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 investment as a share of national income. The model
with low human capital may not benefit from the predicts that without minimum intellectual-property
strengthening of intellectual property rights. The authors protection, additional education may result in more
extend an influential theoretical framework to highlight imitation rather than innovation. The preponderance of
the role of intellectual property rights in the process of the econometric evidence presented in this paper suggests
innovation and structural change. The resulting theory that interactions between human capital and intellectual
is consistent with a stylized fact that appears in the data, property rights determine global patterns of research
namely that countries with poor intellectual-property and development effort, and intellectual property rights
protection may accumulate human capital without a tend to raise the effect of education on the incidence of
corresponding increase in research and development 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
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 dierent (perhaps negative) eects 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 tradeos 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 prots 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 eort to incorporate the decision to imitate by rms is Gallini (1992), who consid-
ers the eect 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) pro-
posed a model in which rms decide simultaneously how much to innovate and imitate (through a
spillover-absorption coecient) in a Cournot setting, but institutions play no role in shaping invest-
ment 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 dierent IPR regimes and the associated
welfare gains or losses (Grossman and Helpman 1991; Helpman 1993). Zigic (1998) explores situa-
tions where leakages due to imperfect IPRs might produce counter-intuitive results. For example,
spillovers might make the strengthening of IPRs in the South benecial for the welfare of developing
economies as R&D in the North rises, with subsequent positive spillovers for the South in the form
of prot leakages from prots driven by scale. An interesting feature of most of these models of
international technology diusion 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 coun-
tries engaged in trade. Their main results establish that the benets 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
aects the instantaneous monopolistic prots; neither risk nor the process of enforcement of IPRs
is considered.
More recently, Branstetter and Saggi (2009) explored the relationship between IPRs and for-
eign 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 oset the decline in imita-
tion. 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 un-
derstand 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 ac-
tivities. 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 eort and imposition of nes, helps
determine the allocation of labor across these two sectors by aecting the risk-adjusted relative
discount rate for innovators and imitators as well as the stream of prots. The discount rate aects
the present value of labor productivity, which is also aected 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 eect on the incidence of R&D expenditures, and, under fairly nonrestrictive assumptions,
the marginal eect 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 deter-
minants (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 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 dierence between the two sectors is that in the innovation sector each innovator
must incur a xed cost of infrastructure of magnitude K.1
The government enforces patent rights, and, for the sake of clarity, patents are innitely 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 ecacy 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 unaected 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 protable imitating rm.
We further assume that a monopolistic rm enjoys an instantaneous monopolistic rent, M . In
the case of Cournot competition, both rms get an instantaneous duopolistic rent of D . 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:
WRD = · V (1)
Analogously, in the imitation sector the wage will be the expected value of one hour spent
1
Imitation might also entail costs in infrastructure, but they tend to be smaller in relative terms than the cost of
innovation. See, for example, Manseld et.al. (1981).
4
in reverse engineering activities. Given that a product can be protably imitated only once, the
marginal product of human capital in this sector is:
WI = · I (2)
where I represents the value of an illegal imitation.
In equilibrium, wages are equalized across sectors and the labor market clears:
WRD = WI (3)
and
ERD + EI = ET (4)
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) = · 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 prots for rms in the R&D sector (characterized by either monopolistic or duopolistic
rents) can be written as follows:
^ ^ ^
V = e-rt M e-ERD t e-µEI t dt + µEI e-µEI t e-rv D e-ERD v e-µEI (v-t) e-px(v-t) dvdt
0 0 t
+EP V (F ) - K
(5)
5
The rst two terms in (5) correspond to the expected present value from monopolistic and duopolis-
tic prots respectively. In these two terms, prots are weighted by the probability of successful
innovations, imitations and enforcement. In the rst term, the higher the values of and µ, the
lower the expected value of the monopolistic prots as the emergence of successful innovation or
imitation will end this stream of prots. In contrast, the second term, contains two eects. The rst
is analogous to the one already discussed for monopolistic prots, hence part of this second term
(within the right integral) decreases with and µ. But there is a second eect whereby expected
present value of R&D partially increases with µ as the likelihood of imitation raises the probability
of a stream of duopolistic prots.
In sum, when the probability of a new innovation is high, existing innovations become obsolete
and thus monopolistic prots decline. When the probability of imitation increases, monopolistic
prots also decline, but the expected value of duopolistic prots partially increases with the prob-
ability of duopolistic competition, but also partially declines given that a second imitation ends
duopolistic competition. Finally, note that the ow of duopolistic prots 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 eects:
M D µ · EI
V = + + EP V (F ) - K (6)
r + · ERD + µ · EI (r + · ERD + µ · EI + px)(r + · ERD + µ · EI )
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 prots.
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 prots will be halted by the enforce-
ment 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 prots of the imitating rm can be expressed as follows:
6
^ ^
-µEI t
I= µEI e e-rv D e-ERD v e-µEI (v-t) e-px(v-t) dvdt
0
^
t
^ (7)
-µEI t -rv -pxv -ERD v -µEI (v-t)
-F µEI e e px · e e e dvdt
0 t
The rst term corresponds to the duopolistic prots, 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 eects 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 eects can
be seen more clearly in the second term of equation (8), which is derived by solving the previous
integrals:
D µ · EI F · µ · EI · px
I= - (8)
(r + · ERD + µ · EI + px)(r + · ERD + µ · EI ) (r + · ERD + µ · EI + px)2
This equation corresponds to the expected duopolistic prots 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:
F ·µ·EI ·px
EP V (F ) = (r+·ERD +µ·EI +px)2
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:
M D µ · EI
+ + EP V (F ) - K
r + · ERD + µ · EI (r + · ERD + µ · EI + px)(r + · ERD + µ · EI )
D µ · EI F · µ · EI · px
= -
(r + · ERD + µ · EI + px)(r + · ERD + µ · EI ) (r + · ERD + µ · EI + px)2
7
which reduces to:
M F · µ · EI · px
+2 =K (9)
r + · ERD + µ · EI (r + · ERD + µ · EI + px)2
Thus, equation (9) implicitly denes ERD and EI .2
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, prots with zero innovation,
and prots with zero imitation must be the following:
M
M F · µ · ET · px M
+2 >K>
r + µ · ET (r + µ · ET + px)2 r + µ · ET
We also assume that there is no waste of public resources. This implies that the monitoring
sampling rate must be smaller that the eective rate of innovation plus imitation:
Assumption 2. The monitoring sampling rate is smaller than the eective rate of innovation plus
imitation.
µ · ET > px
For the sake of clarity regarding the eect of IPRs on the marginal eect 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. =µ
To simplify the proof of the propositions discussed below we implicitly dierentiate the equi-
librium condition (9) with respect to the relevant variables imposing = 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.
2
In 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 = V · 1 + r(T ) + r(T1 )2 + r(T1 )3 .... . The same will happen with I = I · 1 + r(T ) + r(T1 )2 + r(T1 )3 .... .
1 1
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 dierentiating equation (9) with respect to r, we obtain:
3
ERD
r = 2µpxF rM
with = 2M rF 2
+ 2µpxF (ET - ERD ) - K(2rF rM + rF )
rM = r + µET
rF = rM + px,
Where rM is the risk adjusted discount rate of the monopolistic prots of innovators, and rF is
the risk adjusted discount rate of imitator's prots. The equilibrium condition implies that < 0,
ERD
and therefore
r < 0.
The previous proposition is consistent with existing literature that highlights the eect of a low
interest rate, which increases the present value of monopolistic prots 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 prots in both innovative and imitative activities, with the eect
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 dierentiating equation (9) with respect to F:
ERD 2µpxEI rM EI
F = 2µpxF rM = F
Given that the share of workers in the imitation sector is greater or equal than zero then
ERD
F > 0.
By the same token:
ERD 2M rF +2F µEI rM -2KrF rM
px = 2µpxF rM
ERD
The equilibrium condition implies that the numerator is positive, and thus
px > 0. Indeed,
the derivative simplies to:
ERD 2M rF +2F µEI rM -2KrF rM EI (ET µ-px+r)
px = 2µpxF rM = px(ET µ+px+r) , which under Assumption 2 is clearly positive.
Corollary 1. Depending on the parameters, increases in the eective sampling rate, px, or the ne,
F , can have equivalent eects 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 eect on the allocation of human capital to R&D than a marginal
increase in the sampling probability as long as the following inequalities hold:
3
This implicit dierentiation implies dierentiating 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
ERD ERD EI EI (ET µ-px+r)
F > px and therefore F > px(ET µ+px+r) .
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 eect 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 dierentiating equation (9) with respect
to ET :
ERD µ+2µpxF rM
ET = 2µpxF rM
The numerator is composed of a positive and a negative term, hence the sign of this derivative is
undened, 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 :
2ERD M (ET µ+px+r)2 2EI M (ET µ+px+r)2
F ET = F (ET µ+px+r) + 2F 2 px(ET µ+r)2 > 0
2F 2 px(ET µ+r)2
=
ERD
Furthermore, there is an F such that
ET = 0, and for F > F the derivative with respect to human
capital will be strictly positive. This threshold ne can be expressed as follows:
M (ET µ+px+r)3
F = 2px(ET µ+r)2 (2ERD µ-ET µ+px+r)
Proposition 4. The eect 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:
2ERD 4EI µ(ET µ+r) M 1 1
pxET = 1/2( (px(ET µ+px+r)2 ) ) + F ( px2 - (ET µ+r)2 )
) >0
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 eects
of human capital and IPRs on the R&D share in the GDP. The R&D share in GDP is dened as
RD wERD
Y = wET 1. The following corollary is obtained by dierentiating 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:
(RD/Y ) 1 ERD
F = ET F >0
(RD/Y ) 1 ERD
px = ET px >0
The decreasing marginal returns are proved by noting that the following second derivatives are
negative:
2 (RD/Y ) 1 2 ERD 1 ERD EI
F 2
= ET F 2 = ET - F - F 2 < 0
2
2 (RD/Y ) 1 ERD 1 EI (ET µ-px+r)
(px)2
= ET (px)2 = ET px px(ET µ+px+r)
2 (RD/Y ) 1 ERD (ET µ-px+r) (-1)px(ET µ+px+r)-(ET µ-px+r)2px
(px)2
= ET - px px(ET µ+px+r) + EI (px(ET µ+px+r))2
<0
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 eects of F
and px on the incidence of R&D are positive:
M (ET µ+px+r)2 2(2ET µ+Erd(-ET µ+px+r))
2
(RD/Y ) 1 ERD 1 ERD ET 2 - F px(ET µ+r)2
- ET µ+px+r
= - = 2 (10)
ET ET ET ET ET 2ET
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 dierentiating the equation 10 with respect to px and F we obtain:
2 (RD/Y ) M (ET µ+px+r)2 2EI F (ET µ-px-r)
F ET = 2EtF 2 px(ET µ+r)2
+ 2Et2 F 2 (ET µ+px+r)
>0
1 1
M -
2 (RD/Y ) EI (ET µ2 +px2 -r2 )
2 px2 (ET µ+r)2
pxET = ET px(ET µ+px+r)2
2 + 2EtF >0
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 dier-
ences 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 (dis-
cussed 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 identication
The historical R&D series from 1960-2000 were compiled by Lederman and Saenz (2005) from vari-
ous sources, but the data are derived ultimately from national surveys that use a common denition
of R&D expenditures that includes fundamental and applied research as well as experimental de-
velopment.
4 The data thus include not only investments in labor and materials needed to conduct
basic scientic 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 specically, 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
4
See UNESCO Statistical Yearbook (1980) p. 742. The denition 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 denitions 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 denition 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).
12
(namely working requirements, compulsory licensing, and revocation of patents), three types of
enforcement mechanisms, and the duration of patents relative to international standards.
5 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 1960-
2000 available from Park's web site.
6 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 reects 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 dicult to believe that the
index is caused by subsequent realizations of R&D.
3.2 Model specication
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 esti-
mating 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 eects.
7 A more tractable alternative is to apply linear estimators
to exible functional forms using Taylor or Fourier approximations to non-linear functions of un-
known 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 specication tests, such as the t-statistic, and thus we are unable to ascer-
tain the statistical signicance of each element in the high-order functions. On the other hand, we
can apply standard F-tests to test the null hypothesis of insignicant higher-order and interactive
terms in the chosen functions.
8 We apply three econometric approaches to assess the existence of
5
Regarding 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).
6
http://www.american.edu/cas/econ/faculty/park.htm
7
See, for example, Stone (1980), White (1980) and Yatchew (2003).
8
We thank Francisco Rodriguez of Wesleyan University for highlighting these econometric issues. See also his
paper on growth empirics, Rodriguez (2007).
13
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-specic xed eects, 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 aect the estimated elasticities, and
thus we report results from specications 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:
RD
= + · ln HKit-1 + i + t + it (11)
GDP it
HK is human capital observed in the initial year of each ve-year period, as reected in its t-1
subscript, i is the country xed eect, and t is time-period eect.
Figure 1 shows the estimated coecients over the number of interactions corresponding to a
rolling window of 60 observations.
9 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.
9
We 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.
14
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:
RD 2 2
= 0 + 1 HKit-1 + 2 IP Rit-1 + 3 HKit-1 + 4 IP Rit-1 + 5 HKit-1 IP Rit-1 (12)
GDP it
where subscripts i and t are countries and years. The null hypothesis that the function is linear
is:
3 = 4 = 5 = 0 (13)
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 signicance 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:
5 = 0 (14)
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 signicance 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 coecients on the additional interactive terms.
As a preliminary step to explore the dierences 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 eect of the
explanatory variables on R&D over GDP for the global sample and for various regions (groups of
countries) when appropriate.
10
10
We also present econometric estimates that control for time dummies, which capture any period specic eects
that are common to all countries, such as variations in global interest rates.
15
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 signicantly correlated with the estimated quasi elasticities from the
rst stage estimation, thus suggesting that the eect of schooling is not linear. In addition, this
suggestive evidence also seems to show that the level of the IPR index also tends to aect 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 sucient 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 third-
order functional forms
Table 2 contains the results from random eects, xed-eects, and time-eects specications of the
second order polynomial functional form. The table includes the coecient estimates, the p-values
of the null hypotheses of linearity and separability, as well as the Hausmann specication test for
equality of the random- and xed-eects estimations.
As expected, few coecients are statistically dierent from zero. In this regard, it is actually
surprising that the interactive term between schooling and the IPR index is highly signicant across
all specications. 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 signicant, although each one of them does not appear
to be individually signicant. 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 condence 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 specications. The High-Income countries tend to have
the highest marginal eects of schooling on R&D eort as a share of GDP.
Table 3 presents the specication tests for the null of linearity and separability, as well as the
test of equivalence of the random- and xed-eects specications 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-eects specications unable to reject separability. However, the Haus-
mann tests for equivalence between the random- and xed-eects specications suggest the more
ecient random-eects estimation is preferable, as we cannot reject that the set of coecients from
the random- and xed-eects estimations are statistically similar. Since the preferred random-eects
specication 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 eects of schooling on R&D expenditures as a share of GDP is positively aected
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 func-
tion. These results, which are available upon request, also rejected the null of separability of human
capital and IPRs.
11
11
The Fourier expansion implemented is the Taylor second order expansion but with additional trigonometric terms.
The advantage of this specication is that the resulting functions are more exible. More formally, following Yatchew
(2003), the Fourier expansion can be written as:
k 3 3 3
RD
= X + b i zi + cij zi zj + µij cos(jki z) + ij sin(jki z) (15)
GDP ij i=1 i=1 j=1 i=1
where the linear part of the equation is · 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-specied 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 coecients on the terms involving interactions between dierent 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 signicance. There is not linearity test specic 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%
condence level.
17
5 Concluding Remarks
We extended the model by Aghion and Howitt (1992) to take into account the role of intellectual-
property 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 aects 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 dierential eects 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 pre-
determined. 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 eects 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 specic eects. Non-parametric estimators cannot estimate such func-
tions, and thus the applied literature has focused on polynomial and trigonometric approximations
to non-linear functional forms.
18
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 conrm the positive marginal eects of
human capital and IPRs on R&D as well as the signicance of their interactions. It is noteworthy
that the eect of education on R&D eort can depend on intellectual property rights across countries
of diverse levels of development, even after controlling for time-invariant heterogeneity.
19
References
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60(2): 323-51.
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Implications. Oxford Economic Papers 53(3): 541-63.
Branstetter, L. and K. Saggi. 2009. Intellectual Property Rights, Foreign Direct Investment, and
Industrial Development. NBER Working Paper No. 15393, Cambridge, Massachusetts.
Chen, Y. and T. Puttitanum. 2005. Intellectual Property Rights and Innovation in Developing
Countries. Journal of Development Economics 78: 474-93.
Gallini, N. 1992. Patent Policy and Costly Imitation. The RAND Journal of Economics 23(1):
52-63.
Ginarte, J. and W. Park. 1997. Determinants of Patent Rights: A Cross-National Study. Research
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Grossman, G. and E. Lai. 2005. International Protection of Intellectual Property. American
Economic Review 94: 1635-53.
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Higino-Schneider, P. 2005. International Trade, Economic Growth and Intellectual Property Rights:
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Hopenhayn, H., G. Llobet, and M. Mitchell. 2006. Rewarding Sequential Innovators: Prizes,
Patents, and Buyouts. Journal of Political Economy 114(6): 1041-68.
Jim, J. and M. Troege. 2006. R&D Competition and Endogenous Spillovers. The Manchester
School 74(1): 40-51.
Lederman, D. and L. Saenz. 2005. Innovation and Development around the World, 1960-2000.
World Bank Policy Research Working Paper No. 3774, Washington, DC.
Maskus, K.E. 2000. Intellectual Property Rights in the Global Economy. Washington, DC: Institute
for International Economics.
Nordhaus, W. 1969. Invention, Growth and Welfare: A Theoretical Treatment of Technological
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Park. W. 2008. International Patent Protection: 1960-2005. Research Policy 37: 761-66.
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Not Simple. Mimeographed, Wesleyan University, Connecticut.
20
Appendix
Descriptive Statistics
Variable Observations Mean Std. Dev. Min. Max.
R&D/GDP (%) 228 1.091 0.915 0.001 4.399
Average Years of Schooling 228 6.502 2.716 0.308 12.247
IPR Index 228 2.742 0.910 0.330 4.857
List of Countries with Regional Identiers
1. ARGENTINA LAC 2. AUSTRALIA HI 3. AUSTRIA HI 4. BELGIUM HI 5. BOLIVIA LAC
6. BRAZIL LAC 7. CAMEROON SHA 8. CANADA HI 9. CHILE LAC 10. CHINA P.REP.
EAP 11. COLOMBIA LAC 12. COSTA RICA LAC 13. CYPRUS MENA 14. DENMARK HI 15.
ECUADOR LAC 16. EGYPT MENA 17. EL SALVADOR LAC 18. FINLAND HI 19. FRANCE
HI 20. GERMANY HI 21. GHANA SHA 22. GREECE HI 23. GUATEMALA LAC 24. GUYANA
LAC 25. HONDURAS LAC 26. HONG KONG EAP 27. HUNGARY ECA 28. INDIA SA 29.
INDONESIA EAP 30. IRAN MENA 31. IRELAND HI 32. ISRAEL MENA 33. ITALY HI 34.
JAMAICA LAC 35. JAPAN HI 36. JORDAN MENA 37. KENYA SHA 38. MALAWI SHA 39.
MAURITIUS SHA 40. MEXICO LAC 41. NETHERLANDS HI 42. NEW ZEALAND HI 43.
NORWAY HI 44. PAKISTAN SA 45. PANAMA LAC 46. PERU LAC 47. PHILIPPINES EAP
48. PORTUGAL HI 49. SENEGAL SHA 50. SINGAPORE EAP 51. SOUTH AFRICA SHA 52.
SOUTH KOREA EAP 53. SPAIN HI 54. SRI LANKA SA 55. SUDAN SHA 56. SWEDEN HI 57.
SWITZERLAND HI 58. THAILAND EAP 59. TRINIDAD/TOBAGO LAC 60. TUNISIA MENA
61. TURKEY ECA 62. UGANDA SHA 63. UNITED KINGDOM HI 64. UNITED STATES HI
65. URUGUAY LAC 66. VENEZUELA LAC 67. ZAMBIA SHA
21
Table 1: Second Stage Regression Estimates of the Determinants of the R&D/GDP Quasi-Elasticity
with Respect to Schooling across Sample-Window Sizes
Sample-Window Size
30 40 50 60 70 80
Average Years of Schooling 0.134 0.032 0.051 0.092 0.114 0.111
[0.000]*** [0.278] [0.000]*** [0.000]*** [0.000]*** [0.000]***
Intellectual Property Rights Index 0.064 0.289 0.18 0.059 -0.002 0.015
[0.492] [0.000]*** [0.000]*** [0.001]*** [0.926] [0.411]
Obs. 165 155 145 135 125 115
R-Squared 0.449 0.71 0.821 0.872 0.933 0.959
Notes: Fixed Eects were included in the First Stage. Variables were calculated as the country mean
for each window. The original units are 5-year averages of the R&D/GDP variable, and the value of the
schooling and IPR index variables in the initial year of each 5-year period. The data cover the period
from 1960-2004, but the panel is unbalanced. P-values from bootstrapped standard errors for the null
appear within brackets; p < 0.1, p < 0.05, p < 0.01.
22
Table 2: Regression Results for the Second-Order Polynomial Function
No FE FE RE FE&TE RE&TE
Average Years of Schooling (H) -0.147 -0.143 -0.151 -0.195 -0.152
[0.060]* [0.144] [0.039]** [0.105] [0.045]**
Intellectual Property Rights (IPR) Index 0.095 0.064 0.153 0.079 0.156
[0.671] [0.856] [0.514] [0.825] [0.512]
Schooling Squared -0.003 0.010 0.008 0.013 0.008
[0.663] [0.154] [0.162] [0.102] [0.184]
IPR Squared -0.111 -0.085 -0.101 -0.073 -0.090
[0.056]* [0.175] [0.051]* [0.258] [0.088]*
Schooling*IPR 0.127 0.074 0.086 0.064 0.080
[0.000]*** [0.020]** [0.002]*** [0.053]* [0.005]***
Obs 228 228 228 228 228
R-Squared 0.555 0.380 0.406
R-Squared: Overall 0.519 0.538 0.518 0.549
Linearity Test: P-Value 0.000 0.001 0.000 0.003 0.000
Separability Test: P-Value 0.000 0.020 0.002 0.053 0.005
FE=RE: P-Value 0.023 0.997
First Derivative by Region: H
R&D
GDP
World Sample 0.165 0.198 0.189 0.145 0.171
East Asia and the Pacic 0.117 0.152 0.142 0.100 0.126
Europe and Central Asia 0.085 0.089 0.085 0.034 0.071
High-Income Countries 0.232 0.281 0.270 0.230 0.248
Latin America/Caribbean 0.075 0.115 0.104 0.065 0.090
Middle East/N. Africa 0.155 0.173 0.167 0.118 0.150
South Asia 0.084 0.066 0.065 0.007 0.052
Sub-Saharan Africa 0.202 0.114 0.128 0.042 0.110
Notes: P-values for the null appear within brackets; p < 0.1, p < 0.05, p < 0.01.
FE=Fixed Eects; RE=Random Eects; TE=Time Eects. The Regional groups are those of the
World Bank. Derivatives are calculated at regional means.
23
Table 3: Regression Results for the Third-Order Polynomial Function
Specication Test No FE FE RE FE&TE RE&TE
Linearity Test: P-Value 0.000 0.007 0.000 0.007 0.000
Separability Test: P-Value 0.000 0.261 0.016 0.315 0.014
FE=RE: P-Value 0.348 0.991
Obs 228 228 228 228 228
Implied First Derivative by Region: H
R&D
GDP
World Sample 0.230 0.247 0.231 0.172 0.201
East Asia and the Pacic 0.170 0.192 0.179 0.117 0.149
Europe and Central Asia 0.062 0.070 0.069 -0.012 0.035
High-Income Countries 0.253 0.302 0.280 0.225 0.241
Latin America/Caribbean 0.106 0.138 0.127 0.064 0.097
Middle East/N. Africa 0.213 0.215 0.204 0.139 0.174
South Asia -0.001 0.000 0.008 -0.083 -0.025
Sub-Saharan Africa 0.106 0.049 0.082 0.014 0.089
Implied Cross Derivative by Region:
HIP R
R&D
GDP
World Sample 0.133 0.073 0.081 0.063 0.071
East Asia and the Pacic 0.148 0.084 0.091 0.074 0.086
Europe and Central Asia 0.176 0.109 0.118 0.119 0.132
High-Income Countries 0.101 0.046 0.054 0.024 0.028
Latin America/Caribbean 0.160 0.093 0.097 0.081 0.096
Middle East/N. Africa 0.144 0.083 0.092 0.082 0.091
South Asia 0.188 0.122 0.132 0.145 0.157
Sub-Saharan Africa 0.184 0.127 0.148 0.189 0.192
Note: Derivatives are calculated at the regional means of the relevant variables.
24
Figure 1. The Marginal-Effects Coefficient of log(Human Capital) Depends on the Ranking of
Observations in Terms of Intellectual Property Protection
Human Ca pital Coefficient: Rolling Regressions with Fixed Effects
Observations ranked by IP
.8
.6
.4
Coefficient
.2
0
-.2
0 20 40 60 80 100 120
Iteration
al
90% confidence interv reported. Regressions include 60 observations.
Figure 2. R&D over GDP versus Years of Education across Functional Forms
Linear Prediction Quadratic Prediction Cubic Prediction
.04
.04
.04
.03
.03
.03
R &D over GD P
R &D over GD P
R &D over GD P
.02
.02
.02
.01
.01
.01
0
0
0
0 2 4 6 0 2 4 6 0 2 4 6
Scho ol ing Schoo ling Schoo ling
Fourier Prediction:J=1 Fourier Prediction:J=2 Fourier Prediction:J=3
.04
.04
.04
.03
.03
.03
R &D over GD P
R &D over GD P
R &D over GD P
.02
.02
.02
.01
.01
.01
0
0
0
0 2 4 6 0 2 4 6 0 2 4 6
Scho ol ing Schoo ling Schoo ling