Kiel Institute for World Economics Duesternbrooker Weg Kiel (Germany) Kiel Working Paper No. 1120

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1 Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng papers rests wth the author, not the Insttute. Snce workng papers are of a prelmnary nature, t may be useful to contact the author of a partcular workng paper about results or caveats before referrng to, or quotng, a paper. Any comments on workng papers should be sent drectly to the author.

2 Path Dependences n enture Captal Markets Abstract Ths paper examnes the mpact of venture captalsts reputaton buldng and experence accumulaton on the geness of venture captal markets. enture captalsts must accumulate experence to successfully support hgh-technology enterprses. They must buld reputaton,.e., a track record for successfully fnancng hgh-technology enterprses, n order to rase new funds from outsde nvestors that have lttle nformaton about the proftablty of venture captal nvestments. Smulatons are used to solve the model. The smulaton results demonstrate that reputaton buldng and experence accumulaton lead to path dependences: f venture captalsts lack experence, successve waves of unsuccessful venture-captal-backed enterprses undermne the geness of venture captal markets. Keywords: JEL classfcaton: Reputaton buldng, experence accumulaton, dynamc effcency, path dependences, venture captal G4, O6, O4 Andrea Schertler Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel, Germany Tel.: +49/43/ Fax: +49/43/884-5 E-mal:

3 Introducton Several emprcal studes ndcate that venture captalsts need experence to select, montor and support hgh-technology enterprses successfully, and that they need reputaton n order to rase funds from outsde nvestors. For example, Baker and Gompers (999) fnd evdence that the presence of experenced venture captalsts reduces the fracton of nsders on the board. Reducng the fracton of nsders can be nterpreted as lowerng the power of CEOs who are nterested n a hgh fracton of nsders on the board n order to establsh busness polces that are benefcal for them. The emprcal analyss by Lerner (994) suggests that experenced venture captalsts are more profcent n tmng ntal publc offerngs of the hghtechnology enterprses than ther less experenced counterparts. Moreover, as the study by Gompers (996) ndcates, venture captalsts take care to sgnal ther experence to the market n order to buld up reputaton: young venture captalsts take ther portfolo frms publc earler than older venture captalsts do. The beneft of takng ther portfolo frms publc earler,.e., sgnallng ther experence to outsde nvestors, seems to exceed the costs of dong ths,.e., the greater underprcng of the shares. The purpose of ths paper s to nvestgate whether venture captalsts experence accumulaton and reputaton buldng can lead to path dependences n venture captal markets. The mpact of venture captalsts experence accumulaton and reputaton buldng on the development of venture captal nvestments s analysed n a model n whch venture captalsts can affect postvely the proftablty of hgh-technology enterprses and n whch venture captalsts have to rase money from outsde nvestors. These outsde nvestors ntally have lttle nformaton about the proftablty of venture captal nvestments. Because of ths asymmetrc nformaton, outsde nvestors base ther portfolo selecton decson on past realsatons of returns on venture captal nvestments and alternatve nvestment opportuntes. In addton, they base ther portfolo selecton decson on venture captalsts reputaton. In order to analyse the mpact of reputaton buldng and experence accumulaton on the development of venture captal nvestments, the model wll be analysed by means of smulatons.

4 Wth smulatons, trajectores of nnovatng economes can be determned. Trajectores result from the uncertanty of the nnovaton process combned wth past events that affect the behavour of agents,.e., venture captalsts, outsde nvestors and nnovators. Innovators have to make dscrete choces when ntroducng a new product or a new process nnovaton. The venture captalsts also make dscrete choces when decdng about nvestments. However, most mportant s that the uncertanty of the nnovaton process s partly a dscrete choce process: the techncal realzaton of a hghtechnology product can ether be successful or unsuccessful. Because of ths, economc states at a certan pont n tme can be explaned by the trajectores of the past. Thus, dfferent trajectores lead to dfferent economc states and the events n each economc state wll affect the trajectory n the future. The model used to analyse the mpact of reputaton buldng and experence accumulaton on the development of venture captal markets takes nto account some of the systematc nterdependences among outsde nvestors, venture captalsts, banks, nnovators, and consumers. Recent lterature analysng venture captal markets has also consdered some of the systematc nterdependences among the partes nvolved. For example, Keuschngg and Nelsen () analyse the relaton between general taxes, entrepreneural nvestment and venture captal fnance wthn a general equlbrum model. Ther model results show that a tax on captal ncomes reduces the number of entrepreneurs n equlbrum, whle t ncreases the venture captalsts ncentves to advse the management teams. A tax on wage ncome causes the opposte effects. Kannanen and Keuschngg () analyse a stuaton n whch the demand for venture captal through many hgh-technology entrepreneurs s hgh, whle the supply of venture captal s low because of a lack n experenced venture captalsts that offer advce. In ths stuaton, venture captalsts demand hgh returns and have ncentves to nclude many enterprses n ther portfolos. Wth a comparatve statc analyss, Keuschngg () examnes the effects of several exogenous shocks. A permanent ncrease n the manageral For a comprehensve dscusson of the smulaton method see Glbert and Trotzsch (999).

5 3 productvty of venture captalsts, for example, magnfes the number of successful nnovatons n the long-run. However, the lterature so far has not addressed the mpact of reputaton buldng and experence accumulaton on the development of venture captal nvestments. The smulaton results presented n ths paper demonstrate that f the venture captalsts have not yet accumulated experence and f they have not yet bult reputaton, successve waves of unsuccessful venture-captalbacked enterprses can undermne the geness of venture captal markets that would ultmately mprove welfare. In the case of nexperenced venture captalsts, the probablty to realze successve waves of unsuccessful venture-captal-backed enterprses s comparatvely hgh because the venture captalsts lack experence to select the most promsng entrepreneurs. If a venture captal market s struck by successve waves of unsuccessful venture-captal-backed enterprses, the venture captalsts wthout reputaton cannot rase new funds from outsde nvestors. And, f nexperenced venture captalsts cannot rase new funds, they cannot accumulate experence necessary to add value to hgh-technology enterprses. By contrast, f a venture captal market s not struck by successve waves of unsuccessful venture-captal-backed enterprses, venture captalsts can accumulate experence effcently. Ths paper s organzed as follows. In the second, thrd, and fourth secton, I descrbe the basc model, venture captalsts reputaton buldng, and experence accumulaton, respectvely. In the ffth secton, I present the development of the average venture captal nvestments of a large number of smulaton runs, whle n the sxth secton, I examne factors causng dfferent developments n venture captal actvty. Secton seven summarzes the man fndngs of ths paper.

6 4 Overvew of the Basc Model The basc model comprses two scenaros. In the frst scenaro, only products are demanded and suppled whose development s rsk-less. The development of these tradtonal products can be fnanced by bank credts. In ths scenaro, there s no demand for venture captal. In the second scenaro, whch s depcted n Fgure, the consumers demand hghtechnology products n addton to the tradtonal products (for a detaled descrpton see Schertler ). The development of hgh-technology products s rsky. enture captalsts can reduce these rsks through management support and, thus, ncrease the expected profts of hghtechnology product developments. In the second scenaro, venture captalsts have already accumulated experence to successfully support hgh-technology enterprses and have already bult reputaton to rase new funds from outsde nvestors. In order to produce a tradtonal or hgh-technology product, an entrepreneur must make a start-up nvestment for the development of the respectve product. Ths start-up nvestment s used for research and development actvtes f a hgh-technology product should be developed, and for organzng the busness f a tradtonal product s developed. Whle the development of tradtonal products s certan,.e., the nvestment results n the development of a tradtonal product, the development of a hgh-technology product s uncertan. Thus, n ths case, the start-up nvestment can be lost. The entrepreneur has to rase captal n the fnancal market because she does not have the means to fnance the start-up nvestment herself. After successfully establshng the enterprse, both tradtonal and hgh-technology products are produced usng only labour at constant margnal costs. In both scenaros, a homogeneous basc product s Recent lterature analysng generally the development of fnancal markets also uses ths approach. For example, Bencvenga and Smth (998) focus on the transton from the equlbrum wthout ntermedaton to the equlbrum wth ntermedaton n whch the servces of ntermedaton are costly. Boyd and Smth (996, 998) examne the transton from the equlbrum wth banks to the equlbrum wth bank and equty markets, whle Cooley and Smth (998) examne the transton between equlbrum wthout fnancal markets to the equlbrum n whch agents are specalzed ether as savers or captal nvestors.

7 5 also produced usng only labour nput to determne the wage rate n the economy. Fgure : Overvew of the model Consumers Employees Outsde nvestors Basc product Enterprses that produce tradtonal products Bank credts Enterprses that produce hgh-technology products enture captal enture captalst s management support Resource flows (Payments n the opposte drecton) Product flows (Payments n the opposte drecton) The probablty of a successful development of hgh-technology products, whch s determned by a random varable realzed only after fnancng decsons have been taken and the start-up nvestment has been made, depends on venture captalsts actve nvolvement. enture captalsts nfluence the probablty of a successful development because they have a comparatve advantage n fnancng hgh-technology products. Ths comparatve advantage s based on the venture captalsts stage- and technology-specfc knowledge and experence that they need to support the management teams of the hgh-technology enterprses. Tradtonal and hgh-technology products are suppled under monopolstc competton. In the steady states, free entry leads to zero profts n the market for tradtonal products and hgh-technology products: tradtonal and hgh-technology products are sold at average costs. The zero-proft condtons are used to determne the number of tradtonal and hghtechnology enterprses n the steady state. The number of tradtonal

8 6 enterprses determnes the volume of bank credts, whle the number of hgh-technology enterprses determnes the maxmum volume of venture captal n the steady state. In each perod, the ndvduals, who own the resources n the economy, maxmze ther consumpton utlty that s gven by a love of varety functon. In the frst scenaro, the consumpton utlty functon contans only a basc homogeneous product and an aggregate of tradtonal products. In the second scenaro, t contans the basc homogeneous product, an aggregate of tradtonal products as well as an aggregate of hgh-technology products. The ndvduals maxmze ther consumpton utlty under the restrcton of ther budget constrant,.e., n the optmum ther ncome s equal to ther consumpton expendtures. In the frst scenaro, the ncome s gven by wage ncome because I assume that the rsk-less rate of nterest s equal to zero. In the second scenaro, the ncome s gven by the wage ncome and captal ncome because ndvduals demand, as rsk-averse outsde nvestors, a rsk premum for captal nvested n hgh-technology enterprses. The consumpton expendtures are gven by the sum of product quanttes multpled by the respectve product prces. In the steady states of both scenaros, the ndvduals ncome s constant and the savng rate s equal to zero. The story behnd ths s as follows. The start-up nvestments are totally sunk after they have been nvested, and each enterprse s actve for only one perod. The enterprses do not have to pay nterest but they have to repay the start-up nvestment, and enterprses producng hgh-technology products addtonally have to pay a rsk premum. The rsk premum s part of the ncome and s thus consumed, whle the start-up nvestments are repad to the rsk-averse outsde nvestors. In the next perod, the outsde nvestors offer ths captal to the next generaton of entrepreneurs for start-up nvestments. Therefore, n the steady states of both scenaros, the ndvduals ncome s constant, and the savng rate of the economy s equal to zero. Between the steady states of the frst and second scenaro, venture captalsts have to buld reputaton to rase new funds from outsde nvestors, and they have to accumulate experence to successfully select, montor and support hgh-technology enterprses. enture captalsts

9 7 reputaton buldng and experence accumulaton are to be descrbed n the next sectons. 3 Asymmetrc Informaton between Outsde Investors and enture Captalsts The outsde nvestors can observe only the average return on all venturecaptal-backed hgh-technology enterprses n a partcular perod but not the return of sngle nvestments. Moreover, they are not nformed about partcular characterstcs of venture captalsts: they nether know the venture captalsts experence n supportng the management teams nor can they observe the behavour of venture captalsts after they have nvested ther captal n venture captal funds. Thus, there s an asymmetrc dstrbuton of nformaton between the venture captalsts and the outsde nvestors. Therefore, the outsde nvestors base ther portfolo selecton decsons on the past observatons of average returns on venture captal nvestments. In each perod, the outsde nvestors nvest ther portfolo captal n bank assets and n venture captal funds. The volume of the portfolo captal s dentcal to the volume of the captal stock so that there s suffcent captal to fnance the steady state number of tradtonal enterprses and hghtechnology entrepreneurs. Bank assets are nvested only n tradtonal enterprses and are therefore rsk-less. The return on bank assets s equal to zero because the nterest rate s set equal to zero. enture captal funds are nvested only as start-up nvestments n hgh-technology entrepreneurs and are therefore rsky. The share of the portfolo captal whch the outsde nvestors supply to venture captal funds n a partcular perod T depends on the degree of ther rsk averson, the venture captalsts reputaton, and on the frst two moments of the unknown dstrbuton of the returns on venture captal nvestments. The two moments of the unknown dstrbuton are calculated from past observatons of average returns on venture captal nvestments. Specfcally, I assume that the share of the portfolo captal suppled to venture captal funds s gven by:

10 8 [] v ( T ) where = ξ f rˆ else ( T ) * ( T ) rˆ ( T ) ξ σ S f < rˆ ( T ) < ( + σˆ ( T )) a hat denotes expected values, ξ wth ξ > denotes the rsk-utlty parameter, ( + ˆ ( T )) ( T ) r denotes the return on venture captal nvestments, σ denotes the standard devaton of the returns on venture captal nvestments, and wth < denotes the venture captalsts reputaton. Note that the share of the portfolo captal suppled to venture captal funds gven n equaton [] does not result from an optmsaton calculus of the outsde nvestors. However, the functonal form of the share of the portfolo captal suppled to venture captal funds has some smlarty to the one that results from a squared rsk-utlty functon (for a dscusson of portfolo selecton approaches, and rsk-utlty functons see, for example, Ingersoll (987)). The reason for assumng ths specfcaton gven n equaton [] s as follows. For the smulaton model, the share of the portfolo captal suppled to venture captal funds must ncrease wth the expected average return on venture captal nvestments; t must decrease wth the rsk averson of the outsde nvestors, and the varance of the returns on venture captal nvestments. Moreover, n the steady state of the second scenaro, the relaton between the share of the portfolo captal suppled to venture captal funds and the rsk premum must be postve: the hgher the rsk premum s, the hgher the share of the portfolo captal suppled to venture captal funds must be. If the outsde nvestors would base ther portfolo decson on a squared rsk-utlty functon, an ncrease n the expected return on venture captal nvestments would not necessarly lead to a hgher share of the portfolo captal suppled to venture captal funds. In addton, n the steady state, n,

11 9 whch the returns on venture captal nvestments are constant and the varance of the returns s (theoretcally) equal to zero, the relaton between the rsk premum and the share of the portfolo captal suppled to venture captal funds s negatve. If the outsde nvestors would base ther portfolo decson on an exponental rsk-utlty functon, I could not determne the steady state relaton between the rsk premum and the share of the portfolo captal suppled to venture captal funds. Ths relaton s, however, necessary to specfy the rsk premum that equalzes the venture captal demand and supply n the steady state of the second scenaro. It should also be noted that, even f the varance of the returns s equal to zero, the outsde nvestors do not necessarly nvest ther whole portfolo captal n venture captal funds because of the specfcaton of the share of the portfolo captal suppled to venture captal funds gven n equaton []. Only f rˆ ( T ) ξ ( T ), the outsde nvestors nvest ther whole portfolo captal n venture captal funds, f the varance of the returns s equal to zero. However, for the smulatons, ths extreme case s not so mportant because the varance of the returns on venture captal nvestments wll never be equal to zero; the varance wll become even n an extreme case only very small and not zero. In each perod, n whch the venture captalsts are comparatvely successful at fnancng hgh-technology entrepreneurs they ncrease ther reputaton untl they reach the maxmum level of reputaton, whch I fx to unty. In partcular, I assume that the venture captalsts reputaton ncreases by the amount τ f the realzed rate of success of the venturecaptal-backed hgh-technology enterprses ψ ) s at least as large as the exogenously gven rate of success ψ. Thus, the reputaton of the venture captalsts n a partcular perod T results from: [] ( T ) = wth ( ) >. ( T ) f ( T ) < and ψ ( T ) ) ( T ) + τ f ( T ) < and ψ ( T ) else ) < ψ ψ,

12 Note that the venture captalsts reputaton does not decrease f the venture-captal-backed hgh-technology entrepreneurs realze an extraordnary hgh rate of falure. Snce the outsde nvestors cannot observe the proftablty of hghtechnology enterprses, they base ther portfolo decson n the perod T on past observatons of average returns on venture captal nvestments. In the perod T, they expect the return on venture captal nvestments and the varance of these returns to be T t T t= t r ˆ ( T ) = r () t and ˆ ( T ) = r () t r () t T T σ. T t t= t t= t The average return on venture captal nvestments n a partcular perod T results from the dfference between the repayment of the successful hgh-technology enterprses and the venture captal nvested n hgh-technology entrepreneurs, all dvded by the venture captal nvested n hgh-technology entrepreneurs. The realzed return n a partcular perod T s therefore gven by: [3] r ( T ) = ( I + P( T ) ) N ( T ) ψ I N ( T ) I N ( T ) ψ ψ P T = I ( ) Thus, the return on venture captal nvestments ncreases wth the rsk premum of the outsde nvestors and decreases wth the volume of the start-up nvestment. enture captalsts use the rsk premum to encourage the outsde nvestors to nvest ther portfolo captal n venture captal funds. To put t dfferently, venture captalsts try to balance the share of the captal stock demanded for venture captal nvestments and the share of the portfolo captal suppled for venture captal nvestments by usng the rsk premum. Whch rsk premum do venture captalsts offer? On the transton path between the steady state n the frst scenaro and the steady state n the second scenaro, the venture captalsts offer a hgher rsk premum to encourage the outsde nvestors to supply captal to venture captal funds because they have not yet bult reputaton. To put t dfferently, venture.

13 captalsts who have not yet bult reputaton must pay a hgher rsk premum to receve a partcular share of the portfolo captal than venture captalsts who have already bult reputaton. In the steady state of the second scenaro, n whch the venture captalsts have already bult reputaton,.e., =, the rsk premum must only compensate for the rsk averson of the outsde nvestors. If the venture captalsts have bult reputaton, the rsk premum s constant (for a gven venture captal demand) snce ths rsk averson s constant over tme. A constant rsk premum leads to constant returns on venture captal nvestments and to a varance of the returns that s equal to zero. Wth constant returns on venture captal nvestments and a varance of the returns equal to zero, one can re-wrte equaton [] and get for the share of the portfolo captal suppled to venture captal funds n the steady state of the second scenaro: [4] v * S = P ξi, wth v * <. < S The venture captalsts compensate an ncrease n the rsk averson of the outsde nvestors wth a hgher rsk premum n order to receve a fxed share of the portfolo captal n the steady state of the second scenaro. On the transton path between the steady states of the frst and second scenaro, the venture captal demand by the venture captalsts does not have to be equal to the venture captal supply by the outsde nvestors because of the asymmetrc dstrbuton of nformaton and the venture captalsts reputaton buldng. However, n the steady state of the second scenaro, I assume that the venture captal supply s equal to the venture captal demand. Thus, the rsk premum whch compensates the rsk-averse outsde nvestors must be approprate for the degree of rsk averson of the outsde nvestors so that the venture captal supply and the venture captal demand s equalzed. In order to determne the relatonshp between the rsk premum and the degree of rsk averson of the outsde nvestors n the steady state of the second scenaro, I set the share of the captal stock demanded by the venture captalsts v * d gven n equaton [A8] equal to the share of the

14 portfolo captal whch s suppled to venture captal funds v * S gven n equaton [4]. Solvng ths for the rsk premum gves: [5] ( ρ ) ( ρ ) A 3 A3 ξi P = + + t A ( ρ ) ( ρ ) 3 = I + C +. t I, wth Thus, n the steady state of the second scenaro, the rsk premum balancng the venture captal supply and demand only depends on the exogenous parameters of the model. But what about the rsk premum f the venture captalsts buld reputaton,.e., f the venture captal market s on the transton path between the steady state of the frst scenaro and the steady state of the second scenaro? Then the rsk premum depends on the venture captalsts reputaton, on the past returns on venture captal nvestments whch depend n turn on the rsk premums of past perods, and on the varance of these returns. For venture captalsts, t s mpossble to calculate an adequate rsk premum on the transton path,.e., n some perods, the demand wll be larger than the supply, whle n other perods the supply wll be larger than the demand. The reason for ths s that the chosen rsk premum n a partcular perod has two effects on the venture captal market. These effects happen, however, at dfferent ponts n tme. Frst, the rsk premum drectly affects the venture captal demand by hgh-technology entrepreneurs because the rsk premum s part of the fxed costs and the hgher the fxed costs, the lower ceters parbus the demand for venture captal s. Second, the rsk premum of the current perod affects the portfolo decson of the outsde nvestors n the next perods but not n the current one. Therefore, t s mpossble to calculate an adequate rsk premum smultaneously accounts for both effects. However, for the smulaton analyss, t s sensble to specfy a rsk premum that changes when the level of reputaton changes because otherwse venture captalsts wthout reputaton have no mechansm to

15 3 receve larger amounts of the portfolo captal. Therefore, I assume that the venture captalsts (who choose the rsk premum) gnore the effect of the rsk premum n a partcular perod on the venture captal supply n the successve perods. Then, the rsk premum n a partcular perod T can be calculated as: [6] P( T ) I ( ρ ) ( T )( ρ ) A 3 A3 ξ = + + t for <, Thus, the hgher the level of venture captalsts reputaton s, the lower the rsk premum wll be. 4 Experence and Success Probablty enture captalsts accumulate the experence necessary to make hgh-rsk nvestments proftable durng ther actvtes as actve fnancal ntermedares. Certanly, they typcally start ther career wth some basc experence because they have often founded ther own hgh-technology enterprses and they have often also experence n sellng enterprses successfully at a stock market. Wth ther experence, venture captalsts can early recognze on crss stuatons n the enterprses they have chosen to fnance. Thus, the management support of experenced venture captalsts adds more value than the support of nexperenced venture captalsts. Moreover, venture captalsts use ther experence to select new enterprses. The more experence venture captalsts have accumulated, the better busness plans and busness deas can be evaluated. Thus, experenced venture captalsts select ceters parbus enterprses that are more successful than the ones selected by ther nexperenced counterparts. enture captalsts experence can be nterpreted as a mechansm wth whch they can reduce the uncertanty of the nnovaton process. In order to capture the venture captalsts experence accumulaton n the model, I assume that the more enterprses the venture captalsts have fnanced successfully, the hgher ther experence s. Suppose that the experence n perod T s gven by:

16 4 [7] H ( T ) where T T H = t= t= else * ( ) + N ( t) ϖn f H ( ) + N ( t) < ϖn ϖ wth ϖ > denotes a shft parameter whch determnes the speed of the experence accumulaton, N () t denotes the number of successful hgh-technology entrepreneurs n perod t, * N denotes the steady state number of hgh-technology enterprses, and H ( ) wth ( ) > H denotes the basc experence of venture captalsts. Snce ϖ >, venture captalsts need some perods to accumulate the experence to support hgh-technology enterprses successfully. Therefore, an ncrease n the captal provded to venture captal funds does not necessarly lead to an ncrease n the speed of experence accumulaton. The ntuton behnd ths s that each sngle venture captalst has a maxmum level of experence that he can accumulate n a partcular perod. As n the basc model, I assume that the venture captalsts affect the probablty of venture-captal-backed hgh-technology entrepreneurs to be successful. But the sze of ths effect depends now on the venture captalsts experence. The probablty of a hgh-technology entrepreneur to be successful n perod T s gven by: [8] ( T ) where, ( T ) ψ f H ( T ) f H ( T ) H < ψ =, ψ = ψ wthout the perod ndex denotes the exogenously gven probablty of a hgh-technology entrepreneur to be successful f the venture captalsts have already accumulated the necessary experence to fnance hghtechnology enterprses successfully. *,

17 5 For a venture captal market to develop, the startng value of the venture captalsts experence must exceed a crtcal level. Ths crtcal level s determned mplctly by a condton that states that a venture captal market wll emerge only f the value-added by venture captalsts management support s large compared to the costs of management support (equaton [6] n Schertler ()). Replacng the probablty of hgh- technology entrepreneurs to be successful ψ by the startng value of the H multpled by the probablty to be successful ψ leads to the followng crtcal startng value for the venture captalsts experence: venture captalsts experence ( ) [9] H ( ) ( I + P + C) ( I + P) ψ ψ >. Thus, f the venture captalsts do not have suffcent basc experence, a venture captal market n whch fnancal means are offered n combnaton wth management support would not develop. The demand for venture captal does not change f only the experence accumulaton process of the venture captalsts s taken nto account. The reason for ths s that the hgh-technology entrepreneurs probablty to be successful ψ that depends on the venture captalsts experence affects the number of hgh-technology enterprses producng hgh-technology products but not the number of hgh-technology entrepreneurs that try to develop hgh-technology products. Thus, f I do not consder reputaton buldng, the venture captal demand on the transton path s equal to the demand n the steady state. However, f the venture captalsts have not bult suffcent reputaton, the venture captal demand s lower on the transton path than n the steady state because of the hgher rsk premum on the transton path. Whle the experence accumulaton of the venture captalsts does not affect the venture captal demand, t does affect the number of hgh-technology enterprses because ths number depends on the probablty to be successful and, thus, on the experence of the venture captalsts. The reason for ths s that the probablty of the hgh-technology entrepreneurs to be successful affects the repayment that the venture captalsts demand from the hghtechnology enterprses: the hgher the probablty of the hgh-technology

18 6 entrepreneurs to be successful s, the lower the demanded repayment s. Ths repayment s a part of the fxed costs of the hgh-technology enterprses, and the steady state number of enterprses ncreases f the fxed costs decrease. Thus, the hgher the experence of the venture captalsts becomes, the closer the number of hgh-technology enterprses on the transton path to the steady state number s. The number of perods that the venture captalsts need to reach the maxmum level of experence depends on the shft parameter ϖ that determnes the speed of the experence accumulaton. The hgher ths shft parameter s, the more perods the venture captalsts need to accumulate the experence necessary to fnance hgh-technology enterprses successfully. And the more perods the venture captalsts need to accumulate experence, the more perods the smulaton runs wll need to reach the steady state number of hgh-technology enterprses. 5 Smulaton of enture Captal Investments The reputaton buldng and experence accumulaton of the venture captalsts have a substantal mpact on the level of venture captal actvty. Smulaton runs 3 that started wth dentcal ntal parameters show sgnfcant dfferent levels of venture captal nvestments after some perods of tme. Each graph n Fgure depcts the development of the venture captal nvestments for the average and the upper and lower bound usng a large number of smulaton runs. The average s defned as the average venture captal nvestments of all smulaton runs n a partcular perod. The upper bound s defned as the average plus the standard devaton of the venture captal nvestments n a partcular perod, and the lower bound s defned as the average mnus ths standard devaton. The graphs n Fgure dffer because of dfferent ntal parameters. In partcular, I vary the value of the ntal reputaton, the speed of reputaton buldng, the probablty of hgh-technology entrepreneurs to be successful, 3 A descrpton of the smulaton procedure s n appendx.

19 7 the tme horzon of the outsde nvestors, and the past returns on venture captal nvestments. 4 The dfference between the graphs n column (a) and n column (b) of Fgure results from varous past returns on venture captal nvestments that must be gven n order to start the smulatons. In column (a), the venture captal supply n the frst perod s comparatvely low because the chosen values of past returns on venture captal nvestments leads to an expected return of r ˆ () =. 6 wth a varance of σ ˆ () = 8. 4 whch results n a share of the portfolo captal suppled to venture captal funds that s much lower than one per cent. In column (b), by contrast, the venture captal supply n the frst perod s comparatvely hgh because the values of past returns on venture captal nvestments have an expected return of r ˆ () =. wth a varance of only σ ˆ () =. 67. For these past returns, the outsde nvestors supply more than seven per cent of the portfolo =.. captal to venture captal funds f ( ) 5 4 Most of the other exogenous parameters of the model affect the sze of the venture captal market so that varatons of these parameters are not presented here. Increasng the number of ndvduals or the share of the ncome spent of aggregated products, decreasng the start-up nvestment of nnovatve enterprses, the rskaverson of the outsde nvestors, or the dfferentaton parameter of nnovatve products ncreases the sze of the venture captal markets. No mpact on the sze of the venture captal market has the dfferentaton parameter of tradtonal products and the start-up nvestment of tradtonal enterprses.

20 8 Fgure : enture captal nvestments (n,) on the transton path BASELINE: =. 6 ψ, H ( ) =. 5, ( ) =. 5, ϖ = 5, τ =. 4, T t = REPUTATION: =. 6 ψ, H ( ) =. 5, ( ) =. 5, ϖ = 5, τ =. 4, T t = EXPERIENCE: =. 6 ψ, H ( ) =. 5, ( ) =. 5, ϖ = 5, τ =. 4, T t = 8.

21 SPEED OF REPUTATION BUILDING: =. 6 τ =.4, 8 ψ, H ( ) =. 5, ( ) =. 5, ϖ = 5, SPEED OF EXPERIENCE ACCUMULATION: =. 6 ϖ =5, τ =. 4, 8, ψ, H ( ) =. 5, ( ) =

22 SUCCESS PROBABILITY: =. 3 T t = 8. ψ, H ( ) =. 5, ( ) =. 5, ϖ = 5, τ =. 4, TIME HORIZON OF OUTSIDE INESTORS: =. 6 ϖ = 5, τ =. 4,, ψ, H ( ) =. 5, ( ) =. 5 (a) (b),5 average upper bound lower bound Note: Average denotes the average venture captal nvestments of 5 smulaton runs n a partcular perod. Upper bound denotes the average plus one standard devaton of the venture captal nvestments n a partcular perod, and lower bound denotes the average mnus one standard devaton. Addtonally the followng parameters have been used: ρ t = ρ = β B = βt =.5, I = It = C =, L = 5,, ξ =. In (a) the past returns on venture captal nvestments are r ( ) =, r ( ) =. 9, r ( ) =., whle n (b) these =. values are r ( ), r ( ) 9, ( ) =. = 9. r. Lowerng the basc reputaton of the venture captalsts as t s done n the REPUTATION smulaton seems to have an abnormal effect on the average level of venture captal nvestments compared to the BASELINE smulaton: the reducton n the basc reputaton leads to a hgher average level of venture captal nvestments on the transton path. The mechansm behnd ths works as follows. In the REPUTATION smulaton, the venture captalsts buld ther reputaton faster than ther counterparts n the BASELINE smulaton. Remember that venture captalsts buld reputaton f the realzed success rate exceeds the exogenously gven success rate of the steady state. Thus, f nexperenced venture captalsts fnance a large number of hgh-technology enterprses, the probablty to buld reputaton

23 s equal to zero because the low level of experence leads to a low expected and a low realzed probablty to be successful. However, f they fnance only one hgh-technology enterprse, the probablty to buld reputaton s larger than zero because ths enterprse can be ether successful or unsuccessful resultng n a realzed success rate that s ether equal to one or equal to zero. And ths s what happens n the REPUTATION smulaton: n the frst perods, the venture captal supply s comparatvely low so that the venture captalsts can fnance only few hgh-technology entrepreneurs. In ths smulaton, the venture captalsts buld reputaton even f they have not yet accumulated the experence necessary to fnance hgh-technology enterprses successfully. The reducton n the basc reputaton causes stll another nterestng effect compared to the BASELINE smulaton. Whle n the BASELINE smulaton, the number of smulaton runs s comparatvely low n whch the outsde nvestors do no longer supply captal to venture captal funds after some perods, the respectve number n the REPUTATION smulaton s about nne tmes as hgh as n the BASELINE smulaton. Thus, a lower value of the venture captalsts basc reputaton does not mprove welfare as suggested by the hgher average level of venture captal nvestments. A decrease n the basc experence of the venture captalsts depcted n the EXPERIENCE smulaton reduces the average level of the venture captal nvestments, ncreases the tme that the smulaton runs need to reach the steady state level of the venture captal nvestments, and ncreases the volatlty of venture captal nvestments on the transton path. However, the effects are comparatvely small. Whle n the BASELINE smulaton, the average level of venture captal nvestments s about,63 currency unts n perod, the respectve value n the EXPERIENCE smulaton s,3 currency unts. The dfference wth respect to the standard devaton s more substantal: the BASELINE smulaton has a standard devaton of about 434 n perod, whle the EXPERIENCE smulaton has a standard devaton of about 595 n the respectve perod. An ncrease n the speed of reputaton buldng or n the speed of experence accumulaton has a postve mpact on the development of venture captal markets because the steady state level of venture captal nvestments s reached n shorter tme. In comparson to the BASELINE

24 smulaton, the SPEED OF EXPERIENCE ACCUMULATION smulaton has a hgher average level of venture captal nvestments n all perods except some few perods at the begnnng of the smulaton. An ncrease n the speed of experence accumulaton affects the standard devaton postvely. However, after perod, the standard devaton n the BASELINE smulaton s hgher than n the SPEED OF EXPERIENCE ACCUMULATION smulaton. An ncrease n the speed of reputaton buldng depcted n the SPEED OF REPUTATION BUILDING smulaton has smlar effects than an ncrease n the speed of experence accumulaton. Reducng the success probablty from 6 per cent n the BASELINE smulaton to 3 per cent n the SUCCESS PROBABILITY smulaton has only lttle effects on the development of the average level of venture captal nvestments and on the standard devaton n the smulaton presented n column (a). However, the mpact s much larger n the smulaton presented n column (b) n whch the past returns on venture captal nvestments lead to a hgh share of the portfolo captal that s suppled to venture captal funds. The TIME HORIZON OF OUTSIDE INESTORS smulaton shows the effect of an ncrease n the number of perods that the outsde nvestors consder n ther portfolo decson. In comparson to the BASELINE smulaton, ths smulaton has a lower average level of venture captal nvestments on the transton path and the smulaton runs need a longer tme to reach the optmal allocaton of captal n the steady state. Thus, f the outsde nvestors revew many perods of the venture captal markets hstory, the venture captal nvestments grow at a lower rate. It s the hgher varance of the returns on venture captal nvestments whch manly causes ths result: hgh volatlty of the returns n the ntal stage of a venture captal market keep the market away from growng. 6 Interpretaton of the Smulaton Results: The Importance of Path Dependences The standard devatons of the smulatons ndcate sgnfcant dfferences between the runs of a sngle smulaton wth respect to the development of venture captal nvestments. In the followng, I wll present therefore two

25 3 smulaton runs selected out of the BASELINE smulaton. The smulaton run MIN denotes a run n whch the steady state allocaton of captal s not reached even after perods, whle the smulaton run MAX denotes a run n whch the optmal allocaton of captal s realzed after perod 6. Fgure 3: Probablty dstrbuton of venture captal nvestments enture Captal Investments (,) A MAX Per Cent MIN Note: The graph shows the percentage of smulaton runs of the BASELINE smulaton that reached partcular levels of venture captal nvestments n perod. MIN denotes the smulaton run wth a comparatvely low level of venture captal nvestments, and MAX denotes the run that has already reached the steady state level of venture captal nvestments. For parameter values used see Fgure. Fgure 3 depcts that the smulaton run MIN has a very low level of venture captal nvestments n perod, whle the smulaton run MAX has already reached the steady state level of venture captal nvestments. Moreover, Fgure 3 depcts how lkely t s to reach dfferent levels of venture captal nvestments. The probablty to reach the steady state level of venture captal nvestments n the perod, whch s equal to,7 currency unts, s about 3 per cent. By contrast, the probablty to reach a venture captal nvestment level of about currency unts (the venture captal nvestments n the MIN run are 4 currency unts) s below one per cent. The dfferences between the smulaton runs MIN and MAX are caused by dfferences n the venture captal supply and demand condtons. The smulaton run MAX has low levels of venture captal nvestments n the

26 4 frst 4 perods, whle the run MIN has hgher levels of nvestments n ths tme. Around the perod 5, the levels of venture captal nvestments start to ncrease n both smulaton runs. However, n the run MAX the venture captal nvestments ncrease up to, currency unts and stay there for about 6 perods, whle n the run MIN the venture captal nvestments drop down to a low level after some perods. Interestngly, the run MIN shows several ups and downs durng the observaton perod wthout ncreasng the average level of venture captal nvestments substantally. In order to dscuss the dfferences between these two smulaton runs, I dvde the observaton perod n three development stages. The dstncton of the three stages s based on the smulaton run MAX. In the frst stage, called the ntal stage, the realzed falure rates have hgh levels and are very volatle. Ths stage s from the begnnng of the smulaton to perod 58. The second stage, called the expanson stage, s characterzed by droppng realzed falure rates. It comprses the perods 59 to 4. In the thrd stage, called the mature stage, the realzed falure rates are constant at a low level. The nteracton of the venture captalsts experence accumulaton and the reputaton buldng causes the dfferences between the two smulaton runs. If the venture captalsts buld some reputaton n the ntal stage, the outsde nvestors ncrease the venture captal supply. If the venture captal supply ncreases, the venture captalsts can fnance more hgh-technology entrepreneurs. If venture captalsts fnance more hgh-technology entrepreneurs, the number of hgh-technology enterprses ncreases as well and, thus, venture captalsts accumulate experence at a hgher rate. Note, that an ncrease n the number of hgh-technology entrepreneurs fnanced does lead to an ncrease n the number of hgh-technology enterprses only f the venture captal demand exceeds the venture captal supply. What are the effects at work n the ntal stage n partcular? In the smulaton run MAX, the realzed falure rates, whch are the drvng force n the model, vary between zero and per cent, whle n the smulaton run MIN they vary only between 75 and 95 per cent. In the smulaton run MAX, the venture captalsts can buld some reputaton because they are extraordnarly successful n several perods,.e., the realzed success rates exceed the exogenously gven probablty of hgh-technology enterprses to

27 5 be successful. An ncrease n reputaton has ceters parbus a postve mpact on the venture captal supply by the outsde nvestors. In the smulaton run MIN by contrast, the venture captalsts do not buld reputaton because ther realzed falure rates are too hgh n all perods. In the smulaton run MAX, the ncrease n the reputaton lowers the rsk premum for the outsde nvestors, whle n the run MIN the rsk premum does not change because the reputaton does not change. In the ntal stage of the smulaton run MAX, the reducton n the rsk premum ncreases the demand for venture captal because the rsk premum s a ntegral part of the fxed costs of the hgh-technology enterprses, and decreasng fxed costs ncreases the number of hgh-technology entrepreneurs demandng venture captal. However, n the ntal stage, the venture captal demand exceeds the venture captal supply n both smulaton runs. What are the effects at work n the expanson stage n partcular? In the smulaton run MAX, the realzed falure rates vary only slghtly n the frst few perods of the expanson stage. Ths, n combnaton wth the lower rsk premum, encourages the outsde nvestors to ncrease the venture captal supply because the lower returns on venture captal nvestments are overcompensated by a lower volatlty n the returns. There s a smlar effect n the smulaton run MIN. However, ths effect s much smaller and not persstent as n the smulaton run MAX. In the smulaton run MAX, the venture captal supply stays at a comparatvely hgh level, whle n the smulaton run MIN t drops after some perods because the volatlty of the realzed falure rates ncreases agan. After the smulaton run MAX reaches the expanson stage, the rsk premum equalzes the venture captal demand and supply n many perods. Moreover, the dfference between venture captal supply and demand s compared to the level of venture captal nvestments small. Thus, although the venture captalsts are not fully nformed about the decson rule of the outsde nvestors wth respect to the share of the portfolo captal nvested n venture captal funds (see equaton [6]), they are capable to rase suffcent funds for a gven venture captal demand.

28 6 Fgure 4: Dfferences between the smulaton runs MIN and MAX enture Captal Investments A enture Captal Supply A enture Captal Demand A Realzed Falure Rates A

29 7 Rsk Premum A Returns on enutre Captal a Investments A enture Captalsts' Reputaton A enture Captalsts' Experence A MIN MAX Note: see Fgure 3.

30 8 In the smulaton run MAX, the hgh supply of venture captal allows the venture captalsts to fnance a large number of hgh-technology entrepreneurs. Fnancng a large number of hgh-technology entrepreneurs leads to a large number of hgh-technology enterprses and ths ncreases the venture captalsts experence. Hgher experence of the venture captalsts leads to lower realzed falure rates, whch n turn ncrease the venture captal supply so that venture captalsts can fnance a larger number of hgh-technology entrepreneurs. What are the effects at work n the mature stage n partcular? The effects n the smulaton run MIN do not dffer from those n the expanson stage, whle the smulaton run MAX experences the last changes on the way to reach the optmal allocaton of captal n the steady state. In the smulaton run MAX, the venture captalsts start agan to buld reputaton for successfully fnancng hgh-technology entrepreneurs after they have accumulated suffcent experence. Each ncrease n the reputaton leads ceters parbus to an ncrease n the venture captal supply. Moreover, each ncrease n the reputaton leads to a decrease n the rsk premum that affects only scarcely the returns on venture captal and, thus, the supply of venture captal. However, the decrease n the rsk premum affects sgnfcantly the demand of venture captal. In the smulaton run MIN, the venture captal demand exceeds persstently the venture captal supply n the expanson as well as n the mature stage. The reason for ths s that the venture captalsts gnore the effect of the volatlty of the returns on venture captal nvestments on the share of the portfolo captal suppled to venture captal funds. Due to the hghly volatle realzed falure rates, the returns on venture captal nvestments are also hghly volatle leadng to a small share of the portfolo captal whch the outsde nvestors supply to venture captal funds. Ths n turn leads to low nvestments n hgh-technology entrepreneurs so that venture captalsts accumulate very slowly the experence necessary to fnance hgh-technology entrepreneurs successfully. However, there s no reason to beleve that the smulaton run MIN wll not reach the steady state level of venture captal nvestments. It wll only need a very long tme. An alternatve specfcaton of the rsk premum gven n equaton [6] may partly solve the persstent dvergence of the venture captal supply and

31 9 demand n the smulaton run MIN. Promsng seems the dea to model a learnng process of venture captalsts: how do venture captalsts recognze that ther offered returns are too low for gven nvestment rsks, and how they can encourage the outsde nvestors to ncrease the share of ther portfolo captal suppled to venture captal funds. However, t s most mportant to note that the smulaton runs demonstrate how the trajectores of an nnovatng economy dffer even f the ntal condtons are dentcal. In the smulaton run MAX, the specfed rsk premum leads to an equalzaton of the venture captal demand and supply after some perods, whle n the smulaton run MIN t undermnes the development of a venture captal market that would ultmately mprove welfare. The dfferences n the trajectores, whch are substantal, result from venture captalsts accumulaton of experence and ther buldng of reputaton, the uncertanty of the nnovaton process, the asymmetrc dstrbuton of nformaton between the partes that are nvolved n venture captal markets (such as the outsde nvestors and the venture captalsts), and the past events that determnes the behavour of these agents. These nteractons takng place on venture captal markets offer one explanaton why venture captal actvty dffers substantally between countres. 7 Concludng Remarks Ths paper has examned the effects of venture captalsts reputaton buldng and experence accumulaton on the development of venture captal nvestments. enture captalsts have to buld reputaton,.e., a track record for successfully fnancng hgh-technology enterprses, because they have to rase funds from outsde nvestors that ntally have lttle nformaton about the proftablty of venture captal nvestments. Moreover, venture captalsts have to accumulate stage- and technologyspecfc experence n order to add value to hgh-technology enterprses. The smulaton model that has been used to analyse the development of venture captal nvestments captures the man agents of these markets: venture captalsts, outsde nvestors, and entrepreneurs. enture captalsts nvest management support n addton to fnancal means n enterprses developng hgh-technology products. Through ther management support, venture captalsts ncrease the probablty of the hgh-technology

Kiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1119

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