metadata: authors: 0: author: Bravo-Ortega,Claudio
1: author: Lederman,Daniel
count: World
docna: 0: docna: Intellectual property rights, human capital
            and the incidence of R&D expenditures
docty: Policy Research Working Paper
subtopic: Social Policy,Legal Products,Real & Intellectual Property Law,Judicial System Reform,Skills Development and Labor Force Training,Common Property Resource Development,Educational Sciences,International Trade and Trade Rules,Legal Reform,Legislation,Regulatory Regimes,Intellectual Property Rights
teratopic: Private Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,Education,Finance and Financial Sector Development
abstracts: cdata!: Numerous studies predict that developing
            countries with low human capital may not benefit from the
            strengthening of intellectual property rights. The authors
            extend an influential theoretical framework to highlight the
            role of intellectual property rights in the process of
            innovation and structural change. The resulting theory is
            consistent with a stylized fact that appears in the data,
            namely that countries with poor intellectual-property
            protection may accumulate human capital without a
            corresponding increase in research and development
            investment as a share of national income. The model predicts
            that without minimum intellectual-property protection,
            additional education may result in more imitation rather
            than innovation. The preponderance of the econometric
            evidence presented in this paper suggests that interactions
            between human capital and intellectual property rights
            determine global patterns of research and development
            effort, and intellectual property rights tend to raise the
            effect of education on the incidence of research and development.
repnme: repnme: Intellectual property rights, human capital
            and the incidence of R&D expenditures
display_title: Intellectual property rights, human
            capital and the incidence of R&D expenditures
listing_relative_url: /research/2010/02/11837117/intellectual-property-rights-human-capital-incidence-rd-expenditures
topicv3: Patents m1326812 1041,Trade m1326924 698,Education m1327048 470,Intellectual Property Rights m1327290 851,Human Capital Accumulation m1504139 2816
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,Education,Finance and Financial Sector Development
no_of_pages: 29
author_keys: 0: author_key: 645872
1: author_key: 125180
model_extractions: WPS5217 Policy Research Working Paper 5217 Intellectual Property Rights, Human Capital and the Incidence of R&D Expenditures _Claudio Bravo-Ortega Daniel Lederman_ The World Bank Development Research Group Trade and Integration Team & Latin America and the Caribbean Region Office of the Chief Economist February 2010
Policy Research Working Paper 5217

# **Abstract**

Numerous studies predict that developing countries with low human capital may not benefit from the strengthening of intellectual property rights. The authors extend an influential theoretical framework to highlight the role of intellectual property rights in the process of innovation and structural change. The resulting theory is consistent with a stylized fact that appears in the data, namely that countries with poor intellectual-property protection may accumulate human capital without a corresponding increase in research and development investment as a share of national income. The model predicts that without minimum intellectual-property protection, additional education may result in more imitation rather than innovation. The preponderance of the econometric evidence presented in this paper suggests that interactions between human capital and intellectual property rights determine global patterns of research and development effort, and intellectual property rights tend to raise the effect of education on the incidence of research and development.

This paper—a product of the Trade and Integration Team, Development Research Group, and the Office of the Chief Economist, Latin America and the Caribbean Region—is part of a larger effort in these departments to understand the role of innovation in the process of development.. Policy Research Working Papers are also posted on the Web at http:// econ.worldbank.org. The author may be contacted at dlederman@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Intellectual Property Rights, Human Capital and the Incidence of R&D Expenditures**<sup>∗</sup>

Claudio Bravo-Ortega Department of Economics University of Chile Daniel Lederman Development Research Group The World Bank

**Abstract**

Numerous studies predict that developing countries with low human capital may not benefit from the strengthening of intellectual property rights. The authors extend an influential theoretical framework to highlight the role of intellectual property rights in the process of innovation and structural change. The resulting theory is consistent with a stylized fact that appears in the data, namely that countries with poor intellectual-property protection may accumulate human capital without a corresponding increase in research and development investment as a share of national income. The model predicts that without minimum intellectual-property protection, additional education may result in more imitation rather than innovation. The preponderance of the econometric evidence presented in this paper suggests that interactions between human capital and intellectual property rights determine global patterns of research and development effort, and intellectual property rights tend to raise the effect of education on the incidence of research and development.

Keywords: Research and Development, Intellectual Property Rights, Human Capital, Education JEL Classification: O11, O31, O34

> ∗ We thank Javier Cravino and Valentina Paredes for stellar research assistance. We had helpful discussions with Francisco Rodriguez about non-linear functional forms in econometrics. We thank Bill Maloney, Edwin Goni, Juan Carlos Muñoz and Jose Miguel Benavente for helpful discussions about R&D models and data. We are particularly grateful to Keith Maskus for his detailed comments on an earlier version of this paper. We gratefully acknowledge financial support from Fondecyt Grant 1061137, from the World Bank's Latin America and the Caribbean Regional Studies Program, and from the World Bank executed Multi-Donor Trust Fund on Trade, Intellectual Property and Innovation. The usual disclaimer applies and all remaining errors are ours.
# 1 Introduction and Related Literature

The quality of institutions and their impact on economic development is an important eld in economic inquiry, and the literature on intellectual property rights (IPRs) and innovation can be viewed as a sub eld. Much of the existing literature on intellectual property rights predicts that these institutions may have dierent (perhaps negative) eects on developing economies than on rich countries (e.g. Higino-Schneider 2005; Maskus 2000; Helpman 1993; Grossman and Lai 2005). In an extension of the work of Aghion and Howitt (1992), we model interactions between the institutional setting and innovation in the presence of costly imitation. We derive a set of predictions about the relationship between the level of research and development expenditures (R&D), human capital and IPRs. The subsequent econometric evidence rejects linear and separable functional forms, which is consistent with the model predictions. The evidence thus suggests that poor countries may accumulate human capital without a corresponding increase in the incidence of R&D as a share of national income without strengthening IPRs.

One longstanding strand of the literature on institutions and innovation focuses on the optimal design of IPRs, taking into account tradeos between the provision of information that can help spur future innovations while providing inventors an institutional solution to their appropriability problem. Nordhaus (1969, Chapter 5) provided an early contribution, which focused on the policy maker's concern about raising social welfare through the design of IPRs. A more recent literature on the optimal design of IPRs is rooted in the idea of cumulative or sequential innovation, whereby new innovations produce the ideas for future innovations. Hopenhayn et al. (2006) is an example of recent theoretical treatments in this vein. Throughout this literature, rms are characterized only in terms of the prots received from innovations, and the optimal patent design depends on the breadth and scope of innovation. However, the decision to innovate or imitate is not modeled explicitly.

An important eort to incorporate the decision to imitate by rms is Gallini (1992), who considers the eect of costly imitation on the optimal patent length. However, in this framework there is no imitation when the patent length is optimal. This is due to uniformity of patent lengths within a class of patents that supposedly ts all innovations, when in fact the optimal patent length depends on technological parameters that vary across goods. More recently, Jim and Troege (2006) proposed a model in which rms decide simultaneously how much to innovate and imitate (through a spillover-absorption coecient) in a Cournot setting, but institutions play no role in shaping investment decisions. We depart from previous literature by taking patent length as given and allowing simultaneously costly imitation and innovation. In addition, we explicitly model the role of IPRs in determining the incentives of rms to choose between innovation and imitation.

There is a literature on the role of IPRs in economic development. This literature has mainly 1
focused on North-South patterns of trade associated with dierent IPR regimes and the associated welfare gains or losses (Grossman and Helpman 1991; Helpman 1993). Zigic (1998) explores situations where leakages due to imperfect IPRs might produce counter-intuitive results. For example, spillovers might make the strengthening of IPRs in the South benecial for the welfare of developing economies as R&D in the North rises, with subsequent positive spillovers for the South in the form of prot leakages from prots driven by scale. An interesting feature of most of these models of international technology diusion is that developing countries are characterized as only having rms involved in imitation, and the rm-level decision about whether to innovate or imitate is ignored. Firms in the developed North decide how much to spend in R&D, but the option of imitation is not considered, and thus these models are silent with respect to economic structure within countries. Grossman and Lai (2005) extend traditional models by considering a two-country setup with costless imitation, enforcement and national treatment of patents. Unlike other models, in Grossman and Lai (2005) Southern countries are allowed to innovate. They study optimal patent policies for countries engaged in trade. Their main results establish that the benets from IPRs rise with market size and human capital. Thus, considering that Northern countries have larger markets and greater capacity to innovate, it follows that they have stronger incentives to strengthen IPRs compared to Southern countries. However, the enforcement of patents is modeled as a constant probability that aects the instantaneous monopolistic prots; neither risk nor the process of enforcement of IPRs is considered.

More recently, Branstetter and Saggi (2009) explored the relationship between IPRs and foreign direct investment (FDI). In their model, the South imitates, but imitation is endogenously determined as is FDI in a North-South model. The strengthening of IPRs in the South reduces imitation and FDI increases. More importantly, FDI gains more than oset the decline in imitation. In a previous model proposed by Chen and Puttitanum (2005), a Southern rm is allowed to imitate a foreign (Northern) product while another domestic rm can carry out R&D activities facing domestic competition. These authors study the optimal IPR regime through the course of development. They model IPRs as the ability to imitate in an static setting without explicitly modeling IPR structure. Their main nding is that optimal IPRs follow a U-shaped function with respect to income.

This article proposes a new modeling approach, based on Aghion and Howitt (1992), to understand observed patterns of R&D shares in national income across countries. The theoretical contribution entails a model of two sectors that operate simultaneously with costly imitation and innovation, where rms decide endogenously whether to participate in innovative or imitative activities. In contrast with the North-South literature, our model is a closed economy model. This allows us to focus on and carefully model the enforcement of IPRs. The gains of modeling an open economy would complicate the mathematical exposition and would change the focus of our model, 2
which is to model the interactions between IPRs and human capital. The endogenous allocation of rms embodying human capital across sectors results in endogenous aggregate innovation and imitation rates. We derive a set of results for the steady state equilibrium of our model; that is, for constant allocations of human capital across sectors.

In contrast to Aghion and Howitt's seminal contribution, we omit transitional dynamics. In equilibrium, the enforcement of IPRs, through monitoring eort and imposition of nes, helps determine the allocation of labor across these two sectors by aecting the risk-adjusted relative discount rate for innovators and imitators as well as the stream of prots. The discount rate aects the present value of labor productivity, which is also aected by the fees and compensations derived from the enforcement of the IPRs. A second result is that certain conditions are required to ensure that an increase in the endowment of human capital increases the share of labor devoted to R&D activities. This result is driven by inter-sector human capital mobility, and human capital will move into innovation only if IPRs are strong enough. Perhaps more importantly, the model predicts that aggregate R&D shares will depend on complex interactions between the quality of IPRs and human capital endowments. In spite of this complex relationship, the model predicts that IPRs will have a positive eect on the incidence of R&D expenditures, and, under fairly nonrestrictive assumptions, the marginal eect of human capital depends on IPRs. Hence, with lax IPRs, the accumulation of human capital may not raise the incidence of R&D.

The model yields a testable prediction, namely that the share of R&D expenditures in GDP is a non-linear but positive function of IPRs and is generally a positive function of human capital. The existing empirical literature, however, has focused exclusively on log-linear functions of R&D determinants (e.g., Varsakelis 2001; Chen and Puttitanum 2005). We provide empirical tests of functional linearity and separability of human capital and IPRs in an R&D model. The preponderance of the evidence supports the theoretical model.

The rest of the paper is organized as follows. Section 2 presents the theoretical model. Section 3 discusses the empirical methodology, and section 4 discusses the econometric results. Section 5 concludes.

# 2 The Model

Our model is an extension of Aghion and Howitt (1992). However, instead of competition between R&D activities and production, we present a trade-o between R&D and illegal imitation. There is one input, human capital, which is allocated between these two activities. Each person has one unit of human capital and there are _ET_ total units of human capital in the economy. Each person is an entrepreneur who sets up a rm and decides whether she will use her unit of human capital in R&D or imitation activities, which can be interpreted as patent infringement.

3
As in Aghion and Howitt (1992), innovation follows a Poisson process with a ow probability parameter _λ_ and exhibits constant returns to scale in the human capital dedicated to R&D. Illegal imitation follows a Poisson process with ow probability parameter parameter _μ_ and also exhibits constant returns to scale in employed human capital. The randomness represents in one case the success rate of an innovation, and in the other the success rate of reverse engineering per unit of human capital. Given the additivity property of Poisson processes and the constant returns to scale, for each sector the resulting stochastic processes will also follow a Poisson distribution with a parameter that depends on the original ow probability and the human capital allocated to each sector. One crucial dierence between the two sectors is that in the innovation sector each innovator must incur a xed cost of infrastructure of magnitude _K._<sup>1</sup> The government enforces patent rights, and, for the sake of clarity, patents are innitely lived. We assume that the enforcement process follows a Poisson distribution with ow probability _p_ , which represents the sampling probability for any given imitating rm. There are also constant returns to scale in government expenditure, _x_ , which increases the ecacy of the enforcement process. The government imposes a ne of size _F_ on imitating rms that have not paid royalties. For the sake of simplicity, we assume that the ne is transferred to the innovating rm, but the model predictions would be unaected if the transfer is a fraction of the ne. Another interpretation is that _F_ is a court-mandated transfer from the imitating to the innovative rm.

With respect to industrial organization, we assume monopolistic rents for a rm that has been successful in developing R&D activities and whose invention has not been imitated. Once a rm's invention has been imitated, the imitating and innovative rms compete as a Cournot duopoly. We assume Bertrand competition with the successive entry of imitating rms, given similar cost structures among them. These assumptions ensure that there is only one protable imitating rm.

We further assume that a monopolistic rm enjoys an instantaneous monopolistic rent, Π<sup>_M_</sup> . In the case of Cournot competition, both rms get an instantaneous duopolistic rent of Π<sup>_D_</sup> . Finally, the risk free interest rate in the economy is denoted by _r_ .

# 2.1 Labor market equilibrium

In equilibrium, the wage or income of the rm or entrepreneur is the same across sectors. Let _V_ represent the value of an invention. The wage (income) paid to the innovator ( _R_ & _D_ ) equals the expected value of one hour of research: Analogously, in the imitation sector the wage will be the expected value of one hour spent

> 1Imitation might also entail costs in infrastructure, but they tend to be smaller in relative terms than the cost of innovation. See, for example, Manseld et.al. (1981).

4
in reverse engineering activities. Given that a product can be protably imitated only once, the marginal product of human capital in this sector is: where _I_ represents the value of an illegal imitation.

In equilibrium, wages are equalized across sectors and the labor market clears: and where _ERD_ , _EI_ , and _ET_ stand for the human capital employed in the R&D sector, imitating sector and total human capital respectively. Thus, by using (3), we reduce equations (1) and (2) to just one equation. Equation (4) completes a system of two equations and two unknowns, _ERD_ and _EI_ , because _V_ and _I_ can be expressed as functions of exogenous parameters and _ERD_ and _EI_ , as shown in the following section.

# 2.2 Expected value of innovation and imitation

With constant returns to scale in both sectors, the rates of success for each sector are given by: _Rate_ ( _innovation_ ) = _λ · ERD Rate_ ( _illegal_ imitation_ ) = _μ · EI_ Note that in spite of the constant ow probabilities, economy wide (aggregate) innovation and imitation stochastic processes are determined in equilibrium by the human capital allocated to each activity.

The respective Poisson processes are parametrized with those rates, and the expected present value of prots for rms in the R&D sector (characterized by either monopolistic or duopolistic rents) can be written as follows: 5
The rst two terms in (5) correspond to the expected present value from monopolistic and duopolistic prots respectively. In these two terms, prots are weighted by the probability of successful innovations, imitations and enforcement. In the rst term, the higher the values of _λ_ and _μ_ , the lower the expected value of the monopolistic prots as the emergence of successful innovation or imitation will end this stream of prots. In contrast, the second term, contains two eects. The rst is analogous to the one already discussed for monopolistic prots, hence part of this second term (within the right integral) decreases with _λ_ and _μ_ . But there is a second eect whereby expected present value of R&D partially increases with _μ_ as the likelihood of imitation raises the probability of a stream of duopolistic prots.

In sum, when the probability of a new innovation is high, existing innovations become obsolete and thus monopolistic prots decline. When the probability of imitation increases, monopolistic prots also decline, but the expected value of duopolistic prots partially increases with the probability of duopolistic competition, but also partially declines given that a second imitation ends duopolistic competition. Finally, note that the ow of duopolistic prots are conditioned by the existence of a previous imitation and the presence of enforcement, px, hence the second term also decreases with px.

The third and fourth terms in (5) correspond to the expected present value of the ne or transfer (EPV(F)) minus the xed cost of R&D infrastructure, _K_ . The solution of the previous integrals show more clearly these eects: Equation (6) corresponds to the expected present value of the income ow of a rm in the R&D sector discounted by a risk-adjusted interest rate for the case of monopolistic and duopolistic prots.

A rm in the imitation sector faces the possibility of replacement of an innovation by a new innovation or imitation, and the possibility that the stream of prots will be halted by the enforcement of intellectual property rights, which we model as Poisson process with rate _px_ . If the rm is caught imitating without paying royalties, the government imposes a ne or transfer _F_ . Thus, the expected discounted ow of prots of the imitating rm can be expressed as follows: 6
The rst term corresponds to the duopolistic prots, while the second term corresponds to the expected present value of the ne or transfer imposed on imitating rms when property rights are enforced. The enforcement rate, px, has two eects on the expected present value of the ne (transfer). On the one hand it increases its present value by increasing the probability of occurrence of a successful enforcement, but on the other hand it decreases the expected value by reducing the probability of a duopoly and hence the possibility of having to pay the ne. These two eects can be seen more clearly in the second term of equation (8), which is derived by solving the previous integrals: This equation corresponds to the expected duopolistic prots of a rm in the imitation sector, discounted by a risk-adjusted interest rate, minus the expected value of the ne (transfer) for illegal imitation. From (8), we derive an expression of the expected present value of the transfer received by the innovating rm:

# 2.3 Equilibrium

Wages or entrepreneur's incomes are equalized across sectors in equilibrium. Considering that the expected wages depend on the expected value of inventions and imitations, the wage equalization condition can be re-written as follows: 7
which reduces to: Thus, equation (9) implicitly denes _ERD_ and _EI_ .<sup>2</sup>

# 2.4 Comparative statics

Equilibrium across the two sectors requires the following assumptions: Assumption 1. The relationship between the xed cost of R&D, _K_ , prots with zero innovation, and prots with zero imitation must be the following: We also assume that there is no waste of public resources. This implies that the monitoring sampling rate must be smaller that the eective rate of innovation plus imitation: Assumption 2. The monitoring sampling rate is smaller than the eective rate of innovation plus imitation.

For the sake of clarity regarding the eect of IPRs on the marginal eect of human capital accumulation on the incidence of R&D, the innovation arrival rate is set to be equal to the imitation arrival rate.

## Assumption 3. _λ_ = _μ_

To simplify the proof of the propositions discussed below we implicitly dierentiate the equilibrium condition (9) with respect to the relevant variables imposing _λ_ = _μ_ and the equilibrium condition _ERD_ + _EI_ = _ET_ , after these steps in some cases we use again the equilibrium condition to simplify the resulting expressions.

From the model we derive the following set of propositions and corollaries: Proposition 1. A reduction in the risk-free discount rate increases the share of the labor force in innovation activities.

> 2In the determination of the innovation and imitation values we considered one complete sequence of events. This sequence of events can be repeated endlessly. Thus, the more general innovation and imitation values will be _V_<sup>_′_</sup> = _V ·_ �1 + _r_ ( _T_ <u>1</u><sup>_<u>∗</u>_</sup> )<sup>+</sup> _r_ ( _T_ <u>1</u><sup>_∗_</sup> )<sup>2+</sup> _r_ ( _T_ <u>1</u><sup>_∗_</sup> )<sup>3</sup><sup>_...._</sup> � . The same will happen with _I_<sup>_′_</sup> = _I ·_ �1 + _r_ ( _T_ <u>1</u><sup>_<u>∗</u>_</sup> )<sup>+</sup> _r_ ( _T_ <u>1</u><sup>_∗_</sup> )<sup>2+</sup> _r_ ( _T_ <u>1</u><sup>_∗_</sup> )<sup>3</sup><sup>_...._</sup> � . Once the innovation and imitation values are equalized, the factors associated with the repetitions of the sequence will cancel each other out.

8
Proof. By implicitly dierentiating equation (9) with respect to r, we obtain:<sup>3</sup> _<u>∂E∂rRD</u>_ = 2 _μpxFr_ <u>Ω</u> _M_ with Ω= 2Π<sup>_M_</sup> _rF_ + 2 _μpxF_ ( _ET − ERD_ ) _− K_ (2 _rF rM_ + _rF_<sup>2)</sup> _rM_ = _r_ + _μET rF_ = _rM_ + _px_ , Where _rM_ is the risk adjusted discount rate of the monopolistic prots of innovators, and _rF_ is the risk adjusted discount rate of imitator's prots. The equilibrium condition implies that Ω _<_ 0 , and therefore<sup>_<u>∂ERD</u>_</sup> _<_ 0 . _∂r_ The previous proposition is consistent with existing literature that highlights the eect of a low interest rate, which increases the present value of monopolistic prots thus increasing the incentives to innovate. In our model with two sectors this result is no longer obvious. A decline of the discount rate increases the present value of prots in both innovative and imitative activities, with the eect on the former being larger than on the latter, thereby moving workers towards the innovation sector.

Proposition 2. An increase in the sampling rate, _p_ , or in the government expenditure, _x_ , or in the ne, _F_ , increases the share of the labor force allocated to R&D activities.

Proof. The proof is obtained by implicitly dierentiating equation (9) with respect to F: _<u>∂ERD</u>_ =<sup>2</sup><sup>_<u>μpxEI</u>rMEI_</sup> _∂F_ 2 _μpxFrM_<sup>=</sup> _F_ Given that the share of workers in the imitation sector is greater or equal than zero then _<u>∂ERD</u> >_ 0 . _∂F_ By the same token:

> _<u>∂ERD</u>_ =<sup>2Π</sup><sup>_MrF_</sup><sup><u>+2</u></sup><sup>_F_</sup><sup>_<u>μEI</u>rM−_2</sup><sup>_KrFrM_</sup> _∂px_ 2 _μpxFrM_ The equilibrium condition implies that the numerator is positive, and thus<sup>_<u>∂ERD</u>_</sup> _>_ 0 . Indeed, _∂px_ the derivative simplies to:

> _<u>∂ERD</u>_ =<sup>2Π</sup><sup>_MrF_</sup><sup><u>+2</u></sup><sup>_F_</sup><sup>_<u>μEI</u>rM−_2</sup><sup>_KrFrM_</sup> =<sup>_EI_</sup><sup><u>(</u></sup><sup>_ET μ−px_</sup><sup><u>+</u></sup><sup>_r_</sup><sup><u>)</u></sup> _∂px_ 2 _μpxFrM px_ ( _ET μ_ + _px_ + _r_ )<sup>, which under Assumption 2 is clearly positive.</sup>

Corollary 1. Depending on the parameters, increases in the eective sampling rate, _px_ , or the ne, _F_ , can have equivalent eects on the incidence of R&D.

Proof. The results are derived from the following inequalities and assumption 1. A marginal change in the ne will have a larger eect on the allocation of human capital to R&D than a marginal increase in the sampling probability as long as the following inequalities hold:

> 3This implicit dierentiation implies dierentiating both sides of the equilibrium condition with respect to the variable of interest. _ERD_ should be considered a function of the parameters of the model. And as explained in the previous paragraph this should be done after imposing _ERD_ + _EI_ = _ET_ . Finally, we factorize and solve for the derivative of interest.

9
However, governments may prefer to increase the ne rather than the expenditure associated with the sampling rate due to budget constraints. In general, as stated in the previous proposition proof, this alternative will be preferable for low levels of imitation.

The following proposition concerns the eect of changes in human capital endowments on the share allocated to R&D. The relationship has no obvious sign under the model assumptions. This is due to the fact that human capital can move into either innovation or imitation activities. Thus, the following proposition establishes the conditions under which a marginal increase in human capital endowment increases innovation.

Proposition 3. An increase in total human capital, depending on the parameters, may or may not increase the share of human capital allocated to the R&D sector.

Proof. The derivation of the proof is obtained by implicitly dierentiating equation (9) with respect to _ET_ :

> _<u>∂ERD</u>_ =<sup>Ω</sup><sup>_<u>μ</u>_</sup><sup><u>+2</u></sup><sup>_<u>μpxFrM</u>_</sup> _∂ET_ 2 _μpxFrM_

The numerator is composed of a positive and a negative term, hence the sign of this derivative is undened, but there is an F that makes this derivative positive. That is, if there are no incentives for innovation, additional human capital moves into the imitation sector. The derivative of human capital in R&D with respect to total human capital and the fee F can be expressed as : _<u>∂</u>_ 2 _ERD_ 2 _EI ∂F∂ET_<sup>=Π</sup> 2<sup>_M_</sup> _F_<sup>2(</sup><sup>_E_</sup> _px_<sup>_<u>T</u>_</sup> (<sup>_<u>μ</u>_</sup> _E_<sup><u>+</u></sup> _T μ_<sup>_<u>px</u>_</sup> +<sup><u>+</u></sup> _r_<sup>_r_</sup> )<sup><u>)22</u>=</sup> _F_ ( _ET μ_ + _px_ + _r_ )<sup>+Π</sup> 2<sup>_M_</sup> _F_<sup>2(</sup><sup>_E_</sup> _px_<sup>_<u>T</u>_</sup> (<sup>_<u>μ</u>_</sup> _E_<sup><u>+</u></sup> _T μ_<sup>_<u>px</u>_</sup> +<sup><u>+</u></sup> _r_<sup>_r_</sup> )<sup><u>)22</u></sup><sup>_>_0</sup> Furthermore, there is an F such that<sup>_<u>∂</u>_</sup> _∂E_<sup>_ERD_</sup> _T_ = 0 , and for _F > F_ the derivative with respect to human capital will be strictly positive. This threshold ne can be expressed as follows: _F_ = 2 _px_ ( _ET μ_ +Π<sup>_M_</sup> _r_ )<sup>2</sup> <u>(</u> _E_ (2 _<u>TE μRD</u>_ <u>+</u> _<u>pμx−</u>_ <u>+</u> _Er_ <u>)</u> _T_<sup>3</sup> _μ_ + _px_ + _r_ ) Proposition 4. The eect of human capital on R&D is increasing in px and F.

Proof. The previous proposition stated that the derivative of human capital dedicated to R&D with respect to total human capital is increasing on F. This derivative is also increasing on px: _∂px∂E∂_ 2 _ERDT_<sup>= 1</sup><sup>_/_2(</sup> ( _px_ 4 _E_ ( _EITμ μ_ <u>(</u> _E_ + _<u>Tpx μ</u>_ <u>++</u> _rr_ <u>))</u><sup>2</sup> )<sup>) +</sup><sup><u>Π</u></sup> _F_<sup>_M_(</sup> _px_<sup><u>12</u></sup><sup>_−_</sup> ( _ET μ_ <u>1+</u> _r_ )<sup>2</sup> )<sup>)</sup><sup>_>_0</sup> Since the level of human capital in R&D activities depends on institutions, and GDP depends positively on total human capital, we can derive the following corollaries about the nonlinear eects of human capital and IPRs on the R&D share in the GDP. The R&D share in GDP is dened as _<u>RDY</u>_ =<sup>_<u>w</u>_</sup> _wE_<sup>_ERD_</sup> _T_ ≦ 1 . The following corollary is obtained by dierentiating this expression: 10
Corollary 2. The share of R&D in GDP increases with the sampling probability, _p_ , or with the government expenditure, _x_ , or with the amount of the ne, _F_ . These variables show decreasing marginal returns. These relationships are non-linear.

Proof. The respective derivatives can be expressed as functions of the derivatives of human capital in R&D divided by total human capital, hence is straightforward to show that the impacts of F and px are positive: The decreasing marginal returns are proved by noting that the following second derivatives are negative: Corollary 3. Depending on the parameters, the share of R&D in GDP may or may not increase with total human capital, and this relationship is non-linear.

Proof. The respective derivatives can be expressed as functions of the derivatives of human capital in R&D divided by total human capital, hence it is straightforward to show that the eects of F and px on the incidence of R&D are positive: Corollary 4. If _Eμ >_ px + _r_ the cross derivatives of share of R&D in GDP with respect to total human capital and enforcement of IPRs, px, and F are positive.

Proof. By dierentiating the equation 10 with respect to px and F we obtain: Corollaries 1-4 suggest that under nonrestrictive assumptions there is non-separability of IPRs and human capital accumulation in the determination of the incidence of R&D. These relationships are also non-linear and the impact of IPRs protection is positive whereas the impact of human capital 11
is positive under particular conditions. Thus, in our empirical section we depart from traditional estimation of linear and separable functional form of the relationship between R&D, IPRs, and human capital.

# 3 Empirical Evidence

The theoretical model provides testable hypotheses. In brief, we expect that international dierences in R&D as a share of GDP depend on human capital, intellectual property rights (including enforcement), and non-linear interactions between these variables. The econometric models (discussed below) that assess the validity of our theoretical predictions rely on data on R&D, educational attainment, and IPRs that are commonly used in empirical applications.

## 3.1 Data and identication

The historical R&D series from 1960-2000 were compiled by Lederman and Saenz (2005) from various sources, but the data are derived ultimately from national surveys that use a common denition of R&D expenditures that includes fundamental and applied research as well as experimental development.<sup>4</sup> The data thus include not only investments in labor and materials needed to conduct basic scientic research in advanced countries, but also corresponding investments in the adoption and adaptation of existing technologies often thought more germane to developing countries. The series were constructed from data published by UNESCO, the OECD, the Ibero American Science and Technology Indicators Network (RICYT) and the Taiwan Statistical Data Book. The Lederman and Saenz data were updated to the latest year available for 2000-2004 from the UNESCO web site. We work with ve year averages of R&D as a share of GDP from 1960-2004.

The educational attainment data come from Barro and Lee (2001). More specically, we use the variable on the average years of education of the adult population (25-64 years) as the proxy of total human capital. These data are available every ve years, beginning in 1960, thus corresponding to the initial year of each ve-year average of the R&D variable.

We use the aggregate Ginarte-Park IPR index (Ginarte and Park 1997), which is the simple average of ve component indexes concerning each country's IPR laws in terms of its coverage and enforcement. The index's ve components are the coverage of patent laws across seven industries, membership in three international agreements, loss of protection due to three potential reasons

> 4See UNESCO Statistical Yearbook (1980) p. 742. The denition of R&D is the same across secondary sources, including the OECD, Ibero American Science and Technology Indicators Network (RICYT), World Bank, and Taiwan Statistical Yearbook. All these organizations follow the denitions provided by the Frascati Manual with the 2002 edition published by the OECD being its latest incarnation. For the purposes of this study, it is worth reproducing here the denition of experimental development, which is systematic work, drawing on existing knowledge gained from research and/or practical experience, which is directed to producing new materials, products or devices, to installing new processes, systems and services, or to improving substantially those already produced or installed (OECD 2002, p. 30).

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(namely working requirements, compulsory licensing, and revocation of patents), three types of enforcement mechanisms, and the duration of patents relative to international standards.<sup>5</sup> Each component ranges between zero and one, and thus the composite index we use in the empirical exercises also varies between 0 and 1, with higher values indicating stronger IPR protections and enforcement. Summary descriptive statistics of the three variables and the list of 67 countries that appear in our sample are reported in the Appendix.

Finally, the data on IPRs are available in ve year intervals, with the updated data from 19602000 available from Park's web site.<sup>6</sup> These data, like the educational attainment data, are thus also available for the initial year of each ve-year period in our estimation sample. And both variables therefore can be treated as pre-determined or weakly exogenous with respect to the R&D variable in a temporal sense. Moreover, the educational attainment variable reects educational enrollment decisions made roughly during ages 6-25, and therefore are unlikely to be due in a causal sense to the share of R&D observed in the subsequent 4 years. The IPR index is largely a summary indicator of the laws that establish the coverage and enforcement of IPR laws, which are the result of past international negotiations and legislative activity. Consequently it is dicult to believe that the index is caused by subsequent realizations of R&D.

# 3.2 Model specication

As mentioned, the theoretical model predicts that the relationship between R&D as a share of GDP and human capital and IPRs can be characterized by a non-linear function. Under the expectation of non-linear relationships, the ideal estimator would be a non-parametric estimator capable of estimating local derivatives over the data sample. Unfortunately, non-parametric estimators commonly used in empirical analyses tend to breakdown in the presence of multi-variate relationships and especially in the presence of xed eects.<sup>7</sup> A more tractable alternative is to apply linear estimators to exible functional forms using Taylor or Fourier approximations to non-linear functions of unknown form. The disadvantage of this general approach is the well known curse of dimensionality, whereby the addition of higher-order polynomials or trigonometric terms in linear functions reduces the power of standard specication tests, such as the t-statistic, and thus we are unable to ascertain the statistical signicance of each element in the high-order functions. On the other hand, we can apply standard F-tests to test the null hypothesis of insignicant higher-order and interactive terms in the chosen functions.<sup>8</sup> We apply three econometric approaches to assess the existence of

> 5Regarding the enforcement mechanisms, the sub-index includes three de jure enforcement mechanisms: (a) Preliminary (pre-trial) injunctions, (b) Contributory infringement, and (c) Burden of proof reversal (see Ginarte and Park 1997, p. 287-88; and Park 2008).

> 6http://www.american.edu/cas/econ/faculty/park.htm

> 7See, for example, Stone (1980), White (1980) and Yatchew (2003).

> 8We thank Francisco Rodriguez of Wesleyan University for highlighting these econometric issues. See also his paper on growth empirics, Rodriguez (2007).

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# non-linearities among R&D, initial education, and initial de jure IPR.

# 3.2.1 Two-stage rolling regressions

The rst approach entails a two-stage estimation procedure, which is purely descriptive. In the rst stage, we estimate the semi-elasticity of R&D over GDP with respect to (the natural logarithm of) initial educational attainment, while controlling for country-specic xed eects, over a moving window of observations ranked by the initial IPR index. In turn we estimate the correlation between the elasticities estimated in the rst stage and each country's level of educational attainment and IPRs. Since the dependent variable in the second stage is not a precise statistic, but rather an estimated elasticity, the standard errors of the second-stage estimations are bootstrapped. Also, it is likely that the sample size of the window of observations can aect the estimated elasticities, and thus we report results from specications with various window sizes.

More formally, the regression model to be estimated over each window of a subset of observations ranked by the level of IPRs is: _HK_ is human capital observed in the initial year of each ve-year period, as reected in its t-1 subscript, _ηi_ is the country xed eect, and _ηt_ is time-period eect.

Figure 1 shows the estimated coecients over the number of interactions corresponding to a rolling window of 60 observations.<sup>9</sup> This preliminary evidence shows that, in fact, the semi-elasticity of R&D over GDP with respect to educational attainment is generally positive, but it is clearly a non-linear function. The relationship between R&D and human capital is unstable and rising with the rank of the IPR index. Furthermore, the changes in the semi-elasticity seem to be discrete and unpredictable. It is zero in the samples with the worst levels of IPRs, then abruptly rises in the middle of sample, and stabilizes towards the end of the sample. These abrupt changes in the relevant semi-elasticity are not due to abrupt changes in the IPR index as we move up the rankings of IPRs. Considering that the each iteration involves a set of observations with increasing IPR index, the slope of the curve in Figure 1 corresponds approximately to the cross derivative of R&D share with respect to human capital and the IPR rank. Thus, we expect that this cross derivative could be positive on average for the whole sample. In any case, we discuss the results from our two-stage estimations further below.

> 9We excluded one observation from the data, namely for El Salvador in 1980, as the Lederman and Saenz data had a value of 2.27% of GDP. This data point is consistent with the RICyT data, but it is impossibly high for a poor developing economy, and there were no data points within ve years of this observation. Estimations with this observation also yielded notable unpredictable non-linearities. The corresponding graph is available from the authors upon request. We are grateful to Bill Maloney and Edwin Goni for pointing out this outlier.

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# 3.2.2 Formal linearity and separability tests

As mentioned, we study non-linearities in the R&D function by estimating polynomial expansions of the linear function. The second order Taylor expansion is: where subscripts i and t are countries and years. The null hypothesis that the function is linear is: In other words, for the function to be linear, the quadratic and interactive terms in equation (11) need to be jointly zero. Equation (11) can be estimated with Ordinary Least Squares, and a traditional F-test for joint signicance of the relevant parameters can be applied to ascertain whether the function is linear. In addition, the null hypothesis of the separability test concerns the cross derivative: The third order Taylor expansion includes additional terms, namely the cubic of each explanatory variable and the interaction between the square of each explanatory variable and the other. Hence the test for linearity would entail the F-test for the joint signicance as in (11) above, but with the additional terms included in the equality condition. Likewise, the separability test for the cubic expansion would include the coecients on the additional interactive terms.

As a preliminary step to explore the dierences across the linear, second order, third order functional forms, Figure 2 contains graphs of the resulting tted functions. The graphs show the scatter plot of R&D over GDP as functions of the schooling variable. It is evident that the slope of the function depends on the value of schooling for all functional forms, except the linear function. Hence the discussion of the results includes an exploration of the average slope or eect of the explanatory variables on R&D over GDP for the global sample and for various regions (groups of countries) when appropriate.<sup>10</sup>

> 10We also present econometric estimates that control for time dummies, which capture any period specic eects that are common to all countries, such as variations in global interest rates.

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# 4 Results

We discuss the three sets of results separately, starting with the descriptive two-stage estimations with rolling windows of observations ranked by the IPR index variable. In turn, we discuss the results from the second order, third order, and Fourier functional forms, with special attention given to the tests of the null hypotheses of linearity and separability.

## 4.1 Suggestive evidence of non-linearities from two-stage estimations

Figure 1 shows the estimated quasi-elasticities linking R&D over GDP to the (log of) years of schooling of the adult population, based on the ve-year averages panel data discussed earlier. Table 1 shows the results from the second-stage regressions, where the dependent variable is the vector of quasi-elasticities estimated with the various windows of observations. That is, we used windows of between 30 and 80 observations, as listed in the rst row of the table. The level of schooling itself seems to be signicantly correlated with the estimated quasi elasticities from the rst stage estimation, thus suggesting that the eect of schooling is not linear. In addition, this suggestive evidence also seems to show that the level of the IPR index also tends to aect the quasi elasticities of R&D over GDP with respect to schooling, but these results are less robust across the window sizes. This type of sensitivity is expected, since we do not know what would be the optimal window size for this type of estimation. Nevertheless, there is sucient evidence of non-linearities and perhaps of non-separability to turn our attention to the formal tests of linearity and separability.

## 4.2 Formal tests of linearity and separability based on second-order and thirdorder functional forms

Table 2 contains the results from random eects, xed-eects, and time-eects specications of the second order polynomial functional form. The table includes the coecient estimates, the p-values of the null hypotheses of linearity and separability, as well as the Hausmann specication test for equality of the random- and xed-eects estimations.

As expected, few coecients are statistically dierent from zero. In this regard, it is actually surprising that the interactive term between schooling and the IPR index is highly signicant across all specications. Thus we can safely reject the null of separability. Moreover, the p-value of the corresponding F-test safely rejects the null of linearity. That is, we cannot reject the possibility that the squared terms in the model are jointly signicant, although each one of them does not appear to be individually signicant. The curse of dimensionality comes out loud and clear, even in the second-order functional form.

The lower panel of Table 2 shows the average derivatives for the global sample and for the geographic regions. As mentioned earlier, we cannot know the condence interval around each 16
average derivative. But it is interesting to note that all derivatives are positive and seem to be consistently estimated across the various specications. The High-Income countries tend to have the highest marginal eects of schooling on R&D eort as a share of GDP.

Table 3 presents the specication tests for the null of linearity and separability, as well as the test of equivalence of the random- and xed-eects specications of the third-order functional form. It also reports the average rst derivatives of the R&D over GDP with respect to schooling, as well as the average cross derivatives (i.e., how the rst derivative changes with marginal changes in the IPR index).

The results suggest, again, that we can safely reject the null of linearity. The test of separability is more mixed, with the xed-eects specications unable to reject separability. However, the Hausmann tests for equivalence between the random- and xed-eects specications suggest the more ecient random-eects estimation is preferable, as we cannot reject that the set of coecients from the random- and xed-eects estimations are statistically similar. Since the preferred random-eects specication rejects separability, we conclude that in the third-order polynomial function there is evidence that the underlying function is both non-linear with potentially important interactions between IPRs and schooling. In this regard, the estimates of the average cross-derivatives suggest that the marginal eects of schooling on R&D expenditures as a share of GDP is positively aected by the level of IPR protection as the model predicts. This result appears for all regions of the world, but the point estimates tend to be larger for developing countries than for the High-Income countries.

As a robustness check we estimated various Fourier trigonometric expansions of the R&D function. These results, which are available upon request, also rejected the null of separability of human capital and IPRs.<sup>11</sup> 11The Fourier expansion implemented is the Taylor second order expansion but with additional trigonometric terms. The advantage of this specication is that the resulting functions are more exible. More formally, following Yatchew (2003), the Fourier expansion can be written as: where the linear part of the equation is _α · X_ . The z's are our two explanatory variables. The second and third terms in (14) are the terms from the second order expansion. The k's are vectors whose elements are integers with absolute values summing to a number k less than a pre-specied value K*. Given a value of K* and J, the parameter vector can be estimated by OLS. The choices of K* and J are somewhat arbitrary. In our case, K*=3. The total number of terms in the expansion is supposed to grow with sample size. In practice, researchers look at the ratio of the total number of parameters in the expansion to the number of observations. We can obtain a restricted estimator by restricting the coecients on the terms involving interactions between dierent z variables to equal zero. Thus, the separability test for the Fourier expansion is the test used for the second order expansion but including the trigonometric parameters in the set to be tested for joint signicance. There is not linearity test specic to the Fourier expansion. In any case, the point is that the trigonometric terms add exibility to the function, but also add complexity. Tests for the cases of K=2, K=3, J=1 and J=2 rejected the null of separability at less than the 5% condence level.

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# 5 Concluding Remarks

We extended the model by Aghion and Howitt (1992) to take into account the role of intellectualproperty institutions in the process of innovation. Our model consists of two sectors that operate simultaneously, one relying on costly imitation and the other on innovation. Firms or entrepreneurs decide endogenously whether to participate in innovative or imitative activities. The enforcement of intellectual property rights aects the incentives of labor to move between the two sectors. That is, institutions determine the risk-adjusted relative discount rate between employment in the two sectors. A second theoretical result is that an increase in the endowment of human capital increases the share of labor devoted to R&D activities under strong protection of IPRs.

Perhaps more importantly, the model predicts that aggregate patterns of the R&D shares across countries depend on complex interactions between IPRs and human capital. In spite of these complex interactions, the model also predicts, under fairly nonrestrictive assumptions, that IPRs provide incentives for the allocation of human capital into R&D activities. Economies with lax IPRs may not experience increases in the incidence of R&D over GDP as a result of increases in the stock of human capital. The model suggests that a minimum level of protection of IPRs can ensure that human capital accumulation increases the share of R&D. Thus, the model yields a testable prediction, namely that the share of R&D in GDP is a non-linear function of IPRs and human capital. While existing theories predict dierential eects of IPRs on poor versus rich countries, the existing empirical literature has focused exclusively on log-linear functions of R&D determinants (e.g., Varsakelis 2001; Chen and Puttitanum 2005). The analyses here thus contributed to both micro-founded theory and evidence by highlighting an ignored aspect of the role of IPRs as institutions shaping incentives for human capital to be allocated to R&D within countries.

The empirical section of the paper focused on international data on R&D shares of GDP, years of schooling of the adult population, and the Ginarte and Park (1997) data on de jure intellectual property rights. The data on educational attainment and IPRs were safely treated as being predetermined. Preliminary and descriptive estimations of the quasi-elasticity of R&D over GDP as a function of schooling suggested that in fact the data do seem to behave as if the underlying data generation process were unpredictably non-linear, and highlighting a new stylized fact: at low levels of IPRs, marginal increases in the stock of education have negligible eects on R&D.

We estimated basic models of the determinants of R&D expenditures as a share of GDP to test for non-linearities and interactions between the schooling of the labor force and the quality and enforcement of intellectual property rights, while also controlling for unobserved international heterogeneity with country specic eects. Non-parametric estimators cannot estimate such functions, and thus the applied literature has focused on polynomial and trigonometric approximations to non-linear functional forms.

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The estimation of second-order, third-order and Fourier polynomial functions allowed us to test the validity of the null of linearity and separability in the R&D functions. The preponderance of the evidence suggests that we can reject linearity and separability, thus lending credence to the theoretical model. Moreover, the point estimates we obtain conrm the positive marginal eects of human capital and IPRs on R&D as well as the signicance of their interactions. It is noteworthy that the eect of education on R&D eort can depend on intellectual property rights across countries of diverse levels of development, even after controlling for time-invariant heterogeneity.

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