changing over ime. 14

15 unemployed. The coninuaion value V sais es he recursive condiion Moreover, he coninuaion value U sais es V 1 = su + (1 s) V : (13) U 1 = b + ( ) [! () e () ( V + U )] df () + U : (14) A naural generalizaion of he saic analysis, gives ha a conrac C is incenive-compaible and individually raional whenever e (:) is non-increasing and he following condiions hold: v (; ) = v ; + e (y) dy for all 2 ; (IC D ) v ; U : (IR D ) Following he saic analysis, equaion IC D de nes v (; ) v ;, ha is, he informaional rens for a worker of ype who mees a rm a ime. 3.1 Dynamic Compeiive Search Equilibrium In his secion, I de ne he dynamic version of he Compeiive Search Equilibrium. Generalizing he saic de niion, a dynamic Compeiive Search Equilibrium, in sequenial erms, is a sequence of ses of incenive-compaible and individually raional conracs C a sequence of ighness funcions 1 =0, where 1 =0 and : C 7! R + [ 1, such ha, a any employers maximize pro s and workers apply opimally for jobs, aking as given he fuure sequence of ses of conracs C 1 =+1, and ighness funcions 1 =+1. In order o simplify he analyical reamen, I inroduce an equivalen de niion of he equilibrium in recursive erms. The crucial hing o noice is ha he pair of coninuaion uiliies for unemployed and employed workers a ime, U and V, are su cien saisics for he fuure ses of conracs C 1 =+1 and he ighness funcions me o derive he following de niion in recursive erms. 1. This allows =+1 De niion 3 In he dynamic economy, a symmeric Compeiive Search Equilibrium is a sequence of ses of incenive-compaible and individually raional conracs C of funcions uiliy levels U ; V 1 =0, where 1 =0, where U 1 =0, a sequence : C 7! R + [ 1, and a sequence of pairs of coninuaion ; V 2 R 2 + for any, saisfying 15

16 (i) employers pro maximizaion and free-enry a each ime : 8C fe () ;! ()g 2, (C ) [e () y! ()] df () k 0; (C ) subjec o incenive compaibiliy IC D C 2 C ; and individual raionaliy IR D, wih equaliy if (ii) workers opimal job applicaion a each ime : 8C fe () ;! ()g 2, for given V and U ; U 1 b + and ( U 1= max (C )! () e () V (C )) 1 wih complemenariy slackness, where C 02C b + or U 1 = b + U if C C 0! 0 () e 0 () V is empy, and V 1 = su + (1 s) V : + U df () +U ; + U df () +U ; This de niion is a naural generalizaion of he saic equilibrium. A each poin in ime employers maximize pro s and workers apply opimally for jobs, boh aking as given he fuure values of being employed and unemployed and he ighness funcion ha associaes a marke ighness o all poenial conracs, including hose no o ered in equilibrium. Moreover, pro s are driven o zero a each poin in ime by free enry. Generalizing he saic resul, nex proposiion gives a characerizaion of a symmeric compeiive search equilibrium in recursive erms. Proposiion 5 If C pair C ; ; wih C 2C ; U ; V 1 =0 and = is a Compeiive Search Equilibrium, hen any saisfy he following: C (i) for a given pair U ; V, a any ime, C = e () ;! () and 2 solve max b + ( )! () e () V e (:);! (:); subjec o e () 2 [0; 1], he consrains IC D assumpion on e (), and he free-enry condiion ( ) + U df () + U (P4) and IR D, ogeher wih he monooniciy [e () y! ()] df () = k; (15) 16

17 (ii) he sequences C ; 1 =0 and U ; V 1 saisfy equaions (13) and (14). =0 Conversely, if a sequence C solves he program P4, hen here exiss an equi- = C and = C. librium C ; ; U ; V ; 1 =0 1 =0 such ha C The equilibrium unemploymen rae evolves according o u C = u 1 C 1 " 1 Proposiion 5 shows ha, for given U C e () df () # + 1 u 1 C 1 s: and V, an equilibrium pair C and mus solve Problem P4. The nex lemma shows ha, for given U and V, he equilibrium can be equivalenly described by a hiring funcion e () and a ighness ha solve a simpli ed program P5. Moreover, given e () and, an associaed wage funcion! () can be consruced so ha he consrains IC D and IR D are sais ed. 21 Lemma 3 For given U and V, any funcion [e ()] 2 and which solve Problem P4, solve also s.. and e (:) non-increasing. max ( ) e (:); e () [y + V U ] df () + b k + U (P5) ( ) e () y F () f () + V U df () k; (16) Furhermore, for any funcion [e ()] 2 and which solve problem P5, here exiss a funcion [! ()] 2 such ha he conrac C = [e () ;! ()] 2 and solve problem P4. Equilibrium Characerizaion. In he dynamic seing, he di erence U V represens he e ecive ouside opion of he workers a ime. The characerizaion of he equilibrium allocaion a ime, for a given U subsiue he saic ouside opion b wih U by a cu-o value ^ such ha e () = V, is simple and analogous o he saic one, once one ( V. The hiring margin can be fully described 1 if 0 if > ^ ^ 21 The proof of Lemma 3 is similar o he one of Lemma 1 and is herefore omied. ; 17

18 Similarly o he saic seing, de ne ^ =(1 + ^ ), where ^ is he Lagrangian muliplier aached o consrain (16). When his consrain is binding, he equilibrium can be characerized, for given U V, by an array ^, and saisfying he rs order condiions ^ F (^ ) = y (U V ) f(^ ; ) (17) 0 ^ y (U V ) F () df () = k; f () (18) and he binding consrain (16). The analogous o Lemma 2 can be proved in he dynamic seing o show ha whenever he cos of posing a vacancy k is posiive, hen > 0 and he equilibrium is away from he full informaion allocaion. Nex proposiion shows ha here exiss a unique equilibrium, which is characerized by consan ^,, U and V. The consan values of U and V mus saisfy (13) and (14) and, hence, U = R ^ [y ] df () + b k h (1 ) (1 s) ( ) F (^ i ; (19) ) V = s 1 (1 s) U : (20) In urns, given hese values of U and V, (16), (17) and (18) can be used o deermine ^ and. 22 Hence, he equilibrium is found by solving a xed poin problem as shown in he proof of he following proposiion. Proposiion 6 In he dynamic economy, here exiss a unique compeiive search equilibrium. In equilibrium ^,, U and V are consan and independen on he iniial condiion u 0. I follows ha he only non rivial ransiional dynamics of he compeiive search equilibrium are hose of he unemploymen rae: u = u 1 [1 F (^ )] + (1 u 1 ) s: (21) In seady sae no only e (),, V and U are consan, bu also he unemploymen rae. The seady sae unemploymen rae is given by h u SS = s s + F (^ 1 )i : (22) 22 Noe ha in equilibrium he coninuaion uiliy of he employed urns ou o be smaller han he coninuaion uiliy of he unemployed. This is naural once I de ne he coninuaion value of he employed ne from wage and disuiliy. 18

19 4 Dynamic E ciency In his secion, I explore he e ciency properies of he dynamic compeiive search equilibrium. Firs, I characerize he social planning problem and show ha he compeiive equilibrium is consrained ine cien whenever he iniial unemploymen rae is di eren from is seady sae level. Second, I show ha he combinaion of a non-linear ax/subsidy on job posing and a linear ax/subsidy on hiring can implemen he consrained e cien allocaion of resources. 4.1 Social Planning Problem As in he saic seing, he social planner does no observe he ypes of he mached workers and has o induce hem o ruhfully reveal hem. Moreover, here is lack of commimen on he side of he workers, who can always decide no o produce and remain unemployed. The planner faces he same anonymiy resricion presen in he decenralized economy. If a worker eners he unemployed pool, his hisory is indisinguishable from ha of any oher unemployed worker. Given hese consrains, ogeher wih he resource consrain of he economy, he social planner conrols he maching process by deciding how many vacancies o open a he beginning of each period and which jobs o creae, and decides how o allocae ineremporally non-negaive consumpion o employed and unemployed workers. An allocaion is a sequence of funcions fe ( ~ )g ~2 represening he hiring decision for a worker who mees an employer a ime and repors ype ~, a sequence of funcions fc ( ~ )g ~2 denoing he expeced value of consumpion of a worker hired a ime reporing ype ~, a sequence of consumpion values for unemployed workers C U, a sequence of consumpion values C V for employed workers mached a ime, and a sequence of ighness values. Noice ha he consumpion pro le over ime is irrelevan for he analysis, given ha agens have linear uiliy, ypes are xed over ime wihin a mach, and here is no commimen problem afer he mach is implemened. Le V 1 denoe he coninuaion value of being employed a ime 1, ne from consumpion and disuiliy. I represens he value of he curren ransfer plus he discouned expeced value of being separaed and becoming unemployed in he fuure, ha is, V 1 = C V 1 + su + (1 s) V : (23) Moreover, he value of being unemployed a ime 1 is given by 19

20 U 1 = b + C U 1 + ( ) [c () e () ( + U V )] df () + U : (24) Le he uiliy of a mached worker of ype reporing ype ~ a ime be v (; ~ ) = c ( ~ ) e ( ~ )( V ) + [1 e ( ~ )]U for all ~ ; 2 : (25) As in previous secions, an allocaion is incenive-compaible when e (:) is non-increasing and v (; ) = v ; + e (y) dy for all 2 : (26) Workers can choose a any poin in ime o ener he anonymous pool of he unemployed. Afer some algebra, I can show ha under incenive-compaibiliy he paricipaion consrains can be wrien as c () e () + F () f () V + U df () 0: (27) The ineremporal resource consrain ensures ha aggregae consumpion is covered by aggregae oupu and ha consumpion is non-negaive, ha is, C U 0, C V 0, c () 0 for all and. Assume ha he social planner can ransfer resources ineremporally a he xed ineres rae r = 1 1, by borrowing a he beginning of ime a price and paying back a he beginning of ime + 1. De ne P as he ne resources of he planner a ime. 23 I assume ha he social planner, as he marke economy, does no have access o any exernal resource. Then, he resource consrain can be wrien in recursive erms as # P 1 u 1 " ( ) [e () y c ()] df () C U 1 k (1 u 1 ) C V 1 + P ; for any, where u follows he law of moion # u = u 1 "1 ( ) e () df () and saring wih P 0 = 0. + (1 u 1 ) s; (28) 23 Tha is, ( " 1X P j # u j j+1 [e j+1 () y c j+1 ()] df () Cj U j+1 k j= (1 u ) C V j ) : 20

21 De niion 4 An allocaion is feasible when i sais es (i) incenive-compaibiliy, (ii) he paricipaion consrain, and (iii) he resource consrain. For each feasible allocaion and a given iniial rae of unemploymen u 0, here is an associaed pair (U 0 ; V 0 ), de ned by expressions (23) and (24), represening he promised uiliy o unemployed and employed workers a ime 0. The social planner will choose a poin on he Pareo fronier in he uiliy possibiliy space de ned by (U 0 ; V 0 ). De niion 5 For given u 0, an allocaion is consrained e cien if i is feasible and maximizes U 0 subjec o he consrain V 0 V. 4.2 General Characerizaion: Dual Problem In order o analyze consrained e cien allocaions, i is convenien o approach he social planner problem from a dual perspecive, ha is, maximizing he ne resources of he economy P 0 (which is equivalen o minimize he ne coss), subjec o U 0 U and V 0 V, for given U and V. This problem can be characerized in recursive erms. The planner Bellman equaion, a ime, is a funcion of hree sae variables: he promised uiliy o employed workers V 1, he promised uiliy o unemployed workers U 1, and he unemploymen rae u 1. The planning problem can be wrien as P (V 1 ; U 1 ; u 1 ) = max u 1 ( ) [e () y c ()] df () (P6) C U ;CV ; ;feg;fcg V ;U ;u u 1 C U 1 + k (1 u 1 ) C V 1 + P (V ; U ; u ) subjec o he promise-keeping consrains for V 1 and U 1, (23) and (24), he law of moion for u 1, (28), and he incenive-compaibiliy and paricipaion consrains, summarized by (27) and e (:) non-increasing. I sudy a relaxed version of he problem, where I do no impose he monooniciy of e (:) and where I use he consrain (24) o subsiue for c (), so ha consrain (27) reduces o ^ U 1 b + C U 1 + ( ) F () d + U : (29) Once I solve his problem, I can solve for c () from equaions (25) and (26). Poinwise maximizaion, as in he compeiive equilibrium analysis, implies ha here exiss a hreshold 21

22 ^ such ha e () = 1 if ^, and e () = 0 oherwise. This shows ha he soluion o he relaxed problem is characerized by a monoone e (:), so ha i also solves he full planning problem. Given he value funcion P (; ; u 0 ) for a given u 0, he Pareo fronier is de ned by he pairs U; V such ha P V ; U; u0 = 0. Nex, I show he main resul of he paper: he compeiive equilibrium is consrained ine cien whenever he iniial unemploymen rae is di eren from is seady sae level. Proposiion 7 In he dynamic economy, if u 0 6= u SS, hen he compeiive search equilibrium is consrained ine cien. The crucial di erence beween he saic and he dynamic environmen is ha he worker s ouside opion is exogenously given in he former, while in he laer, i is endogenously deermined. Dynamic ine ciency arises because rms do no inernalize he fac ha he worker s ouside opion a ecs he cos of informaion revelaion. The social planner can inernalize his informaional exernaliy, and, hus, achieve a Pareo improvemen. To explain he mechanism behind his resul I illusrae he special case where u 0 = 1 > u SS, leaving he general proof o he appendix. The planner rs order condiion wih respec o he promised uiliy of he unemployed workers a dae 1 = [1 ( 1 )F (^ 1 )] u 1 (1 0 ) + (1 1 ) u 1 = 0; (30) where L denoes he Lagrangian associaed o he planner problem and is he Lagrange muliplier aached o consrain (29). The rs wo erms capure he direc e ec of increasing U 1 by one uni. The planner can reduce he consumpion of he unemployed workers who remain unemployed a he end of period 0, of mass 1 ( 1 )F (^ 1 ), bu is forced o increase he consumpion of he unemployed workers in period 1, of mass u 1. Since u 1 = 1 ( 1 )F (^ 1 ), hese wo erms cancel ou. However, changing he promised uiliy U 1 also a ecs he informaional rens for he workers hired in periods 0 and 1. Noe ha U 1 appears on he righ-hand side of consrain (29) in period 0, and on he lef-hand side of he same consrain in period 1. This implies ha he expeced informaional rens ( ) R ^ F () d, and hence job creaion, will decrease in period 0 and increase in period 1. These wo e ecs are capured by he las wo erms in (30), given ha 1 represens he shadow informaional bene of increasing he promised uiliy of a worker employed a dae Proceeding by conradicion, suppose 24 The envelope heorem implies =@U 1 = u 1. Absen informaional asymmery, he cos of 22

23 ha he compeiive equilibrium solves he planner problem. Then, I can show ha has o be consan over ime, given ha a he compeiive equilibrium job creaion is consan over ime. When u 0 = 1, i follows from equaion (30) 1 < 0. This means ha he planner can locally improve upon he compeiive equilibrium by decreasing U 1. The argumen is more general han his speci c example. A perurbaion argumen can show ha whenever u 1 > u he planner can improve upon he equilibrium by reducing U. 25 In his case, here is a larger mass of unemployed workers a ime 1, for whom a reducion in U ighens consrain (29), relaive o he mass of unemployed a ime, for whom a reducion in U makes he consrain looser. Since a he compeiive equilibrium he shadow cos of informaion per worker is consan, he oal informaional bene a ime U is higher han he oal informaional cos experienced a ime. u 1 < u, here is a gain from increasing U. 1 of reducing Symmerically, when This suggess ha he direcion of he ine ciency depends on he iniial condiions of he economy. In paricular, when he iniial unemploymen rae is above is seady sae level, hen equaion (28) implies ha he unemploymen rae is decreasing over ime. Then a any, he planner has an incenive o reduce U, hus increasing job creaion and speeding up he convergence of he unemploymen rae o he seady sae. On he oher hand, when he iniial unemploymen rae is below is seady sae level, he reverse applies. Finally, if he iniial unemploymen rae is a is seady sae level, hen he compeiive search equilibrium sais es he necessary condiions of he social planning problem. In his case, he mass of unemployed workers is consan over ime and he exernaliy described above is mued Implemenaion Given ha i is generically possible o improve upon he compeiive equilibrium, a naural quesion arises: which policy can correc he marke ine ciency? I now show ha he governpromising one exra uni of uiliy o unemployed workers a ime 1 would correspond o 1 per worker, ha is, would be equal o 1. When informaional asymmery is presen, on op of his direc cos, he planner receives an indirec bene from increasing his promised uiliy, since he can increase job creaion a ime 1 owards is e cien level. This reduces he cos o he planner of increasing U 1 and implies ha < Noe ha, if u < 1, when U changes also V mus adjus o saisfy he promise keeping consrain for V 1. In urns, his requires U +1 o change as well. This is he reason why i is easier o make he perurbaion argumen for u 0 = Unforunaely problem P6 is no concave and I canno conclude ha a he seady sae he equilibrium is consrained e cien, alhough i seems a reasonable conjecure. 23

24 men can implemen he consrained e cien allocaion by combining a non-linear ime-varying ax on vacancy posing, V (), ogeher wih a linear ime-varying ax on job hiring, H. Boh can be negaive, in which case, hey represen subsidies. Imagine ha rms pay V beginning of ime and a ax H () o pos a conrac associaed o he marke ighness a he if hey hire a worker a ime. The compeiive equilibrium can be characerized using naural generalizaions of Proposiion 5 and Lemma 3. A each ime 1, agens ake as given he axes V () ; H and he coninuaion uiliies V and U, and solve he following problem: ^ max () y H + V U df () + b k + V () + U (P7) ^; s.. () ^ y H F () f () + V U df () k + V () : To complee he characerizaion of he equilibrium one has o nd he sequences fu ; V g 1 =0 evolving according o (13) and (14), using he opimal sequences f^ ; g 1 =0. order for his equilibrium o be feasible, he sequences of axes V he ineremporal governmen budge consrain 1X =0 () ; H Moreover, in 1 need o saisfy =0 h i ( ) F (^ )u H + v V ( ) = 0: (31) Proposiion 8 The consrained e cien allocaion can be implemened wih a linear ax/subsidy on hiring H 2 R and a non-linear ax/subsidy on vacancy posing V (), ha akes he form V () = T =, wih T 2 R. The ine ciency discussed in he previous secion can be described as an ineremporal exernaliy among employers. An employer a ime chooses wheher o pos a vacancy, and in ha case, a wage and a hiring cu-o. These decisions deermine he ouside opion of workers who mee employers a ime 1. An higher ouside opion ighens he incenivecompaibiliy consrain of hese workers and resrics he se of he conracs ha employers can pos a ha ime. Employers a ime do no inernalize he informaional cos ha hey impose on employers a ime 1. The planner akes his cos ino consideraion and, hence, wans o correc job creaion depending on he unemploymen rae level. Marke e ciency can be resored by cross-subsidizing rms across periods. In order o do so, he governmen needs 24

25 o use wo ypes of axes because he needs o correc he hiring margin, wihou disoring he vacancy posing ex-ane. If he governmen wans o increase hiring in periods of high unemploymen and hence pay a subsidy on i, he needs simulaneously o ax vacancies o avoid excessive vacancy posing by subsidized rms. 4.4 Transferabiliy resores Full Informaion. An essenial ingredien o obain he ine ciency resul discussed above is ha he nonnegaiviy consrain on consumpion of unemployed workers is binding. To illusrae he role of his consrain, I now consider an alernaive environmen where b is freely ransferable. In his case, I inerpre b as home producion. The money burning exercise, in Secion 4, shows ha if he planner can wasefully desroy b, in some cases, he can obain a Pareo improvemen. When b is ransferable, boh he planner and he privae economy can do beer han ha, since hey can ake resources away from workers who do no paricipae and redisribue hem. Hence hey can reduce he workers ouside opion, wihou wasing aggregae resources. In he nex proposiion, I show ha when b is su cienly large he compeiive search equilibrium can achieve he full informaion allocaion. Proposiion 9 Suppose ha b is ransferable and he following inequaliy holds b kf I ( F I ) ; hen he compeiive search equilibrium achieves he full informaion allocaion. When b is ransferable he opimal wage schedule akes he form (!! () = () + ^ + U V if ^! () if > ^ ; where rms can se a negaive value for!() as long as!() b: (32) This conrac has a naural inerpreaion as bond posing. Afer he mach, he rm asks he worker o sign a promise o pay a fee! () before he observes he realizaion of he shock. If he worker is hired, he will receive a wage of value ^ + U V before paying he fee back. If he is no hired he will produce b a home and use i o pay back he fee 25