J EconDOI 10.1007/s00712-014-0410-8

Economic growth under two forms of intellectualproperty rights protection: patents and trade secrets

Keishun Suzuki

Received: 20 December 2013 / Accepted: 15 June 2014© Springer-Verlag Wien 2014

Abstract This paper analyzes the effects on growth of strengthened patent protec-tions, where trade secrets are introduced as an additional protection method. Strength-ening patent protection decreases the amount of common knowledge, which has twoasymmetric effects on incentives to innovate. First, as competitors cannot freely usetechnological information, it helps successful innovators earn higher profits. Second,less disclosure of information reduces R&D productivity. The model shows that therelative importance of patents versus trade secrets determines whether the formerpositive effect dominates the latter negative effect. As a result, strengthened patentprotection can increase economic growth when the risk of leakage of trade secretsis high. Conversely, when the risk is low, stronger patent protection hinders growth.Similar opposing results are also found in welfare analysis.

Keywords Innovation · Patent · Trade secret · Dynamic general equilibrium

JEL Classification: O31 · O34 · L16

1 Introduction

In the traditional view, strong intellectual property rights (IPR) protection enhanceseconomic growth because it secures innovator’s profits and provides inventors with

K. Suzuki (B)Graduate School of Economics and Management, Tohoku University, 27-1 Kawauchi Aoba-ku,Sendai, Japane-mail: keishun.suzuki@gmail.com

K. SuzukiJapan Society for the Promotion of Science, Tokyo, Japan

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K. Suzuki

incentives to innovate. On the basis of this common understanding, enhancing IPRprotection has been recently promoted by the OECD countries, especially after 1994,when the TRIPS Agreement was implemented.1 However, empirical results do notnecessarily show a positive relationship between the strength of IPR protection andeconomic growth (e.g., Falvey et al. 2006; Horii and Iwaisako 2007).2 Furthermore, itremains unclear whether strong IPR protection always stimulates innovative activity.For example, Allred and Park (2007a) find a U-shaped relationship between firm-levelR&D and the strength of patent rights in developed countries.

Is patent protection really considered as an effective way for R&D firms to appro-priate the benefits of their innovations? In a questionnaire conducted by Cohen et al.(2002), most US firms respond that trade secrets are more effective than patents inproduct innovation, and both US and Japanese firms depend on trade secrets ratherthan other protection methods in process innovation. Arundel (2001) also found that ahigher percentage of firms view patents as less important than secrecy. Trade secretsdo not disclose any information to competitors, unless the secrets are leaked. On theother hand, a patent holder can transmit detailed information to rivals even beforethe patent expires.3 While the patent system is meant to protect intellectual prop-erty, during the patent prosecution process, applicants for patents must disclose sometechnological information to the public in return for patent protection. This partialdisclosure of information gives competitors clues that help them catch up and eveninnovate further. Such disclosure actually causes some firms to avoid patenting theirinnovations. For example, Cohen et al. (2002) found that 46 % of Japanese firms report“over-disclosure” as the most important reason for not applying for a patent.

The purpose of the present paper is to show that the relative importance of patentsversus secrecy is a determinant of the growth effect of strengthened patent protection.Although many empirical studies have highlighted the role of trade secrets in IPR pro-tection, theoretical studies have exclusively focused on patent protection, even thoughthe latter is just one form of IPR protection (e.g., Horowitz and Lai 1996; Futagamiand Iwaisako 2007). There are few theoretical frameworks in which trade secrets areexplicitly introduced.4 Many models assume that inventions are protected only bypatents for simplicity. Such a setup enables us to focus strictly on the role of patents.However, this assumption is far from realistic because actual firms simultaneouslyemploy different protection mechanisms, including both patents and trade secrets, for

1 Park (2008) created an index that represents the level of patent protection. The index is composed of fivescores, some of which are duration of protection, patentable coverage, and enforcement mechanisms. Usingthis index, he showed that the strength of patent protection has increased over time globally.2 At this point, we may need to pay attention to time lag as one reason. Generally speaking, R&D projectstake time to complete, especially for commercialization; therefore, the growth effect may not appear imme-diately after the policy change.3 For example, the detail of the technological information of numerous patent applications can be accessedfreely on the Internet. The amount of access to the website of the Japan Patent Office (JPO) from China isvery large, and experts note that the website is used for imitative activities in China.4 Some studies do not specify the protection method by treating the probability that costless imitation occursas a level of IPR protection [e.g., Horii and Iwaisako (2007)]. This specification is feasible for simplificationand contributes to an analysis of the abstract effects of IPR protection. However, the result of such studiesmay be too generic to be employed as an actual IPR policy.

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an innovation (e.g., Cohen et al. 2000; Thomä and Bizer 2013). In addition, Arundeland Kabla (1998) found that the percentages of innovations for which patent appli-cations were made are only 35.9 % for product innovations and 24.8 % for processinnovations. The fact that firms do not patent all patentable inventions implies thatstrengthening patent protections would have a more limited effect on a firm’s appro-priability than existing models suggest. In other words, the unrealistic assumptionthat firms only seek to protect innovations through patents leads to incorrect evalua-tions of the impact of strengthened patent protection on firms’ incentives to innovate.Therefore, to overcome this shortcoming of existing models, we must consider a morerealistic situation where firms protect their innovations through different methods ofIPR protection. Moreover, to analyze IPR policy more accurately, we must incorporatethe firm’s endogenous choice between several forms of IPR protection. Arundel andKabla (1998) also showed that firms that prefer secrecy have small propensities topatent. This indicates that the relative importance of patenting versus secrecy affectsa firm’s optimal patenting strategy. The lack of an effect on patenting behavior willalso lead to incorrect evaluations of IPR policy.

In contrast to existing literature, the model presented in this paper explicitly con-siders two forms of IPR protection, patents and trade secrets. In the model, innovatorsdevelop a good that consists of many fractional parts. A successful innovator endoge-nously decides how many parts of the good are to be protected by patents, whilethe remaining parts are maintained as trade secrets. Patents ensure stable profits in thelong-run, but short-term profits are relatively low because patents disclose informationto competitors, who can utilize a portion of this information due to the imperfection ofpatent protection. On the other hand, by keeping information secret, an innovator canearn high profits in the short run. However, if the secret leaks to competitors, profitswill fall drastically. Unprotected information becomes common knowledge, and otherfirms can use it for partial imitation and further innovation. Strengthening patent pro-tection decreases the amount of common knowledge, which has two opposing effectson the incentive to innovate. First, it increases the profits of innovators because thereduction of common knowledge lowers the productivity of imitators. This naturallystimulates incentives to innovate. Second, a reduction of common knowledge alsoreduces the R&D productivity of potential innovators, as they cannot easily accessexisting technological information. This increases their R&D costs and discouragesinnovative activities. If the former positive effect overwhelms the latter negative effect,strengthening patent protection can enhance innovation.

The model presented in this paper shows that the probability of leakage of tradesecrets determines whether strengthening patent protection can enhance economicgrowth. When the risk of leakage is high, strengthening patent protection increasesthe growth rate. In this case, because innovators heavily depend on patents, strongerpatent protection dramatically increases profits, which stimulates incentives to inno-vate. On the other hand, when the risk of leakage is low, stronger patent protectiononly slightly increases profits because innovators protect many parts by trade secret.Because the negative impact on R&D productivity is relatively strong in this case,strengthened patent protection is detrimental to the economic growth. Interestingly,when the leakage risk is at middle levels, the relationship between the strength ofpatent protections and economic growth is U-shaped. The intuition is as follows: In

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the model, stronger patent protection leads firms to increase the proportion of theirinnovations that are under patent protection. Therefore, when patent protection is ini-tially weak, innovators still continue to depend on trade secrets. In this case, similarlyto the low leakage risk case, strengthening patent protection has limited effects onprofits and cannot enhance economic growth. However, when the strength of patentprotection exceeds some critical value, such that innovators are sufficiently dependenton patents, stronger patent protection dramatically increases firm profits. Because thispositive effect dominates the aforementioned negative impact in this case, strongerpatent protection accelerates growth.

To my knowledge, no previous study has considered the endogenous choice betweenpatenting and secrecy in a Dynamic General Equilibrium (DGE) model. Some studies,employing a partial equilibrium framework, address decisions to patent.5 For example,Takalo (1998) considered the innovator’s choice between patenting and secrecy in aone-shot innovation model. In contrast to the present paper, his model demonstratedthat broader patent breadth always stimulates R&D investment because such protectionincreases firm value. The essential difference between his model and that of the presentpaper is that, in his model, innovation is not cumulative, and the dynamic effects ofpatent protection on follow-on innovation are not considered. In the framework of thepresent paper, we conclude that the absence of negative effects on R&D productivitygenerates the monotonic effect on R&D. By incorporating this negative effect on R&Dinto a DGE model, the present model demonstrates non-monotonic effects of patentprotection on growth, as is observed empirically. In addition, Takalo (1998) does notfully capture the characteristics of trade secrets. In his model, trade secrets are neverleaked to imitators, while patent length is finite. By considering the leakage of tradesecrets, which can be interpreted as the strength of trade secrets, the present paper alsoderives implications for optimal policy with respect to trade secrets and “mixed” IPRpolicies.

The remainder of the paper is structured as follows. Sect. 2 briefly introduces therole of patents and trade secrets in the model. Sect. 3 develops an endogenous growthmodel that incorporates two IPR protections. In Sect. 4, we obtain the growth effectsof strengthening patent protection, using a numerical method, and welfare effects arealso examined. Finally, Sect. 5 concludes the paper.

2 Basic setup of patent and trade secret

First, this section briefly shows the role of two IPR protections by calculating thefirm’s profit. Suppose that there is only one good that comprises many fractional parts,and the good is produced by a monopolist. Let μ ∈ [0, 1] denote the percentageof “patented parts” in the good. Then, 1 − μ indicates the portion of “secret parts”.Although μ is exogenous here, we will derive it from firm’s optimization in the next

5 Anton and Yao (2004) established a model in which an innovator decides whether to protect his innovationby patent or as a trade secret, as well as what aspects of the invention are the innovator wishes to disclose.Similarly, Ottoz and Cugno (2008) constructed a model in which an innovator can protect the innovation bya patent-secret mix. These studies focus on how innovation size and strength of protection change a firm’sprotection strategy, and do not include an analysis of how such a change affects the economic growth.

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Fig. 1 The transition of protected parts of the innovation. The protected parts in each stage are representedby the shaded area. The left panel depicts the stage before the trade secrets are leaked out (stage-1), andthe right panel shows the stage after leakage (stage-2)

section. For simplicity, I assume that the patent protection goes forever as long as thefirm pays the patent maintenance fee.

Patents are an imperfect form of protection because all the technology of the inno-vation must be disclosed during patent application. Furthermore, this process enablesimitators to access partial information about a product’s composition or the productionmethod. I simply assume that a fraction of δ ∈ [0, 1] in the patented parts is unpro-tected and that other firms can use this information without infringing on the patent.Therefore, a small δ indicates strong patent protection.

Similarly, the trade secret approach does not offer perfect protection because thesecret leaks out with a probability of �. The firms can keep the trade secret as privateinformation at first, but once the leakage occurs, all the secret parts of the good aredisclosed. For convenience, we call the situation before (after) the leakage “stage-1(stage-2)”.

Figure 1 shows how the two ways of protection individually classify the innovationinto protected parts and disclosed parts for each stage. The innovation is divided intopatented parts μ (left side) and secret parts 1 − μ (right side). In stage-1, the secretparts are perfectly protected, but the patented parts are partially protected due to theinformation disclosure by patent application. Thereby, the patented parts are bisectedinto protected parts and disclosed parts, as shown in the left panel of Fig. 1. As a result,the protected parts of the innovation in stage-1 are all secret parts and partial patentedparts. In stage-2, all the secret parts are disclosed and the protected parts are only thepartial patented area, as depicted in the right panel of Fig. 1.

I define dn(μ) as the percentage of unprotected parts of the good in stage n = 1, 2.From Fig. 1, dn(μ) is evaluated as follows.

d1(μ) = δμ, (1)

d2(μ) = 1 − (1 − δ)μ. (2)

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The monopolist has a technological advantage against the imitators according to theamount of protected information. He can produce one good by employing one worker.On the other hand, imitators can produce χn ≤ 1 units of the same good with one unitof labor.6 I assume that χn depends on dn and specify χn as following the function ofμ.

χn(μ) = λ−1 + (1 − λ−1)dn(μ), n = 1, 2. (3)

λ−1 is the minimum value of χn , which is attained when no information is disclosed(dn = 0). We can check χ1(μ) = 1 when dn(μ) = 1 and χ1(μ) = λ−1 whendn(μ) = 0 hold.7 Because imitators can use additional information (1 − μ) afterthe leakage, the amount of information disclosure in both stages may be different(d1 ≤ d2). For this reason, χ1(μ) ≤ χ2(μ) holds, which implies the advantage instage-1 is larger than 1 in stage-2 when μ < 1.

In the market, the monopolist and the imitators are engaged in Bertrand competitionand the monopolist employs the limit-pricing strategy. The unit production cost of theimitator in stage-n is χ−1

n w, and the unit cost of monopolists is w. Therefore, themonopolist can exclude the imitators from the market with a price p = χ−1

n w.To derive the profit of the monopolist, I assume that the demand function is an

inverse of the price, x(t) = 1/p(t), and the total consumer expenditure equals 1.8

Then, the monopolist’s profit is

πn = p · x − w · x

= 1 − w · χn

w

= (1 − λ−1)(1 − dn).

Finally, we can calculate πn in each stage as follows:

π1(μ) =(

1 − λ−1)

(1 − δμ), (4)

π2(μ) =(

1 − λ−1)

(1 − δ)μ. (5)

Figure 2 shows the profit curve for each stage. πn is the linear function of μ andsatisfies π1(1) = π2(1) and π2(0) = 0. The upper downward-sloping straight linerepresents the profit for stage-1 and the lower upward-sloping straight line is the profitfor stage-2.

Here, there is a trade-off between π1 and π2. To see this briefly, consider the case thatthe innovator protects a small fraction of the innovation by patent (μL ). Then, he canearn a relatively high profit before leakage (π L

1 ) because most of the technological

6 We can also interpret χn as the cost disadvantage for imitators. When χn is very small, imitators mustinput a large number of workers for production. In contrast, imitators can perfectly copy in the case ofχn = 1.7 The case of δ = 0 and μ = 1 corresponds to the model of Grossman and Helpman (1991) in which thetechnological advantage of the monopolist is λ−1.8 In the full model, I will show that the assumption is endogenously obtained in the equilibrium. Here, wetake the results in advance.

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Fig. 2 Patented fraction and the profit in each stage

information is concealed from other firms. However, after the leakage occurs, heobtains a low profit (π L

2 ) because the patented parts that still remain are relativelysmall. Next, we consider the case where the innovator patents a large fraction of theinnovation (μH ). Because the technological information about the patented parts ispartially disclosed to other firms, he earns a relatively small profit in stage-1 (π H

1 ).After the leakage, however, the reduction size of the profit is relatively small becausethe innovator does not overly depend on maintaining the trade secret. Therefore, hecan still earn a relatively high profit in stage-2 (π H

2 ).

3 The rest of the model

The model is an extension of Grossman and Helpman (1991), which is a quality-laddermodel. There is a continuum of the sector indexed by j ∈ [0, 1] and a monopolistin each sector. The monopolist can earn profit until a potential firm succeeds in aninnovation in that sector. Because the quality of a new product is higher than theprevious one, the incumbent is replaced by the new innovator. For a more detaileddescription of the model, see Grossman and Helpman (1991).

3.1 Households

The economy consists of L identical households and there is no population growth.Each household serves a unit of labor inelastically and gains a wage w in every period.They maximize intertemporal utility over an infinite horizon as follows:

Ut =∞∫

t

e−ρ(τ−t) ln C(τ )dτ, (6)

where ρ is the subjective discount rate, and C(τ ) is an index of consumption at timeτ . The instantaneous utility is given by

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ln C(τ ) =1∫

0

ln

⎛⎝

m j∑m=0

λm( j)xmt ( j)

⎞⎠ d j, (7)

where xmt ( j) is the consumption of the good whose quality is m in industry j at time t ,and θ is the number of the industries from whom the monopolist has shielded the tradesecret (the situation in stage-1). For convenience, we call such industries “sector-1”.Then, 1 − θ is the number of the industries to whom the monopolist’s trade secret hasbeen disclosed; we call these industries “sector-2”.

The quality of each good is represented as an integer m power of λ > 1, whichmeans that the quality of the new good is λ times as high as the previous one. Inindustry i , there are mi types of goods, and the quality of the latest good is λmi . Inthe equilibrium, households buy only the good of the highest quality in each sectorbecause of limit-pricing.

Under the logarithmic utility function, households equally spend their budget acrossthe industries. Therefore, the demand of a good in the industry i is xmi (t) = E/pmi (t),where E is expenditure and pmi is the price of the good whose quality is mi .

In this setting, the ideal price index associated with the consumption index C is

P = exp

⎡⎣

θ∫

0

ln

(pmi

λmi

)di +

1∫

θ

ln

(pm j

λm j

)d j

⎤⎦ . (8)

Given the aggregate price index, households spend to maximize their intertemporalutility. From the result of the maximization, household’s optimal time path of spendingis represented by E/E = r − ρ. By using aggregate expenditure as the numeraireaccording to Grossman and Helpman (1991), we get E = 1 and r = ρ.

3.2 Firms

The time schedule in an industry is as follows. At first, a successful innovator choosesoptimal mixed protection between patent and trade secret. Then, he produces goodsand earns profit in stage-1 until innovation occurs in the industry with a probability ofz1. In addition, the secret parts of the innovation leak out with a constant probability �

in stage-1. After that, the incumbent moves to stage-2 and his profit decreases due tothe information disclosure of the secret parts. Furthermore, once another firm succeedsin its R&D with an innovation rate z2, it replaces the incumbent and emerges as thenew incumbent.

I assume that the patent cost is a maintenance fee for simplicity and that the incum-bents must pay c(μ) = γμ2/2 in every period, where γ > 0.9 To analyze the role of

9 While the specification of convex patent cost enables us to obtain an interior solution, most fees (e.g.,filing fees) may be proportional to the number of patents. However, the patent cost in the model includesnot only application cost but also other costs. For example, to be granted a patent of an invention of whichit is difficult to determine the non-obvious aspects (e.g., program code), innovators need to pay additionalcosts for the patent-issuing. Suppose a good comprises many parts and each part has a peculiar difficulty in

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trade secret, I focus on the case that γ is not so small and therefore the optimal μ is lessthan 1 in the equilibrium. Their period payoff is the profit obtained in Sect. 2 minusthe patent cost. An incumbent decides μ for maximizing the value of innovation V1,defined as a total expected payoff after the innovation occurs. First, we calculate V2,which is the expected sum of the payoff after the trade secret leakage.10

V2 =∫

t∞e−(r+z2)s [π2(μ) − c(μ)] ds.

= π2(μ) − c(μ)

r + z2. (9)

Then, from a no-arbitrage condition, V1 is derived as follows:

r V1 = π1(μ∗) − c(μ∗) + � (V2 − V1) − z1V1

⇔ V1 = π1(μ∗) − c(μ∗) + �

[π2(μ

∗) − c(μ∗)]/(r + z2)

r + � + z1. (10)

Each incumbent chooses his μ to maximize V1 with a given z. From the first-ordercondition, we obtain an optimal μ as follows:

μ∗(z2) =⎧⎨⎩

0γ −1

(1 − λ−1

)[�/ (r + � + z2) − δ]

1(11)

3.3 R&D sector

In the economy, all innovations stem from the R&D activities by potential firms.11

The preceding R&D cost is covered by issuing equities whose value is equal to V1.The blueprints are invented according to the Poisson process so that the success

probability in any time interval dt is zndt = [L R�n/An(μ)]dt , where L R is thenumber of researchers, �n/An(μ) indicates the R&D productivity, �1 = θ , and�2 = 1 − θ . I assume that R&D becomes more efficient when the number of targetedsectors �n is higher.12 In addition, in this model, potential firms can obtain some

Footnote 9 continuedbeing granted the patent. At first, innovators will apply first for patents of the easiest parts, but eventuallythey will be required to pay additional costs to file subsequent patents.10 In the calculation, we assume that the economy is in a steady state and ignore capital gains or losses.11 This is called “allow effect” or “replacement effect.” All incumbents in sector-1 have no incentive toinnovate by paying some cost because they cannot increase their profit through the new innovation. Themonopolists in sector-2 can raise their profit by successful innovation, although the incentive to innovateis lower than the incentive of the potential firms because they have zero-profit now and because the R&Dtechnology is a constant return here. Therefore, all researchers are employed in the potential firms.12 This spillover can be interpreted as follows. Each industry potentially has a different R&D difficulty andpotential firms may find it easy to discover a suitable industry in which to innovate when the number of the“target” is large.

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clues for further innovation from the disclosed information. I specify An(μ), whichindicates R&D inefficiency, as the following decreasing function of dn .

An(μ) = A − dn, (12)

where A is a parameter larger than 1.

3.4 Free entry

A successful innovator earns expected payoff V1. On the other hand, the innovatormust pay R&D cost wAn(μ)/�n for innovation in sector-n. Therefore, free entry intoR&D in each sector requires that

wA1(μ)

θ≥ V1, equality holds whenever z1 > 0. (13)

wA2(μ)

1 − θ≥ V1, equality holds whenever z2 > 0. (14)

3.5 Labor market

In the economy, the labor supply L is allocated between production and R&D; there-fore, the labor market clearing condition is

L = θχ1(μ)

w+ (1 − θ)

χ2(μ)

w+ A1(μ) · z1 + A2(μ) · z2. (15)

3.6 Equilibrium

At first, we derive the condition that the fractions of sector-1 and sector-2 are constantover time. A monopolist in sector-1 moves into sector-2 with a constant probability �.On the other hand, a firm in sector-2 is replaced by a new incumbent in sector-1 with aprobability z2. Then, the instantaneous change of θ is presented as θ = (1−θ)z2 −�θ .Therefore, in the steady state, the following equation holds:

θ = z2

z2 + �. (16)

There are two types of equilibrium in the model.13 The first case is that all R&D con-centrate in sector-2, z1 = 0 and z2 > 0. Recall that A1 ≥ A2 necessarily holds. If theinitial number of sector-2 is sufficiently large, potential firms target only the industriesin sector-2 because the R&D productivity is high. Although larger z2 decreases the

13 The model does not have third case in which z1 > 0 and z2 = 0 are satisfied. In this case, A1/θ <

A2/(1 − θ) initially holds. However, some industries in sector-1 continuously move to sector-2 due toinformation leakage, and θ gradually decreases until A1/θ = A2/(1 − θ) holds.

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(1 − θ), the equilibrium of this case becomes stable when � is sufficiently large. Inthis case, next equation holds in the equilibrium:

A1

θ>

A2

1 − θ. (17)

The second case is that innovation simultaneously occurs in two sectors, z1 > 0 andz2 > 0. In this case, the R&D productivity across the sector is the same, and innovatorsare indifferent with regard to the sector. Therefore, the next equation holds:

A1

θ= A2

1 − θ. (18)

Once the long-run equilibrium is determined, we can calculate the growth rate of theconsumption index C as below:

g∗ = [θ z1 + (1 − θ)z2] ln λ. (19)

4 Simulation

This section examines the growth effects of strengthening patent protection (δ ↓).Because the equilibrium in the model is very complex to examine analytically, I assumethat there exists a trajectory to the steady state. We then analyze the policy effects,using a numerical method. The existence and uniqueness of a steady state in thissimulation are numerically shown in the Appendix.

4.1 R&D concentration: z1 = 0 and z2 > 0

First, we consider a case where all R&D is concentrated in sector-2 and derive therelationship between δ and the growth rate, given high, medium, and low leakage rates.The simulation uses the following parameters: L = 4, λ = 1.2, ρ = 0.03, A = 2,and γ = 1/4.14 When the leakage probability is sufficiently high, (17) holds, andequilibrium in R&D concentration case is attained. The simulation uses � = 0.35,� = 0.45, and � = 0.8, and we denote each case by “L”, “M”, and “H”, respectively.The numerical results are shown in Figs. 3 and 4. Figure 3 shows that the growth effectis ambiguous and varies across the 3 cases. The results are summarized as follows:

Numerical Result 1 Strengthening patent protection (lowering δ),

(i) reduces the growth rate when the leakage rate is low,(ii) increases the growth rate when the leakage rate is high,

(iii) has unclear growth effects, a U-shaped relationship between patent protectionand growth, when the leakage rate is middle.

14 The results presented in this section remain robust to parameter values not employed here. For example,when we assume small L or large A, by setting a low leakage rate, we still obtain three different patternsof relationship between the growth rate and the strength of patent protection.

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Fig. 3 Growth rate and the patent protection. Each curve becomes horizontal under weak patent protectionbecause firms then depend wholly on trade secrets

Interpretation

In this case, as shown in (19), the growth rate is influenced by both of (1 − θ) and z2.However, as shown in Panel (a) of Fig. 4, the relationship between z2 and δ determinesthe growth effect shown in Fig. 3. Therefore, to interpret this result, we focus only onthe effect on the innovation rate.

Before proceeding to the interpretation of the growth effect, we confirm the impor-tant results represented in Fig. 4 to discuss the mechanism more clearly. As depicted inPanel (b) of Fig. 4, stronger patent protection or a higher leakage rate leads innovatorsto employ patents rather than secrets.15 Moreover, strengthening patent policy (δ ↓)has two opposing effects on the incentives of innovators. The first effect is the “R&Dinefficiency effect”, which discourages innovation. When δ is low, potential R&D firmsobtain only limited information on existing technologies. Then, as depicted in Panel(c) of Fig. 4, the costs of R&D rises as δ falls, impeding R&D investment. The secondeffect is the “cost advantage effect”, which accelerates innovation. When δ is low,imitators have only limited information regarding inventions, so that the cost advan-tages of the monopolists increase. Panel (f) of Fig. 4 indicates that lower δ necessarilydecreases the productivity of imitators in sector-2 (χ2 ↓). Monopolists can then earnhigh profits, as their cost advantages enable them to charge high prices in stage-2.Panel (g) of Fig. 4 also shows that strong patent protection always increases firm value(V1). After all, these opposing effects account for the full impact of stronger patentprotection on innovation. These results can be summarized as follows:

Numerical Result 2 Stronger patent protection (lower δ) and a higher leakage rate oftrade secret (higher �) always increases a firm’s patenting propensity (μ). In addition,strengthening patent protection (δ ↓) increases both of R&D inefficiency (A2) andfirm value (V1).

15 We can derive this result analytically from (11) if we ignore the indirect effect on z2.

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Economic growth under two forms

(a) (b)

(c) (d)

(f)(e)

(g)

Fig. 4 Other variables and the patent protection

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Fig. 5 Protected area andunprotected area in stage-1

(a) (b)

The strength of the cost advantage effect is very important in understanding differ-ences in the growth effects. Panel (g) of Fig. 4 indicates that the strength of the costadvantage effect varies across the 3 cases, H, M, and L. In Case H, firm value dramati-cally increases as δ falls, relative to the other cases. When � is high, incumbents protectmany parts of an invention through patenting because trade secrets provide relativelyweak protection. The incumbent can then conceal a significant amount of informationinvolved in the invention and earn high profits. In contrast, in Case L, innovators pro-tect many parts of inventions through trade secrets. In this case, strengthening patentprotection (δ ↓) cannot increase the protected parts as effectively as in Case H, asdepicted in Panels (e) and (f) of Fig. 4. Therefore, lowering δ has only limited effectson the increase in V1. Figure 5 illustrates this mechanism. Initial patented parts aredepicted in regions A, B, and C, and secret parts are depicted in regions D, E, and F inboth panels of Fig. 5. When the government increases the strength of patent protection(δ → δ′), firms increase the fraction of patented parts (μ → μ′). The additional pro-tected parts are represented by the surface of B − E . Clearly, the fraction of protectedparts is relatively large when the initial μ is high. Consequently, we obtain followingresult:

Numerical Result 3 The higher is a firm’s patenting propensity (μ), the greater isthe cost advantage effect (the size of increase of V1) of strengthening patent protection(lowering δ).

In Case H, strengthening patent protection can increase the growth rate because thecost advantage effect is relatively strong, dominating the R&D inefficiency effect. InCase L, conversely, strengthening patent protection negatively affects the innovationrate because the cost advantage effect is weak and dominated by the R&D inefficiencyeffect. In Case M, the effect of the policy on the innovation rate is ambiguous. We caninterpret this result as follows: When patent protection is initially weak, innovators donot heavily depend on patent protection. In this case, strengthening patent protectionhas a very small positive effect on a firm’s profits and also decreases the innovation rate,as in Case L. However, when the level of patent protection exceeds a critical value, suchthat innovators are sufficiently dependent on patents, stronger patent protection candramatically increase profits, as shown in Panel (g) of Fig. 4. Consequently, because thecost advantage effect belatedly becomes strong, the relationship between the growthrate and δ is U-shaped. Put differently, the critical value is extremely large in CaseL; therefore, the cost advantage effect cannot dominate the R&D inefficiency effect,even if patent protection is very strong.

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(a) (b)

Fig. 6 Innovation rates and the patent protection

In addition, Fig. 3 also indicates that lowering the leakage rate of the trade secretsalways enhances the economic growth rate under a constant δ. This result is naturalbecause lowering the leakage rate always increases firm value and decreases R&Dinefficiency, as shown in Fig. 4.16 When the leakage rate is low, firms depend on tradesecrets rather than patents, and the amount of unprotected information in stage-2 isvery large. Because all R&D is concentrated in sector-2, this necessarily stimulatesthe incentive to innovate.

4.2 R&D in both sectors: z1 > 0 and z2 > 0

In this case, unlike in the previous case, θ = A1/(A1 + A2) holds, and innovationoccurs in both sectors. By using this equation and (16), we can obtain z2 in the steadystate. Then, from (1)–(5) and (10)–(15), we can also solve for z1 in the steady state.The simulation uses the following parameters: L = 4, λ = 1.2, ρ = 0.03, A = 2,and γ = 1/10. The equilibrium in this case requires a sufficiently small � becausethere is no innovation in sector-1 under large � as in the previous case. Therefore, thesimulation uses � = 0.02 (Case LL), � = 0.05 (Case LM), and � = 0.18 (Case LH).The results, shown in Figs. 6 and 7, are summarized as follows:

Numerical Result 4 When R&D occurs in both sectors, strengthening patent protec-tion (lowering δ)

(i) always decreases the innovation rate in sector-2,(ii) always decreases the innovation rate in sector-1 when the leakage rate is

extremely low,(iii) has ambiguous effects on the innovation rate in sector-1 when the leakage rate is

high, and(iv) always decreases the growth rate when the leakage rate is low.

16 Strictly speaking, lowering the leakage rate also decreases the number of firms in sector-2, whichdiscourages innovation in that sector. However, this effect is numerically small, as shown in Panel (d) ofFig. 4.

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Fig. 7 Growth rate and the patent protection

First, we discuss the effect of strengthening patent protection (δ ↓) on the innovationrate in each sector (z1 and z2). As shown in Panel (b) of Fig. 6, z2 decreases through alower δ in all cases. As in the R&D concentration case, Panel (d) of Fig. 8 indicates thatR&D inefficiency in sector-2 necessarily increases when δ falls. Panel (f) of Fig. 8shows that there is a cost advantage effect in this case; however, the effect is notstrong because firms mainly depend on trade secrets under a low leakage probability.Therefore, the R&D inefficiency effect always dominates the cost advantage effect inthis case. Consequently, strengthening patent protection cannot enhance innovation insector-2.

On the other hand, the effect of lowering δ on z1 is ambiguous. Panel (a) of Fig. 6shows a weak U-shaped relationship between them in Cases LM and LH, while in CaseLL, z1 necessarily decreases through a lower δ. Unlike A2, as shown in Panel (c) ofFig. 8, the effect of lowering δ on A1 is very small. This indicates that, in this case, theR&D inefficiency effect is not strong and might be dominated by the cost advantageeffect. 17 As discussed in the R&D concentration case, the lower is the leakage rate,the stronger patent protection is required for the cost advantage effect to becomesignificant. To understand this mechanism again, let us examine Panel (g) of Fig. 8. Inall cases, the relationship between market competitiveness and the strength of patentprotection is an inverted U shape. However, the critical value at which strengtheningpatent protection leads to a decrease in χ1 differs across the 3 cases, with the criticalvalue of δ in Case LL smaller than in the other cases. Moreover, from Numerical Result3, the cost advantage effect is initially weak in Case LL. Therefore, the cost advantageeffect cannot dominate the R&D inefficiency effect, even if patent protection is verystrong. Conversely, in Cases LH and LM, strengthening patent protection can enhancethe innovation rate in sector-1 (z1) when δ is sufficiently low.

17 Recall that lowering δ has a limited effect on the amount of protected information (equal to B − E inFig. 5) when � is sufficiently small because it simultaneously induces innovators to seek protection throughpatenting. Therefore, the negative effect on R&D inefficiency (A1) is mitigated. This tendency is moresignificant when R&D occurs in both sectors because � is extremely low in this case.

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Economic growth under two forms

(a) (b)

(c) (d)

(f)(e)

(g) (h)

Fig. 8 Other variables and the patent protection

Next, we discuss the growth effects of the strengthening patent protection. Unlikein the previous case, the growth rate is determined not only by z2 and θ but also by z1.As shown in Fig. 7, a lower δ primarily decreases the growth rate in all cases becausethe negative effect on z2 is too strong and directly decreases the growth rate. As notedabove, lowering δ drastically increases R&D inefficiency in sector-2 but has limitedeffects on R&D inefficiency in sector-1. This asymmetric effect lowers the relativeimpact of z1 versus z2 on the growth rate. The result of the growth-reducing effect isquite similar in Case L in the R&D concentration case, but it is natural because theleakage rate is extremely low in this two-sector R&D case. Therefore, we can viewthe result as an extension of Case L. In Case LH, z1 is increased by lowering δ, whichhas a growth-enhancing effect. However, sector-1 simultaneously narrows through areduction in z2 because θ is decreased through (16). This mitigates the positive effectof z1, and the growth rate remains unchanged, even if δ is close to zero.

Figure 6 also shows that the R&D-intensive sector differs between Case LL andCase LH. While many firms engage in R&D in sector-1 in case LL, almost all inno-

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vative activities concentrate into sector-2 in Case LH. The logic is simple. When �

is sufficiently small, the fraction of sector-1 (θ ) is relatively large, as shown in Panel(a) of Fig. 8. This reduces R&D costs in sector-1 (A1/θ ↓), and it stimulates theinnovation in that sector. Conversely, in Case LH, a smaller θ raises R&D costs insector-1, and innovation is discouraged. Moreover, Fig. 6 shows that a lower leakagerate decreases the innovation rate in sector-2. This is completely different from theR&D concentration case, where a smaller � always increases z2. In this case, firmvalue is small when the leakage rate is low, as shown in Panel (f) of Fig. 8. Unlike inthe previous case, the firm in this case may be replaced by another firm before tradesecrets are leaked because innovation also occurs in sector-1. As noted above, a lowerleakage rate directly increases the fraction of sector-1 (θ ), and this stimulates inno-vation in that sector. This result implies that the expected survival time is relativelyshort when the leakage rate is low, which reduces firm value. As a result, through thenegative impact on firm value, a lower leakage rate decreases the innovation rate insector-2.18

4.3 Welfare effect

We now analyze the welfare effects of strengthening patent protection in the R&Dconcentration case. From the lifetime utility function, we can calculate total discountedconsumption over time in the steady state:

W =∞∫

0

e−ρ(τ−t) [θ

(g∗τ + ln χ1 − ln w

) + (1 − θ)(g∗τ + ln χ2 − ln w

)]dτ

= g∗/ρ2︸ ︷︷ ︸

quality effect

+ [θ ln χ1 + (1 − θ) ln χ2 − ln w] /ρ︸ ︷︷ ︸price effect

. (20)

The first term on the RHS of (20) reflects the quality improvement effect, while thesecond term reflects the price effect.

Table 1 shows that strengthening patent protection has differing effects on theseterms. As discussed above, a smaller δ increases the growth rate in Case H anddecreases in Case L. This effect directly influences welfare through the qualityimprovement term on the RHS of (20). On the other hand, strengthening patent pro-tection negatively affects welfare through a high markup. As illustrated in Panel (f)of Fig. 4, stronger patent protection decreases competitiveness in sector-2 (χ2 ↓), andfirms charge higher prices. The effect on χ1 is ambiguous, but this does not signifi-cantly impact the price term when the leakage rate is high because θ , the coefficientof χ1, is relatively small in this case. However, when the leakage rate is small, theeffect of lowering δ on the price term is not monotonic, due to the ambiguous effecton χ1. In the simulation, the welfare effect exhibits a pattern nearly identical to that of

18 Strictly speaking, the lower leakage rate decreases R&D inefficiency in sector-2, which encourages theinnovation in sector-2. However, this effect is mitigated by a reduction in the fraction of sector-2, as shownin Panel (d) of Fig. 8. Consequently, the lower leakage rate always decreases the innovation rate in sector-2.

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Economic growth under two forms

Table 1 Welfare effect

δ Case L (� = 0.35) Case H (� = 0.8)

0.01 0.2 0.4 0.6 0.01 0.2 0.4 0.6

Quality term 27.82 27.89 29.06 30.75 26.02 21.29 15.40 8.08

Price term 43.42 43.76 43.89 43.79 44.13 44.85 45.43 45.84

Welfare 71.24 71.66 72.95 74.54 70.15 66.14 60.83 53.92

δ Case M (� = 0.45)

0.01 0.1 0.2 0.3 0.4 0.5 0.6

Quality term 27.66 26.86 26.05 25.31 24.78 24.46 24.78

Price term 43.74 43.99 44.19 44.37 44.54 44.61 44.65

Welfare 71.40 70.85 70.23 69.68 69.32 69.07 69.44

the growth effect. The different patterns (upward-sloping, downward-sloping, and U-shaped) are preserved, as shown in Table 1. This implies that the quality improvementhas strong effects on welfare.19 In this case, the strengthening patent protection doesnot strongly decrease χ2 because firms do not perfectly depend on patent protection(μ < 1), even under the strongest patent protection (δ = 0), as shown in Panel (b)in Fig. 4. In addition, conversely, the strengthening patent protection may increaseχ1 because firms may disclose substantial information by applying for many patents.Therefore, the price effect is not strong and is always dominated by the quality effect.The above discussion also holds when R&D occurs in both sectors. As depicted inPanel (b) in Fig. 8, the welfare effect is nearly identical to the growth effect. Conse-quently, even in terms of welfare, policy makers should be mindful of the leakage ratein determining patent policy.

4.4 Policy implications and empirical validity

The model shows that the leakage risk of secrecy determines whether strengtheningpatent protection enhances growth and welfare. The results indicate that policy makersshould consider the relative importance of patenting versus trade secret for actual firms.

We can interpret leakage risk as the strength of protection of trade secrets. Thesimulation in the R&D concentration case shows that, for a given strength of patentprotection, a lower probability of leakage enhances innovation. This result would beconsistent with the findings of Png (2012) that enactment of trade secret laws in theU.S. has increased R&D. In this case, the model suggests that policy makers should

19 This result does not depend on the parameter settings. For example, there is an anticipation that λ = 1.2is a very crucial parameter setting for the result, and under smaller λ, the welfare implications may differfrom those of the growth effect. According to Sener (2006), the size of the quality improvement (λ) isalso the size of the markup, which is estimated to be between 1.05 and 1.4. However, under very small λ

(� 1.05), the innovation rate falls to zero because the value of innovation is too small. This is a nonsensicalresult.

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K. Suzuki

strengthen protections of trade secrets for as long as possible. However, as shown inthe model, the growth effect of strengthening patent protection becomes negative whenthe leakage rate is sufficiently low. Therefore, in the IPR policy mix, policy makersshould consider the interaction between the two forms of IPR protection.

In fact, the expected duration of secrecy may largely relate to the specific featuresof products (e.g., the difficulty of reverse-engineering) rather than the environmentof trade secrets law. For example, Naghavi et al. (2014) found that the level of com-plexity of a good can provide a shield against imitation and thus mitigate the relativeimportance of patent protection. Taking into account these ideas, the results in thepresent model suggest that patent protection should be strengthened in industries inwhich the components of products can easily be analyzed by other firms. How validis this implication? To illustrate, pharmaceuticals are generally regarded as a typicalexample of this type of industry because the costs of innovation are extremely high,while the costs of imitation are low. In an earlier study, Mansfield (1986) found that, forfirms in the pharmaceutical and chemical industries, which are relatively dependenton patents compared with firms in other industries, the effect of the patent system oncommercial introduction of inventions is very substantial, while it is minimal in otherindustries. Recently, Allred and Park (2007b) also showed that firm-level innovationin the chemical and scientific instruments industries, in which inventions are easilyimitated, responded positively to the level of patent rights. Thus, evidence supportsthe plausibility of the implications of the present model. Although these results arehighly intuitive, existing theory largely fails to account for them.

5 Conclusion

I extended the quality-ladder model of endogenous growth by considering two formsof IPR protection and a choice problem between them. The results show that theleakage risk of trade secrets determines whether the growth effect of strengtheningpatent protection is positive or negative. In the model, the degree of a firm’s depen-dence on patent protection, which is affected by the leakage rate of trade secrets,determines the extent of the impact of strengthening patent protection on firm value.When the leakage risk is low, firms do not depend on patent protection, and therefore,the effect of strengthening patent protection on innovators’ profits is very limited.In this case, strong patent protection negatively affects economic growth. In otherwords, when trade secrets provide relatively strong protection for innovators, patentprotection should be weak. Conversely, when the leakage risk is high, firms protecttheir inventions through patenting, and strengthening patent protection dramaticallyincreases firm profits. In this case, strengthening patent protection enhances growth.Consequently, differences in leakage rate generate the opposing growth effects. Inaddition, for a middle leakage probability, the relationship between economic growthand patent protection is represented by a U-shaped curve. In this case, policy makersshould consider the current strength of patent protection.

In this paper, the leakage probability is regarded as an exogenous parameter. Asan extension, we can consider the case where the leakage probability is endogenouslydetermined in the model. For example, leakage probability plausibly depends on the

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volume of trade secrets. If a firm has many trade secrets, it may be difficult for thefirm to secure all of them. Alternatively, using the leakage mechanism as a means tospy on or reverse-engineer an innovation may be another way to endogenize leakageprobability. However, whatever extensions are considered, the model presented in thispaper can serve as a starting point for the introduction of two forms of IPR protectionin a DGE model.

Acknowledgments I would like to thank Ryo Horii, Akiomi Kitagawa, Koki Oikawa, Yunfang Hu,numerous people who commented on earlier versions of the paper in the 2012 Japan Economic AssociationSpring Meeting at Hokkaido University, attendees at the 2013 Asian Meeting of Econometric Society inSingapore, and three anonymous referees for their helpful comments and suggestions on the manuscripts.This study was financially supported by Grant-in-Aid for Japan Society for the Promotion of Science (JSPS)Fellows (No.25-10619). Of course, all remaining errors are my own.

Appendix

The existence and uniqueness of the steady-state

Using the first-order condition, the free-entry condition and the labor market clearingcondition, we obtain a following function:

θ = V1(μ(z2)) [L − z2 A2(μ(z2))] − χ2 A2(μ(z2))

A2(μ(z2)) [χ1(μ(z2)) − χ2(μ(z2))] + V1(μ(z2)) (L − z2 A2(μ(z2))). (21)

The RHS of (21) is a function of z2. The steady state (θ∗, z∗2) in the R&D concentration

case can be calculated by solving (16) and (21). Figure 9 shows that the steady stateexists under the parameters used in the simulation. The upward-sloping curve in each

(a) (b)

(c)

Fig. 9 The Steady state in R&D concentration case. The x-axis denotes the innovation rate in sector-2 (z2)and the y-axis is the number of sector-1 (θ )

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K. Suzuki

panel is the RHS of (16), and the downward-sloping curves are the RHS of (21) underδL = 0.01, δM = 0.3 and δH = 0.6, respectively.

Next, we consider the case where R&D occurs in both sectors. Rewriting (18), weobtain:

θ = A − δμ(z2)

2 A − 1 + (1 − 2δ)μ(z2). (22)

This equation and (16) determine z2 in the steady state. The upward-sloping curvein the left-hand side of each panel of Fig. 10 is the RHS of (16), and the downward-sloping curve is the RHS of (22) under a given δ, using δL L = 0.01, δL M = 0.15 andδL H = 0.3.

(a)

(b)

(c)

Fig. 10 The determination of z∗1 and z∗

2

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Economic growth under two forms

Once z∗2 is determined, μ, A1, A2, χ1 and χ2 are determined. Finally, we obtain z1

in equilibrium through the following equation, which is derived from the free-entrycondition and the labor market clearing condition.

A1χ1

V1(z1, μ(z∗2))

+ A2χ2

V1(z1, μ(z∗2))

+ A1z1 + A2z∗2 = L . (23)

The right-hand side in each panel of Fig. 10 shows that z∗1 is determined so as to satisfy

the labor market clearing condition.

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Allred B, Park W (2007b) The influence of patent protection on firm innovation investment in manufacturingindustries. J Int Manag 13:91–109

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of multinational firms. Canad J Econ, forthcomingOttoz E, Cugno F (2008) Patent-secret mix in complex product firms. Am Law Econ Rev 10:142–158Park W (2008) International patent protection: 1960–2005. Res Policy 37:761–766Png I (2012) Law and innovation: evidence from state trade secrets laws. Working paperSener F (2006) Intellectual property rights and rent protection in a North–South product-cycle model.

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