Beyond Cash: Venture Capital, Firm Dynamics, and Economic Growth *

Transcription

1 Beyond Cash: Venure Capial, Firm Dynamics, and Economic Growh * Sînâ T. Aeş Universiy of Pennsylvania Job Marke Paper Absrac This paper presens a new dynamic general equilibrium model of innovaion wih heerogeneous firms ha incorporaes an explici venure capial (VC) marke. The daa show ha VC financing accouns for a disproporionae share of sales and employmen in he US compared wih is limied share of oal invesmen. VC firms inves heavily in young and innovaive firms, bringing operaional knowledge, ogeher wih financing, o heir porfolio companies. The goal of his paper is wofold. Firs, I measure he paricular channels hrough which VC firms influence heir underakings, using a srucural model. Second, I explore he implicaions of VC invesmens for aggregae produciviy and innovaion policy. To address hese goals, I combine and srucurally esimae an endogenous echnical change model wih a VC seing ha includes (i) he new feaure of experise, and (ii) he endogenous maching marke where firms and VCs mee. In his model, firms improve he qualiy of heir innovaive produc hrough risky R&D. VC experise raises he efficiency of produc developmen, and firms obain VC financing a he cos of selling an endogenously deermined share of he company. The enry cos ha VC companies face also inroduces a selecion margin: VCs inves in firms ha presen a high poenial for growh. The esimaed model capures cerain feaures of he VC maches and innovaion observed in he US daa. Counerfacual experimens imply ha operaional knowledge accouns for abou 1/3 of VCs impac on aggregae growh. Policy experimens sugges ha changes affecing he VC marke could resul in a 7 basis poin gain in he long-run growh rae of he economy. *This version: November For he laes version, see: ØØÔ»»Ø ÒÝÙÖкÓÑ» Ò ¹ Ø. I am deeply indebed o my advisors Jesús Fernández-Villaverde, Ufuk Akcigi, and Harold Cole for heir insighful guidance and encouragemen. I am very graeful o Bilge Yilmaz, Faih Karahan, Olga Ienberg, Daniel Neuhann, Diego Amador, Felipe Saffie, Harun Alp, and Tzuo Hann Law for very helpful commens, and o Mura Alp Celik and Ekim Cem Muyan for all heir ime and consan suppor. I would also like o hank seminar paricipans a he Board of Governors of he Federal Reserve Sysem, Bilken Universiy, Penn Macro Club, and Penn Growh Reading Group. All errors are my own. Universiy of Pennsylvania, Deparmen of Economics, 3718 Locus Walk, Philadelphia, PA Ò Ø ºÙÔ ÒÒº Ù

2 ... We were cash posiive. We didn have a year where we los money... We evenually... sold 5% of he company for a million dollars... us o ge a venure capial company o oin our board and give us some adul advice... Tha money sa in he bank. Bill Gaes, ex-chairman and co-founder of Microsof 1 Inroducion Invesmens by venure capial (VC) companies have a disproporionae impac on he US economy. In 2010, he revenues of firms ha had ever received VC suppor accouned for 21% of GDP, and heir employmen share was 11% of oal privae secor employmen, alhough VC invesmens o heir porfolio companies amoun o less han 0.2% of GDP. 1 VC financing is of paricular relevance for firm creaion and innovaion because VC firms srive o find young and innovaive firms ha lack marke experience. VC firms are unique in ha hey do no only provide financing: They also acively engage in managemen by bringing heir operaional knowledge o bear in heir invesmens. 2 Despie his disincive srucure, he conribuion of operaional knowledge o firm produciviy and is implicaions for aggregae economic growh lack a horough invesigaion. This paper presens a rigorous quaniaive framework o explore he disinc mechanisms by which VC firms influence innovaive firms and, hrough hem, aggregae produciviy. Invesing in a young company ha needs o develop an innovaive business idea enails considerable uncerainy and is subec o pervasive moral hazard problems (Gompers, 1995). In such environmens, Casamaa (2003) shows ha he opimal conrac specifies a dual role for he VC firm. The opimal conrac bundles financing and advice so ha a VC firm s financial sake in he company moivaes i o provide valuable advice. By conras, consuling firms are no preferred by young and innovaive firms because hey do no acquire sakes in he laer. 3 As a consequence of his lack of skin in he game, enrepreneurs have o pay a very high price in order o obain valuable advice from he consulan. Therefore, young and innovaive companies prefer VC advising o consuling advice. Taking he srucure of he opimal conrac as given, I develop a srucural model conaining an explici VC marke. This model serves wo main purposes: Firsly, I use he model o measure 1 Naional Venure Capial Associaion (NVCA, 2013). Well-known examples include Amazon, Google, Sarbucks, and FedEx. 2 By operaional knowledge, I refer o a general body of experises concerning organizaional srucure, markeing, produc developmen, and oher business domains. This role of venure capial financing reflecs he idea ha he ypical founder is an incomplee businessman, wih gaps in experience in maers such as financial managemen and markeing. An acive board of direcors, saffed by represenaives of he [venure capial] invesors, is expeced o help fill hese gaps (Barle, 1995). For evidence on differen mehods, see Gorman and Sahlman (1989), Sahlman (1990), Gompers (1995), and Hellmann and Puri (2000), among ohers. Da Rin e al. (2011) provide an exensive survey. 3 The resul assumes ha he enrepreneurial effor is cheaper and is key for he success of he proec. 2

3 he imporance of he VCs operaional experise o firm growh. To idenify his channel, i is fundamenal o separae i from he provision of financing and he overall selecion of porfolio firms by VCs. Esablishing a unified srucure ha accouns explicily for differen aspecs of he VC marke, he srucural model is an effecive ool o accomplish his ask. Quanifying he operaional knowledge channel is useful for evaluaing he advanages commonly aribued o VC finance in fosering firm produciviy and growh. To he exen ha VC companies add valuable knowledge o heir underakings, hey become a more efficien opion for financing innovaion han more radiional financing sources such as bank loans. Secondly, he model provides a suiable ground o shed ligh on various policy discussions such as he relaionship beween an acive public equiy marke and VC financing. To address hese issues, I propose a new dynamic general equilibrium model of innovaion wih heerogeneous firms, in he radiion of Romer (1990), Grossman and Helpman (1991), and Acemoglu e al. (2013), among ohers. 4 In his model, enrepreneurs/privae firms produce differeniaed goods of heerogeneous qualiy which hey can improve hrough risky research and developmen. The efficiency of his developmen process can only be increased wih he help of a VC and is oherwise fixed. I inroduce o his model a deailed venure capial marke hrough (i) he feaure of VC experise and (ii) he endogenous maching marke for firms and VCs. Every privae firm ha is no in a relaionship wih a VC can search for VCs and mee hem in he maching marke. VCs improve he efficiency of produc developmen hrough heir operaional knowledge. They also provide financing and relax he cos of inpus ino he producion of goods. This financial suppor o a priori unconsrained firms reflecs he dual srucure of he opimal conrac for VC invesmen. The heerogeneiy in he qualiy level of privae firms deermines he magniude of he improvemen ha VC firms can poenially creae. VC firms are subec o enry coss, which induce hem o selec firms for invesmen ha presen more room for growh. Thus, in addiion o financing and operaional knowledge channels, he VC seing also accouns for he effecs of selecion by VC firms. Because he preferred opion for VC firms o exi heir porfolio companies is o sell hem via iniial public offerings, he model also includes a public equiy marke. To complee he general equilibrium framework, he res of he srucure builds on he shoulders of endogenous echnical change models in which enrepreneurs own inermediae produc lines. Enrepreneurs ener he marke wih a new produc line while inermediae good producers who canno develop he qualiy of heir good sufficienly exi he economy. Togeher wih enry and exi margins, he innovaions generaed by hese inermediae good firms deermine he endogenous rae of growh of he aggregae economy. 4 The model shares feaures such as produc variey expansion wih Romer (1990), qualiy laer srucure wih Grossman and Helpman (1991), and innovaion by incumben firms wih Acemoglu e al. (2013), whose deails are explained below. 3

4 The main idenificaion problem in his model is o disinguish he financing channel from operaional knowledge in heir relaive influence on firms receiving VC invesmen. The assumpion ha disenangles hese wo channels is ha he former mainly affecs he level of he profis while he laer changes is growh rae. The financial help of VC decreases he cos of inpus in he inermediae good producion. Therefore, he enrepreneur earns higher profis for a given qualiy level of he inermediae good ha he firm produces. Operaional knowledge, on he oher hand, direcly affecs he efficiency of he enrepreneur s effor in generaing innovaions ha increase he produc qualiy. 5 To discipline he size of he financial impac in he model, I arge he raio of VC invesmen o GDP. Deermining he size of VCs conribuion o efficiency in he daa is a more delicae ask. A well-known concern is selecion: VCs migh be cherry-picking already good firms insead of improving hem in some oher way. I address his issue by applying he mehod of indirec inference in my esimaion. To do so, I uilize he findings of Puri and Zaruskie (2012). In heir empirical sudy, Puri and Zaruskie (2012) provide saisics on growh raes of VC-backed and non-vc-backed privae firms, conrolling for selecion on observable characerisics. In a nushell, Puri and Zaruskie (2012) creae samples of privae firms wih and wihou VC suppor ha are mached on some measurable feaures. Following similar seps, I creae he analogues of such samples from he saionary firm disribuion of my model. Finally, I use he model-generaed samples o mach he regression saisics on VCs effec on firm growh provided in he same paper. I esimae his model by he mehod of momens, using US daa on he venure capial marke, public equiy issuances, and research and developmen expendiures. The model does a successful ob in maching momens ha perain o venure capial and innovaion aspecs of he model, such as he duraion of VC maches, firm age a he issuance of iniial public equiy, and aggregae share of R&D. Moreover, he model-generaed regression resuls accuraely predic he coefficien esimae found in Puri and Zaruskie (2012). Successfully hiing his arge via indirec inference is crucial because i deermines he scope of he influence of he operaional knowledge channel. Before using he esimaed model for counerfacual analyses, I compare is auxiliary predicions o daa momens in order o obain ou-of-sample validaion. This comparison reveals ha he model is very precise in capuring he high IPO frequency among VC-backed firms and he share of IPOs issued by VC-backed companies, boh of which are definiive characerisics of he VC marke in he US. 5 Gonzalez-Uribe (2014) is a recen empirical work ha poins owards he efficiency enhancing role of VC. By using he inroducion of he Pruden Invesor Rule (PIR) across saes as a source of exogenous variaion in VC financing, she firs documens a 50% rise in he annual ciaions of paens of a firm afer i obains VC financing. More ineresingly, she shows ha he probabiliy of receiving a ciaion from a company in he porfolio of he same VC firm increases wice as much as from a company ouside he VC s porfolio. This resul indicaes ha VCs faciliae he diffusion of knowledge among heir porfolio companies. Similarly, Lindsey (2008) argues ha by miigaing informaional and conracual problems, VC firms increase he probabiliy of sraegic alliances among heir porfolio companies. The empirical esimaes imply a 70% increase in he probabiliy of R&D alliances, a significan consiuen of sraegic cooperaions. 4

5 The firs se of counerfacual experimens deermines he relevance of VCs operaional knowledge o firm and aggregae growh. I creae hypoheical economies in which I srenghen paricular channels of VC finance in each experimen. Comparing he responses of he aggregae growh rae o hese changes demonsraes ha he knowledge channel accouns for 1/3 of VCs impac. Hence, he conclusion is ha VC suppor maers significanly beyond financing. Then I consider a 15% increase in he fixed cos of IPO o capure he average level of underwriing spreads in he US before heir secular decline afer he 1980s. 6 As a resul, fewer privae firms issue IPOs, and he equilibrium probabiliy of a mach wih a VC firm decreases. Thus, he increase in he fixed IPO cos resuls in a smaller share of VC-backed privae firms in he economy. This leads o a 1.5 basis poin loss in he long-run growh rae. As an example for he policy implicaions of he model, I consider a recen regulaion ha he European Union inroduced in 2013 regarding European VC firms. In order o decrease he fundraising coss of VC firms, his policy aims o harmonize he legislaive environmen hese firms face when invesing across he borders of European counries. I map his change ino he model as lower enry coss for VC firms hrough lump-sum subsidies. I find ha his policy can increase he long-run growh rae by 7 basis poins a a cos of subsidies ha corresponds o approximaely 8% of he VC invesmen in he model. This increase in he growh rae hinges on he reallocaion of privae firms owards he VC marke. Moreover, a rise in he median duraion of he VC-firm relaionship amplifies he effec of he operaional knowledge. These resuls highligh he significance of he general equilibrium effecs for he policy evaluaion. Relaed Lieraure. This paper draws on several srands of he lieraure. Firs, by embedding he VC marke ino he endogenous echnical change environmen, i conribues o he lieraure ha concenraes on innovaion and firm dynamics (Klee and Korum, 2004; Akcigi, 2010; Akcigi and Kerr, 2010; Lenz and Morensen, 2008; Acemoglu e al., 2013). 7 Lenz and Morensen (2008) and Acemoglu e al. (2013) are recen examples ha paricularly focus on allocaion of resources across firms wih heerogeneous capaciies o innovae. This paper conribues o he analysis by inroducing a link beween his heerogeneiy and he financing decisions of innovaive firms. In ha regard, his paper also relaes o work on finance of innovaion (Aghion and Tirole, 1994; Aghion e al., 2004; Korum and Lerner, 2000; Lerner e al., 2011; Brown e al., 2009; Amore e al., 2013). 8 As an example in he seing of endogenous growh, Ienberg (2014) explores he effec of developmens in he US public equiy marke on R&D decisions of small firms. By conras, he 6 An underwriing spread, also known as gross spread, measures he fees paid o he underwrier of he issue in compensaion for expenses such as legal expenses, managemen fees, ec. as a fracion of he oal proceeds raised. This spread is a direc cos associaed wih he issue, which I model as a fixed cos. 7 For a deailed discussion of innovaion and firm dynamics in he conex of Schumpeerian growh heory, see Aghion e al. (2013). 8 Hall and Lerner (2009) is a seminal survey on his opic. 5

6 focus of his paper is he venure capial marke. This sudy exends he venure capial lieraure by analyzing VC financing in a dynamic quaniaive framework. The heoreical work in his area uncovers he condiions in a saic seing ha leaves room for he use of venure capial in he exisence of alernaive financing or in advising agens such as banks and consulans (Ami e al., 1998; Casamaa, 2003; Ueda, 2004; de Beignies and Brander, 2007). 9 While my work acknowledges hese heoreical foundaions, and borrows he feaures of he opimal VC conrac from his lieraure, i focuses on quaniaive analysis of he VC marke. In paricular, my model improves he undersanding of VC financing in a dynamic general equilibrium seing ha enables he measuremen of he disinc channels hrough which VC firms affec firm dynamics. A realisic srucure for he VC marke in a model of endogenous firm dynamics also allows he analysis of venure capial from he perspecive of innovaion policy. Due o hese characerisics, his work also conribues o answering empirical quesions in VC lieraure. 10 In paricular, Korum and Lerner (2000) show he significan effec of VC finance on firm-level innovaion in erms of boh paen couns and ciaions, whereas papers such as Hellmann and Puri (2000, 2002) examine he effeciveness of paricular managemen pracices applied by VC firms using hand-colleced daa. My paper advances hese exercises o quanify VCs impac by using a new srucural model as a measuremen ool ha akes ino accoun imporan margins such as selecion and reallocaion. Furhermore, he seing should also be helpful in shedding ligh on various policy debaes, such as he relaionship beween public equiy and VC markes (Black and Gilson, 1998; Boazzi and Rin, 2002). Finally, a relaed lieraure focuses on he role of he financial sysem in evaluaing and selecing invesmen proecs. For insance, Jayarane and Srahan (1996) show empirically ha inersae branch reform in he US banking sysem has led o a igher selecion in lending hrough increased compeiion. This in urn has resuled in higher lending qualiy and growh raes in liberalized saes. In he conex of VC, Casamaa and Harichabale (2007) provide evidence on how VC firms use syndicaion pracices o obain a second opinion when deciding on early rounds of invesmen. By esimaing a heoreical framework using Bayesian mehods, Sørensen (2007) finds imporan effecs of assoraive maching in he VC marke. In relaion o his lieraure, my paper formalizes he idea ha VC firms search for high growh poenial by embedding an endogenous search and maching marke ha accouns for selecion. This aspec is inegral o idenifying he effec of value-adding pracices of VC firms in he model. Furhermore, building 9 There are a few recen papers ha include venure capial in a dynamic seing. Silveira and Wrigh (2013) model VC firms in a search and maching environmen and analyze is heoreical predicions for he life cycle of VC firms. Pinheiro (2012) examines he heoreical underpinnings of he opimal duraion in maches beween VC firms and heir underakings. Opp (2014) analyzes he cycles in he venure capial marke. None of hese sudies consider he effecs on firm-level innovaion and economic growh. 10 For a recen survey, see Da Rin e al. (2011). 6

7 on he endogenous growh framework, his paper relaes o he lieraure ha analyzes he effecs of selecion on economic growh (King and Levine, 1993; Jaimovich and Rebelo, 2012). 11 A recen paper in his srand, Aeş and Saffie (2014), argue ha financial selecion inroduces a rade-off beween he mass and he qualiy in firm enry, and analyzes is impac on aggregae produciviy growh in he conex of sudden sops. 12 In comparison o his lieraure, my work focuses on a specific, bu one ha is more relevan o innovaion and growh, namely venure capial finance. The nex secion inroduces he main ingrediens of my model. Secion 3 explains he daa used in he esimaion, and discusses idenificaion. Secion 4 presens counerfacual and policy experimens, and Secion 5 concludes. 2 Model In his secion, I presen he componens of he model economy. Enrepreneurs produce differeniaed inermediae goods and sell hem o a represenaive final good producer ha combines hese inermediae goods ino a final oupu. The enrepreneurs ener he business wih an innovaive produc, he qualiy of which hey can improve over ime by invesing in risky research and developmen (R&D) aciviies. The efficiency of he R&D process is a firm characerisic ha is fixed unless he firm uses he addiional business experise of a VC. VC suppor also enails a reducion in he cos of inermediae good producion. An inermediae good producer can search for and mach wih a VC firm in he endogenous search and maching marke. The conribuion of he VC o firm growh sems from increased R&D efficiency ha makes produc developmens likelier. However, i comes a he cos of firm diluion, and carries an exogenous risk of running he proec idle. Any privae firm can issue public equiy o expand he size of is enerprise, bu here is an associaed fixed cos. By improving he efficiency of produc developmen, VC firms help heir underakings raise adequae resources faser o afford he IPO cos. 2.1 Preferences Consider he following closed economy in discree ime. The represenaive household maximizes he expeced discouned sum of he period uiliy from consumpion wih he following preferences U = τ= β τ C1 ε τ 1 1 ε 11 Levine (2005) provides an excellen survey on his opic, and on he relaionship beween finance and growh, in general. 12 In a relaed paper, Aeş and Saffie (2013) provide a heoreical characerizaion of he nexus beween financial selecion and he long-run produciviy growh by analyzing he mass-qualiy rade-off in a closed economy seing. 7

8 where C denoes consumpion a ime. β is he discoun facor and ε is he coefficien of relaive risk aversion. The household consumes a final good, and supplies labor inelasically o he final good producer, which I normalize o 1 wihou loss of generaliy. Households own all he firms in he economy, and heir budge consrain is C J Π d+w (1) where Π is he flow profi of he inermediae firm in he inerval J of acively operaing firms, and w is he wage level a ime. 2.2 Final Good Producion The final good, which is used for consumpion, R&D, and inermediae good producion, is produced in a perfecly compeiive marke. The producion echnology combines labor and differeniaed inermediae varieies in he following srucure: Y = 1 1 α Lα q α k1 α d. (2) J Here, L denoes he labor inpu, k refers o inermediae good J a ime, and q is he associaed qualiy of produc. (1 α) sands for he physical facor share. Y is he numeraire good in he economy. The represenaive final good producer chooses a bundle of inermediae goods and labor in order o maximize is profis. Taking he price of he inermediae produc, p, as given, he problem of he final good producer reads as: { 1 Π Y, = max L,{k } J 1 α Lα J } q α k1 α d p k d w L. (3) J The soluion of his maximizaion problem yields in equilibrium he following inverse demand for inermediae good : p = q α ( k d ) α (4) where k d is he opimal amoun of good demanded by he final good producer. 2.3 Inermediae Good Firms Inermediae firms are disribued across produc lines whose measure, J, is deermined endogenously. There are hree ypes of inermediae good firms: privae firms ha are no mached wih a VC, privae firms ha are mached wih a VC, and public firms. Each firm is characerized mainly 8

9 by wo sae variables which are he produc qualiy and he R&D efficiency. An enrepreneur ha has an innovaive proec eners a produc line as a privae firm wihou a VC. Firs I inroduce decisions ha are common o all inermediae good firms, and hen I go ino he specific choices of differen ypes of firms Producion Each inermediae good is a monopolis in producing is differeniaed good k. To maximize he operaing profis, he monopolis solves he following problem ( ) { ( )} Π q = max p k C k k k ( ) α p = q α k d subec o where C k ( k ) denoes he cos of inpus o produce k amoun of inermediae good in erms of he final good and has he following form: C k ( k ) = η k. In his specificaion, η {η H, η} denoes he marginal cos of producion wih η H > η. For any firm ha does no have VC suppor, his parameer has he higher value. Therefore, his srucure capures he financial conribuion of VC firms o heir underakings. An inerpreaion for his srucure is ha i reflecs cash-in-hand consrains in a reduced form way. In line wih realiy, VC relaxes his financial consrain wih is moneary commimen. In equilibrium, he opimal level of inermediae good producion becomes k = α [ ] 1 α α 1 α η q. (5) Wih a consan mark-up over price, his opimal quaniy generaes profis ha are linear in produc qualiy q. Thus, Π = π q where π = π L π H if C k ( k ) = η H k if C k ( k ) = η L k is a consan depending on he marginal cos η. Hence, he operaional profis are higher if he marginal cos of inermediae good producion is lower due o VC suppor. 9

10 2.3.2 Research and Developmen Each firm invess in R&D o improve he qualiy of is produc and hence o increase is operaing profis. Le i and Z ( ) i denoe he (process) innovaion rae and he R&D effor required o generae his rae, respecively. The R&D cos funcion in erms of he final good has he following form: Z ( ) h ( ) i i = where h( ) is a convex, sricly increasing funcion. In his specificaion, θ denoes he efficiency in developing he produc qualiy. In order o analyze he effec of VC firms operaional knowledge, he parameer θ can ake hree differen values: θ q θ = θ pb θ L θ H for privae firms wihou VC for privae firms wih VC { θ L, θ M} for public firms In his economy, he privae firms conduc R&D wih low efficiency, θ L, unless hey receive help from a VC firm. Once mached, a VC firm raises he efficiency level of is porfolio company o θ H hanks o is experise. In urn, a higher efficiency in generaing innovaions increases he expeced growh rae of he privae firm. In addiion o his direc effec, I allow for he possibiliy ha VC firms also cause a permanen effec. Produc developmen efficiency afer IPO, θ pb, depends on wheher he firm used VC finance or no. The underlying moivaion is ha, alhough he enrepreneur separaes from he VC, she reains some of he operaional skills brough o he firm by he venure capialis. Therefore, for a firm ha becomes public under he supervision of a VC, I assume ha θ pb = θ M. Alhough deermined by he daa hrough esimaion, i is expeced ha θ H > θ M > θ L, as validaed in Secion 3.4. The ordering θ H > θ M reflecs he loss of VC supervision, whereas θ M > θ L reflecs he VC s permanen impac on he firm s operaional knowledge sock. The produc developmen efficiency remains consan unless he firm changes is ype due o a financial decision. A successful process innovaion improves he produc qualiy of he firm by an amoun ha is aken o be proporional o he average qualiy of he firm, q : q +1 = q + λ q. where q J q d. If he R&D is unsuccessful, q remains he same. These addiive incremens in produc qualiy inroduce decreasing reurns o innovaion, and imply smaller incenives o 10

11 innovae for larger firms. Limiing he growh poenial of larger firms, his srucure enables he model o generae a saionary size disribuion in equilibrium Free Exi Every inermediae firm has an ouside opion χ o = χ o q which is proporional o he average qualiy q. If he value of he firm goes below his level, he firm exis he economy. Noice ha he opion value grows a he rae of he aggregae economy. Therefore, if a firm fails o innovae for a long period of ime, i will necessarily exi he marke. Therefore, in addiion o he profi enhancing moive, here is anoher incenive o moivae, namely o survive in he business Free Enry The economy has a uni measure of poenial enrans. These ouside firms need o generae an innovaion o ener he marke. An enering firm observes he iniial qualiy of is produc upon successful innovaion. This iniial qualiy is drawn from he saionary disribuion of he previous period, bu from a range ha is small enough such ha he enran does no go public immediaely. 13 An enran opens a new inermediae produc line and sars wih he low level of produc developmen efficiency θ L. 14 The cos of generaing a produc innovaion for enry is quadraic in probabiliy of innovaion, x : C e (x) = χ e q f(j 1 )x 2 where χ e denoes he scale of he cos funcion. There are wo imporan feaures in his cos srucure. Firs, i is proporional o aggregae produciviy level q. Since he expeced value of an innovaion also shares his proporionaliy he opimal innovaion rae becomes independen of q. Second, he cos depends on he previous measure of he inermediae firms hrough a convex and increasing funcion. 15 This srucure relaes he measure of firms o he size of enry, and enables he economy o reach a sable size. 13 Given he median age of US firms a he IPO sage, his assumpion is a plausible one. Moreover, he average size of enry firms in he US are drasically smaller han he average size of incumben firms (Scarpea e al., 2004; Barelsman e al., 2009). 14 The fac ha enrans open new produc lines inroduces a source for growh due o expanding produc markes, à la Romer (1990). However, as explained below, he measure of inermediae produc lines, J, remains consan in a balanced growh pah equilibrium. 15 In he esimaion, f( ) is assumed o have a quadraic form. This ype of relaionship has he inerpreaion ha he resources o innovae are scarce, and he coslier i is for enrans o use hese resources, he larger he share of incumben firms becomes. 11

12 2.3.5 Timing of Evens The iming of evens is summarized in Figure 1. The period sars wih he enrans decision o pay he enry fee and draw heir produciviy. Then, he privae inermediae good producers make heir financial decisions, which are searching for VC and going public. Then, he final good producer and inermediae good producers decide on producion. Inermediae good producers also deermine heir innovaion inensiies. Lasly, he R&D oucomes are realized, and inermediae producers make heir exi decisions. Figure 1: Flow of Evens +1 Enrans draw q sar w/ θ L IPO decision f or privae VC decision f or single privae i) Producion k, Y ii) R&D, i R&D oucome q,+1 Exi decision Nex, I explain he differen ypes of inermediae firms and heir specific financial choices. In paricular, a public firm will consider only he decisions inroduced above. Every privae firm considers going public a he onse of a period, in addiion o he aforemenioned common decisions. Lasly, a privae firm ha is no mached wih a VC can search for a VC if i has already chosen o remain privae Firm Types and Financial Decisions Public Firm. A privae firm can choose o go public by issuing an iniial public offering (IPO) and raise public funds o expand is operaions. 16 I assume ha a firm canno look for a VC and canno raise any public funds once i is public. Therefore, he only decisions ha a public firm needs o consider are producion, R&D, and exi decisions. Specifically, le V pb denoe he value of a public company. Then he problem of he public firm becomes V pb ( q, θ pb ) = max i [ i W pb π L q h ( ) pb i /θ q + 1 ( ) q + λ q, θ pb 1+r +1 + ( 1 i ) W pb where r +1 denoes he ineres rae. The coninuaion value is defined as W pb ( ) ( q+1, θ = max {χ o q, EV pb +1 q +1, θ pb ( q, θ pb )] (6) )}. (7) 16 This ype of modelling IPO is in line wih he invesmen financing explanaion of equiy finance. Using exensive daa on iniial and seasoned equiy offerings across 38 counries during he period , Kim and Weisbach (2008) show ha firms subsequenly use proceeds from selling equiy for R&D and CAPEX invesmens. When I explain he decision o do an IPO below, i will be clear ha going public also provides an exi channel for he VC. 12

13 Every period, he public firm collecs flow profis and decides on he opimal size of process innovaion. 17 In case of successful R&D, i increases is produc qualiy wih which i sars he nex period, unless i chooses o use he ouside opion and exis. If R&D effors do no resul in an incremenal innovaion, he produc qualiy remains he same. In his regard, produc developmen enables he firm o decrease he likelihood of exiing he marke, besides increasing he profis. Noe ha he produc developmen efficiency remains consan in any case. VC decision. A privae firm wihou VC backing can search for a VC in every ime period. To undersand he benefi of becoming mached wih a VC, firs consider he problem of a privae firm wih a VC ha decided no o go public. This pos-ipo-decision value is he one ha a privae firm wihou VC obains when i is mached wih a VC firm, because he process of searching for a VC follows he IPO decision. I is defined as πq h ( ) i /θh q + ( ) 1 V pr q, θ H, I vc = 1 = max i i W pr ( q + λ q, θ H, 1 ) + ( ) pr( 1 i W q, θ H, 1 ) 1+r +1. (8) where I vc is an indicaor funcion ha akes he value 1 if he firm is mached o a VC. This problem is very similar o he one of he public firm, wih hree excepions. Firs, as he firm ges he experise of VC, is efficiency increases o level θ H > θ L, and his is he operaional knowledge channel hrough which a VC adds value o he firm. Second, due o is financial suppor, VC increases he profis of he firm o π > π L for a given qualiy level. The hird difference reflecs he fac ha many relaionships beween he VC and he firm end up unsuccessfully, i.e. hey do no lead o any IPO or acquisiion by anoher firm where VC can have a profiable exi. To capure his, I assume ha he VC and he firm can separae wih an exogenous probabiliy σ vc in which case he firm exis he marke. The coninuaion value W pr (, 1) incorporaes hese differences. A privae firm mees wih VCs in a random maching environmen. 18 probabiliy ha a privae firm maches wih a VC firm is defined by Λ m f (Λ) = ρ 1+Λ The endogenous where n vc and n f denoe he number of VC firms and available privae firms, respecively, Λ n vc /n f is he marke ighness, and ρ refers o he efficiency parameer (Shi, 2009). 19 Then he 17 Noice he low level of profis because public firms do no have VC suppor. 18 The main fricion in his marke is he process of evaluaion by he VC. I is a cumbersome process in which only one ou of a hundred applicans ges funded on average, according o NVCA figures. A direced search on he firm side is also unlikely given he low probabiliy of accepance. Moreover, his would require he applican o gain informaion abou oher companies in he porfolio he VC firm of ineres, heir financing sages, he human capial consrains of he VC firm, ec., which is probably no he case wih mos of he applicaions in realiy. 19 Correspondingly, he oal number of maches is given by he so-called elegraph maching funcion. 13

14 value of a privae firm wihou a VC, afer deciding no o issue an IPO, becomes: 20 V pr ( ( ) q, θ L, I vc = 0 = m f n vc n f [(1 m f ( max i ) [ i W pr I s vc >0 V pr ( n vc ))+m n f f ( ) q, θ H, 1 + n vc n f ) (1 I s vc >0) π L q h ( i ) /θl q + 1 ] 1+r +1 ( q + λ q, θ L, 0 ) + ( 1 i ) W pr ( q, θ L, 0 )]. (9) Here, m f ( ) denoes he probabiliy ha he firm will mee wih a VC. The share of he firm o be lef o VC, s vc, is deermined endogenously via Nash bargaining. The firs line of his value simply ells ha, if here is a mach ha generaes a posiive surplus he firm, maches wih a VC. Oherwise, i moves on o make producion, R&D and exi decisions where is R&D efficiency remains consan. Privae firms and IPO decision. Any privae firm, wih or wihou a VC, can issue an IPO in any period. The upside of IPO is an increase in he size of operaions. Moreover, i enables he VC firm sell is share in he company and collec he reurn. 21 Le V pr refer o he value of a privae firm ha considers going public or remaining privae. Then he IPO decision is deermined by he following maximizaion V pr ( q, θ, I vc ) { ( = max V pr q, θ, I vc ) (,(1 ) V pb κq, θ pb ) χ ipo q }. ( ) The firs par of his maximizaion is he value of he firm if i remains privae. V pb κq, θ pb in he second par denoes he value of he public firm wih larger size of operaions, where κ > 1 denoes he increase. Firms ha issue an IPO wihou any previous relaionship wih a VC do no experience any change in he efficiency of produc developmen. A las, he firm incurs various coss of issuing an IPO, which are capured by χ ipo q. Moreover, a share of he firm value is sold a IPO. The firm finances is invesmen in improving is produc qualiy wih he proceeds from his ransacion. In addiion, if he firm ha goes public is mached wih a VC, IPO allows he VC o liquidae is socks in he company in order o obain he reurn on is iniial invesmen, s vc. 20 No search coss are assumed in his seing. 21 IPO is considered as he mos profiable exi opion and a measure of success for VC funds (Brander e al., 2002; Sørensen, 2007). According o he 2013 Yearbook of Naional Venure Capial Associaion, 16% of porfolio companies end up going public. 14

15 2.4 Venure Capial Firms Venure capial firms are agens ha provide operaional knowledge and finance o privae firms. There is an ouside pool of VC firms. To ener he maching marke, a VC firm has o pay an enry cos. The enry cos is given by χ vc χ vc q, and is proporional o he average produciviy in he economy. A any poin in ime, a VC firm can be mached wih only one firm. When he VC exis is invesmen, i is assumed o exi he economy. The value of a VC ha is no mached o a privae firm is A = m vc ( n vc n f ) ( ( ) s vc q, θ L ; Ψ q (dq)+ [1 m vc n vc n f )] A +1 1+r +1 (10) where Ψ q denoes he disribuions over q of he privae firms ha are in he maching marke. The firs par of equaion (10) explains ha, wih probabiliy m vc ( ), he VC mees a privae firm and ges a share s vc. Oherwise i coninues o search nex period. The share of he firm ha he VC gains, s vc (q, θ), is he soluion of he following Nash bargaining problem s vc [ ( ) ( ) ] [ (q, θ) = arg max V pr s q, θ H, 1 V pr 1 φ q, θ L, 0 s s A +1( ) 1+r +1 ] φ (11) where φ is he bargaining power of he VC. Noice ha, for a mach o form beween a VC firm and a privae company, he paymen o he VC firm needs o be a posiive amoun because he VC firm is subec o an enry cos. This implies ha he VC firms inves in companies only if he expeced surplus is larger han zero. This selecion margin is inegral for he idenificaion purposes Equilibrium Throughou his paper, I will focus on he Markov Perfec Equilibrium. In paricular, he analysis will be based on he balanced growh equilibrium where aggregae variables grow a a consan rae. To his end, i will be necessary o ransform he economy ino a saionary one by normalizing he growing variables by he aggregae produciviy q. Firs, I denoe ˆq q / q as he normalized qualiy. Nex, I define he Markov Perfec Equilibrium where he aserisk refers o equilibrium values. Definiion 1 (Equilibrium) Le ξ d {0, 1}, d {exi,vc,ipo}, denoe he decisions of firm regarding exi, VC search, and going public, respecively. A Markov Perfec Equilibrium consiss of aggregae prices {r, w }; aggregae oupu, consumpion, R&D expendiure, and inermediae inpu expendiure 22 See Secion 3.2 for deails. 15

16 {Y, C, Z, K }; inermediae prices and quaniies {k, p }; R&D, exi, search, and floaing decisions {i, ξd } d {exi,vc,ipo} ; firm value funcions {V f, W f } f {pb,pr} and VC value A ; VC pricing funcion s vc ; he normalized qualiy disribuion and he mass of firms { ˆΨ ( ˆq), J } where [0, ), J such ha 1. {k, p } are given by (5) and (4), and maximize he operaing profis, 2. {V f, W f } f {pb,pr} saisfy (6), (7), (9), and (8), 3. i maximize he expeced profis, and {ξd } d {exi,vc,ipo} solves he value funcions, 4. ˆΨ ( ˆq) is consisen wih R&D, enry, exi, VC, and IPO decisions of he firms, 5. J suppors he free enry condiion o hold wih equaliy, 6. A is given by (10), 7. s vc as in (11) is deermined by Nash bargaining; 8. {Y, C } are given by (2) and (1), 9. and aggregae prices {r, w } clear he marke. Accordingly, a balanced growh equilibrium is defined as follows: Definiion 2 (Balanced Growh Pah) A Balanced Growh Pah (BGP) is an equilibrium where ˆΨ ( ˆq) defines an invarian disribuion, he measure of firms, J, has a fixed value, and he average qualiy q and he aggregae variables grow a a consan rae g. Given he invarian disribuion of normalized qualiy levels and he saionary R&D decisions, I can now derive he consan growh rae of he economy in a BGP: 23 J ( g = 1 ξ exi ){ i λ+ξ ipo (κ 1) ( ˆq + i λ )} d J { ξ exi + I vc σ vc( )} 1 ξ exi ˆq d+ ˆq d. (12) J enry There are several facors ha conribue o he balanced growh rae. The firs inegral on he righhand side of equaion (12) capures he effec of surviving firms. Condiional on remaining in he business, inermediae firm adds he sep size λ if i generaes an innovaion, which happens a rae i. Moreover, if firm issues public equiy in he beginning of he nex period, is qualiy 23 See Appendix A for he derivaion. 16

17 increases by a facor κ 1. The second inegral capures he loss due o exiing firms. Noice ha exi happens due o boh he opimal decision of he firm and he ariion rae if he firm is mached wih a VC. The las componen of equaion (12) denoes he conribuion of enry. 24 Finally, he following condiion holds for he represenaive household. Proposiion 1 (Euler Equaion) In BGP, he household maximizaion implies he equilibrium ineres rae r = (1+g) ε /β 1. 3 Esimaion In order o measure he specific effecs of differen channels hrough which VC financing affecs firm-level innovaion and aggregae growh, I esimae he parameers of he model via he simulaed mehod of momens (SMM). In his secion, I firs describe he idenificaion and compuaion procedures. Then, I presen he esimaion resuls and discuss he goodness of fi. As a brief overview, he model successfully capures he duraion of firm-vc maches and he firm age a he ime of iniial public offering as well as he aggregae paerns of R&D and growh. The model also replicaes he difference in firm growh paerns beween VC-backed and non-vc-backed firms observed in he daa. I sar by describing he parameers ha are deermined ouside he model. 3.1 Pre-deermined Parameers Because he model a hand is a fairly rich one wih a large number of parameers, assigning some of hem a priori miigaes he burden of esimaion. There are 10 parameers ha are chosen exernally. The ime period in he model corresponds o 1 year in he daa. On he household side, he period uiliy funcion is assumed o have logarihmic form such ha he curvaure of he CRRA uiliy funcion, ε, equals 1, he midpoin beween various esimaes surveyed in Mehra and Presco (1985). The discoun rae, β, is picked o imply a reasonable long run ineres rae level, given he argeed rae of growh of 2%. Seing β = 0.98 implies approximaely a 4% real ineres rae. On he final good producion, he share of inermediae goods, α, is se o This is in he ballpark of Akcigi e al. (2014), who find a calibraed share of 0.9 for angible facors of producion using US daa on firm profiabiliy. Akcigi e al. (2013) also assign a value of 0.85 o physical facors in heir final good producion funcion. Wihou loss of generaliy, he marginal cos of producing inermediae goods is normalized o (1 α) for privae firms ha do no have 24 Noe ha he enran firms do no conribue hrough IPO because he suppor of he disribuion from which hey draw he iniial produc qualiy does no exend over values ha lead o IPO. 17

18 VC suppor. 25 The funcion h( ) ha defines he cos of doing R&D is assumed o have he form γ 0 x γ 1. The curvaure parameer, γ 1, is se o 2 so ha he funcion has quadraic shape. This in urn implies ha he R&D elasiciy in he innovaion producion funcion is 0.5, a value in line wih he empirical lieraure. 26 The lowes produc developmen efficiency, θ L, is normalized o 1. The parameer ha governs he exogenous separaion of maches beween firms and VC funds, σ vc, is se as follows. In NVCA (2013), he Naional Venure Capial Associaion (NVCA) repors ha, among VC-backed firms ha received heir firs round of funding beween , abou 16% made i o he IPO sage. Anoher 18% are repored o fail. The res of he maches end in ways ha I do no include in my model. 27 The exogenous separaion parameer, σ vc, capures he yearly ariion rae due o hese exernal reasons. 28 For he average share sold a IPO,, Rier (1998) repors a range of 20%-40%. The elegraph maching funcion inroduces a single scale parameer ha is normalized o 1. Lasly, he bargaining power of he VC, φ, is assumed o be 0.5. Table (1) summarizes he predeermined values. Table 1: Parameers Fixed A Priori Value Descripion Source β = 0.98 Discoun Rae Real Ineres Rae ε = 1 CRRA curvaure Mehra and Presco (1985) α = Share of physical facor Akcigi e al. (2014) η H = 1 α Cos of capial, high normalized γ 1 = 2 R&D cos elasiciy Blundell e al. (2002) θ L = 1 Produc developmen efficiency, low normalized ρ = 1 Scale of elegraph maching imposed φ = 0.5 Bargaining power imposed σ vc = 8.7% Ariion rae of VC-firm maches Unsuccessful separaions =.28 Share sold a IPO Rier (1998) 25 This normalizaion simplifies he derivaion of he profi funcion. The corresponding value for VC-backed and public firms, η, is deermined in he esimaion. 26 Measuring innovaions by paens, he empirical lieraure on paens and R&D provides esimaes for his elasiciy. Griliches (1990) gives a range from 0.3 o 0.6 while Blundell e al. (2002) find Among hese remaining maches, half of hem resuled in acquisiion of he privae firm by anoher one. The oher half is couned as sill privae or no known, and mos of hem are believed o have failed. Because he success of a VC firm is generally measured by is IPO performance, I focus on IPOs. 28 The oal ariion rae is assumed o be he cumulaive hazard rae over 7.5 years. This lengh of ime represens he median enure of VC invesmens, which is esimaed o vary from 7 o 10 years in he daa. 18

19 3.2 Idenificaion of he Esimaed Parameers There are 10 parameers o be esimaed. Perhaps he mos crucial parameers are{θ L, θ H } because hey deermine he magniude of he impac on firm growh of he operaional knowledge provided by VCs. Having normalized θ L o 1, I make use of Puri and Zaruskie (2012) in esimaing θ H. Puri and Zaruskie (2012) make a fundamenal conribuion o he empirical lieraure ha invesigaes he effec of venure capial on firm dynamics by employing survey daa on firms. In paricular, hey combine he VenureXper and Longiudinal Business Daabase of US Census Bureau so ha hey are able o deermine he firms ha received VC financing. Conrolling for he number of employees, age, geographical locaion, and he indusry a four-digi SIC level, hey creae a mached sample of non-vc-backed firms and firms ha are a he firs round of geing VC funding. 29 The auhors observe he firms in hese wo caegories unil hey exi in some form (exi he daa, become public, ec.) for a maximum of 10 years. Then, using hese samples, hey regress he logarihm of firm sales on a number of covariaes and, in paricular, provide he OLS esimae on he ineracion erm beween a dummy for VC use and he ime elapsed afer maching. 30 This esimae deermines he differenial impac of VC financing on firm growh. To deermine θ H, I creae analogous samples from he saionary disribuion of my model. I simulae firms in hese samples for 10 years, and conduc he same regression analysis. The esimaion procedure ries o mach he model counerpar of he OLS esimae wih he one provided Puri and Zaruskie (2012). The size of VC firms financial impac is governed by he difference beween η and η H, he marginal coss of producion for privae firms wih and wihou VC backing, respecively. To discipline his difference, I assume ha he decline in he cos of capial due o VC invesmen reflecs all he pecuniary suppor of VC companies. Then, including he raio of VC invesmen o GDP as one of he daa momens deermines he size of his financial suppor in my model. 31 In order o complee he esimaion of he VC marke, he enry cos for VC firms needs o be deermined. The enry cos of he venure capialis, χ vc, creaes a hreshold for he inermediae good qualiies above which VC firms would no agree o form a mach wih a firm, because hey could no generae a grea deal of improvemen on already high qualiy levels due o decreasing reurns o innovaions. Moreover, his enry cos deermines he ex-ane value of a venure capialis before enering he marke. Therefore, once he oher parameers ha describe he maching funcion and Nash bargaining are fixed, χ vc is closely correlaed wih he probabiliy of firms ob- 29 I should be emphasized ha Puri and Zaruskie (2012) do no conrol for he amoun of VC invesmen received, and do no uncover paricular mechanisms hrough which VC affecs firm dynamics. One conribuion of my paper is o esablish his. 30 The OLS regression resuls are presened in Appendix B. 31 Venure capial invesmens do no only include funding of early- and growh-sage companies, bu also buyous, laer-sage invesmens, ec. no relevan o he poin of his paper. Therefore, when calculaing he raio of VC invesmen o GDP, I ake ino accoun only he early- and expansionary-sage invesmens by VC. 19

20 aining VC financing. Hence, o discipline χ vc, I include as a arge he NVCA (2013) esimae ha, roughly, only one ou of a hundred applicaions succeeds in securing VC financing. One cavea: in my model, every meeing in he maching marke resuls in a mach. This happens boh because here is no search cos for he firms, and because VC firms are idenical. Any firm ha knows ha a mach would creae a posiive surplus goes ino he marke, and he ones wih he expecaion of a negaive surplus say ou. To map he NVCA saisic o my model, I inerpre he 1% success on applicaions as he chance of meeing a VC company ha would accep he firm. When solving he model, I fix he probabiliy of maching wih a VC a his level, and solve for he level of enry cos ha suppors he equilibrium by looping over χ vc. To complee he cos srucure of an IPO, he fixed cos of IPO, χ IPO, needs o be deermined. This parameer maps o direc coss of IPO observed in he daa, such as regisraion fee and underwriing coss. The saisics provided by Rier (1998) indicae ha, on average, hese coss amoun o 11% of he oal proceeds raised by IPO. Using his figure, I can direcly esimae χ IPO. The benefis of an IPO are deermined by wo parameers: κ, he abrup increase in qualiy level, and θ M, he permanen produc developmen efficiency ha VC-backed firms reain afer becoming public. Deermining he gains from IPO, hese parameers are crucial for he decision of he opimal ime o go public. To pin down κ and θ M, I herefore use he median age across all privae firms a he ime of IPO, ogeher wih he median lengh of firm-vc maches ha lead o an IPO. Because produc developmen efficiency is assumed o remain fixed for non-vc-funded privae firms afer going public, κ is he only parameer ha deermines he gains from going public for hese ype of firms. Then, he median ime o IPO for VC-backed companies is helpful primarily in idenifying θ M. Boh κ and θ M are negaively relaed o hese age momens. The res of he parameers are λ, γ 0, χ o, and χ e. The firs one deermines he qualiy gain due o process innovaions and is mosly ied o he average growh, for which he arge value is he average US pos-war annual growh rae of 2%. The scale parameer of R&D cos funcion γ 0 is used o mach he R&D share of GDP. The ouside opion for inermediae firms, χ o, is esimaed by argeing a 5.5% equilibrium exi rae. I ake his value from Lee and Mukoyama (2012), who calculae esimaes using US plan-level daa from I se he enry cos, χ e, ha he poenial enrepreneurs face, such ha he equilibrium measure of inermediae good firms is equal o uniy. As a resul, he se of 11 parameers o be esimaed wihin he feasible se Ω is ω [ η, γ 0, χ vc, ρ, χ IPO, κ, θ M, θ H, λ, χ e, χ o ] T Ω. 20