Do Stronger Patents Stimulate or Stifle Innovation? The Crucial Role of Financial Development

Transcription

1 MPRA Munch Personal RePEc Archve Do Stronger Patents Stmulate or Stfle Innovaton? The Crucal Role of Fnancal Development Angus C. Chu and Gudo Cozz and Shyuan Pan and Mengbo Zhang Fudan Unversty, Unversty of St. Gallen, Zhejang Unversty, Unversty of Calforna, Los Angeles September 2016 Onlne at MPRA Paper No , posted 7 May :02 UTC

2 Do Stronger Patents Stmulate or Stfle Innovaton? The Crucal Role of Fnancal Development Angus C. Chu Gudo Cozz Shyuan Pan Mengbo Zhang Aprl 20, 2017 Abstract Ths study explores the effects of patent protecton n a dstance-to-fronter R&D-based growth model wth fnancal frctons. We fnd that whether stronger patent protecton stmulates or stfles nnovaton depends on credt constrants faced by R&D entrepreneurs. When credt constrants are non-bndng (bndng), strengthenng patent protecton stmulates (stfles) R&D. The overall effect of patent protecton on nnovaton follows an nverted-u pattern. An excessvely hgh level of patent protecton prevents a country from convergng to the world technology fronter. A hgher level of fnancal development nfluences credt constrants through two channels: decreasng the nterest-rate spread and ncreasng the default cost. Through ether channel, a hgher level of fnancal development stmulates nnovaton, but the two channels of fnancal development nteract wth the effects of patent protecton dfferently. Va the nterest-spread (default-cost) channel, patent protecton s more lkely to have a negatve (postve) effect on nnovaton under a hgher level of fnancal development. We test these results usng cross-country regressons and fnd that patent protecton and fnancal development have a negatve nteracton effect on nnovaton. JEL classfcaton: O31, O34, E44 Keywords: Patent protecton, credt constrants, economc growth, convergence Chu: angusccc@gmal.com. Chna Center for Economc Studes, School of Economcs, Fudan Unversty, Shangha, Chna. Cozz: gudo.cozz@unsg.ch. Department of Economcs, Unversty of St. Gallen, St. Gallen, Swtzerland. Pan: shyuanpan@zju.edu.cn. School of Economcs, Zhejang Unversty, Hangzhou, Chna. Zhang: mbzhangucla@g.ucla.edu. Department of Economcs, Unversty of Calforna, Los Angeles, Unted States. The authors would lke to thank Margaret Davenport for her excellent research assstance. The usual dsclamer apples. 1

3 1 Introducton In ths paper, we explore the effects of patent protecton n a dstance-to-fronter R&D-based growth model, n whch a country nvests n R&D to adopt technologes from the world technology fronter and may gradually converge to the technology fronter. A novelty of our growth-theoretc analyss of patent polcy s that we consder fnancal frctons n the form of potentally bndng credt constrants on R&D entrepreneurs. As n Aghon et al. (2005), due to moral hazard, R&D entrepreneurs may not be able to borrow as much as they want for ther R&D nvestment. When these credt constrants are non-bndng, we fnd that strengthenng patent protecton by ncreasng patent breadth leads to a larger amount of monopolstc proft, whch stmulates R&D and technologcal progress. Ths postve monopolstc-proft effect captures the tradtonal vew of patent protecton. However, when the credt constrants are bndng, we fnd that the monopolstc dstorton arsng from patent protecton leads to more severe fnancal frctons, whch stfle R&D and slow down technologcal progress. The ntuton of ths negatve fnancal dstortonary effect of patent protecton can be explaned as follows. Strengthenng patent protecton causes more severe monopolstc dstorton, whch n turn reduces aggregate ncome and tghtens credt constrants faced by R&D entrepreneurs. As a result, the rates of nnovaton and economc growth decrease. Ths fndng s consstent wth recent studes that often fnd the presence of negatve effects of patent protecton on nnovaton. 1 Furthermore, we fnd that the postve monopolstc-proft effect of patent protecton prevals when the level of patent protecton s below a threshold value, whereas the negatve fnancal dstortonary effect of patent protecton prevals when the level of patent protecton s above the threshold. Therefore, the overall effect of patent protecton on R&D and nnovaton follows an nverted-u pattern that s commonly found n emprcal studes. 2 An excessvely hgh level of patent protecton even prevents a country from convergng to the world technology fronter. In ths case, the country s technology level relatve to the world technology fronter converges to zero n the long run. We consder the case n whch a hgher level of fnancal development nfluences credt constrants through two channels: ncreasng the default cost as n Aghon et al. (2005) and decreasng the nterest-rate spread. Emprcal studes, such as Lerner and Schoar (2005), Qan and Strahan (2007) and Lbert and Man (2010), often fnd that fnancal development reduces nterest rates, the contractng cost of fnancng and the collateral spread of captal. We fnd that by decreasng the nterest-rate spread or ncreasng the default cost, a hgher level of fnancal development stmulates nnovaton. Intutvely, by decreasng the nterest-rate spread, the nterest rate becomes lower, whch n turn ncreases the present value of future monopolstc profts and the value of nventons. By ncreasng the default cost, R&D entrepreneurs are less lkely to default, and hence, banks are more wllng to lend to entrepreneurs for ther R&D nvestment. Interestngly, the two channels of fnancal development nteract wth the effects of patent protecton dfferently. We fnd that va the nterest-spread (default-cost) channel, patent protecton s more lkely to have a negatve (postve) effect on nnovaton under a hgher level of fnancal development. The ntuton of these results can be explaned as follows. When the nterestrate spread decreases, the present value of future profts and the value of nventons ncrease. Consequently, entrepreneurs are ncentvzed to borrow more fundng for R&D, renderng the 1 See for example Jaffe and Lerner (2004), Bessen and Meurer (2008) and Boldrn and Levne (2008). 2 See for example Qan (2007) and Lerner (2009). 2

4 credt constrants more lkely to be bndng n whch case patent protecton has a negatve effect on nnovaton. When the default cost ncreases, banks become more wllng to lend to R&D entrepreneurs, renderng the credt constrants less lkely to be bndng n whch case patent protecton has a postve effect on nnovaton. We test the above theoretcal mplcatons usng cross-country regressons. We fnd that patent protecton and fnancal development have drect postve effects on economc growth. Ths fndng s consstent wth Ang (2010, 2011) who also emprcally explore the effects of both patent protecton and fnancal development on R&D actvty. We complement the analyss n Ang (2010, 2011) by consderng the nteracton effect of patent protecton and fnancal development on economc growth. In summary, we fnd that patent protecton and fnancal development have a negatve nteracton effect on nnovaton, whch s consstent wth the nterest-spread channel through whch patent protecton s more lkely to have a negatve effect on nnovaton under a hgher level of fnancal development. Therefore, to capture the complete effects of patent polcy on economc growth, t s useful to take nto consderaton the nteracton between patent protecton and fnancal development. Ths study relates to the lterature on patent polcy. In ths lterature, Nordhaus (1969) provdes the semnal study n whch he shows that ncreasng patent length causes a postve effect on nnovaton and a negatve statc dstortonary effect on welfare. Whle Nordhaus (1969) focuses on a partal-equlbrum framework, we consder a dynamc general-equlbrum (DGE) model n whch the monopolstc dstorton caused by patent protecton nteracts wth fnancal frctons to affect credt constrants and stfle nnovaton. Subsequent studes n ths lterature, such as Glbert and Shapro (1990) and Klemperer (1990), explore patent breadth n addton to patent length. Scotchmer (2004) provdes a comprehensve revew of ths patent-desgn lterature. Our study nstead explores the effects of patent polcy n a DGE model n whch the fnancal dstortonary effect of patent polcy arses through a general-equlbrum channel. Therefore, ths study relates more closely to the macroeconomc lterature on patent polcy and economc growth based on DGE models. The semnal DGE analyss of patent polcy s Judd (1985), who fnds that an nfnte patent length maxmzes nnovaton and elmnates the relatve-prce dstorton because all ndustres charge the same markup. Our model features an nfnte patent length under whch the relatveprce dstorton s absent as n Judd (1985). However, we show that patent breadth nteracts wth a fnancal dstorton that affects credt constrants and R&D. Subsequent studes n ths lterature explore patent breadth as an alternatve patent-polcy nstrument; see for example, L (2001), Goh and Olver (2002) and Iwasako and Futagam (2013). 3 Some of these studes also fnd that strengthenng patent protecton has an nverted-u effect on nnovaton and growth. Our study dffers from these prevous studes by explorng the effects of patent protecton n the presence of fnancal frctons and n a dstance-to-fronter R&D-based growth model that enables us to explore the technology convergence of countres. Chu, Cozz and Gall (2014) also analyze the effects of patent protecton n a dstance-to-fronter model and show that the nnovaton-maxmzng level of patent protecton depends on the ncome level of a country. However, the abovementoned studes 3 For other patent-polcy nstruments, see O Donoghue and Zwemuller (2004) and Kedasch (2015) on patentablty requrement, Furukawa (2007) and Hor and Iwasako (2007) on protecton aganst mtaton, Dnopoulos and Syropoulos (2007) and Davs and Sener (2012) on rent protecton actvtes, and Chu (2009), Chu, Cozz and Gall (2012), Chu and Pan (2013) and Cozz and Gall (2014) on blockng patents. These studes nether consder fnancal frctons nor the dstance-to-fronter approach. 3

5 nether feature fnancal frctons nor consder the nteracton between patent protecton and credt constrants, whch are the novel contrbutons of ths study. The rest of ths paper s organzed as follows. Secton 2 descrbes the model. Secton 3 presents the theoretcal results. Secton 4 dscusses the regresson results. The fnal secton concludes. 2 An R&D-based growth model wth credt frctons In ths secton, we consder a dstance-to-fronter R&D-based growth model wth fnancal frctons based on the semnal work of Aghon et al. (2005) and Acemoglu et al. (2006). We extend ther model by allowng for varable patent breadth, the value of nventons beng dependent on multple perods of profts and an nterest-rate spread that affects the present value of future profts. We consder a dscrete-tme model and use the model to explore the nteracton effects of patent protecton and credt constrants on the technology convergence of countres. 2.1 Households and workers/entrepreneurs There s a contnuum of countres, ndexed by a superscrpt, that are behnd the world technology fronter. 4 For smplcty, we follow prevous studes to assume that countres do not exchange goods or factors but are subject to nternatonal technology spllovers from the fronter. There s a unt contnuum of nfntely-lved households n each country. These households own ntangble captal (n the form of patents that generate monopolstc profts) and consume fnal goods (numerare). The lfetme utlty functon of the representatve household n country s gven by U = t=0 C t (1 + ρ) t, where the parameter ρ > 0 s the subjectve dscount rate and Ct s consumpton of the representatve household n country at tme t. The asset-accumulaton equaton s A t+1 = (1+rt)A t Ct. From standard dynamc optmzaton, the lnear utlty functon mples that n equlbrum the real nterest rate s equal to the dscount rate, such that rt = ρ. In addton to the nfntely-lved households n the economy, we follow prevous studes to assume the presence of overlappng generatons of workers/entrepreneurs n each perod to create a need for the entrepreneurs to borrow fundng for R&D. At the begnnng of each perod t, L workers enter the economy, and they work to earn wage Wt. At the end of the perod, each worker becomes an entrepreneur and devotes part of her wage ncome κ Wt to R&D, where κ (0, 1). 5 At the begnnng of the next perod, those entrepreneurs who have succeeded n ther R&D projects sell ther nventons to households and use the proceeds for consumpton. Wthout loss of generalty, we normalze L to unty. A worker who enters the economy n perod t has the utlty functon u t = yt + E t [o t+1]/(1 + ρ), where yt denotes consumpton when young and E t [o t+1] denotes expected consumpton when old. If the amount of her R&D spendng Zt s 4 In ths study, we do not model the behavor of the technology fronter and smply take t as gven. 5 Here we assume that the entrepreneur may not be able to devote her entre wage ncome to R&D. Our results also hold when κ = 1. 4

6 less than κ Wt, then a worker/entrepreneur smply consumes Wt Zt n perod t or saves part of t subject to the market nterest rate rt. However, f Zt > κ Wt, then the worker/entrepreneur would need to apply for a loan subject to credt constrants, whch wll be descrbed n detals n Secton Fnal goods The fnal goods sector s perfectly compettve. Frms n ths sector employ workers and a contnuum of dfferentated ntermedate goods v [0, N t ] to produce fnal goods usng the followng producton functon: Y t = (L t) 1 α N t 0 [x t (v)] α dv, (1) where the parameter α (0, 1) determnes labor ntensty 1 α n producton. L t s labor nput. x t (v) s the amount of ntermedate goods v [0, Nt ], and Nt s the number of avalable ntermedate goods n country at tme t. Compettve frms take the prces of fnal goods and factor nputs as gven to maxmze proft. The condtonal labor demand functon s gven by Wt = (1 α)yt /L t, where L t = L = 1 from the market-clearng condton. The condtonal demand functon for ntermedate goods s gven by x t (v) = where p t (v) s the prce of ntermedate goods v n country. [ ] 1/(1 α) α, (2) p t (v) 2.3 Intermedate goods Each dfferentated ntermedate good v s produced by a frm that owns the patent of the product and has market power, whch s determned by the level of patent protecton to be explaned below. In ndustry v, the frm produces x t (v) unts of ntermedate goods usng x t (v) unts of fnal goods as nputs. Therefore, the proft functon of the frm n ndustry v s Π t (v) = p t (v) x t (v) x t (v) = [ p t (v) 1 ] [ ] 1/(1 α) α, (3) p t (v) where the second equalty follows from (2). Usng (3), one can derve the proft-maxmzng prce p t (v) gven by 1/α. To capture the effects of patent protecton, we follow Goh and Olver (2002) to model patent breadth β (1, 1/α) as a polcy varable. 6 In ths case, p t (v) = β. (4) 6 The dea s that the unt cost for other frms to produce an dentcal product s β, whch s ncreasng n the level of patent protecton. Therefore, stronger patent protecton allows the producer who owns the patent to charge a hgher markup; see also L (2001) and Iwasako and Futagam (2013) for a smlar formulaton. Ths formulaton captures Glbert and Shapro s (1990) semnal nsght on breadth as the ablty of the patentee to rase prce. 5

7 Combnng (3) and (4), we obtan the amount of proft as a functon of patent breadth gven by whch s ncreasng n β for β 1/α. Π t (v) = ( β 1 ) ( ) 1/(1 α) α β π(β ), (5) 2.4 Aggregate producton functon Substtutng (2) and (4) nto (1) yelds ( ) α/(1 α) α Yt = β Nt. (6) Equaton (6) shows that the growth rate of Yt s determned by the growth rate of Nt and that the level of Yt s decreasng n patent breadth β, whch captures the effect of markup dstorton on the level of output. In other words, by ncreasng the prce of ntermedate goods, a larger markup leads to less ntermedate goods beng produced and also less fnal goods beng produced. 7 In the presence of credt constrants, patent protecton would then generate a negatve effect on R&D as a result of ths markup dstorton as we wll show later. 2.5 R&D and the value of patents In each country, there s an R&D sector. In each perod t, workers/entrepreneurs devote fnal goods to R&D at the end of the perod to nvent new ntermedate goods that wll be produced n the next perod. To ensure balanced growth, we assume that each entrepreneur spreads her R&D spendng Zt over Nt R&D projects. 8 Therefore, the amount of fnal goods that an entrepreneur devotes to each of her R&D projects s Zt/N t, and the probablty of her R&D projects beng successful s Pt = mn{zt/(n t η t), 1}, 9 where 1/η t captures the productvty of R&D n country. We follow Acemoglu (2009, chapter 18) to assume that η t s an ncreasng functon n Nt /N t, where N t s the level of technology at the world technology fronter. N t grows at a constant rate g > 0, whch s taken as gven by other countres. Let s defne country s relatve technology level to the fronter as µ t Nt /N t (0, 1), whch s an nverse measure of the country s dstance to the world technology fronter. We adopt the followng specfcaton for η t: ( ) Z η t = [γ(µ t) φ θ + η] t, (7) Nt 7 If we follow Romer (1990) to assume that ntermedate goods are produced from captal, nstead of fnal goods, ths markup dstorton would stll exst because the presence of markup and profts lowers captal ncome and reduces captal accumulaton. However, allowng for captal accumulaton would complcate the transton dynamcs substantally. 8 To ensure the nnovaton probablty Pt 1 n the presence of growth n Zt, we only need to assume that entrepreneurs spread ther R&D spendng Zt over ςnt R&D projects, where ς > 0. Wthout loss of generalty, we set ς = 1. 9 For smplcty, we assume that an entrepreneur s R&D projects ether all succeed or all fal. 6

8 where the parameters {γ, η} > 0 and {θ, φ} (0, 1) are common across countres. Ths specfcaton features the catchng-up effect under whch a less developed country that has a smaller µ t s able to grow faster by absorbng more world technologes. The term (Z t/n t ) θ captures an ntratemporal duplcaton externalty of R&D as n Jones and Wllams (2000). Gven the unt contnuum of R&D entrepreneurs and the ndependence of R&D projects (across entrepreneurs), the law of large numbers apples, so that the accumulaton of nventons at the aggregate level follows a determnstc process gven by N t N t+1 N t = Z t η t = ( ) Nt Z 1 θ t, (8) γ(µ t) φ + η Nt where Zt/η t = Nt Zt/(N t η t) s the number of successful R&D projects n perod t. Each R&D project has a probablty Pt to gve rse to a new varety of ntermedate goods. When a new varety s successfully nvented at the end of perod t, producton of the ntermedate goods begns n perod t + 1. We denote the value of an nventon created n perod t as Vt (v). Here we assume that the dscount rate for future profts s gven by r + ɛ = ρ + ɛ, where ɛ 0 denotes an exogenous nterest-rate spread n country. For example, Lerner and Schoar (2005), Qan and Strahan (2007) and Lbert and Man (2010) fnd that fnancal development reduces nterest rates, the contractng cost of fnancng and the collateral spread of captal. Here we use ɛ to capture these fnancal frctons n a smple way. Under the assumpton above, Vt (v) can be expressed as V t (v) = s=t Π s+1 (v) (1 + r + ɛ ) s+1 t = π ( ) β ρ + ɛ, (9) whch s ncreasng n patent breadth β and decreasng n ɛ. The postve effect of β captures the postve effect of patent protecton on the value of nventons. In a country that s more fnancally developed, there are less fnancal frctons, whch n turn reduce the nterest-rate spread ɛ and ncrease the value of nventons. Fnally, we make the followng parameter restrcton, whch guarantees that Pt (0, 1) and µ t (0, 1). Assumpton 1 (g θ η) 1/(1 θ) < π ( β ) /(ρ + ɛ ) < mn{η 1/(1 θ), [g θ (γ + η)] 1/(1 θ) } Equlbrum wthout credt constrants In ths secton, we explore the equlbrum level of R&D n the absence of credt constrants. The zero-expected-proft condton of R&D s gven by Pt Vt = Zt/N t, whch can be expressed as ( ) Vt = η t π(β ) Z ρ + ɛ = [γ(µ t) φ θ + η] t. (10) Nt 10 The assumpton π ( β ) /(ρ + ɛ ) < η 1/(1 θ) ensures P t < 1 for µ t (0, 1). Dervatons avalable upon request. 7

9 Therefore, the level of R&D n any perod t s gven by Z t = [ π(β ] )/(ρ + ɛ 1/θ ) N γ(µ t) φ t, (11) + η whch s ncreasng n β for a gven level of relatve technology µ t. The growth rate of technology s gven by g t N t N t = 1 ( ) Z 1 θ t = γ(µ t) φ + η Nt 1 [γ(µ t) φ + η] 1/θ [ π(β ] (1 θ)/θ ), (12) ρ + ɛ whch s also ncreasng n patent breadth β, for a gven µ t, capturng the postve monopolstc proft effect of patent protecton on nnovaton. Furthermore, a hgher level of fnancal development n the form of a decrease n the nterest-rate spread ɛ ncreases the growth rate of technology. We summarze these results n Proposton 1. Proposton 1 In the absence of credt constrants, stronger patent protecton leads to a hgher growth rate of technology. A hgher level of fnancal development n the form of a decrease n the nterest-rate spread also leads to a hgher growth rate of technology. Proof. Proven n text. In the long run, µ t converges to a steady state, n whch N t grows at the same rate as N t. 11 Settng g t to the world technology growth rate g n (12) yelds the steady-state level of relatve technology µ t gven by { µ = 1 1 γ 1/φ g θ [ π(β ] (1 θ) } 1/φ ) η µ 1 (β ρ + ɛ +, ɛ ), (13) whch s ncreasng n the level of patent breadth β and decreasng n the nterest-rate spread ɛ. Note that Assumpton 1 ensures µ 1 (0, 1) n the steady-state equlbrum. The balanced-growth level of R&D s gven by Zt = π(β g ) ρ + ɛ N t, (14) whch s ncreasng n patent breadth β and decreasng n the nterest-rate spread ɛ. In other words, a decrease n the nterest-rate spread ɛ causes the entrepreneurs to want to do more R&D. 11 We show the stablty of ths steady state n Secton

10 2.7 Equlbrum wth credt constrants Before the end of a perod, each entrepreneur devotes her wage ncome κ Wt to Nt R&D projects wthout borrowng. If the R&D spendng Zt exceeds her wage ncome κ Wt, then she would have to borrow Dt = Zt κ Wt from a bank to fnance her R&D projects. If her R&D projects succeed, she repays the loan plus an nterest payment equal to (1 + Rt+1)D t at the end of the perod. If her R&D projects fal, she becomes bankrupt and repays nothng to the bank. Therefore, f the entrepreneur truthfully reveals the outcome of her R&D projects, the expected payment receved by the bank s Pt (1 + Rt+1)D t + (1 Pt )0. When banks make zero expected proft, we have Pt (1 + Rt+1)D t = Dt, whch mples Pt (1 + Rt+1) = 1. What makes t dff cult to borrow s that an entrepreneur may want to default even when her projects are successful. We follow Aghon et al. (2005) to assume that banks do not observe the outcome of R&D projects, and hence, the problem of moral hazard arses. Specfcally, by payng a default cost h Zt where h (0, 1), an entrepreneur can hde the outcome of her projects and avod repayng the loan. The cost parameter h s an ndcator of banks effectveness n securng repayment and partly measures the level of fnancal development n the country. In case an entrepreneur decdes to default, the entrepreneur must ncur the default cost before observng the outcome of her R&D projects. Therefore, entrepreneurs would not default f and only f the followng ncentve-compatblty (IC) constrant holds: where D t = Z t κ W t = Z t κ (1 α)y h Z t P t (1 + R t+1)d t = D t, (15) Zt κ (1 α)yt = κ (1 α) 1 h 1 h t. Substtutng ths condton nto (15) yelds ( α β ) α/(1 α) N t, (16) where the last equalty uses (6). We refer to ths IC constrant as a credt constrant, whch becomes tghter as patent breadth β ncreases capturng an nteracton between the monopolstc dstorton of patent protecton and the fnancal dstorton of the credt constrant. The ntuton can be explaned as follows. When patent breadth β ncreases, aggregate ncome Yt decreases due to the markup dstorton. As a result, a larger β reduces the ncome of entrepreneurs and ther ablty to borrow. Ths effect exsts so long as entrepreneurs ablty to borrow s affected by ther ncome and n turn entrepreneurs ncome s related to aggregate ncome. For convenence, we defne f κ (1 α)/(1 h ) (0, ) as a composte parameter that s ncreasng n the default cost h. Equatons (14) and (16) show that the balanced-growth level of R&D spendng Zt satsfes { Zt = mn π ( β ) ( ) } α/(1 α) g α ρ + ɛ, f β Nt. (17) There exsts a unque value of patent breadth β below (above) whch the credt constrant does not bnd (s bndng) n the long run. Ths threshold value of β s gven by 12 β 1 (f, ɛ ) αg + αg (ρ + ɛ )f, (18) + 12 To ensure that the threshold value β 1 < 1/α, we assume f < (1 α)αg/(ρ + ɛ ), whch s equvalent to h < 1 (ρ + ɛ )/(αg). 9

11 whch s ncreasng n the country s default cost f and the nterest-rate spread ɛ. The ntuton of these two results can be explaned as follows. Frst, a larger default cost f reduces entrepreneurs ncentves to default and enables them to borrow more fundng for R&D. In ths case, the credt constrant s less lkely to be bndng, whch n turn ncreases the threshold value of patent breadth. Second, a lower nterest-rate spread ɛ ncreases entrepreneurs ncentves to nvest n R&D. As a result, the credt constrant becomes more lkely to be bndng, whch n turn decreases the threshold value of patent breadth. In ths case, a hgher level of fnancal development has dfferent mplcatons on the threshold value of patent breadth dependng on whether fnancal development s reflected by an ncrease n the default cost or a decrease n the nterest-rate spread. Fnally, whenever the credt constrant s bndng, the growth rate of technology n country s gven by g t = N t N t = ( ) ] α/(1 α) 1 θ 1 [f αβ, (19) γ(µ t) φ + η whch s decreasng n the level of patent breadth β, for a gven µ t, capturng the fnancal dstortonary effect of patent protecton on nnovaton. Furthermore, a hgher level of fnancal development n the form of an ncrease n the default cost f ncreases the growth rate of technology. We summarze these results n Proposton 2. Proposton 2 In the presence of bndng credt constrants, stronger patent protecton leads to a lower growth rate of technology. A hgher level of fnancal development n the form of an ncrease n the default cost leads to a hgher growth rate of technology. Proof. Proven n text. 2.8 Convergence Usng the defnton of relatve technology level µ t, we can derve ts law of moton gven by µ t+1 µ t = N t+1 / N t+1 µ Nt t+1 = N t ( ) 1 + g t µ 1 + g t. (20) In the absence of credt constrants, we use (12) to express the law of moton for µ t as { [ µ t+1 = µ t 1 π(β ] (1 θ)/θ } ) 1 + H 1 + g [γ(µ t) φ + η] 1/θ ρ + ɛ 1(µ t). (21) Even f the credt constrant does not bnd n the long run, t may be bndng n the short run when µ t s small. When the credt constrant s bndng, we can use (19) to express the law of moton for µ t as µ t+1 = µ t 1 + g γ(µ t) φ + η [f ( αβ ) α/(1 α) ] 1 θ H 2(µ t). (22) 10

12 Combnng (21) and (22) mples that country s technology level relatve to the fronter evolves accordng to the followng law of moton: µ t+1 = mn{h 1(µ t), H 2(µ t)}, from whch we derve a threshold value ˆµ of relatve technology level below (above) whch H2 < H1 (H1 < H2). In other words, when relatve technology level µ t s below ths threshold ˆµ, µ t+1 evolves accordng to H2(µ t) that s subject to the credt constrant. In contrast, when relatve technology level µ t s above the threshold ˆµ, µ t+1 evolves accordng to H1(µ t) that s free from the credt constrant. The threshold value ˆµ s gven by { [ ˆµ (β, f, ɛ ) 1 π(β ( ) β ) αθ/(1 α) ]} 1/φ η, (23) + γ (f ) θ (ρ + ɛ ) α whch s ncreasng n patent breadth β but decreasng n the default cost f and n the nterestrate spread ɛ. Intutvely, at a hgher level of patent protecton, the credt constrant s more lkely to be bndng, whch n turn expands the range of µ t wthn whch µ t+1 evolves accordng to H 2(µ t) that s subject to the credt constrant. In contrast, when ether the default cost or the nterest-rate premum ncreases, the credt constrant becomes less lkely to be bndng, whch n turn shrnks the range of µ t wthn whch µ t+1 evolves accordng to H 2(µ t). In the followng lemmata, we derve some propertes of the functons {H 1 (µ t), H 2 (µ t)}, whch wll be useful n determnng the value of µ t at the steady state. Lemma 1 H 1 (µ t) s ncreasng and concave w.r.t. µ t, and satsfes the followng propertes: Proof. See Appendx A. H1 (0) = 0, H1 (1) < 1, H 1 µ µ t =0 > 1. t Lemma 2 H 2 (µ t) s ncreasng and concave w.r.t. µ t, and satsfes the followng propertes: Proof. See Appendx A. H 2 (0) = 0, H2 µ µ t =0 = 1 t 1 + g η [f ( αβ ) α/(1 α) ] 1 θ. In addton to the frst threshold value β 1 of patent breadth defned n (18), we also defne a second threshold value β 2 of patent breadth below (above) whch H 2 µ t [ β 2 (f ) α + µ t =0 > 1 ( H 2 µ µ t t =0 < 1). ] (1 α)/α f ( ) 1/(1 θ), (24) ηg whch s ncreasng n the default cost f. We now consder three possbltes. 11

13 Case 1 When β β 1 (f, ɛ ), we have ˆµ µ 1 (β, ɛ ). In ths case, although the credt constrant may be bndng n the short run dependng on the ntal value of µ 0, the credt constrant does not bnd n the long run. Therefore, the steady-state value of relatve technology µ t s gven by µ = µ 1 (β, ɛ ), whch s ncreasng n patent breadth β as shown n (13). The long-run growth rate of technology n ths country s g. Fgure 1 shows that the steady state s stable. µ t + 1 µ µ = t+ 1 t ( ) H 2 µ t ( ) 1 t H µ 0 ˆµ µ 1( β) µ t Fgure 1: Convergence under β β 1 Case 2 When β 1 (f, ɛ ) < β < β 2 (f ), 13 we have ˆµ > µ 1 (β ) and H 2 µ µ t t =0 > 1. In ths case, the credt constrant s bndng even n the long run. The steady-state value of relatve technology level µ t s determned by the fxed pont µ = H 2 (µ ), whch yelds µ 1 = 1 ( ) ] α/(1 α) 1 θ [f αβ η γ g 1/φ µ 2 (β, f ), (25) + whch s decreasng n patent breadth β and ncreasng n the default cost f. The long-run growth rate of technology n ths country s g. Fgure 2 shows that the steady state s stable. 13 To ensure β 1 < β 2, we assume η < f [αg (ρ + ɛ )f ] α(1 θ)/(1 α) /g (1 αθ)/(1 α). 12

14 µ t + 1 µ µ = t+ 1 H 2 ( µ t ) H 1( µ t ) t 0 2( ) µ 1( β) µ β ˆµ µ t Fgure 2: Convergence under β 1 < β < β 2 Case 3 When β β 2 (f ), we have ˆµ > µ 1 (β ) and H 2 µ µ t t =0 1. In ths case, µ t converges to 0 as shown n Fgure 3, and µ t+1 lm t µ t = lm µ t 0 H 2 (µ t) µ t = g η [f ( αβ ) α/(1 α) ] 1 θ ξ (β, f ) 1. (26) Therefore, the balanced growth rate n country n ths case s [ ] g = lm (1 + g) µ t+1 1 = (1 + g) ξ 1 g, (27) t µ t where ξ s decreasng n patent breadth β and ncreasng n the default cost f. + 13

15 µ t + 1 µ µ = t+ 1 t H 1 ( µ t ) H 2 ( µ t ) 0 µ 1( β) µ t Fgure 3: Dvergence under β β 2 3 Patent breadth and credt constrants Based on the results n the prevous secton, we can dvde countres nto three groups. Wthout loss of generalty, we rearrange the order of the countres and denote the three groups as group 1, 2 and 3. For countres n group 1, ther R&D actvtes are not restrcted by the credt constrant, and ther technologes grow at the same rate as the world technology fronter n the long run. The levels of patent protecton n these countres satsfy β β 1 (f, ɛ ), whch s ncreasng n the default cost f and the nterest-rate spread ɛ. For countres n group 2, ther R&D actvtes are restrcted by the credt constrant, but these countres can stll keep pace wth the growth rate of the world technology fronter n the long run. The levels of patent protecton n these countres satsfy β 1 (f, ɛ ) < β < β 2 (f ), where β 2 (f ) s ncreasng n the default cost f but ndependent of the nterest-rate spread ɛ. For countres n group 3, ther R&D actvtes are strongly restrcted by the credt constrant. In ths case, the technology growth rate n these countres s slower than that of the world technology fronter n the long run. The levels of patent protecton n these countres satsfy β β 2 (f ). Accordng to ths classfcaton, the relatve technology level µ of a country n the steady state s gven by µ 1 (β, ɛ ), f + β β 1 (f, ɛ ) + + µ = µ 2 (β, f ), f β 1 (f, ɛ ) < β < β 2 (f ), (28) + 0, f β β 2 (f ) 14 +

16 and the balanced growth rate of technology s gven by g, f β β 1 (f, ɛ ) + + g = g, f β 1 (f, ɛ ) < + + β < β 2 (f ) + (1 + g) ξ (β, f ) 1 g, f β β 2 (f ) + +. (29) We summarze these results n Proposton 3. Proposton 3 There are three types of balanced growth paths n the world. Frst, when β β 1 (f, ɛ ), relatve technology level µ converges to µ 1, and the growth rate of technology converges to g. In ths case, µ 1 s ncreasng n patent breadth β and decreasng n the nterest-rate spread ɛ. Second, when β 1 (f, ɛ ) < β < β 2 (f ), relatve technology level µ converges to µ 2, and the growth rate of technology converges to g. In ths case, µ 2 s decreasng n patent breadth β and ncreasng n the default cost f. Thrd, when β β 2 (f ), relatve technology level µ converges to zero, and the growth rate of technology converges to (1 + g) ξ 1, whch s decreasng n patent breadth β and ncreasng n the default cost f. Proof. Proven n text. Fgure 4 Fgure 4 llustrates the three groups of countres. Countres n group 1 are not fnancally constraned due to a hgh default cost f. In ths case, stronger patent protecton ncreases the amount of monopolstc proft, whch n turn stmulates R&D and ncreases the relatve technology level µ 1 n the long run. A hgher level of fnancal development n the form of a lower nterest-rate spread ɛ ncreases the value of nventons and the relatve technology level µ 1 n the long run. Countres n group 2 are fnancally constraned due to a moderate default cost f. In ths case, stronger patent protecton amplfes monopolstc dstorton and reduces the level of output, whch n turn tghtens the credt constrant on R&D and decreases the relatve technology level µ 2 n the long run. A hgher level of fnancal development n the form of a hgher default cost f enables the 15

17 entrepreneurs to borrow more fundng for R&D, whch n turn ncreases the relatve technology level µ 2 n the long run. For a gven value of the default cost f, an ncrease n the level of patent protecton may cause a country n group 1 to fall nto group 2. Therefore, there exsts a technology-maxmzng level of patent protecton β 1. Ths technology-maxmzng level of patent protecton β 1 s affected by the level of fnancal development. Frst, t s ncreasng n the default cost f. As mentoned before, a larger default cost f reduces entrepreneurs ncentves to default, whch enables them to borrow more fundng for R&D. In ths case, the credt constrant s less lkely to be bndng, whch n turn ncreases the threshold value β 1 of patent breadth. Second, the technology-maxmzng level of patent protecton β 1 s ncreasng n the nterest-rate spread ɛ. Intutvely, a hgher nterest rate decreases the value of nventons and reduces entrepreneurs ncentves to nvest n R&D. As a result, the credt constrant becomes less lkely to bnd, renderng patent protecton to be more lkely to have a postve effect on R&D. A hgher level of fnancal development ncreases the cost of default but decreases the nterest-rate spread n a country. Therefore, under a hgher level of fnancal development, t s not clear whether patent protecton would become more lkely to have a postve or negatve effect on nnovaton. Ths depends on whether fnancal development ncreases the default cost or decreases the nterest-rate spread. We summarze all the above results n Proposton 4. Proposton 4 Fnancal development has a postve effect on nnovaton whereas patent protecton has an nverted-u effect on nnovaton. If fnancal development ncreases the default cost, then patent protecton would be more lkely to have a postve effect on nnovaton under a hgher level of fnancal development. If fnancal development decreases the nterest-rate spread, then patent protecton would be more lkely to have a negatve effect on nnovaton under a hgher level of fnancal development. Proof. Proven n text. Fnally, countres n group 3 have a very low default cost f. Gven that R&D entrepreneurs have strong ncentves to default n ths case, they are not able to borrow much fundng for R&D. In ths case, the steady-state growth rate s gven by (1 + g) ξ 1 g, where ξ s decreasng n the level of patent breadth. An ncrease n the default cost helps to mtgate ths problem and rases the steady-state growth rate. 4 Emprcal analyss In ths secton we examne the emprcal evdence of our theoretcal predctons. The mplcatons of our theory that wll be tested are the followngs: 1. The lkelhood that a country converges to the fronter growth rate ncreases wth ts level of fnancal development but decreases wth ts level of patent protecton. 2. In a country that converges to the fronter growth rate, fnancal development has a postve effect on the steady-state level of per-capta GDP relatve to the fronter. 16

18 3. In a country that converges to the fronter growth rate, patent protecton has an ambguous effect on the steady-state level of per-capta GDP relatve to the fronter. 4. Under a hgher level of fnancal development, patent protecton can be more lkely to have a negatve or postve effect on the steady-state level of relatve per-capta GDP. 4.1 Data The dataset conssts of 98 countres from 1980 to 2009 featurng varables of economc growth, patent protecton, fnancal development and other controls. 14 We transform the dataset nto a cross secton by takng annual average of each varable for each country. The growth rate of a country s taken to be the average annual growth rate of GDP per capta between 1980 and For the measure of patent protecton wthn a country, we consder the commonly used ndex of patent rghts developed by Gnarte and Park (1997) and Park (2008). 15 The data for fnancal development s based on the Fnancal Development and Structure Dataset from Chak et al. (2012). Followng Kng and Levne (1993) and Beck et al. (2010), we take advantage of three ndcators of fnancal ntermedaton that can proxy the overall development of a country s fnancal system. The frst measure s the prvate credt by depost money banks and other fnancal nsttutons as a rato to GDP, denoted as prvate credt. The second ndcator s depost money banks assets as a rato to GDP, denoted as bank assets. The thrd ndcator s lqud labltes as a rato to GDP, denoted as lqud labltes. We use prvate credt as our preferred measure of fnancal development as n Ang (2010, 2011) and consder the other two measures as robustness checks because as stated n Levne et al. (2000), prvate credt excludes credt granted to the publc sector and credt granted by the central bank and development banks. In our theoretcal model, the amount of borrowng as a rato to output s gven by { Dt = Z t κ Wt = mn π ( β ) ( g β ) α/(1 α) }, f κ (1 α), Yt Yt ρ + ɛ α where the second equalty follows from (17) and (6). Therefore, Dt/Y t s ncreasng n the default cost f and decreasng n the nterest-rate spread ɛ. In other words, an ncrease n Dt/Y t n the data may reflect the effect of a larger f or the effect of a smaller ɛ. 4.2 Convergence regresson We frst use the convergence regresson model based on Aghon et al. (2005) to test our theoretcal mplcatons. The startng pont of ths model s that each country s assumed to be on a transton 14 See Appendx B for descrpton and sources of data. 15 The ndex covers fve dmensons: 1) extent of coverage; 2) membershp n nternatonal patent agreements; 3) provsons for loss of protecton; 4) enforcement mechansms; and 5) duraton of protecton. Each dmenson s assgned a value between zero and one. The overall ndex s the unweghted sum of these fve values, wth a larger value reflectng a hgher level of patent protecton. 17

19 path towards ts steady state. From (20)-(22), patent protecton and fnancal development affect the relatve growth rate of a country that s convergng to the fronter gven by (1 + gt)/(1 + g) = µ t+1/µ t. In partcular, (21) and (22) show that the ntal relatve technology level has a negatve effect on the transtonal relatve growth rate and that fnancal development always has a postve effect regardless of whether t ncreases the default cost f or decreases the nterest-rate spread ɛ. In countres wthout bndng credt constrants, patent protecton postvely affects the transtonal relatve growth rate, whereas n countres wth bndng credt constrants, patent protecton negatvely affects the transtonal relatve growth rate. Ths emprcal analyss s an extenson of Aghon et al. (2005) wth the addton of patent protecton, so we follow them to approxmate our theoretcal model by the followng cross-sectonal regresson, whch can be used to nvestgate the effects of patent protecton and fnancal development on the steady-state level of per-capta GDP growth relatve to the fronter: g g 1 = γ 0 + γ β β + γ F F + γ βf β F + γ y (y y 1 ) +γ βy β (y y 1 ) + γ F y F (y y 1 ) + γ x x + ε, (30) where g denotes the average annual growth rate of per-capta GDP, β denotes the average level of patent protecton, F denotes the average level of fnancal development, y s the log of ntal per-capta GDP, x s a set of other control varables and ε s the dsturbance term wth mean zero. The subscrpt denotes country, and country 1 s the technology leader, whch we take to be the Unted States. Defne country s ntal relatve per-capta GDP as ŷ y y 1. Then we can rewrte (30) as g g 1 = λ (ŷ ŷ ), where the steady-state value ŷ s gven by settng the rght-hand sde of (30) to zero (.e., when the growth rate dfference s zero): ŷ = γ 0 + γ β β + γ F F + γ βf β F + γ x x + ε. (31) (γ y + γ βy β + γ F y F ) In (30), λ s a country-specfc convergence parameter gven by λ = γ y + γ βy β + γ F y F. (32) It s useful to note that a country converges to the technology fronter f and only f the growth rate of ts relatve per-capta GDP depends negatvely on the ntal ŷ ; that s, f and only f λ < 0. Thus, from mplcaton 1 we know that the lkelhood of convergence would ncrease wth fnancal development and decrease wth patent protecton f and only f γ F y < 0 and γ βy > 0. (33) From (31), the long-run effects of fnancal development and patent protecton on the relatve output of a country that converges are as follows: ŷ = 1 (γ F λ F + γ βf β + γ F y ŷ ), (34) }{{} }{{}? + 18

20 and ŷ = 1 (γ β λ β + γ βf F + γ βy ŷ ). (35) }{{} }{{}? Relatve-technology-level regresson In addton to the convergence regresson, we also consder the followng relatve-technology-level regresson: ȳ ȳ 1 = ζ 0 + ζ β β + ζ F F + ζ βf β F + ζ y (y y 1 ) + ζ x x + ν, (36) where ȳ s the average log of per-capta GDP, ν s another dsturbance term wth mean zero, and the other varables are defned n the same way as n the convergence regresson. Ths regresson model also captures the mplcatons from (21) and (22) that patent protecton and fnancal development affect a country s relatve technology level wth respect to the technology fronter. It s useful to note that our data sample covers 30 years, so we try to approxmate the steady-state level of relatve per-capta GDP by ȳ ȳ 1, and hence, ths regresson model s used as an addtonal test of mplcatons Regresson results Consderng the endogenety of fnancal development as dscussed n Aghon et al. (2005) and also the endogenety of patent protecton, we estmate the regresson models usng nstrumental varables. We use legal orgns as the nstrument for fnancal development F. As for the nstruments for patent protecton β, we combne two sets of nstruments. The frst set of nstruments s chosen accordng to Gould and Gruben (1996), ncludng ntal relatve output y y 1 and ntal degree of openness. We do not use the other nstruments n ther paper to avod overdentfcaton. The second set of nstruments s a smulated nstrumental varable (SIV). For country, we use the average degree of patent protecton of all the other countres (except country ) n 1980 as an nstrument for country s average patent protecton over We refer to ths nstrument as smulated patent protecton and denote t as sv_pr. Ths varable s to control for the endogenous response of patent protecton to changes n nnovaton actvtes wthn a country, and we assume that the changes are not correlated across countres. 16 The nteracted terms between nstruments are also used as nstruments for the nteracted terms of the endogenous varables. Tables I and III report the estmaton results from the generalzed method of moments (GMM), and Tables II and IV report the results from two-stage least squares (2SLS). We consder both GMM and 2SLS for robustness. 16 For a dscusson of SIV, see for example Curre and Jonathan (1996) and Mahoney (2015). We use SIV to deal wth the ssue of weak nstruments. We fnd that f we only use ntal relatve GDP and ntal openness as nstruments for patent protecton, the two varables suffer from the problem of weak nstruments. Moreover, we tred usng lagged patent protecton, whch s the degree of patent protecton wthn each country (from 1960 to 1979) before our sample perod. All these regressons results are avalable upon request. 19

21 [Insert Tables I and II here] From Tables I and II, we fnd that the followng results are robust and sgnfcant for most of the regressons: (1) γ βy > 0, γ F y < 0, γ y < 0; and (2) γ β > 0, γ F > 0, γ βf < 0. The frst set of results {γ βy > 0, γ F y < 0, γ y < 0} supports mplcaton 1. It s useful to recall that a country converges to the technology fronter f and only f λ = γ y + γ βy β + γ F y F < 0. Therefore, γ F y < 0 and γ βy > 0 mply that the lkelhood of convergence ncreases wth fnancal development but decreases wth patent protecton. To understand the mplcatons of the second set of results {γ β > 0, γ F > 0, γ βf < 0}, let s beng by assumng that all countres lag behnd the Unted States n the steady state;.e., ŷ < 0. Fnancal development would have a postve long-run effect on the relatve ncome of each country that converges f and only f γ F + γ βf β + γ F y ŷ > 0. In ths term, γ βf β s negatve because the estmated γ βf s negatve, whereas γ F y ŷ s postve because the estmated γ F y s negatve. The result γ F > 0 mples that fnancal development s lkely to have a postve long-run effect, and ths postve effect s unlkely to vansh or become negatve because γ F +γ F y ŷ > 0. Ths fndng s consstent wth mplcaton 2. We also consder the magntude of the coeff cents. From regresson 1 of Table II, we have γ F + γ βf β = β. Gven a mean of for β, γ F + γ βf β s postve for the average country. Together wth γ F y ŷ > 0, fnancal development has a postve long-run effect on the relatve ncome of the average country. Moreover, we use equaton (34) to compute the long-run effect of fnancal development and fnd that fnancal development has a postve long-run effect n the vast majorty of countres. As for patent protecton, t would have a postve long-run effect on each country that converges f and only f γ β + γ βf F + γ βy ŷ > 0. In ths term, γ βf F s negatve because the estmated γ βf s negatve, and γ βy ŷ s also negatve because the estmated γ βy s postve. The result γ β > 0 mples that patent protecton may have a postve long-run effect, but ths postve effect may turn negatve because γ βf F + γ βy ŷ < 0. From regresson 1 of Table II, we have γ β + γ βf F = F. Gven a mean of for F, the average country has γ β + γ βf F > 0. However, gven that γ βy ŷ < 0 and that F can be as large as 1.776, patent protecton would have a negatve long-run effect n countres wth suff cently large F. In other words, patent protecton has a negatve (postve) long-run effect when the level of fnancal development F s hgh (low). Usng equaton (35) to compute the long-run effect of patent protecton, we fnd that patent protecton has a postve (negatve) long-run effect n about one-thrd (two-thrds) of countres, and these countres have a low (hgh) level of fnancal development. Ths fndng s consstent wth mplcatons 3 and 4 as well as the scenaro n whch the nterest-spread channel domnates n nfluencng credt constrants. In other words, when the level of fnancal development s low (.e., a hgh nterest-rate spread n the model), patent protecton has a postve long-run effect. When the level of fnancal development s hgh (.e., a low nterest-rate spread n the model), the effect of patent protecton becomes negatve. [Insert Tables III and IV here] From Tables III and IV, we fnd that ζ β > 0, ζ F > 0, ζ βf < 0 and ζ y > 0. The mplcatons of ths set of results are smlar to the above, so we do not repeat the dscusson and smply report 20

22 the results as a robustness check. Fnally, we also estmate the lkelhood of convergence for each country. We use the coeff cents n regresson 1 of Table II to compute the estmated value of convergence parameter λ, and ts standard devaton. We follow Aghon et al. (2005) to classfy a country as most lkely to converge n growth f ts estmated λ s at least two standard devatons below zero, as most lkely to dverge n growth f ts estmated λ s at least two standard devatons above zero, and as uncertan to converge otherwse. As reported n Table V, we fnd that none of the countres n our sample s classfed as most lkely to dverge, and there are 54 countres (out of 103) that are classfed as most lkely to converge. [Insert Table V here] 5 Concluson In ths study, we have explored the effects of patent protecton and fnancal development on economc growth. The novelty of our analyss s that we consder the presence of credt constrants on R&D entrepreneurs. We fnd that whether strengthenng patent protecton has a postve or negatve effect on technologcal progress depends on credt constrants. When credt constrants are not bndng, strengthenng patent protecton has a postve effect on economc growth. When credt constrants are bndng, strengthenng patent protecton has a negatve effect on growth. An ncrease n the level of patent protecton may cause the credt constrants to become bndng. As a result, the overall effect of patent protecton on economc growth follows an nverted-u pattern. A hgher level of fnancal development nfluences credt constrants va two channels: decreasng the nterest-rate spread and ncreasng the default cost. These two channels have dfferent mplcatons on the effects of patent protecton. Our regresson analyss fnds evdence that strengthenng patent protecton s more lkely to have a negatve effect on nnovaton under a hgher level of fnancal development, whch s consstent wth the nterest-spread channel. These results show the mportance of an often neglected nteracton between the monopolstc dstorton caused by patent protecton and the fnancal dstorton caused by credt constrants. 21