- Email: [email protected]
Intellectual property, research intensity, and scale effect
Journal of Business Research 69 (2016) 2297–2301
Contents lists available at ScienceDirect
Journal of Business Research
Intellectual property, research intensity, and scale effect☆ Chu-Ping Lo ⁎ Department of Agricultural, National Taiwan University, Economics, No. 1, Section 4, Roosevelt Rd, Da'an District, Taipei City, Taiwan 10617
a r t i c l e
i n f o
Article history: Received 1 September 2015 Received in revised form 1 October 2015 Accepted 1 November 2015 Available online 22 December 2015 Keywords: Trade Technology Research intensity Business services
a b s t r a c t This study revisits a multi-country Ricardian model with a continuum of goods by incorporating the “standingon-shoulder” and “stepping-on-toes” effects into technology-accumulated formation to allow externalities of both knowledge spillovers and duplication of research efforts. Being more in harmony with real practice, and even though all the merits of the trade model remain valid, this study demonstrates the scale effect in research intensity: the larger a country is, the greater the country's research intensity is. © 2015 Elsevier Inc. All rights reserved.
1. Introduction Using a multi-country Ricardian model with a continuum of goods, Eaton and Kortum's (2001) trade model shows that a country's research intensities are invariant to the size of the country, whereas all countries share a common research intensity (relative to the population growth rate). Here, the ratio of researchers in total employment measures the research intensity in a country. However, in real practice, the research intensity varies substantially across countries, even among OECD countries. Empirically, Lo and Yang (2015) use a panel dataset for 64 countries over the period of 1996–2009 to show that the country's size matters: the larger the country is, the greater its research intensity is. The scale also matters in firm-level research activities. Many studies suggest that large size firms tend to be more innovative, because they can use more resources and employ a broad group of researchers (Cohen & Klepper, 1996; Kafouros, 2005; Kafouros, 2006; Kotabe, Srinivasan, & Aulakh, 2002; Lichtenberg & Siegel, 1991). Thus, research activities are more efficient in translating scientific knowledge into new products in large firms than in smaller firms (Mansfield, 1968). Lin and Lee (2006) also argue that research intensity and commercialization of knowledge assets are complementary in enhancing firm performance. Generally, large firms have scale advantages in using this commercialization. ☆ The author is grateful to contributions from Fuhmei Wang, University of Cheng Kung, and Su-Ying Hsu, Southern Taiwan University of Science and Technology for their careful reading and suggestions on revising this essay. The author thanks the “Academic Exchange and Cooperation Project” between the Top University Strategic Alliance (Taiwan, R.O.C.) and the University of California, Berkeley (U.S.A.) and by the National Science Council of Taiwan (NSC102-2410-H-002-010). ⁎ Tel.: +886 2 3366 2653. E-mail address: [email protected].
http://dx.doi.org/10.1016/j.jbusres.2015.12.045 0148-2963/© 2015 Elsevier Inc. All rights reserved.
For a country as a whole, Romer's growth model also implies a scale effect in the research intensity. Having the knowledge spillovers externality, the technology accumulated formation in Romer's (1990) growth model increases not only with the country's involved researchers but also the country's current technology stock, leading to the so-called “standing-on-shoulder” effect. The standing-on-shoulder effect also appears in firm-level data. Kafouros (2008) investigates the relationship between research activities and corporate performance and suggests that the returns to research activities for low-tech firms are significantly higher than those for technologically dynamic firms. Conversely, the simplification of the technology accumulated formation in Eaton and Kortum's trade model increases only with a country's researchers involved in R&D, thus neglecting the standing-on-shoulder effect. As a result, the scale effect disappears in Eaton and Kortum's (2001) trade model. In addition, the technology accumulated formation in Eaton and Kortum's (2001) trade model also neglects the stepping-on-toes effect, which is an externality that indicates duplication of research efforts. The stepping-on-toes effect is more likely when too many people engage in this process, and especially when bureaucracy takes place. The phenomenon appears in historical data. As Jones (1995) argues, research is an essential input to the production function of ideas. Although authors of the most variable ideas patent them, patents count may provide a simple measure of the technology stock. According to the patents issued, the technology stock increases from around 25,000 patents in 1900 to around 96,000 in 1991 in the U.S. This trend represents a four-fold increase in the last century. As for the inputs into the production of ideas (i.e., researchers), Jones (1995) documents that the number of scientists and engineers devoted to research activities increases from around 200,000 in 1950 to about one million in 1990 in the U.S. This rise also represents a four-fold increase, but during a forty-year
2298
C.-P. Lo / Journal of Business Research 69 (2016) 2297–2301
period. France, West Germany, and Japan presented a similar pattern. That is, the fact that the accumulation of technology (in the form of patents granted) increases at almost half rate (four-fold increase during the forty-year period vs. four-fold increase in a century) of researchers in the most advanced countries (e.g., the U.S., Japan, France, and Germany) provides evidence of the stepping-on-toes effect. To establish harmony in real practice, this study revisits Eaton and Kortum's (2001) trade model by simply incorporating the standingon-shoulder and stepping-on-toes effects into their technology accumulated formation to allow for externalities of both knowledge spillovers and duplication of research efforts. As a result, although all of the merits of Eaton and Kortum's (2001) trade model remain, this study demonstrates the scale effect in research intensity: the larger a country is, the greater is the country's research intensity. Section 2 redesigns Eaton and Kortum's (2001) model by adding the standing-on-shoulder effect to the technology accumulated formation. Section 3 demonstrates how a country's intellectual property protection affects the country's research intensity. Section 4 presents the concluding remarks. 2. The model Following Eaton and Kortum's (2001) probabilistic model, a firm from country i draws its productivity zi(ω) from a Fréchet distribution Fi(z) = e−Tiz−θ, in which the parameter θ reflects the amount of variation within the productivity distribution of a continuum of goods to govern the comparative advantages within this continuum. Eaton and t
Kortum (2001) presume T i ðtÞ ≡ ϕi ∫ 0 r i Li ðsÞds to denote the accumulated technology of country i that represents the absolute advantage of the country, in which ϕi denotes the research productivity of researchers and ri is country i’s research intensity. Firms in a country with a higher level of T tend to have a higher probability of drawing a more efficient productivity. This model includes two sectors in an N countries world, in which labor is the only factor of production and is in inelastic supply as Li, ∀i ∈ {1,.....N}. A firm in a country employs an idea from researchers to produce a variety of the final good. Labor is freely mobile between research and production sectors. The technology accumulated function in Eaton and Kortum's (2001) model is seemingly an oversimplified version of Romer's (1990) model that neglects the standing-on-shoulder effect. This study revisits Eaton and Kortum's (2001) probabilistic model by simply restoring the standing-on-shoulder effect. In addition, to be more realistic, the study also incorporates the stepping-on-toes effect into the mode, as Jones (1995) suggests. Similar to Romer's (1990) and Jones (1995) model, this research regulates the technology accumulated function as T_ i ðt Þ ≡ ϕi T i ðt Þλ ðr i Li ðt ÞÞη ;
ð1Þ
where 0 b η ≤1, which Jones names the stepping-on-toes effect, to indicate that the duplication of research efforts is more likely to occur when too many people engage into the research and especially when bureaucracy takes effect. Here, 0 b λ b 1 denotes the standing-onshoulder effect (Jones), capturing whether an economy has wellprotected intellectual property rights. Here, intellectual property refers to all the intangible assets resulting from research activities, including industrial patents, copyrighted works, software patents, and trademarks. Researchers widely acknowledge that a country government encourages innovation by ensuring optimal protection of intellectual property rights, because entrepreneurs assure that they will capture satisfactory private returns from the social returns that their innovations produce (Jones, 1995). With an enforceable legal system protecting patents and copyrights, entrepreneurs are more willing to invest in research activities and unveil their innovations in the form of patent applications, allowing all researchers to study freely the innovations the patent application describes. Protection of intellectual
property ends up encouraging knowledge spillovers, that is, the standing-on-shoulder effect increases with a greater λ. Romer presumes an extreme value λ = 1 (everyone freely applies all patents), whereas Eaton and Kortum presume another extreme as λ = 0 (no standing-on-shoulder effect). This study follows Jones to take the middle and presume 0 b λ b 1, which is the main assumption in this model. Both Romer (1990) and Eaton and Kortum (2001) presume the stepping-on-toes effect as η = 1, whereas Jones (1995) argues 0 b η b 1 because of historical evidence. This model also applies this assumption. In (1), the probability of the fraction of goods that country n buys from country i is time-invariant in equilibrium, implying that
_ TðtÞ TðtÞ
¼
η 1−λ g L ,
where gL is the population growth rate. With the solution of the differentiation equation in (1), the accumulated technology of country i is as 1 1−λ Z t T i ðt Þ ¼ ð1−λÞϕi ðr i Li ðsÞÞη ds 0 1 η ð1−λÞϕi 1−λ ¼ ðr i Li Þ1−λ : gL
ð2Þ
2.1. The utility function As in Eaton and Kortum (2001), the utility function of a representative consumer in each country is a Cobb–Douglas function across the continuum of final goods: Z U ¼ exp
1 0
ln yi ðωÞdω:
ci din , where The price of good ω in country n from country i is pin ðωÞ ¼ zðωÞ
din is the geographical barriers from country i to n. As in the Eaton and Kortum (2001, 2002) model, dii = 1 and din N 1 if n ≠ i. The geographical barriers also obey the triangle inequality: for any three countries i, k, and n, din ≤ dkndik. The goods in country n that come from country i have a price distribution Gin(p) = 1 − e− Ti(cidin)−θpθ. Therefore, the price distribution in country n is Gn ðpÞ ¼ 1− Π Ni¼1 ð1−Gin ðpÞ ¼ 1− N
θ
−θ
e−Φn p , in which Φn ≡ ∑ T i ðci din Þ
. With the Cobb–Douglas prefer-
i¼1
ences, the price index of the final goods in country n is: : P n ¼ eηe =θ Φ−1=θ n
ð3Þ
∞
where ηe ≡ −∫ 0 lnðxÞe−x dx is Euler's constant. The probability that country i is the cheapest source of a particular good exporting to country n is: −θ
T ðw d Þ ; πin ¼ XN i i in −θ T ðwk dkn Þ k¼1 k
ð4Þ
which also represents the fraction of goods that country n buys from i. 2.2. The research activities The third sector is the research sector. At a point of time t, a firm in country i employs an idea from researchers. Suppose that an idea has an efficiency z(ω) and that the idea is the best idea applied to a particular good ω.
C.-P. Lo / Journal of Business Research 69 (2016) 2297–2301
By letting Yin(t) represent the total exports from country i to n at time t, the total profits of i’s research sector around the world are
where ψ ≡
−ð1−λ−ηÞ η 1−λ 1−λ
where Yi(t) denotes the total expenditure of country i when trade is bal1 Y i ðtÞ anced. Note that the preferences are Cobb–Douglas, such that 1þθ represents the total profit attributed to the research activities, ∀i (see Appendix for the derivation and also in Eaton and Kortum's (2001) model). 2.3. Equilibrium in labor market
∀t;
ð6Þ
1 where ð1− 1þθ ÞY i is the total income in country i that goes to production workers and witLit(1 − ri) denotes the total wage income of these workers.
2.4. Equilibrium in goods markets The following expression thus gives the expected discounted value of an idea that succeeds in the world market at time t Z ∞ P ðsÞ bin ðm; sÞ 1 Y ðsÞds ϕi bin ð1; t Þ e−ρðs−t Þ i P i ðt Þ bin ðm; t Þ 1 þ θ in t n¼1 Z ∞ 1 Y ðt Þ ϕ i ¼ e−ðρ−gL =θÞðs−t Þ ds; 1 þ θ i T i ðt Þ t N X
ð7Þ
−1 ηg L
θ 1−λðs−tÞ is inflation, ∀i. Here, fully where ρ is a discount rate and PPii ðsÞ ðtÞ ¼ e N T_ −1 _ differentiating (3) with respect to t, one can obtain PP ¼ −1 θ ∑ πk T ¼ θ k¼1
ηgL 1−λ,
implying that
PðsÞ PðtÞ
−1 ηg L θ 1−λðs−tÞ
¼e
increases with the population growth. In
ri
¼ ψð1−r i Þ
. The
term bbii ðm;sÞ denotes the ðm;tÞ
probabil-
ity that the idea will still be the best by time s, given that such idea was ηg L
ðtÞ the best at time t, and bbii ðm;sÞ ¼ TT ii ðsÞ ¼ e−1−λðs−tÞ , ∀i. When the economy ðm;tÞ
An equilibrium research intensity exists in country i, r⁎i , as appears in Fig. 1. Note that, in the case of λ = 0 and η = 1, according to Eaton and gL Kortum's (2001) model as r i ¼ ρθ , the research intensity does not
3. Intellectual property The duplication externality associated with 0 b λ b 1 is the steppingon-toes effect. The parameter η measures the net effect of knowledge spillovers, and η N 0 represents the standing-on-shoulders effect. Empirically, Jones and Williams (1998) estimate the U.S. data of twelve manufacturing industries, covering the years 1961–1989, to determine a reasonable estimation of λ ≅ 0.48. Here, the calculation builds on the reasonable assumption that the TFP growth rate is 1.8% and the research intensity (share of R&D spending in GDP) is 2.9% in the U.S. Riddel and Schwer (2003) use the U.S. state-level data over the period 1989–1998 to determine that the standing-on-shoulder effect is about η ≅ 0.15 (see their Table 2). Although few empirical estimations on those externalities exist in the literature (Stokey, 1995), the study takes their estimation as given to obtain 0 b λ + η = 0.63 b 1. That is, the technology accumulation is increasing diminishingly with the research inputs as 0 b λ + η b 1. With 0 b λ + η b 1, the Eq. (8) implies that a large country (larger Li) tends to have a greater research intensity (Fig. 2). That is, in line with Romer's (1990) model, the scale matters in the research intensity. This idea is the main implication in this model. This model also shows that an increase in population growth leads to higher research intensity, and this argument is in line with the Eaton and Kortum's (2001) model (Fig. 3). To investigate how intellectual property affects a country's research −ð1−λ−ηÞ
¼ egL ðs−tÞ. The term ϕibin(1, t) in (7) is the instantaneous probability
of having at least one successful idea at time t from country i in market n. With the above conditions and equilibrium in (2), (6) and (7), one can obtain the net present value of a researcher in country i by discovering successful ideas at time t: 0 vi ðt Þ ¼
1
1 B C 1−λ −η 1−λ−η C ϕi Y i ðt Þ B 1 gL 1−λ B " !#C r 1−λ i Li B C −1 1 þ θ Li ðt Þ @ ð 1−λ Þϕ i 1−θ A ρ−gL 1−η 1−λ 0 1
1 B C 1−λ −η 1−λ−η B C 1−ri gL 1−λ C " ! # ¼ wi ϕi B r1−λ i Li B C ð1−λÞϕ −1 i @ A 1−θ ρ−g L 1−η 1−λ
1−λ−η
−η
¼ wi ψð1−ri ÞLi 1−λ r1−λ i ;
ð8Þ
η
intensity, the study first derives the change rate of Li 1−λ ri1−λ and ψ(1 − ri ) regarding the improvement in the intellectual property protection (i.e., an increase in λ), respectively. The equilibrium requires
Li ðsÞ is static, then YY ii ðsÞ ðtÞ ¼ Li ðtÞ. When trade is balanced for all countries, then Y i ðsÞ Y i ðtÞ
ð9Þ
depend on the size of the country.
With (5), the labor market equilibrium for production workers in country i is:
vi ðt Þ ¼
1
−1
ρ−gL ½1−ηð1−θ 1−λ Þ
ð5Þ Li
1 Y it ¼ wit Lit ð1−r i Þ; 1þθ
−1
ϕ1−λ ð1−λÞ1−λ gL 1−λ
equilibrium, vi = wi to equate the returns to labor across sectors, leading to
N X 1 1 Y in ðt Þ ¼ Y ðt Þ; 1 þ θ 1 þ θ i n¼1
1−
−λ
2299
Fig. 1. Research intensity in equilibrium.
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C.-P. Lo / Journal of Business Research 69 (2016) 2297–2301
Fig. 2. When labor size L increases. Fig. 4. When intellectual protection λ improves. −ð1−λ−ηÞ η 1−λ 1−λ
Li
ri
¼ ψð1−ri Þ, as Fig. 1 shows. Then, the study determines the −ð1−λ−ηÞ 1−λ
change rate of Li
−ð1−λ−ηÞ η 1−λ 1−λ
∂ ln Li
ri
∂λ
with respect to an increase in λ as
¼
−ð1−λ−ηÞ ð1−λÞ2
lnLi b 0;
In line with Pathak, Xavier-Oliveira, and Laplume (2013), a country's research intensity increases with the improvement in its intellectual property protection. 4. Concluding remarks
−ð1−λ−ηÞ η 1−λ 1−λ
r i shifts where 0 b λ + η b 1. Fig. 4 then illustrates that the curve Li downward substantially with an increase in the intellectual property protection (i.e., an increase in λ). On the other hand, the change rate of ψ is given with respect to an increase in λ as ∂ lnψ −1 ϒ; ¼ ∂λ ð1−λÞ2 −1
ηð1−θ Þ . The rate paramewhere ϒ ¼ ln ϕ þ ln ð1−λÞ þ η lnr i þ ρ−ggLþg ηð1−θ−1 Þ L
L
ters ϕ , λ , η , ri , gL are 0 b ϕ , λ , η , gL b 1, indicating that 0 N ln ϕ and 0 N ln (1− λ). Note further that parameter θ N N 1 (around 8 in Eaton & −1
ηð1−θ Þ Kortum, 2002), so that 1N ρ−ggLþg N0 . Consider the fact that ηð1−θ−1 Þ L
L
the research intensity in the world has a mean around 0.2% to feasibly ln ψ . In this case, the presume 1 N N ri, leading to 0 N ϒ such that 0b ∂ ∂λ curve ψ(1− ri) moves to the right with an increase in λ. As a result, as Fig. 4 illustrates, the research intensity increases with an increase in λ.
The study adds the standing-on-shoulder and standing-on-toes effects to Eaton and Kortum's (2001) trade model to allow externalities of the knowledge spillovers and duplication of research efforts in the technology accumulated formation. As a result, although all the merits of Eaton and Kortum's (2001) trade model remain, this model demonstrates the scale effect in research intensity: the larger a country is, the greater the country's research intensity is. This study also demonstrates that a country's research intensity increases with the country's population growth rate and the improvement in the country's intellectual property protection. However, this study excludes the recent observation that patents might stagnate and hold up innovation. This research also disallows international knowledge diffusion, which prevails in the real world (e.g., Huarng, Hui-Kuang, & Yu, 2015). Future research should consider these ideas. Appendix The following derivation comes directly from Eaton and Kortum (2001). An idea in a country draws from a Pareto distribution H i ðzÞ ¼ 1−z−θ :
ðA1Þ
A firm in country i employs an idea to produce a specific final good. The chance is that the idea is the best idea that leads to the least cost in production and commands a mark-up of at least m N 1 in country n as Z bin ðmÞ ¼
1
∞
1−Gn ðmci din =zÞdHi ðzÞ ≅
π in : T i mθ
ðA2Þ
The probability of a mark-up of at least m, given that the idea is a successful idea in country n is then bin ðmÞ ¼ m−θ ; bin ð1Þ
Fig. 3. Population growth and research intensity.
ðA3Þ
which implies that the markup that is conditional on the idea being the best idea follows a Pareto distribution with a parameter θ as H(θ) =1 − m−θ. The net profit share from producing the capital good is 1 − m−1,
C.-P. Lo / Journal of Business Research 69 (2016) 2297–2301
so that the expected share of the profits from the best idea in a market is as Z
∞ 1
1−m−1 dHðmÞ ¼
1 : 1þθ
ðA4Þ
References Cohen, W. M., & Klepper, S. (1996). Firm size and the nature of innovation within industries: The case of process and product R&D. The Review of Economics and Statistics, 78(2), 232–243. Eaton, J., & Kortum, S. S. (2001). Technology, trade, and growth: A unified framework. European Economic Review, 45, 742–755. Eaton, J., & Kortum, S. S. (2002). Technology, geography, and trade. Econometrica, 70(5), 1741–1779. Huarng, K. -H., Hui-Kuang, T., & Yu, W. L. (2015). Innovation and diffusion of high-tech products, services, and systems. Journal of Business Research, 68(11), 2223–2226. Jones, C. (1995). R&D-based models of economic growth. Journal of Political Economy, 103(4), 759–784. Jones, C., & Williams, J. (1998). Measuring the social return to R&D. The Quarterly Journal of Economics, 113(4), 1119–1135.
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Kafouros, M. I. (2005). R&D and productivity growth: Evidence from the UK. Economics of Innovation and New Technology, 14(6), 479–497. Kafouros, M. I. (2006). The impact of the Internet on R&D-efficiency: Theory and evidence. Technovation, 26(7), 827–835. Kafouros, M. I. (2008). Economic returns to industrial research. Journal of Business Research, 61(8), 868–876. Kotabe, M., Srinivasan, S. S., & Aulakh, P. S. (2002). Multinationality and firm performance: The moderating role of R&D and marketing capabilities. Journal of International Business Studies, 33(1), 79–97. Lichtenberg, F., & Siegel, D. (1991). The impact of R&D investment on productivity-new evidence using linked R&D-LRD data. Economic Inquiry, 29(2), 203. Lin, B. Y., & Lee, S. H. (2006). R&D intensity and commercialization orientation effects on financial performance. Journal of Business Research, 59(6), 679–685. Lo, C. P., & Yang, C. H. (2015). Business services, trade, and research intensity, working paper. Mansfield, E. (1968). Industrial research and technological innovation: An econometric analysis. Norton for the Cowles Foundation for Research in Economics: Yale University, New York. Pathak, S., Xavier-Oliveira, E., & Laplume, E. O. (2013). Influence of intellectual property, foreign investment, and technological adoption on technology entrepreneurship. Journal of Business Research, 66(10), 2090–2101. Riddel, M., & Schwer, R. K. (2003). Regional innovative capacity with endogenous employment: Empirical evidence from the U.S. The Review of Regional Studies, 33(1), 73–84. Romer, P. M. (1990). Endogenous technological change. Journal of Political Economy, 98(5), S71–S102. Stokey, N. (1995). R&D and economic growth. Review of Economic Studies, 62(3), 469–489.
Contents lists available at ScienceDirect
Journal of Business Research
Intellectual property, research intensity, and scale effect☆ Chu-Ping Lo ⁎ Department of Agricultural, National Taiwan University, Economics, No. 1, Section 4, Roosevelt Rd, Da'an District, Taipei City, Taiwan 10617
a r t i c l e
i n f o
Article history: Received 1 September 2015 Received in revised form 1 October 2015 Accepted 1 November 2015 Available online 22 December 2015 Keywords: Trade Technology Research intensity Business services
a b s t r a c t This study revisits a multi-country Ricardian model with a continuum of goods by incorporating the “standingon-shoulder” and “stepping-on-toes” effects into technology-accumulated formation to allow externalities of both knowledge spillovers and duplication of research efforts. Being more in harmony with real practice, and even though all the merits of the trade model remain valid, this study demonstrates the scale effect in research intensity: the larger a country is, the greater the country's research intensity is. © 2015 Elsevier Inc. All rights reserved.
1. Introduction Using a multi-country Ricardian model with a continuum of goods, Eaton and Kortum's (2001) trade model shows that a country's research intensities are invariant to the size of the country, whereas all countries share a common research intensity (relative to the population growth rate). Here, the ratio of researchers in total employment measures the research intensity in a country. However, in real practice, the research intensity varies substantially across countries, even among OECD countries. Empirically, Lo and Yang (2015) use a panel dataset for 64 countries over the period of 1996–2009 to show that the country's size matters: the larger the country is, the greater its research intensity is. The scale also matters in firm-level research activities. Many studies suggest that large size firms tend to be more innovative, because they can use more resources and employ a broad group of researchers (Cohen & Klepper, 1996; Kafouros, 2005; Kafouros, 2006; Kotabe, Srinivasan, & Aulakh, 2002; Lichtenberg & Siegel, 1991). Thus, research activities are more efficient in translating scientific knowledge into new products in large firms than in smaller firms (Mansfield, 1968). Lin and Lee (2006) also argue that research intensity and commercialization of knowledge assets are complementary in enhancing firm performance. Generally, large firms have scale advantages in using this commercialization. ☆ The author is grateful to contributions from Fuhmei Wang, University of Cheng Kung, and Su-Ying Hsu, Southern Taiwan University of Science and Technology for their careful reading and suggestions on revising this essay. The author thanks the “Academic Exchange and Cooperation Project” between the Top University Strategic Alliance (Taiwan, R.O.C.) and the University of California, Berkeley (U.S.A.) and by the National Science Council of Taiwan (NSC102-2410-H-002-010). ⁎ Tel.: +886 2 3366 2653. E-mail address: [email protected].
http://dx.doi.org/10.1016/j.jbusres.2015.12.045 0148-2963/© 2015 Elsevier Inc. All rights reserved.
For a country as a whole, Romer's growth model also implies a scale effect in the research intensity. Having the knowledge spillovers externality, the technology accumulated formation in Romer's (1990) growth model increases not only with the country's involved researchers but also the country's current technology stock, leading to the so-called “standing-on-shoulder” effect. The standing-on-shoulder effect also appears in firm-level data. Kafouros (2008) investigates the relationship between research activities and corporate performance and suggests that the returns to research activities for low-tech firms are significantly higher than those for technologically dynamic firms. Conversely, the simplification of the technology accumulated formation in Eaton and Kortum's trade model increases only with a country's researchers involved in R&D, thus neglecting the standing-on-shoulder effect. As a result, the scale effect disappears in Eaton and Kortum's (2001) trade model. In addition, the technology accumulated formation in Eaton and Kortum's (2001) trade model also neglects the stepping-on-toes effect, which is an externality that indicates duplication of research efforts. The stepping-on-toes effect is more likely when too many people engage in this process, and especially when bureaucracy takes place. The phenomenon appears in historical data. As Jones (1995) argues, research is an essential input to the production function of ideas. Although authors of the most variable ideas patent them, patents count may provide a simple measure of the technology stock. According to the patents issued, the technology stock increases from around 25,000 patents in 1900 to around 96,000 in 1991 in the U.S. This trend represents a four-fold increase in the last century. As for the inputs into the production of ideas (i.e., researchers), Jones (1995) documents that the number of scientists and engineers devoted to research activities increases from around 200,000 in 1950 to about one million in 1990 in the U.S. This rise also represents a four-fold increase, but during a forty-year
2298
C.-P. Lo / Journal of Business Research 69 (2016) 2297–2301
period. France, West Germany, and Japan presented a similar pattern. That is, the fact that the accumulation of technology (in the form of patents granted) increases at almost half rate (four-fold increase during the forty-year period vs. four-fold increase in a century) of researchers in the most advanced countries (e.g., the U.S., Japan, France, and Germany) provides evidence of the stepping-on-toes effect. To establish harmony in real practice, this study revisits Eaton and Kortum's (2001) trade model by simply incorporating the standingon-shoulder and stepping-on-toes effects into their technology accumulated formation to allow for externalities of both knowledge spillovers and duplication of research efforts. As a result, although all of the merits of Eaton and Kortum's (2001) trade model remain, this study demonstrates the scale effect in research intensity: the larger a country is, the greater is the country's research intensity. Section 2 redesigns Eaton and Kortum's (2001) model by adding the standing-on-shoulder effect to the technology accumulated formation. Section 3 demonstrates how a country's intellectual property protection affects the country's research intensity. Section 4 presents the concluding remarks. 2. The model Following Eaton and Kortum's (2001) probabilistic model, a firm from country i draws its productivity zi(ω) from a Fréchet distribution Fi(z) = e−Tiz−θ, in which the parameter θ reflects the amount of variation within the productivity distribution of a continuum of goods to govern the comparative advantages within this continuum. Eaton and t
Kortum (2001) presume T i ðtÞ ≡ ϕi ∫ 0 r i Li ðsÞds to denote the accumulated technology of country i that represents the absolute advantage of the country, in which ϕi denotes the research productivity of researchers and ri is country i’s research intensity. Firms in a country with a higher level of T tend to have a higher probability of drawing a more efficient productivity. This model includes two sectors in an N countries world, in which labor is the only factor of production and is in inelastic supply as Li, ∀i ∈ {1,.....N}. A firm in a country employs an idea from researchers to produce a variety of the final good. Labor is freely mobile between research and production sectors. The technology accumulated function in Eaton and Kortum's (2001) model is seemingly an oversimplified version of Romer's (1990) model that neglects the standing-on-shoulder effect. This study revisits Eaton and Kortum's (2001) probabilistic model by simply restoring the standing-on-shoulder effect. In addition, to be more realistic, the study also incorporates the stepping-on-toes effect into the mode, as Jones (1995) suggests. Similar to Romer's (1990) and Jones (1995) model, this research regulates the technology accumulated function as T_ i ðt Þ ≡ ϕi T i ðt Þλ ðr i Li ðt ÞÞη ;
ð1Þ
where 0 b η ≤1, which Jones names the stepping-on-toes effect, to indicate that the duplication of research efforts is more likely to occur when too many people engage into the research and especially when bureaucracy takes effect. Here, 0 b λ b 1 denotes the standing-onshoulder effect (Jones), capturing whether an economy has wellprotected intellectual property rights. Here, intellectual property refers to all the intangible assets resulting from research activities, including industrial patents, copyrighted works, software patents, and trademarks. Researchers widely acknowledge that a country government encourages innovation by ensuring optimal protection of intellectual property rights, because entrepreneurs assure that they will capture satisfactory private returns from the social returns that their innovations produce (Jones, 1995). With an enforceable legal system protecting patents and copyrights, entrepreneurs are more willing to invest in research activities and unveil their innovations in the form of patent applications, allowing all researchers to study freely the innovations the patent application describes. Protection of intellectual
property ends up encouraging knowledge spillovers, that is, the standing-on-shoulder effect increases with a greater λ. Romer presumes an extreme value λ = 1 (everyone freely applies all patents), whereas Eaton and Kortum presume another extreme as λ = 0 (no standing-on-shoulder effect). This study follows Jones to take the middle and presume 0 b λ b 1, which is the main assumption in this model. Both Romer (1990) and Eaton and Kortum (2001) presume the stepping-on-toes effect as η = 1, whereas Jones (1995) argues 0 b η b 1 because of historical evidence. This model also applies this assumption. In (1), the probability of the fraction of goods that country n buys from country i is time-invariant in equilibrium, implying that
_ TðtÞ TðtÞ
¼
η 1−λ g L ,
where gL is the population growth rate. With the solution of the differentiation equation in (1), the accumulated technology of country i is as 1 1−λ Z t T i ðt Þ ¼ ð1−λÞϕi ðr i Li ðsÞÞη ds 0 1 η ð1−λÞϕi 1−λ ¼ ðr i Li Þ1−λ : gL
ð2Þ
2.1. The utility function As in Eaton and Kortum (2001), the utility function of a representative consumer in each country is a Cobb–Douglas function across the continuum of final goods: Z U ¼ exp
1 0
ln yi ðωÞdω:
ci din , where The price of good ω in country n from country i is pin ðωÞ ¼ zðωÞ
din is the geographical barriers from country i to n. As in the Eaton and Kortum (2001, 2002) model, dii = 1 and din N 1 if n ≠ i. The geographical barriers also obey the triangle inequality: for any three countries i, k, and n, din ≤ dkndik. The goods in country n that come from country i have a price distribution Gin(p) = 1 − e− Ti(cidin)−θpθ. Therefore, the price distribution in country n is Gn ðpÞ ¼ 1− Π Ni¼1 ð1−Gin ðpÞ ¼ 1− N
θ
−θ
e−Φn p , in which Φn ≡ ∑ T i ðci din Þ
. With the Cobb–Douglas prefer-
i¼1
ences, the price index of the final goods in country n is: : P n ¼ eηe =θ Φ−1=θ n
ð3Þ
∞
where ηe ≡ −∫ 0 lnðxÞe−x dx is Euler's constant. The probability that country i is the cheapest source of a particular good exporting to country n is: −θ
T ðw d Þ ; πin ¼ XN i i in −θ T ðwk dkn Þ k¼1 k
ð4Þ
which also represents the fraction of goods that country n buys from i. 2.2. The research activities The third sector is the research sector. At a point of time t, a firm in country i employs an idea from researchers. Suppose that an idea has an efficiency z(ω) and that the idea is the best idea applied to a particular good ω.
C.-P. Lo / Journal of Business Research 69 (2016) 2297–2301
By letting Yin(t) represent the total exports from country i to n at time t, the total profits of i’s research sector around the world are
where ψ ≡
−ð1−λ−ηÞ η 1−λ 1−λ
where Yi(t) denotes the total expenditure of country i when trade is bal1 Y i ðtÞ anced. Note that the preferences are Cobb–Douglas, such that 1þθ represents the total profit attributed to the research activities, ∀i (see Appendix for the derivation and also in Eaton and Kortum's (2001) model). 2.3. Equilibrium in labor market
∀t;
ð6Þ
1 where ð1− 1þθ ÞY i is the total income in country i that goes to production workers and witLit(1 − ri) denotes the total wage income of these workers.
2.4. Equilibrium in goods markets The following expression thus gives the expected discounted value of an idea that succeeds in the world market at time t Z ∞ P ðsÞ bin ðm; sÞ 1 Y ðsÞds ϕi bin ð1; t Þ e−ρðs−t Þ i P i ðt Þ bin ðm; t Þ 1 þ θ in t n¼1 Z ∞ 1 Y ðt Þ ϕ i ¼ e−ðρ−gL =θÞðs−t Þ ds; 1 þ θ i T i ðt Þ t N X
ð7Þ
−1 ηg L
θ 1−λðs−tÞ is inflation, ∀i. Here, fully where ρ is a discount rate and PPii ðsÞ ðtÞ ¼ e N T_ −1 _ differentiating (3) with respect to t, one can obtain PP ¼ −1 θ ∑ πk T ¼ θ k¼1
ηgL 1−λ,
implying that
PðsÞ PðtÞ
−1 ηg L θ 1−λðs−tÞ
¼e
increases with the population growth. In
ri
¼ ψð1−r i Þ
. The
term bbii ðm;sÞ denotes the ðm;tÞ
probabil-
ity that the idea will still be the best by time s, given that such idea was ηg L
ðtÞ the best at time t, and bbii ðm;sÞ ¼ TT ii ðsÞ ¼ e−1−λðs−tÞ , ∀i. When the economy ðm;tÞ
An equilibrium research intensity exists in country i, r⁎i , as appears in Fig. 1. Note that, in the case of λ = 0 and η = 1, according to Eaton and gL Kortum's (2001) model as r i ¼ ρθ , the research intensity does not
3. Intellectual property The duplication externality associated with 0 b λ b 1 is the steppingon-toes effect. The parameter η measures the net effect of knowledge spillovers, and η N 0 represents the standing-on-shoulders effect. Empirically, Jones and Williams (1998) estimate the U.S. data of twelve manufacturing industries, covering the years 1961–1989, to determine a reasonable estimation of λ ≅ 0.48. Here, the calculation builds on the reasonable assumption that the TFP growth rate is 1.8% and the research intensity (share of R&D spending in GDP) is 2.9% in the U.S. Riddel and Schwer (2003) use the U.S. state-level data over the period 1989–1998 to determine that the standing-on-shoulder effect is about η ≅ 0.15 (see their Table 2). Although few empirical estimations on those externalities exist in the literature (Stokey, 1995), the study takes their estimation as given to obtain 0 b λ + η = 0.63 b 1. That is, the technology accumulation is increasing diminishingly with the research inputs as 0 b λ + η b 1. With 0 b λ + η b 1, the Eq. (8) implies that a large country (larger Li) tends to have a greater research intensity (Fig. 2). That is, in line with Romer's (1990) model, the scale matters in the research intensity. This idea is the main implication in this model. This model also shows that an increase in population growth leads to higher research intensity, and this argument is in line with the Eaton and Kortum's (2001) model (Fig. 3). To investigate how intellectual property affects a country's research −ð1−λ−ηÞ
¼ egL ðs−tÞ. The term ϕibin(1, t) in (7) is the instantaneous probability
of having at least one successful idea at time t from country i in market n. With the above conditions and equilibrium in (2), (6) and (7), one can obtain the net present value of a researcher in country i by discovering successful ideas at time t: 0 vi ðt Þ ¼
1
1 B C 1−λ −η 1−λ−η C ϕi Y i ðt Þ B 1 gL 1−λ B " !#C r 1−λ i Li B C −1 1 þ θ Li ðt Þ @ ð 1−λ Þϕ i 1−θ A ρ−gL 1−η 1−λ 0 1
1 B C 1−λ −η 1−λ−η B C 1−ri gL 1−λ C " ! # ¼ wi ϕi B r1−λ i Li B C ð1−λÞϕ −1 i @ A 1−θ ρ−g L 1−η 1−λ
1−λ−η
−η
¼ wi ψð1−ri ÞLi 1−λ r1−λ i ;
ð8Þ
η
intensity, the study first derives the change rate of Li 1−λ ri1−λ and ψ(1 − ri ) regarding the improvement in the intellectual property protection (i.e., an increase in λ), respectively. The equilibrium requires
Li ðsÞ is static, then YY ii ðsÞ ðtÞ ¼ Li ðtÞ. When trade is balanced for all countries, then Y i ðsÞ Y i ðtÞ
ð9Þ
depend on the size of the country.
With (5), the labor market equilibrium for production workers in country i is:
vi ðt Þ ¼
1
−1
ρ−gL ½1−ηð1−θ 1−λ Þ
ð5Þ Li
1 Y it ¼ wit Lit ð1−r i Þ; 1þθ
−1
ϕ1−λ ð1−λÞ1−λ gL 1−λ
equilibrium, vi = wi to equate the returns to labor across sectors, leading to
N X 1 1 Y in ðt Þ ¼ Y ðt Þ; 1 þ θ 1 þ θ i n¼1
1−
−λ
2299
Fig. 1. Research intensity in equilibrium.
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C.-P. Lo / Journal of Business Research 69 (2016) 2297–2301
Fig. 2. When labor size L increases. Fig. 4. When intellectual protection λ improves. −ð1−λ−ηÞ η 1−λ 1−λ
Li
ri
¼ ψð1−ri Þ, as Fig. 1 shows. Then, the study determines the −ð1−λ−ηÞ 1−λ
change rate of Li
−ð1−λ−ηÞ η 1−λ 1−λ
∂ ln Li
ri
∂λ
with respect to an increase in λ as
¼
−ð1−λ−ηÞ ð1−λÞ2
lnLi b 0;
In line with Pathak, Xavier-Oliveira, and Laplume (2013), a country's research intensity increases with the improvement in its intellectual property protection. 4. Concluding remarks
−ð1−λ−ηÞ η 1−λ 1−λ
r i shifts where 0 b λ + η b 1. Fig. 4 then illustrates that the curve Li downward substantially with an increase in the intellectual property protection (i.e., an increase in λ). On the other hand, the change rate of ψ is given with respect to an increase in λ as ∂ lnψ −1 ϒ; ¼ ∂λ ð1−λÞ2 −1
ηð1−θ Þ . The rate paramewhere ϒ ¼ ln ϕ þ ln ð1−λÞ þ η lnr i þ ρ−ggLþg ηð1−θ−1 Þ L
L
ters ϕ , λ , η , ri , gL are 0 b ϕ , λ , η , gL b 1, indicating that 0 N ln ϕ and 0 N ln (1− λ). Note further that parameter θ N N 1 (around 8 in Eaton & −1
ηð1−θ Þ Kortum, 2002), so that 1N ρ−ggLþg N0 . Consider the fact that ηð1−θ−1 Þ L
L
the research intensity in the world has a mean around 0.2% to feasibly ln ψ . In this case, the presume 1 N N ri, leading to 0 N ϒ such that 0b ∂ ∂λ curve ψ(1− ri) moves to the right with an increase in λ. As a result, as Fig. 4 illustrates, the research intensity increases with an increase in λ.
The study adds the standing-on-shoulder and standing-on-toes effects to Eaton and Kortum's (2001) trade model to allow externalities of the knowledge spillovers and duplication of research efforts in the technology accumulated formation. As a result, although all the merits of Eaton and Kortum's (2001) trade model remain, this model demonstrates the scale effect in research intensity: the larger a country is, the greater the country's research intensity is. This study also demonstrates that a country's research intensity increases with the country's population growth rate and the improvement in the country's intellectual property protection. However, this study excludes the recent observation that patents might stagnate and hold up innovation. This research also disallows international knowledge diffusion, which prevails in the real world (e.g., Huarng, Hui-Kuang, & Yu, 2015). Future research should consider these ideas. Appendix The following derivation comes directly from Eaton and Kortum (2001). An idea in a country draws from a Pareto distribution H i ðzÞ ¼ 1−z−θ :
ðA1Þ
A firm in country i employs an idea to produce a specific final good. The chance is that the idea is the best idea that leads to the least cost in production and commands a mark-up of at least m N 1 in country n as Z bin ðmÞ ¼
1
∞
1−Gn ðmci din =zÞdHi ðzÞ ≅
π in : T i mθ
ðA2Þ
The probability of a mark-up of at least m, given that the idea is a successful idea in country n is then bin ðmÞ ¼ m−θ ; bin ð1Þ
Fig. 3. Population growth and research intensity.
ðA3Þ
which implies that the markup that is conditional on the idea being the best idea follows a Pareto distribution with a parameter θ as H(θ) =1 − m−θ. The net profit share from producing the capital good is 1 − m−1,
C.-P. Lo / Journal of Business Research 69 (2016) 2297–2301
so that the expected share of the profits from the best idea in a market is as Z
∞ 1
1−m−1 dHðmÞ ¼
1 : 1þθ
ðA4Þ
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