Inflation, Investment Composition and Total Factor Productivity

Transcription

1 1 Inflaion, Invesmen Composiion and Toal Facor Produciviy Michael Evers, Sefan Niemann, Marc Schiffbauer Bonn Graduae School of Economics PRELIMINARY VERSION This version: Absrac This paper argues ha he empirically observed negaive relaionship beween inflaion and oal facor produciviy (TFP) can be undersood on he basis of a dynamic sochasic general equilibrium model where causaliy runs from inflaion o aggregae produciviy. Tha is, TFP is no o be seen as an exogenous process, bu as a funcion of economic variables which - among oher hings - are affeced by he rae of inflaion. We develop a heoreical model whose key ingrediens are (i) a limied paricipaion assumpion which generaes non-neuraliy of moneary policy even under flexible prices, (ii) he scope for echnology choice, and (iii) an agency problem which gives rise o financial marke incompleeness. In his environmen, we demonsrae how nominal flucuaions affec no only he overall amoun, bu also he composiion of aggregae invesmen. Our calibraed benchmark economy is compared o alernaive economies where eiher moneary shocks are absen or he seady seady sae rae of inflaion is changed; on he basis of his exercise we conclude ha moneary policy shocks can accoun for a significan proporion of he variaion in TFP. Finally, we subsaniae he relevance of our basic hypohesis ha nominal flucuaions affec he composiion of aggregae invesmen by means of an empirical anlysis of aggregae, secoral and firm level panel daa. 1 Inroducion The saring poin for his paper is he empirical finding of a negaive relaion beween inflaion and oal facor produciviy (TFP), boh a business cycle frequency and over longer horizons. 1 If one ries o give a causal inerpreaion o his correlaion, one can pursue wo ways, depending on he direcion of causaliy ha is sressed. Indeed, in sandard moneary business cycle models feauring an exogenous produciviy process and a quaniy heory relaion beween money, oupu and prices, i is he case ha - ceeris paribus - a negaive produciviy shock is associaed wih a higher rae of inflaion. Hence, he premise in his class of models is a causal negaive effec of TFP on inflaion. However, given ha TFP is aken o be a residual caegory which is no furher modelled, his is an unsaisfacory siuaion; he reason is ha we are lef 1 A deailed assessmen of he relevan empirical evidence will be provided in he subsequen secions.

2 2 wih a measure of our ignorance (Abramoviz, 1956) in order o explain economic processes of firs prioriy. Therefore, his paper akes a differen roue. While we do no quesion he meris of he aforemenioned class of models for he purpose of sudying macroeconomic dynamics or he effecs of sabilizaion policies over he business cycle, we reverse he underlying noion of causaliy beween inflaion and TFP by sressing ha he laer variable can be seen as a funcion of he former one. This implies ha TFP is no longer an exogenous residual, bu becomes an endogenous variable which is deermined in he general equilibrium of our macroeconomic model. Agains his background, he presen paper concenraes on he effec of moneary policy on TFP. Specifically, we argue ha i is no appropriae o rea shocks o moneary policy and echnology as orhogonal. The ransmission mechanism ha we pu forward in order o raionalize he negaive relaionship beween inflaion and TFP is ied o he composiion and effeciveness of aggregae invesmen. To formalize our argumen, we develop a model economy whose underlying srucure is based on he common poin of deparure of boh modern business cycle and growh heory: he neoclassical growh model. This basic model is modified along hree dimensions. Firs, i feaures a cash-in-advance (CIA) consrain and incorporaes he assumpion of limied asse marke paricipaion; his generaes non-neuraliy of moneary policy even in an environmen wih flexible prices via a liquidiy effec. Second, he model does no involve a comprehensive aggregae producion funcion, bu sars from he presumpion ha invesmen can be channelled ino wo disinc echnologies: a safe, bu reurn-dominaed ( basic ) echnology and a superior ( advanced ) echnology which yields higher expeced reurns, bu is subjec o idiosyncraic liquidiy shocks. Firms operaing he laer echnology can insure hemselves agains such idiosyncraic risk by means of holding a precauionary sock of readily markeable asses; however, due o an enrepreneurial moral hazard problem, which is he hird key building block of he model, he scope for insurance is limied. The consequence of his fricion is ha financial markes are incomplee in ha scarce liquidiy - along he lines of Holmsrom and Tirole (1998) - canno be efficienly provided o he producive secor. In paricular, given ha insurance agains liquidiy shocks is cosly, variaions in he coss of insurance generae a composiion effec ha is found o be associaed wih changes in TFP. In he model we pu forward, i urns ou ha hese coss are given by he nominal ineres rae. Specifically, quie similar o is role wih respec o he opporuniy coss of consumpion in a simple cash-in-advance model, he nominal ineres rae consiues an addiional cos of producion by means of he advanced echnology relaive o he basic one. Hence, he model posulaes a novel aspec of moneary ransmission in ha movemens in he nominal ineres rae are associaed wih changes in he composiion of invesmen in he wo available echnologies. In view of above argumens, i is eviden ha he presen paper sands beween business cycle and growh heory: I considers moneary and echnological shocks as well as heir ineracion wih a specific financial markes fricion, bu a he same ime endogenizes he produciviy process via an endogenous echnology choice which is caalyzed by his fricion. 2 Since he in- 2 For a similar approach, compare he recen paper by Aghion e al. (2005) who paraphrase he siuaion as follows: The modern heory of business cycles gives a cenral posiion o produciviy shocks and he role of financial markes in he propagaion of hese shocks; bu i akes he enire produciviy process as exogenous. The modern heory of growh, on he oher hand, gives a cenral posiion o endogenous produciviy growh and he role of financial markes in he growh process; bu i focuses on rends, largely ignoring shocks and cycles.

3 3 cenive problem we posi gives rise o an endogenous form of financial marke incompleeness, we can derive a se of implicaions of he consrained-efficien conracing scheme which governs he provision of liquidiy o firms operaing he advanced echnology. These implicaions relae o he reacion of he producive secor o moneary policy shocks and o he way in which indusry level characerisics affec specific indusries sensiiviy o such shocks. In order o assess he quaniaive relevance of he ransmission mechanism as well as is empirical relevance, we adop a wofold sraegy: One he one hand, we inerpre our model as a lieral business cycle model and calibrae i o he US economy a quarerly frequency. The calibraed benchmark economy is hen compared o alernaive economies whose basic srucure is idenical, bu where eiher echnology shocks or he financial marke fricion are absen. Comparing he respecive model-generaed momens, we conclude ha, by generaing an invesmen-composiion driven variaion in TFP, moneary policy shocks can accoun for a significan proporion of macroeconomic flucuaions. On he oher hand, we use aggregae daa from he US naional accouns ogeher wih secoral and firm-level panel daa o subsaniae he empirical relevance of our basic hypohesis ha nominal flucuaions affec he composiion of aggregae invesmen. Anicipaing resuls, he findings emerging from dynamic panel regressions a quarerly and yearly frequency provide robus evidence in favor of our heoreical proposiions. In paricular, higher inflaion is significanly found o negaively affec TFP (-growh), whereby he exogeneiy of inflaion canno be rejeced; hus, here is evidence ha he negaive relaion beween inflaion and TFP indeed is due o a causal effec. While his resul perains o aggregae level daa, he subsequen analysis of secoral and firm-level daa provides evidence consisen wih (i) he implicaions of consrained-efficien conracing wih respec o he posulaed agency problem, as well as (ii) he noion ha corporae liquidiy holdings are used as a precauionary buffer sock o insure invesmen ino advanced echnologies and ha he scope of such insurance is negaively affeced by he level of inflaion. The res of he paper is organized as follows. The nex secion provides a review of he relaed lieraure as well as a brief synopsis of some relevan empirical evidence, before Secion 3 describes he heoreical model as he basic srucure o formulae our main hypoheses. Secion 4 examines he saisical properies of he posulaed benchmark economy as well as hose of alernaive economies. Then, Secion 5 seeks o empirically corroborae our proposiion ha he composiion of aggregae invesmen is crucially affeced by he condiions of insuring projecs via corporae liquidiy holdings by means of an analysis of panel daa a differen levels of aggregaion. A final secion concludes. 2 Relaed lieraure Theoreical lieraure: The general equilibrium model we will formulae in he nex secion is similar in spiri o he approach aken by Aghion e al. (2005) who examine how credi consrains affec he cyclical behavior of produciviy-enhancing invesmen. To ha end, he auhors develop a simple growh model where invesmen can be sunk ino wo ypes of aciviies which differ in heir respecive ime horizons: a shor-erm projec, and a long-erm projec which enhances fuure produciviy. Imporanly hen, aggregae produciviy has boh an exogenous and an endogenous componen. The exogenous componen is specified as in a convenional real business cycle model, whereas he endogenous componen is driven by he

4 4 mass of long-erm projecs ha have successfully been compleed in he pas. Survival of longerm projecs is uncerain because hey are subjec o idiosyncraic liquidiy shocks which - for reasons lef unspecified - can only be imperfecly insured. In his seup, an opporuniy cos effec makes he demand for long-erm invesmen counercyclical, while credi consrains induce a counervailing liquidiy risk effec and generally depress he level of long-erm invesmen. Hence, under sufficienly igh credi consrains, here a wo effecs: Firs, aggregae invesmen is shifed owards shor-erm aciviies, and second, long-erm invesmen becomes procyclical, hus amplifying he business cycle. Similarly, Angeleos (2006) sudies he effecs of idiosyncraic invesmen risk on he aggregae level and he allocaion of savings wihin he framework of a non-moneary neoclassical growh model. Hence, unlike Bewley-ype economies he model feaures capial raher han labor income risk. One model varian considers he aggregae dynamics resuling from he choice of invesing eiher ino privaely-held projecs or ino public equiy, which allows o pool idiosyncraic risks. The key implicaion hen is ha, quie similar o wha will happen in he model economy developed below, incomplee markes reduce TFP by shifing resources away from he more risky, bu also more producive privae equiy invesmen. One disadvanage wih above approaches is ha heir implicaions for he economy s cyclical dynamics criically hinge on he assumpion ha uninsured idiosyncraic invesmen risk evolves in a counercyclical fashion. In order o improve along his dimension, i is imporan o carefully specify he source of marke incompleeness which gives rise o uninsured idiosyncraic risk. In our sudy, we will do so by embedding he conracing problem discussed in Holmsrom and Tirole (1998) ino a business cycle model. 3 The quesion addressed here is wheher privae claims provide enough liquidiy o guaranee he efficien funcioning of he producive secor. In conras o he classical heory of finance, where here is no corporae demand for liquidiy since firms, a any ime, can issue claims up o he full presen value of heir expeced fuure reurns, he paper inroduces an enrepreneurial moral hazard problem ha creaes a demand for liquidiy in he form of advance financing. If his corporae demand for liquidiy is mached wih an endogenous supply of funds, he key observaion o be drawn is ha he same agency problem ha limis he scope for ex pos refinancing also limis he amoun of resources ha can be raised for invesmen purposes ex ane. Moreover, variaions in he liquidiy premium will endogenously affec he degree of marke incompleeness and hus he composiion of aggregae invesmen. The models menioned above are all based on real economies, bu saring from he conribuions by Bernanke and Gerler (1989, 1995) here is also an exensive lieraure dealing wih he ineracion of financial marke fricions and he moneary ransmission process. Raher 3 Kao (2006) adops a similar approach, bu in a real one-secor model. Meh and Quadrini (2006) consider a model wih endogenous marke incompleeness wih respec o individual invesmen risk. A differen agency problem is sudied in Rampini (2004) who analyzes an economy where enrepreneurs face a choice beween a safe projec and a risky projec which is more producive in expecaion. For incenive reasons, agens who ake he risky projec need o bear par of he idiosyncraic risk. The agens risk aversion implies ha hey are willing o bear more risk when produciviy is high; addiionally, heir incenive consrain is relaxed such ha hey need o bear less risk during a boom. The consequence of such counercyclical agency coss is ha enrepreneurial aciviy is procyclical. Hence, echnology shocks are amplified, and here resuls a firs-order effec on aggregae oupu. The reason is ha a a poin where an agen is indifferen beween he riskless and he risky projec, he expeced oupu of he risky projec exceeds he reurn of he riskless projec since he agen has o be compensaed for aking risk.

5 5 han reviewing his lieraure, we poin o a paricular model whose underlying srucure is quie similar o our own seup: Cooley and Quadrini (2006) develop a general equilibrium model wih heerogenous, long-lived firms facing an exogenous borrowing consrain. All firms have access o he same decreasing reurns o scale echnology, whereby producion is financed wih exernal funds borrowed from a financial inermediary. Since hese funds have o be paid in advance, he model capures he so-called cos channel of moneary ransmission. 4 The paper s focus is on indusry dynamics and on he financial decisions of heerogenous firms which differ in he amoun of equiy hey have accumulaed in he pas as well as he idiosyncraic produciviy shock hey receive in he curren period. The model s key implicaions relae o he overall amoun of invesmen as well as o is cross-secional disribuion across firms and o is dynamics raher han o he composiion of invesmen: A fall in he nominal ineres rae decreases he ineres paymens of firms on shor-erm loans and increases heir profis. 5 Because of reinvesed profis, any operaing firm s financial capaciy is increased in he nex period, and his allows o expand producion. For small firms, i is more imporan o expand he fuure capaciy, while large firms are more concerned abou he volailiy of profis. This implies ha small firms are more highly leveraged in equilibrium, and hence, above ransmission mechanism is more imporan for small firms. Moreover, since a moneary shock affecs he amoun of equiy held by firms in he nex period, here resuls a propagaion mechanism which gives rise o a persisen response of macroeconomic aggregaes o ineres rae shocks. Empirical lieraure and evidence: In he field of business cycle research, here exiss an exensive lieraure on he ransmission of moneary (policy) shocks. We make no aemp o review his branch of he lieraure, bu refer he reader o he work by Chrisiano, Eichenbaum and Evans (1997, 2005) and ohers. Similarly, we largely neglec he lieraure on economic growh which employs low frequency daa and cross-counry panel regressions o invesigae he nexus beween inflaion and growh. 6 Raher, in line wih he presen paper s focus, we organize our reading of he relevan empirical work in wo seps: Firs, we selecively draw on he lieraure o provide evidence (i) on he relaionship beween inflaion on he one hand and growh and aggregae produciviy on he oher hand, as well as (ii) on he linkage beween inflaion and aggregae invesmen. Second, we resor o evidence from disaggregae firm level daa which provides valuable background informaion wih respec o our proposed ransmission mechanism. Applying cross-secional and panel growh regressions for yearly daa, Fischer (1993) finds a negaive correlaion beween inflaion and growh, which is raced back o he effecs of he inflaion ax and increased uncerainy. 7 He invesigaes he causal mechanism behind his correlaion in several ways, arguing ha an empirical discriminaion beween level and 4 See Barh and Ramey (2001) for an empirical accoun. 5 See Lucas (1990) as well as Chrisiano and Eichenbaum (1992, 1995) for conribuions developing general equilibrium models characerized by limied asse marke paricipaion and liquidiy effecs of moneary policy. 6 Imporan conribuions in his branch of research include De Gregorio (1992, 1993), Barro (1996), Bruno and Easerly (1998) and Easerly (2005). 7 Fisher offers hree poenial mechanisms o raionalize he negaive relaionship: (i) a reducion in produciviy growh because of disorions in he informaional conen of he price level due o aggregae uncerainy; (ii) a reducion in capial accumulaion semming from emporary hold up of invesmen decisions in he presence of aggregae uncerainy; (iii) he inflaion ax on reurns from capial and R&D invesmen if invesors mus hold cash-in-advance.

6 6 uncerainy effecs of inflaion is hardly possible since boh measures are highly correlaed, and ha adverse supply shocks are an imporan source for he endogeneiy of inflaion. 8 To assess he relevance of non-lineariies, Fisher uses splines (wih breakpoins a 15% and 40%) and finds he negaive correlaion beween inflaion and TFP-growh o be, if anyhing, larger in low-inflaion (OECD-)counries. Moreover, he auhor decomposes GDP growh ino is componens and deecs a robus negaive relaion beween inflaion on he one hand and he growh rae of capial, bu also of TFP on he oher hand. This las resul implies ha, even afer conrolling for facor accumulaion and employmen, he negaive effec of inflaion on growh persiss; ha is, here mus be some inflaion-driven mechanism which records in erms of decreased aggregae produciviy. The sudy by Ramey and Ramey (1995) 9 esablishes a negaive correlaion beween he level of macroeconomic volailiy and he rend of GDP growh; his finding is robus o he inclusion of he invesmen share of GDP. Ineresingly, Ramey and Ramey are no able o find a robus empirical relaionship beween inflaion and he share of aggregae invesmen in GDP. Furhermore, by considering deviaions from a forecasing equaion, hey are able o show ha mos of he volailiy-growh correlaion is due o variaions in unexpeced innovaions o GDP growh. Hence, heir resuls sugges ha uncerainy induced by nominal or real innovaions is an imporan facor o link volailiy and growh, while he imporance of aggregae invesmen is called ino quesion. In paricular, we noe ha heir empirical findings are inconsisen wih he noion of an AK-model à la Romer (1990), where he ransmission o an economy s growh performance would be via aggregae invesmen. Aghion e al. (2005) elaborae on his issue and use counry-level panel daa o assess he empirical implicaions of heir heoreical model wih respec o he invesmen-driven relaionship beween volailiy and growh. In heir analysis, he auhors focus on he composiion raher han on he level of aggregae invesmen for wo reasons: Firs, as esablished by Ramey and Ramey, he negaive impac of volailiy on growh persiss even afer one conrols for he level of aggregae invesmen; and second, he correlaion beween volailiy and growh may be spurious because, in fac, variaions in boh variables may be due o differences in financial developmen. To operaionalize heir analysis of he composiion of aggregae invesmen, he auhors use daa on R&D expendiures o approximae invesmen in superior echnologies, 10 whereas invesmen in safer, reurn-dominaed echnologies is approximaed by oal invesmen as a fracion of GDP. The evidence generaed via dynamic panel esimaions is ha exogenous shocks negaively influence he R&D share, while he aggregae invesmen share remains unaffeced. This resul hins a he imporance of composiion effecs in invesmen raher han movemens in oal invesmen o accoun for he impac of volailiy on economic growh and he characerisics of he business cycle. Our own sudy sars from he resuls in Aghion e al. (2005) and seeks o analyze how 8 The difficuly in idenifying a causal relaion beween inflaion and growh sems from he lack of appropriae exernal insrumens for inflaion. For cross-counry regressions, a possible insrumenal variable approach is due o Cukierman e al. (1993) who incorporae measures of cenral bank independence as insrumenal variables and deec negaive correlaions wih economic growh. Our own approach circumvens he problem by applying dynamic panel regressions, hus relying on inernal insrumens whose validiy is esable. 9 The auhors apply cross secion and (saic) panel esimaions covering he period for a sample of 92 counries and subse of 24 OECD-counries. 10 Walde and Woiek (2004) provide evidence on he level of R&D expendiure, which ends o be procyclical; conversely, Aghion e al. (2005) focus on he cyclical variaion of R&D as a share of oal invesmen.

7 7 nominal flucuaions impac on firms invesmen decisions. The srucure of he model we develop in he nex secion suggess ha he availabiliy of corporae liquidiy is a crucial deerminan for hese firm-level invesmen decisions. To ge some guidance on he poenial power of his mechanism, we relae our analysis o he findings in Opler e al. (1999) who examine he deerminans and implicaions of holdings of cash and markeable securiies by publicly raded non-financial US firms. The auhors esablish ha firms wih beer ouside financing opporuniies 11 end o hold a lower fracion of heir oal asses in he form liquid asses, and ha firms wih srong growh opporuniies and riskier cash flows hold relaively high raios of cash o oal non-cash asses. 12 Moreover, here is evidence ha firms reain a relaively high fracion of heir earnings as liquid reserves and ha hese reserves are generally no used for capial invesmen, bu raher end o be depleed by operaing losses. As o he quaniaive imporance of corporae cash holdings, he auhors repor he mean over he firms in heir sample of he raio of cash o ne asses o be 17%, while he median amouns o 6.5%. Thus, corporae liquidiy holdings are likely o consiue a relevan caegory; in wha follows we will elaborae on his hypohesis. 3 The model In his secion, we propose a moneary model of a closed economy characerized by limied asse marke paricipaion and subjec o a financial markes fricion. The economy is populaed by wo ses of agens, households and enrepreneurs, each of uni mass. Moreover, here are a financial inermediaion secor and a producive secor, organized in decenralized firms, which has access o wo disinc echnologies, labelled basic and advanced for reasons ha will become apparen in he sequel. 13 Finally, here is a governmen ( moneary auhoriy ) which implemens macroeconomic policies. These policies, ogeher wih a se of exogenous shocks, expose he economy o aggregae uncerainy. The iming srucure underlying our model is as follows. Time is discree, and wihin each period, here are hree poins in ime: one a he beginning of he period, denoed, one a an inerim sage when he vecor s of aggregae shocks maerializes and informaion abou hem is revealed, and finally one a he end of he period, denoed +. The aggregae shocks in our model are produciviy shocks A, V o he wo echnologies as well as o governmen policy J (o be specified laer); hence, we have s = {A, V, J }. Apar from hese aggregae shocks, here are purely idiosyncraic liquidiy shocks ξ i o he subse of firms operaing he advanced echnology. We now urn o a deailed descripion of he environmen in which he economy s agens inerac and define heir relevan decision problems as well as he relevan concep of a compeiive equilibrium. 11 The background for mos heoreical and empirical sudies of corporae cash holdings is he presumpion ha exernal finance is cosly and ha firms hold liquid asses in order o survive bad imes and o have funds readily available if an invesmen opporuniy arises. The benefis of corporae liquidiy mus hen be balanced agains is coss which arises as a consequence of a liquidiy premium. 12 We inerpre hese laer characerisics - high growh poenial and risky cash flows - as he idenifying characerisics of wha we label advanced echnology. 13 As a general rule, variables peraining o he basic secor are indicaed by he variable/superscrip k, while z is he relevan indicaor for he advanced secor.

8 8 3.1 Households The economy is populaed by a uni mass of infiniely-lived, risk averse households. 14 Households ener a given period wih claims o wo disinc capial socks (k, z ) accumulaed from he pas ogeher wih a nominal wealh posiion M. A ime, households divide heir nominal wealh ino resources Q disposable for consumpion laer in he period and deposis M Q wih a financial inermediary ha earn a ne ineres rae ( R 1). 15 Afer aggregae shocks have unfolded, households ren ou heir secor-specific physical capial o he firms operaing he basic and advanced echnology, respecively. Similarly, hey supply labor h k o he basic secor and h z o he advanced secor, and heir aggregae labor supply is h H = h k,h + h z,h, whereby households are indifferen as o he secoral composiion of heir labor supply. A ime +, households receive he reurns from labor and capial and make consumpion and invesmen decisions. However, here is a cash consrain on he goods marke wih he consequence ha he household s curren expendiure for consumpion c H and physical invesmen x mus be covered by he resources Q earmarked for consumpion plus a fracion θ of his curren wage earnings. The household has preferences over sequences of consumpion and labor supply; hence, he household problem is o maximize lifeime uiliy: subjec o he cash consrain: E 0 Q + θ[w k,h h k,h β u(c H, h H ) an equaion describing he evoluion of nominal asses: =0 M +1 = Q + θ[w k h k,h + W z h z,h + Υ + R k k + R z z + (1 θ)[w k,h (1a) + W z,h h z,h ] P [c H + x ], (1b) ] P [c H + x ] + R [M Q + J ] h k,h + W z,h h z,h ], (1c) where J are cash injecions ino he financial marke on behalf of he governmen and Υ are nominal resources redisribued in a lump sum fashion among he consumers a he end of he period, and subjec o a law of moion for aggregae capial K = k + z, which accouns for depreciaion and secor-specific adjusmen coss: x = (k +1 + z +1 ) (1 δ)(k + z ) + Φ(k, k +1 ) + Φ(z, z +1 ) (1d) The soluion o he household problem can be summarized by a se of opimaliy condiions which characerize he household s equilibrium behavior. The firs one is he Euler equaion describing he opimal ineremporal allocaion of nominal wealh: E { uc (c H, h H ) P β R u c (c H +1, h H +1) P +1 } = 0 (2) 14 Where necessary, variables peraining o he household secor will be denoed wih a superscrip H. 15 This iming convenion is sandard in moneary models which feaure a limied paricipaion assumpion on he household side; compare e.g. Lucas (1990). Our iming convenion necessiaes a careful reamen of he informaion ses relevan o he household when i akes decisions. Specifically, here is a disincion beween expecaion operaors a he beginning of a period (ime ) and a he end of a period (ime + ).

9 9 Nex, here are wo Euler equaions which deermine he sequence of dynamic decisions beween consumpion and secor-specific invesmens; for i = k, z, hey read: { u c (c H, h H ) [1 + Φ 2 (i, i +1 )] = βe u c (c H +1, h H +1) [(1 δ) Φ 1 (i +1, i +2 )] + β u } c(c H +2, h H +2) R+1 i (3) P +2 An immediae implicaion of he wo equaions (3) is ha he secor-specific ineres raes mus be equal in expecaion, i.e. E {R+1} k = E {R+1} z = E {R +1 }. Similarly, here are wo opimaliy condiions which govern he household s consumpion-leisure choice, hus deermining he opimal supply of labor o eiher secor i = k, z: u h (c H, h H ) + [ θ u c(c H, h H ) + (1 θ)βe P { uc (c H +1, h H +1) P +1 }] W i,h = 0 (4) Here, i follows ha, in all saes of he world, he secoral wage raes mus be idenical because he household cares only abou aggregae labor supply; hence, we have W k,h = W z,h = W H 3.2 Enrepreneurs Apar from households, here is a uni mass of risk neural enrepreneurs, each one capable of running a specific projec associaed wih he advanced producion echnology. 16 A he beginning of each period, a mass (1 η) of new-born enrepreneurs eners he economy wihou any iniial wealh and replaces an equal measure of reiring enrepreneurs. The remaining measure η of incumben enrepreneurs says acive. An individual enrepreneur arrives in period wih an amoun A i of nominal wealh. Then, if she receives a random exi signal, she wais unil he end of he period o simply consume her accumulaed wealh such ha A i = P c E,i. In conras, new enrans and enrepreneurs who have no received he exi signal have no consumpion moive; raher, each acive enrepreneur inelasically supplies her (uni) labor endowmen h E = h k,e +h z,e = 1 and hus augmens her nominal wealh A i by her curren wage earnings W E. As for consumers, only a fracion θ of hese wage earning is immediaely disposable such ha an individual enrepreneur s effecive wealh posiion is E i = A i + θw E. This posiion E i consiues he enrepreneur s necessary privae equiy sake when she applies for funding of an advanced secor projec wih he financial inermediary. 3.3 Financial inermediary The financial inermediary (equivalenly, a perfecly compeiive financial secor) receives he ime financial deposis M Q from he households as well as lump sum cash injecions J from he moneary auhoriy. These funds are supplied o he loan marke a a gross nominal ineres rae R. A he loan marke, his supply mees he demand for financial asses which comes from wo sources: Firs, boh secors firms demand shor erm credi in order o mee he advance financing requiremen for a fracion θ of heir respecive wage bills (W is he relevan aggregae wage rae, reflecing boh he wage W H received by households and he 16 Where necessary, variables peraining o he enrepreneurial secor will be denoed wih a superscrip E..

10 10 wage W E received by enrepreneurs). Second, here is a demand for liquidiy D coming from firms operaing he advanced echnology. Hence, financial marke clearing requires: M Q + J = θw L + D (5) This condiion simply sipulaes ha he equilibrium ineres rae R balances he supply of loans wih he corporae demand for funds due o is advance financing requiremen and is need for liquidiy. The financial inermediary operaes afer aggregae uncerainy is resolved. While lending o basic secor firms proceeds in a fricionless marke, lending o advanced secor firms is complicaed by an enrepreneurial moral hazard problem which is deal wih by a financial conrac described in Secion 3.5. Two key implicaion of ha conracing scheme are ha firm bankrupcy is an equilibrium phenomenon and ha he inermediary mus commi funds o individual advanced secor projecs before hese projecs respecive liquidiy needs are known. Therefore, i is imporan o reckognize ha he financial inermediary is able o pool idiosyncraic risks across he advanced secor firms because, as a consequence, i is sufficien for he financial inermediary o break even on an individual credi relaionship in expecaion. A he end of he period, he inermediary receives he reurns on is lending and financial invesmen aciviy and pays he amoun R [M Q + J ] o he households in reurn for heir deposis. 3.4 Firms In our economy, producion aciviies proceed in hree ypes of firms. The firs ype produces he final marke good ha can be used eiher for consumpion or invesmen purposes. Firms supplying he marke good use an aggregaion echnology wih wo inermediae inpu goods which are produced by he wo oher ypes of firms operaing in he basic and advanced secor, respecively. In all hree goods markes, firms face perfec compeiion Marke good The marke good producers employ he following CES aggregaion echnology: y = (ζ 1 ρ y k ρ 1 ρ ) ρ + (1 ζ) 1 ρ 1 ρ 1 ρ y z ρ, (6) where y is he final oupu good and y z and y k are he wo inermediae inpu goods. The wo parameers 0 < ζ < 1 and ρ > 0 deermine he share of each inermediae good in producing he aggregae marke good and he elasiciy of subsiuion of he wo facors. Producive efficiency pins down he minimum cos combinaion of he final good firms demands for inermediae inpu goods o be funcions of he relaive prices for he relevan inermediae inpu P j, j = k, z and for he final oupu P : y k = ζ ( ) P k ρ ( ) P y and y z z ρ = (1 ζ) y (7) P P By perfec compeiion on he final goods marke, he aggregae price level is deermined by marginal coss, i.e. he inermediae good prices, which are consan from he final good firm s

11 11 perspecive. Consequenly, zero profis imply: ( P = ζp k ) 1 1 ρ + (1 ζ)p z1 ρ 1 ρ (8) For fuure reference, we also define he elasiciies of aggregae oupu wih respec o he secoral inermediae oupu levels: ω y yk, dy /y dy k /y k = ζ 1 ρ ( y k y ) ρ 1 ρ and ω y yz, dy /y dy z /y z = (1 ζ) 1 ρ ( y z y ) ρ 1 ρ (9) Inermediae goods There are wo perfecly compeiive secors producing inermediae goods. Boh secors employ capial as well as labor as inpu goods, bu are characerized by differen echnologies. On he one hand, here is a safe, bu reurn-dominaed ( basic ) echnology; he oher ( advanced ) echnology yields a higher poenial reurn, bu is subjec o idiosyncraic liquidiy shocks. The scope for an individual advanced firm s insurance agains his idiosyncraic liquidiy risk is endogenously deermined via he financial conrac described in Secion 3.5. The need for his insurance arises as a consequence of an enrepreneurial moral hazard problem prevens he efficien refinancing of projecs and calls for he commimen of liquidiy a an ex ane, raher han an ex pos sage. The oher fricion ha is relevan for boh ypes of inermediae firms is an advance paymen requiremen, which necessiaes he firms borrowing working capial in order o be able o pay wages; he parameer θ [0, 1] represens he fracion of he oulays ha needs o be financed in advance. Basic secor: Firms in he basic secor seek o maximize ime + profis by hiring labor and capial inpus {l k, k }, whereby he vecor of prices {P k, W k, R k, R } is aken as given. A Cobb-Douglas aggregaor convers household and enrepreneurial labor inpus ino heir effecive composie, and similarly agen-specific wages aggregae o a secoral wage rae: l k = (hk,h ) Ω (h k,e ) (1 Ω) and W k (Ω) Ω (1 Ω) (1 Ω) = (W k,h ) Ω (W k,e ) (1 Ω) The echnology characerizing he basic inermediae secor is assumed o be homogenous of degree one and feaures labor augmening echnological progress a he exogenous rae γ. For simpliciy, we employ he Cobb-Douglas form: ϕ(k, l k ) = (k ) αk ( (1 + γ) l k ) 1 α k Hence, he problem of a represenaive firm operaing he basic echnology is: ( max Π k {k,l k} = P k A ϕ(k, l k ) ) W k l k R k k 1 θ( R 1)W k l k = P k y k C(W k, R k, R ; y k ) (10) By consan reurns o scale, efficien facor employmen implies ha marginal coss are independen of he quaniy produced, i.e. C(W k, R k, R ; y k ) = MC k (W k, R k, R ; 1)y k. Then, from

12 12 he assumpion of perfecly compeiive inermediae goods markes, i follows ha he price of he basic inermediae good equals marginal coss, i.e. P k = MC k (W k, R k, R ). Using he Cobb-Douglas specificaion of ϕ(k, l k ), he opimal facor demands in he basic secor read: k = αk P k y k R k Finally, he price for he basic inermediae good is: and l k = (1 αk )P k y k [1 + θ( R 1)]W k (11) P k = 1 A ( R k α k ) α k ([1 + θ( R ) (1 α k 1)]W k ) (1 α k ) (12) Advanced secor: The problem of firms operaing he advanced echnology is complicaed by he risk ha heir producion plan is hi by a liquidiy shock 17 which may rigger he erminaion of projecs before hey yield any reurn. As in he basic secor, here is a Cobb-Douglas aggregaion of he respecive labor inpus by households and enrepreneurs, and he echnology in he advanced secor is given by a Cobb-Douglas producion funcion under consan reurns o scale which allows for exogenous labor augmening echnological progress: f(z, l z ) = (z ) αz ( (1 + γ) l z ) 1 α z Each advanced firm is run by an individual enrepreneur who brings he amoun E i as privae equiy ino he firm. The firm s producion plan and is hedge agains liquidiy shocks ξ, i which are disribued according o a coninuous disribuion funcion G(ξ) i wih associaed (sricly posiive) densiy g(ξ), i are hen deermined as par of a consrained-efficien conrac beween he enrepreneur and he financial inermediary. In paricular, he liquidiy provision sipulaed by he financial conrac will be seen o pin down a hreshold value ˆξ up o which liquidiy shocks are covered; his hreshold, in urn, deermines an individual advanced firm s ex ane survival probabiliy G(ˆξ ). Since he financial conrac, derived in Secion 3.5, urns ou o be linear in E, i he disribuion of equiy across enrepreneurs does no maer and exac aggregaion is possible. 18 Hence, we anicipae resuls and noe in analogy o he basic secor ha he price level for he inermediae goods produced in he advanced secor is: P z = 1 R ˆξ 0 G(ξ )dξ 1 V ( R z α z ) ( α z [1 + θ( R ) (1 α z 1)]W z ) (1 α z ) The deails of he financial conrac are described in he nex secion. 17 The liquidiy shock admis a variey of inerpreaions. I can be hough of as a simple cos overrun, as a shorfall of revenue a an inerim sage which could have been used as an inernal source of refinancing or as adverse informaion relaing o he projec s end-of-period profiabiliy. Hence, we sress ha our noion of liquidiy shock is consisen wih wha Opler e al. (1999) empirically summarize under he heading of operaing losses. 18 From now on, we will herefore drop he supercrip i. (13)

13 Financial conracing Following Holmsrom and Tirole (1998), we now urn o a deailed analysis of he specific conracing problem in our model which - by assumpion - is only relevan for he inermediae goods firms operaing he advanced echnology. Hence, while advanced secor firms face he problem of insuring heir producion agains liquidiy shocks, he oher firms respecive problems are sandard. The sequencing of evens underlying an individual advanced firm s wihin-period 19 conracing problem can be decomposed ino hree sages; compare Figure 1. A sage one, afer aggregae uncerainy wih respec o s = {A, V, J } is unveiled, each advanced firm, run by an enrepreneur holding an equiy posiion E in he firm, conracs wih he financial inermediary o pin down is producion plan and refinancing provisions. 20 In paricular, he refinancing provisions deermine he degree of insurance agains idiosyncraic liquidiy risk. 21 Given s, a conrac beween he financial inermediary (ouside invesor) and he enrepreneur (firm) holding equiy E prescribes (i) he scale of producion as deermined by facor employmen z, l z, (ii) a sae coningen coninuaion rule Γ (ξ ), and (iii) a sae coningen ransfer τ (ξ ) from he firm o he invesor. Hence, a generic conrac akes he form C = {z, l z, Γ (ξ ), τ (ξ )}. A consrain on he conrac is ha i is wrien under limied liabiliy, i.e. in case of projec erminaion facors mus be remuneraed by he ouside invesor. A a subsequen inerim sage (sage wo) afer he facor employmen decisions have been made, he firm is hi by an idiosyncraic liquidiy shock ξ. If he shock is me by appropriae refinancing o be provided by he inermediary, he firm can coninue; oherwise he firm is liquidaed. We assume ha he liquidiy shock is verifiable, bu i is shown in Holmsrom and Tirole (1998) ha nohing changes if only he firm observes he shock as long as he firm does no benefi from divering resources. Afer he coninuaion decision, here is scope for moral hazard on he par of he enrepreneur in ha she can exer effor o affec he disribuion of producion oucomes. Specifically, we make he exreme assumpion ha, condiional on coninuaion, exering effor guaranees a gross reurn of P z V f(z, l z ) = P z ỹ z o producion aciviy, while shirking leads o zero oupu, bu generaes a privae (non-moneary) benefi B. We assume ha he privae benefi is proporional o firm revenue condiional on survival; in paricular, we have: B = bp z V f(z, l z ) = bp z ỹ z wih 0 < b < Finally, a sage hree, he revenue from producion accrues and payoffs are realized according o he rules sipulaed in he financial conrac. The financial inermediary engages in a coninuum of conracs wih advanced secor firms; hence, since liquidiy risk is idiosyncraic, he inermediary is able o pool he risk inheren in he invesmens across individual firms projecs. As an implicaion, we can compleely absrac from he effecs of idiosyncraic uncerainy on he invesor s evaluaion of payoffs. Similarly, he enrepreneur who is exposed o her uninsured privae equiy risk is risk 19 Alhough he firm s producion plan is condiional on he predeermined enrepreneurial equiy posiion E, he firm problem iself is no dynamic because enrepreneurial asse accumulaion proceeds mechanically and here is no ineremporal incenive provision. 20 We assume ha enrepreneurial self-financing is no possible; a sufficien condiion for his o be he case is derived below. 21 I is imporan o realize ha he financial conrac is negoiaed afer fresh cash J has been injeced ino he economy. Consequenly, he resuls of moneary policy ha we will develop in he sequel do no sem from an implici nominal rigidiy. On he conrary, our concep of corporae liquidiy is enirely real; wha is affeced by nominal flucuaions, however, is he price of such liquidiy. 22 Noe, however, ha he specific value of b > 0 will no maer as long as he conrac o be derived below delivers an inerior soluion.

14 14 neural and cares only abou expeced profis as long as she is acive. Hypoheically absracing from boh he enrepreneurial incenive consrain and he cos of obaining liquidiy a he inerim sage, i is easy o see ha here exiss a unique cuoff value of one corresponding o a coninuaion policy which prescribes projec coninuaion if and only if he liquidiy shock is such ha ξ 1. The reason is ha he sage one invesmen is sunk; hence, a he inerim sage, i is opimal o refinance up o he full value of wha can be generaed in erms of revenue a he final sage. However, he need o ake ino accoun he incenive consrain and he coss of liquidiy provision implies ha he consrained-efficien coninuaion policy will ake he form: { 1, if ξ Γ (ξ ) = ˆξ 0, if ξ > ˆξ for some cuoff value ˆξ < 1. Hence, Γ (ξ ) is a simple indicaor funcion wih Γ (ξ ) = 1 in case of coninuaion and Γ (ξ ) = 0 in case of erminaion. A consrained-efficien conrac C = {z, l z, Γ (ξ ), τ (ξ )} wih (z, l z ) deermining he scale of producion, and Γ (ξ ) and τ (ξ ) pinning down he sae coningen policies for projec ( coninuaion and ransfers per uni of producion coss C W z, R z, R ; ỹ z solves he following second bes program of maximizing he enrepreneur s ne reurn: max C { ( Γ (ξ )P z ỹ z τ (ξ )C W z, R z, R )} ; ỹ z dg(ξ ) E ), respecively, hen (14a) subjec o a paricipaion consrain for he invesor ha requires him o break even in expecaion: { ( τ (ξ )C W z, R z, R ) } ( ; ỹ z Γ (ξ )ξ R P z ỹ z dg(ξ ) C W z, R z, R ) ; ỹ z E (14b) and a sae-by-sae incenive compaibiliy consrain for he enrepreneur: ( Γ (ξ )P z ỹ z τ (ξ )C W z, R z, R ) ; ỹ z Γ (ξ )bp z ỹ z ξ, (14c) where: ỹ z = V (z ) αz ( (1 + γ) l z ) 1 α z is firm level oupu condiional on survival and: ( C W z, R z, R ) ; ỹ z = [1 + θ( R 1)]W z l z + R z z are he associaed oal coss which accrue when a oupu level of ỹ z is argeed in case of survival. Noe how he specificaion of his problem, by means of he paricipaion consrain (14b), incorporaes he requiremen ha he invesor who bears he risk of projec failure be willing o finance he firm, whereby he ouside invesor commis boh he facor remuneraion and he inerim resources needed o mee he liquidiy shock. The cos of providing liquidiy a he inerim sage, which has o be obained in he financial marke a he financial rae R,

15 15 will be key in shaping he soluion o problem (14). Opimal facor inpu raio and he cos funcion: Obviously, par of he opimal conrac mus be o use facor inpus in a cos minimizing combinaion. However, since facor demands are deermined via he conrac C, hey will no only reflec he firm s profi maximizaion objecive, bu also he inermediary s need o break even in expecaion. Wih our Cobb-Douglas specificaion, he possibiliy of projec failure( hen requires ha facors earn consan shares no of firm revenue, bu of he oal coss C W z, R z, R ) ; ỹ z associaed wih a argeed producion scale ỹ z. Hence, he demands for capial and labor are: ( α z C W z, R z, R ) ( ; ỹ z (1 α z )C W z = and l z z, R z, R ) ; ỹ z R z = [1 + θ( R (15) 1)]W z Furhermore, from consan reurns o scale and he Cobb-Douglas specificaion of he echnology, we can wrie: C ( W z, R z, R ) ; ỹ z = MC z (W, R z, R ) ỹ z = 1 ( ) ( α z R [1 + θ( R ) (1 α z 1)]W z ) ỹ V α z (1 α z z, ) where MC z ( ) are he per uni coss of producing a argeed oupu level ỹ z ; since he echnology displays consan reurns o scale, hese per uni coss coincide wih marginal coss. Noe ha, as a consequence, he program o find he opimal conrac is linear in he projec size ỹ z. Firs bes - he socially opimal conrac: Le us firs look a he firs bes conrac where b = 0 such ha he enrepreneurial moral hazard probelm plays no role (bu liquidiy is scarce and has an opporuniy cos R ). The quesions asked here are, wha is he maximum overall reurn on invesmen, and how does he corresponding socially opimal conrac look like? Suppose for he momen a binding paricipaion consrain for he invesor; indeed, we will laer verify ha his is he case in a well-specified problem. 23 Subsiuing from he binding paricipaion consrain (14b) ino he enrepreneur s ne reurn (14a) yields: [ Π F = P z Γ (ξ ) MC z ( ) (1 ξ R ) dg(ξ ) 1 ] MC z ( )ỹ z Le ˆξ denoe he cuoff value for he liquidiy shock such ha he projec is coninued if and only if ξ ˆξ ; using his rule for he indicaor funcion hen allows o rewrie he enrepreneur s ne reurn as: Π F (ˆξ ) = λ (ˆξ )MC z ( )ỹ z, (16a) where: λ (ˆξ ) [ ˆξ 0 ] P z ) (1 ξ MC z R dg(ξ ) 1 ( ) (16b) 23 By well-specified, we mean (i) ha here is no self-financing by he firms, and (ii) ha he soluion o he consrained-opimal conrac feaures a finie invesmen level.

16 16 P z MC z ( ) In definiion (16b), λ (ˆξ ) denoes he ne social marginal reurn on one uni invesed in an individual advanced secor projec, given a cuoff value ˆξ. Since > 0, λ(ˆξ ) is maximized a he socially opimal cuoff value ˆξ F B = 1 R. Moreover, from (16a), i is clear ha he enrepreneur is he residual claiman and receives he full social surplus from he projec. Second bes - enrepreneurial moral hazard: Now consider he case where b > 0. Firs of all noe ha general equilibrium consideraions imply ha he marginal ne social reurn under boh he firs and he second bes soluion mus be posiive. 24 Then, given a posiive value for λ (ˆξ ), he enrepreneur will seek o maximize Π F (ˆξ ) by choosing he maximum invesmen volume MC z ( )ỹ z ha sill guaranees invesor paricipaion. Bu from (14b), his is achieved by maximizing he sae coningen per uni ransfer τ (ξ ) o he invesor. Accordingly, he second bes conrac prescribes o reain he minimum amoun of profis in he firm ha is sill consisen wih incenive compaibiliy. Hence, he enrepreneur s incenive compaibiliy consrain (14c) is binding a he maximum pledgeable uni reurn: τ (ξ ) = Γ (ξ )(1 b)p z ỹ z MC z ( )ỹ z (17) We can now solve for he larges invesmen volume MC z ( )ỹ z ha is compaible wih boh he invesor s paricipaion consrain and he enrepreneur s incenive consrain by subsiuing he maximum pledgeable uni reurn (17) ino he invesor s paricipaion consrain (14b) o obain: [ 1 ) Γ(ξ ) ((1 b) ξ R ] P z MC z ( ) dg(ξ ) MC z ( )ỹ z = E (18) Here, he expression in squared brackes represens he difference beween marginal cos of invesmen o an ouside invesor and he expeced marginal reurn o such ouside invesmen. Le ˆξ 0 (1 b) denoe he cuoff value ha maximizes he expeced marginal reurn o ouside R invesors, and noe ha equaion (18) implies ha, given some E > 0, he expeced (subjec o idiosyncraic liquidiy shocks) marginal reurn on ouside invesmen is sricly smaller han one To see his, suppose o he conrary ha λ(ˆξ F B ) 0 such ha he opimal conrac would prescribe z = l z = 0, i.e. zero invesmen for any level of enrepreneurial equiy E. However, his implies ỹ z = 0 which conradics a general equilibrium wih posiive consumpion and invesmen, and he price of he advanced inermediae good would adjus such as o guaranee a posiive marginal ne social reurn. By he same oken, he second bes soluion mus also involve a cuoff rule ˆξ wih posiive marginal ne social reurn. 25 Indeed, if his was no he case, invesmen would be self-financing and here would be no demand for liquidiy a all in ha he invesor s paricipaion consrain would be non-binding. A sufficien condiion for ruling ou self-financing is: ˆξ0 0 ((1 b) ξ R ) P z MC z ( ) dg(ξ ) < 1 Observe ha rewriing his condiion yields λ (ˆξ 0 ) < b MC ( )G(ˆξ 0 z ); hen, i is apparen ha ˆξ F B = ˆξ 0 if b = 0, which leads o he conclusion ha, in order o rule ou self-financing, a posiive wedge ˆξ F B ˆξ 0 > 0 and herefore b > 0 are essenial. P z

17 17 Solving equaion (18) for he maximum invesmen volume condiional on a given cuoff value ˆξ, allows o wrie he firm s invesmen capaciy as: where: µ (ˆξ ) MC z ( )ỹ z = µ (ˆξ )E, (19a) 1 ˆξ 0 1 ( ) P z (1 b) ξ R MC z( )dg(ξ ) (19b) is an equiy muliplier, whose denominaor specifies he amoun of inernal funds ha he firm has o conribue per uni of invesmen in order o compensae he ouside invesor for he shorfall implied by he expression in squared brackes in (18). Finally, using (16a) and (19a), he enrepreneur s expeced ne payoff becomes: Π F (ˆξ ) = λ (ˆξ )µ (ˆξ )E (20) I now remains o deermine he second bes coninuaion hreshold, o be denoed ˆξ. Given an enrepreneurial equiy posiion E, he second bes cuoff ˆξ maximizes (20). I is clear ha ˆξ [ˆξ 0, ˆξ F B ]: If ξ < ˆξ 0, hen boh paries prefer o coninue ex pos because boh paries can realize gains on he sunk sage one invesmen; if ξ > ˆξ F B, hen boh paries prefer o abandon he projec because he ne social marginal reurn of coninuing is negaive. Wihin he inerval [ˆξ 0, ˆξ F B ], here emerges a rade-off: On he one hand, increasing ˆξ implies ha coninuaion is possible in more coningencies, and hus he marginal ne social reurn λ (ˆξ ) on each uni of iniial invesmen is increased. On he oher hand, decreasing ˆξ allows o increase he amoun of iniial invesmen MC z ( )ỹ z by increasing he equiy muliplier µ (ˆξ ). Afer subsiuion from he definiions (16b) and (19b) ino (20), i is sraighforward o show ha he opimal coninuaion value ˆξ can be found as he soluion o he following problem: ˆξ R min ξ 0 dg(ξ ) + MCz ( ) P z, (21) ˆξ G(ˆξ ) which has he inerpreaion ha he second bes cuoff value minimizes he expeced uni cos of oal expeced invesmen. The firs order condiion o his problem is: ˆξ 0 G(ξ )dξ = MCz ( ) P z 1 R (22) Finally, using he opimaliy condiion for he cuoff value allows o rewrie he enrepreneur s expeced ne reurn in he following compac form: Π F (ˆξ ) = 1 R ˆξ ˆξ (1 b) R E = ˆξ F B ˆξ ˆξ ˆξ E (23) 0 Observe how his expression reflecs he rade-off underlying he choice of ˆξ [ˆξ 0, ˆξ F B ]. For fuure reference, we define he expeced ne reurn per uni of enrepreneurial equiy E as: Π F (ˆξ ) 1 R ˆξ ˆξ (1 b) R