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Would Global Patent Protection be Too Weak Without International Coordination?

Edwin L.-C. Lai and Isabel K.-M. Yan

CESifo GmbH Phone: +49 (0) 89 9224-1410 Poschingerstr. 5 Fax: +49 (0) 89 9224-1409 81679 Munich E-mail: office@cesifo.de Germany Web: www.cesifo.de

Would global patent protection be too weak withoutinternational coordination?∗

Edwin L.-C. Lai†

and

Isabel K.-M. Yan‡

February 1, 2011

Abstract

Would global patent protection be too weak without international coordination? Would it

be too strong with the international coordination mandated by the TRIPS agreement (Agree-

ment on Trade-Related Aspects of Intellectual Property Rights)? We try to answer these ques-

tions using a model of patent-setting game between governments. We introduce profit-biased

government preferences, trade barriers and firm heterogeneity. We make use of the estimates

of a parameter from the political economy literature to proxy for the degree of governments’

profit-bias. Then We calibrate the model using this profit-bias parameter, data on innovative

capability of a number of countries and their market sizes for patent-sensitive goods, and data

on the fractions of American firms that export and that carry out FDI in foreign countries. We

analyze and calibrate the Nash equilibrium and global optimum and find that there is global

under-protection of patent rights when there is no international policy coordination. Calibrat-

ing the model with data on market sizes and patent counts, we find that requiring all countries

to harmonize their patent standards with the equilibrium standard of the most innovative coun-

try (the US) does not lead to global over-protection of patent rights. Therefore, there is no

evidence that there will be global over-protection of patent rights when the TRIPS agreement

is fully enforced.

Keywords: intellectual property rights, patents, TRIPS, harmonization

JEL Classification Number : O34, F13

––––—

† Corresponding author. Department of Economics, Hong Kong University of Science and

Technology, Clear Water Bay, Kowloon, Hong Kong. Phone: (852) 2358-7611; Fax: (852)

2358-2084; Email: elai@ust.hk

‡ Department of Economics and Finance, City University of Hong Kong, Tat Chee Avenue,

Kowloon, Hong Kong. Email: efyan@cityu.edu.hk

∗ Lai would like to thank participants in seminars in Michigan State University, Kobe Univer-sity, Erasmus University, and in European Trade Study Group Annual Conference in Warsaw,

AEA Annual Meeting and Otago Workshop in International Economics for helpful comments.

The work in this paper has been supported by the Research Grants Council of Hong Kong,

China (Project no. CityU 1476/05H) and City University of Hong Kong. Lai would also like

to thank the International Economics Section of Princeton University for their support while

he was writing this paper there.

1 Introduction

The global intellectual property rights (IPR) protection system was given a boost by the im-

plementation of the TRIPS agreement (Agreement on Trade-Related Aspects of Intellectual

Property Rights), which started a gradual process of IPR harmonization in 1995. This agree-

ment effectively requires the strengthening of patent protection of many countries, and forces

the world IPR protection policies towards harmonization (albeit a partial one). There have

been nothing nearly as powerful as TRIPS in its ability to coordinate international IPR pro-

tection, not least because of the large number of countries involved (it is under the auspices of

the WTO) and its ability to enforce rulings due to the credibility of the threat of punishment

through trade retaliation. Given the tremendous repercussions of such a coordinated increase

in the strengths of IPR protection, it is fair to ask whether TRIPS is really a solution to a

global coordination problem. It is clear that TRIPS has distributive effect between countries.1

However, the more important question is whether global IPR protection was too weak before

TRIPS. If it was, then TRIPS can potentially be globally welfare-improving and therefore po-

tentially make all countries better off. For example, if less developed countries (LDCs) lose from

strengthening of their IPR and developed countries (DCs) gain from it, but the latter’s gains

outweigh the former’s losses, then it can be mutually beneficial for the LDCs to accept (partial)

harmonization of IPR standards with the DCs in exchange for the DCs’ opening their markets

for labor-intensive manufacturing goods or agricultural products from the LDCs. However, if

global patent protection was already too strong before TRIPS, then no such synergy exists

between negotiations on trade-related IPR and other issues of global trade.

There is no doubt that some countries attempted to coordinate their IPR policies somewhat

even before TRIPS, but empirical studies have shown that even as late as 1990, market sizes

and innovative capabilities significantly affected variation in the strengths of patent protection

across countries, as would be expected of a world where each country sets its own optimal IPR

standard.2 So, we start with the working assumption that the world was in a non-cooperative

equilibrium before TRIPS, and then ask, Would global patent protection be too weak when left

to individual governments to decide their own level of protection?

1McCalman (2001) has shown that the US was by far the largest beneficiary, followed by Germany and

France as distant second and third beneficiaries. On the other hand, the greatest loser was Canada, followed

by Brazil and UK.2See, for example, Ginarte and Park (1997) and Maskus (2000a).

1

To answer this question, we need to (a) have a theory that explains how the global system

of patent protection was determined in a non-cooperative equilibrium; (b) have a theory that

explains how the optimal global system of patent protection should be; and (c) develop a

sufficient condition for global under-protection (or over-protection) of IPR. In order to answer

(c), we need to explain how a global system of patent protection affects incentives to innovate

and how it creates distortions (deadweight losses). Therefore, we need to answer (a) and (b)

first. To do so, we modify and extend a model by Grossman and Lai (2004). In Section 2,

we shall concisely re-state their theory. Then, we extend the model so as to more realistically

evaluate whether there would be under-protection of IPR in non-cooperative equilibrium.

A second and related question We ask is, Would global patent protection be too strong with

international coordination mandated by TRIPS? To answer this question, we need to determine

what TRIPS has done in the context of our model. Adopting the views of Reichman (1995) and

Lai and Qiu (2003), we make the assumption that TRIPS requires all countries in the world to

set their IPR standards equal to that of the most protective country in Nash equilibrium. The

model described in the last paragraph would help us to answer this second question.

In the basic model of Grossman and Lai (2004), countries play a Nash game in setting the

strengths of patent protection. The best response function of a country’s government is obtained

by setting the strength of patent protection that equates the marginal costs (deadweight loss

due to longer duration of monopoly pricing) and marginal benefits (increased incentives of

innovation) of extending protection, given the strengths of protection of other countries. Each

country conveys positive externalities to foreign countries as it extends patent protection, as it

increases profits of foreign firms in the home market, and increases consumer surplus of foreign

consumers due to induced innovations. As a result, there is under-protection of patent rights

in Nash equilibrium relative to the global optimum. In fact, the degree of under-protection

in Nash equilibrium increases with the number of independent decision-makers in the patent-

setting game.

However, two factors prevents us from directly applying Grossman and Lai’s (2004) basic

model to answer whether global patent protection would be too weak without international

coordination. First, as discussed in the political economy literature, governments may put extra

weight on profits as opposed to consumer surplus in their objective functions (e.g. due to firm

lobbying). We shall call this profit-biased preferences of governments. When governments put

more weight on profits, the marginal cost of patent protection decreases since deadweight loss

2

is smaller. Therefore, patent protection in Nash equilibrium is stronger. Second is the existence

of trade barriers and firm heterogeneity. As recent empirical trade literature documents, only

a small fraction of (more productive) firms export to foreign markets. Moreover, the firms

that do export have to bear variable trade costs, which include transportation cost and import

tariffs. When only a fraction of domestic firms would enter a foreign market, and when there

are transportation cost and other trade costs, the positive international externalities of patent

protection is diminished. Both profit-bias and trade barriers tend to diminish the degree of

under-protection in Nash equilibrium relative to the global optimum. If these forces are strong

enough, there may even be over-protection of patent rights in Nash equilibrium. Therefore,

whether or not there is under-protection of patents in the non-cooperative equilibrium is an

empirical question. In this paper, we incorporate these two features in an extension of the basic

Grossman and Lai (2004) model and derive a sufficient condition for under-protection of patent

in the global economy. We then calibrate the model using the profit-bias parameter estimated

from the empirical literature and then find out how small the trade barriers have to be in order

for there to be under-protection of patents in Nash equilibrium.

In the original model of Grossman and Lai (2004), we can find a functional relationship

between the global strength of patent protection and global welfare. The same strength of

global patent protection creates the same amount of total deadweight losses (what We call

static losses) and aggregate flow of new differentiated goods (what We call dynamic gains) in

each period. As long as the global strength of patent protection is the same, global welfare is

the same, regardless of the combination of individual countries’ strengths of patent protection.

Therefore, the global optimum is a continuum of combinations of national strengths of patent

protection that maximize global welfare. However, this will not be true in the present model.

In the present extended model with trade barriers, there does not exist a scalar measure of the

global strength of patent protection such that there is a functional relationship between the

global strength of protection and global welfare. Despite this problem, we are able to calculate

a sufficient condition under which, starting from Nash equilibrium, global welfare must increase

with increases in the strengths of protection in all countries. When this condition is satisfied,

we can conclude that there is under-protection in global IPR protection.

The key features of the present model are: 1. There is only one single combination, not

a continuum, of national strengths of patent protection that maximizes global welfare. 2.

Externalities still exist, but their magnitude decreases with trade barriers. Therefore, the degree

3

of under-protection decreases with trade barriers. 3. The degree of under-protection decreases

with the profit-bias of governments. Based on the estimates of the profit-bias parameter from

the political economy literature, and our judgment of the plausible magnitude of trade barrier,

we conclude that under-protection of global patent rights in the non-cooperative equilibrium is

very likely. This answers our first question.

One interesting result arising from the origingal G-L (2004) model is that requiring all other

countries to increase their equilibrium patent standards so as to harmonize with that of the

most protective country is never over-protective from the global welfare point view, and thus

it is always welfare-improving. In the present model, whether or not such as harmonization

scheme is over-protective depends on trade barriers, the degree of profit-bias and the distribution

of innovative capability and distribution of market size among the countries in the world.

Calibrating the extended model using data and parameter estimates from the literature, we

find that under such a harmonization scheme, there is no over-protection of patent rights. If

such a scheme captures what the TRIPS has done, then we can say that there the model does

not predict that TRIPS would result in over-protection of patent rights in the global economy.

This answers my second question. Taken together, the answers to the two questions indicate

that international coordination of IPR protection is needed to improve global welfare, and that

the coordination scheme mandated by the TRIPS is not over-protecting patent rights from a

global welfare point of view. In other words, TRIPS is globally welfare-improving.

In section 2, we describe a model modified from Grossman and Lai (2004) by introducing

profit-bias, trade barriers and firm heterogeneity. In section 3 we analyze the Nash equilibrium

and global optimum of the model in a two-country setting. In section 4 we answer the two

questions posed above by analyzing and calibrating the multi-country version of the model.

Finally, we conclude in section 5.

2 A basic theory of international protection of IPR

The theory described in this section is basically modified from Grossman and Lai (2004) by

introducing trade barriers, firm heterogeneity and profit-bias of governments.

Noncooperative Patent Protection

In this section, we study the national incentives for protection of intellectual property in

4

a world economy with imitation and trade. For ease of exposition, we shall start with a two-

country case, though we can easily generalize it to the multi-country case. We derive the

Nash equilibria of a game in which two countries set their patent policies simultaneously and

noncooperatively. The countries are distinguished by their wage rates, their market sizes, and

their stocks of human capital. The last of these proxies for their different capacities for R&D.

We shall term the countries “North” and “South,” in keeping with our desire to understand the

tensions that surrounded the tightening of intellectual property rights (IPR) protection in the

developing countries in the last one or two decades. But our model, when generalized to the

multi-country case may apply more broadly to relations among any number of countries that

have different wages, market sizes and capacities for research.

Let us start our description of the model with a two-country model. Consumers in the two

countries share identical preferences. In each country, the representative consumer maximizes

the intertemporal utility function. The instantaneous utility of a consumer in country is given

by

() = () +

Z ()+ ()

0

[( )] (1)

where () is consumption of the homogeneous good by a typical resident of country at time

, ( ) is consumption of the differentiated product by a resident of country at time

and () is the number of differentiated varieties previously invented in country that remain

economically viable at time . There are consumers in the North and consumers in

the South. While we do not place any restrictions on the relative sizes of the two markets at

this juncture, we shall be most interested in the case where .3 It does not matter for

our analysis whether consumers can borrow and lend internationally or not.

In country , it takes units of labor to produce one unit of the homogeneous good or

to produce one unit of any variety of the differentiated product. New goods are invented in

each region according to = ( ) = ()1−

, where is an input whose

quantity determines the innovative capability of country , is the labor devoted to R&D

there. We assume that , which means that labor is uniformly more productive in the

North than in the South. We also assume that the numeraire good is produced in positive

quantities in both countries, so that = 1 for = and hence = 1.

Define = (1− − ), where is the product life of a differentiated good.

3We remind the reader that market size is meant to capture not the population of a country, but rather the

scale of its demand for innovative products.

5

We now describe the IPR regime. In each country, there is national treatment in the granting

of patent rights. Assume for simplicity that all unexpired patents are fully enforced. Under

national treatment, the government of country affords the same protection Ω to all inventors

of differentiated products regardless of their national origins, where Ω = (1 − −), and

is the length of the patents granted by country . In other words, we assume that foreign

firms and domestic firms have equal standing in applying for patents in any country and that

all patents are subject to the same enforcement provisions. National treatment is required

by TRIPS and it characterized the laws that were in place in most countries even before this

agreement.4 In our model, a patent is an exclusive right to make, sell, use, or import a product

for a fixed period of time (see Maskus, 2000a, p.36). This means that, when good is under

patent protection in country , no firm other than the patent holder or one designated by it

may legally produce the good in country for domestic sale or for export, nor may the good

be legally imported into country from an unauthorized producer outside the country. We

also rule out parallel imports – unauthorized imports of good that were produced by the

patent holder or its designee, but that were sold to a third party outside country .5 When

parallel imports are prevented, patent holders can practice price discrimination across national

markets.

Recent empirical trade literature documents that only a small fraction of firms export. To

capture this phenomenon, we assume that each producer of differentiated goods is faced with

trade barriers, which include: a fixed cost in exporting, equal to , a fixed cost in setting up

production facilities in a foreign country (which we call “carrying out FDI”) equal to , and

a variable trade cost of the iceberg type (which consists of transport costs and import tariffs),

4National treatment is required by the Paris Convention for the Protection of Industrial Prop-

erty, to which 127 countries subscribed by the end of 1994 and 164 countries subscribe today (see

http://www.wipo.org/treaties/ip/paris/index.html). There were, however, allegations from firms in the United

States and elsewhere that prior to the signing of TRIPS in 1994, nondiscriminatory laws did not always mean

nondiscriminatory practice. See Suzanne Scotchmer (2004) for an analysis of the incentives that countries have

to apply national treatment in the absence of an enforcible agreement.5The treatment of parallel imports under TRIPs remains a matter of legal controversy. Countries continue

to differ in their rules for territorial exhaustion of IPRs. Some countries, like Australia and Japan, practice

international exhaustion, whereby the restrictive rights granted by a patent end with the first sale of the good

anywhere in the world. Other countries or regions, like the United States and the European Union, practice

national or regional exhaustion, whereby patent rights end only with the first sale within the country or region.

Under such rules, patent holders can prevent parallel trade. See Maskus (2000b) for further discussion.

6

equal to a fraction of the production cost if a good is exported from one country to another. As

a result, only a fraction of domestic firms will export to and/or or set up production facilities in

another foreign country. There is a constant-elasticity demand curve faced by each consumer,

with being the price elasticity of demand. If we assume further that demand of a typical

consumer is = − (where 1) and define = (1 + )−+1

, then , which is less than one,

is an inverse measure of the variable trade costs. As a first cut, we assume that each of the

three parameters , and are the same across countries. It is assumed that not only is

but · , which guarantees that firms who choose to carry out FDI in

a foreign country always have the option of exporting but choose not to do so. Thus, we have

a situtation as depicted in Helpman, Melitz and Yeaple (2004). For any given foreign market,

a firm with a lower unit cost of production will export, and a firm with a still lower cost will

do FDI. For any given firm, a larger foreign market or stronger patent protection induce the

firm to export to that market; further increases in market size or strength of patent protection

will eventually induce the firm to carry out FDI in that market. See Figure 4.

Recent political economy models indicate that politicians’ desire for campaign contribution

tends to bias the objective function of a government towards the contributors. In our model,

owners of research capital are owners of firms, who denote campaign contributions to politicians.

Following the literature, we let 1+ be the weight a government puts on domestic profits when

a weight of one is put on domestic consumer surplus in its objective function. The parameter

a measures the profit-bias of governments. Note that this approach of assigning additional

exogenous weight to firm profits as opposed to consumer welfare is similar to what is done by

Bagwell and Staiger (2002). They essentially put a weight of 1+ on firms in the government’s

objective function, which they treat as a reduced form derived from the analysis of a political-

economy equilibrium a la Grossman and Helpman (1994). Accordingly, is also the weight a

politician puts on campaign contribution when a weight of one is put on social welfare, given

that his objective function is the weighted sum of the two terms.

Assume that firm productivity follows a Pareto distribution: Pr(1 ) = 1 − ¡

¢where

∈ [∞]. This implies that Pr( ) = (). Define as the earnings per consumer for a

monopoly selling a typical brand; define as the (unconditonal) mean surplus that a consumer

derives from purchases of a good produced at a cost of = 1 and sold at the monopoly price

; and define as the (unconditional) mean surplus he derives from a product sold for the

7

competitive price of = 1. It can be shown (see Appendix A) that

=1

− 1 ·

1− + −1

and

= = Λ

where Λ =¡−1

¢.

It can be easily shown that the distribution of profit per consumer (as well as revenue

per consumer) is also Pareto as long as we assume that firm productivity follows a Pareto

distribution:

Pr( ) = 1−µΛ−1

− 1¶

−1· −

−1 where ∈µΛ−1

− 1 ∞¶.

Axtell (2001) found that the size (number of employees) as well as revenue distribution of

American firms followed a Pareto distribution ( ): Pr( ) = 1−() where ∈ (∞).For size distribution, = 1059 while for revenue distribution, = 0994. In other words, the

estimated for both distributions are very close to one. Therefore, we shall assume −1 to be

close to one in our calibration below.6

Now, define as the probability that a foreign firm can profitably export to country ;

and define as the probability that a foreign firm can profitably carry out FDI in country

. According to our assumptions above, if a firm can profitably export to (carry out FDI in) a

larger foreign market it can also profitably export to (carry out FDI in) a smaller foreign market.

Therefore, the probability that a firm in a country can profitably export to (carry out FDI in)

some foreign market(s) is equal to the probability that it can profitably export to (carry out

FDI in) the largest foreign market. If we further define =¡

¢ 1−+ − (1− )

¡

¢ 1−+ ,

then it can be shown (see Appendix D) that in country k each consumer (or user) can only

enjoy a consumer surplus equal to from consuming a foreign-developed product, due to

the existence of trade barriers in , which not only increase the cost of serving the country

market but also prevents some foreign firms from serving the market. Likewise, a foreign firm

can only earn a profit per consumer (or user) equal to from country k market due to the

existence of trade barriers.

6Note that we want to avoid adopting ≤ 1, as this would correspond to infinite mean. We shall thereforeadopt a value of greater than one but very close to one.

8

It follows that the expected value of a patent of an invention by a firm in country is given

by

=

"X 6=

¡Ω

¢+Ω

#−X 6=

£¡ −

¢ +

¤(2)

In general 6= for 6= .

It can also be shown (see Appendix C) that in equilibrium

=Λ−1

− 1 Ω¡

¢ 1− for all (3)

and therefore

Ω

¡

¢ 1− =Ω

¡

¢ 1− for all 6= . (4)

Moreover,

− = (1− )Ω

Λ−1

− 1¡

¢ 1− for all . (5)

and therefore

Ω

¡

¢ 1− =Ω

¡

¢ 1− for all 6= . (6)

Note that 1− 0. (4) and (6) therefore say that a country with stronger patent protectionor a larger market tends to allow a higher fraction of foreign firms to be exported to the country

as well as a higher fraction of foreign firms to set up production facilities there. (3) and (5)

say that given the strengths of patent protection of countries, larger fixed cost of exporting

(carrying out FDI) lowers the fraction of firms that can export to (carrying out FDI in) other

countries. Interestingly, (5) indicates that given the strengths of patent protection of countries,

a larger variable trade cost (smaller ) induces a higher and therefore a higher fraction of

foreign firms doing FDI in any country.

Substituting the above expression for and , (3) and (5), into the expression for ,

(2), and recall that =¡

¢ 1−+ − (1− )

¡

¢ 1−+ , we can re-write (see Appendix D)

the expression for the value of a patent as

= X 6=

µ− 1

¶Ω +Ω

This is an interesting equation as can be expressed in a very simple form though it has

taken into account a myriad of factors including fixed costs of exporting and FDI, variable cost

of exporting, heterogeneous firms and screening of firms by the market. The only assumption we

9

make is that the trade costs and the parameters of the Pareto distribution of firm productivities

are the same across countries.

We solve the Nash game in which the governments set their patent policies once-and-for-all

at time 0. These patents apply only to goods invented after time 0; goods invented beforehand

continue to receive the protections afforded at their times of invention. So long as the gov-

ernments cannot remove protections that were previously granted, the economy has no state

variables that bear on its choice of optimal patent policies at a given moment in time. This

means that the Nash equilibrium in once-and-for-all patents is also a sub-game perfect equilib-

rium in the infinitely repeated game in which the governments can change their patent policies

periodically, or even continuously.

3 Two-country Case

Let us describe, for given patent strengths Ω and Ω, the life cycle of a typical differentiated

product developed in South. During an initial phase after the product is introduced, the

inventor holds an active patent in both countries. The patent holder earns an expected flow of

profits of from sales in the Northern market and an expected flow of profits of

from sales in the Southern market. Each Northern consumer realizes a flow of expected surplus

of from his purchases of the good. A Southern consumer realizes an expected flow of

consumer surplus of from his purchases of the good.

(Since there is no cost of patenting, a firm always patent its good in all countries once it is

developed. Once patented, the technology is disclosed. But the good cannot be legally imitated

in that market until the patent expires. So, when a patent has expired consumer surplus is

whether a good was developed overseas or locally, as countries can always imitate foreign-

developed goods when the patent has expired, and these imitated goods are produced locally,

and so there is no trade barrier when imitated goods are sold.7)

After a while, the patent will expire in one country. For concreteness, let’s say that this

7We assume that an innovator patent his innovation all over the world before he learns to which countries,

or whether, he would be able to export. Note that even if it turns out that a good is not exported to a foreign

country, nobody in the foreign country can legally produce or sell the good locally while the patent for the good

is in force. Under such circumstance, local consumers cannot enjoy the good while its patent is in force locally.

When the patent is not in force, local imitators can produce the good with zero imitation cost, and the market

becomes perfectly competitive.

10

happens first in the South. Then the good will be legally imitated by competitive firms pro-

ducing there, for sales in the local (Southern) market. The imitators will not, however, be able

to sell the good legally in the North, because the live patent there affords protection from such

infringing imports. When the patent expires in the South, the price of the good falls perma-

nently to = 1, and the original inventor ceases to realize profits in that market. The flow

of consumer surplus in the South rises to .

Eventually, the inventor’s patent expires in the North. Then the Northern market can be

served completely by competitive firms producing in the North. At this time, the price of

the good in the North falls to = 1 and households there begin to enjoy the higher flow of

consumer surplus. The original inventor loses his remaining source of monopoly income.

Finally, after a period of length has elapsed from the moment of invention, the good becomes

obsolete and all flows of consumer surplus cease.

3.1 The Best Response Functions

Consider the choice of patent policies Ω and Ω that will take effect at time 0 and apply

to goods invented thereafter. The expressions for government objective function in country ,

discounted to time 0, is given by

(0) = Λ0 +

+ (1 + )

+

£Ω + ( −Ω)

¤+

−

£Ω + ( −Ω)

¤= Λ0 +

( − (1 + ))

+

£Ω + ( −Ω)

¤+−

£Ω + ( − Ω)

¤+

(1 + )

∙Ω + −−Ω−

µ− 1

¶¸, for =

(7)

where Λ0 is the fixed amount of discounted surplus that consumers in country derive from

goods that were invented before time 0. The second equality arises from the fact that there is

zero present-discounted profit for each firm, so that

+ = = £Ω + −−Ω−

¡−1

¢¤, where =

£Ω + −−Ω−

¡−1

¢¤is the value of a new patent developed in country .

We are now ready to derive the best response functions for the two governments. The best

response expresses the strength of patent protection that maximizes a national government’s

objective as a function of the given patent policy of its trading partner. Consider the choice of

11

Ω by the government of the South. This country bears two costs from strengthening its patent

protection slightly. First, it expands the fraction of goods previously invented in the South

on which the country suffers a static deadweight loss of [ − − (1 + )]. Second, it

augments the fraction of goods previously invented in the North on which its consumers realize

surplus of instead of . Notice that the profits earned by Northern producers in

the South are not an offset to this latter marginal cost, because they accrue to patent holders

in the North. The marginal benefit that comes to the South from strengthening its patent

protection reflects the increased incentive that Northern and Southern firms have to engage in

R&D. If the objective-maximizing Ω is positive and less than , then the marginal benefit

per consumer of increasing Ω must match the marginal cost, which implies

[ − − (1 + )] + ( − )

=

£Ω + ( −Ω)

¤+

£Ω + ( −Ω)

¤, (8)

where is the responsiveness of innovation in each region to changes in the value of a patent

(in elasticity form), i.e.=

.8

Similarly, in the North, the marginal benefit of strengthening patent protection must match

the marginal cost at any interior point on the best response curve. The marginal cost in

the North is different from that in the South, because the North’s national income includes the

profits earned by Northern patent holders but not those earned by Southern patent holders. The

marginal benefit differs too, because the effectiveness of patent policy as a tool for promoting

innovation varies according to the importance of a country’s market in the aggregate profits of

potential innovators and because the surplus from a typical product over its lifetime depends

upon a country’s patent regime. The condition for the best response of the North, analogous

to (8) above, is

( − ) + [ − − (1 + )]

=

£Ω + ( −Ω)

¤+

£Ω + ( −Ω)

¤. (9)

8The fact that the two supply elasticities and are equal despite the differences in human capital

endowments, in employment, and in labor productivity is a property of the Cobb-Douglas research technology.

It follows from the observation that

=

(1− )for all

12

The two best response functions can be written similarly as

−¡1− Λ

¢+ [1− Λ− (1 + )Λ0]

=

© [1− (1− Λ)] + −

£1− ¡1− Λ

¢

¤ª + −−

¡−1

¢ for = , (10)

where Λ = ; Λ0 = ; = Ω ; = ( + ) is the share of world innovation

that takes place in country . Moreover, = ( + ) for our Cobb-Douglas research

technology. Thus, both and are independent of the patent policies in the Cobb-Douglas

case. Given that −1 is sufficiently small (i.e. close to one, which has been justified by empirical

research findings), we can show from (10) that the best response functions are downward sloping,

and that the best response function for the South is everywhere steeper than that for the North,

when the two are drawn in (Ω Ω) space. It follows that the curve for the South must be

steeper than that for the North at any point of intersection. This guarantees uniqueness of the

Nash equilibrium and ensures stability of the policy setting game.

Thus, the patent policies of the two countries are strategic substitutes. To understand

the strategic interdependence between the governments in choosing their policies, consider the

choice of patent protection by the South. Suppose the North were to strengthen its patent

protection; i.e., to increase Ω . This would shrink the fraction of total discounted profits that

an innovator earns in the South and so, ceteris paribus, reduce the responsiveness of global

innovation to patent policy in the South. Moreover, the increase in Ω would draw labor into

R&D in the North and South. The South would find that its market is relatively less important

to potential innovators. For this reason, the marginal benefit to the South of strengthening its

patent protection would fall and so the government would respond to the increase in Ω with

a reduction in patent length or an easing of enforcement.

We summarize the most important findings in this section as follows.

Proposition 1 Let the research technology be = ()1−

in country , for = ,

and −1 is sufficiently small (i.e. larger than but close to one). Since the two patent policies

are strategic substitutes in both countries, there exists a unique and stable Nash equilibrium of

the policy setting game.

13

3.2 International Patent Agreements

In this section, we study international patent agreements.9 We begin by characterizing the

combinations of patent policies that are jointly efficient for the two countries.10 Then we

compare the Nash equilibrium outcomes with the efficient policies, to identify changes in the

patent regime that ought to be effected by an international treaty. Finally, we address the issue

of policy harmonization.

Efficient Patent Regimes

Let =Ω + Ω . A Southern firm that earns a flow of expected profits of

for a period of length in the South and a flow of expected profits of for a period of

in the North earns a total discounted sum of expected profits equal to . On the other

hand, a Northern innovator earns a total discounted sum of expected profit equal to where

= Ω +Ω .

Consider the choice of patent policies Ω and Ω that will take effect at time 0 and apply

to goods invented thereafter. Summing the welfare expressions in (7) for = and = , we

find that

[(0) +(0)] = (Λ0 + Λ0) + ( − ) + ( − )

+£ −Ω ( − − )

¤( + )

+£ −Ω ( − − )

¤( + ) (11)

There is clearly a tradeoff as patent strength is increased in either country. For example, as

Ω increases there is a direct effect of an increase in the deadweight loss Ω ( − − ),

which lowers global welfare. But there are indirect effects that tend to increase global welfare:

an increase in leads to an increase in (), which induces faster innovation in the North

(South), thus increasing () and (). These effects are globally welfare-improving.

9See also McCalman (2002), who discusses globally efficient patent policies in his two-country extension of

the Nordhaus (1969) model. Lai and Qiu (2003) consider whether the joint welfare of the two countries would

be increased if the South were to extend its patents so as to be equal in length to those chosen by the North in

a Nash equilibrium.10Ours is a constrained efficiency, because we assume that innovation must be done privately and that patents

are the only policies available to encourage R&D. We do not, for example, allow the governments to introduce

R&D subsidies, which if feasible, might allow them to achieve a given rate of innovation with weaker patents

and less deadweight loss.

14

In fact, it can be shown that when −1 is sufficiently small, there exists a unique globally

optimum combination of Ω and Ω.

How do the efficient combinations of patent policies compare to the policies that emerge

in a noncooperative equilibrium? The answer to this question – which informs us about the

likely features of a negotiated patent agreement – is illustrated in Figure 1. The figure depicts

the best response functions and the efficient policy combinations on the same diagram.

Figure 1 about here

In the figure, the globally optimal policy combination is depicted by point . The iso-

global-welfare lines around are also shown. The diagram shows that simultaneous increases

of Ω and Ω from point leads to an increase in global welfare. This is true when is small,

i.e. when government’s profit-bias is weak. The reasons are clear. Starting from a point on

the South’s best response function, a marginal strengthening of IPR protection in the South

increases world welfare when profit-bias is weak. Such a change in Southern policies has only

a second-order effect on welfare in the South, but it conveys two positive externalities to the

North. First, it provides extra monopoly profits to Northern innovators, which contributes to

aggregate income there. Second, it enhances the incentives for R&D, inducing an increase in

both and . The extra product diversity that results from this R&D creates additional

surplus for Northern consumers.

By the same token, a marginal increase in the strength of Northern patent protection from

a point along increases world welfare. Such a change in policy enhances profit income for

Southern firms and encourages additional innovation in both countries. It follows that when

is small world welfare rises as Ω and Ω simultaneously increase from point . However, if

is not “small”, then it is possible that an efficient patent treaty may require all countries to

reduce their strengths of patent protection. Whether or not is small in practice is an empirical

question, which we seek to answer in the next section.

We define global under-protection of patent rights to be a situation when global welfare rises

as Ω and Ω are both raised from their Nash equilibrium levels. If there is under-protection of

patent rights, then starting from any interior Nash equilibrium, an efficient patent treaty must

strengthen patent protection in both countries. It also implies that the treaty will strengthen

global incentives for R&D and induce more rapid innovation in both countries.

15

4 Multi-country Case

It is useful to consider a multi-country setting, as the number of independent decision-making

governments plays a crucial role in whether there is under-protection of IPR in Nash equilibrium.

Let there be countries in the set N of country-players. Define ≡ − ( − )Ω as

the present discounted value of consumer surplus for a consumer in country i derived from

consumption of a home-developed differentiated good over its product life; and 0 ≡ −¡ −

¢Ω as the corresponding consumer surplus derived from consumption of a product

developed by a foreign country.

Nash Equilibrium

In a multi-country setting, the best-response function of country i is

ÃX 6=

!¡ −

¢+ ( − )− (1 + )

=

ÃX 6=

Ω

0

!+

Ω

=

ÃX 6=

!

0 +

for = 1 2 (12)

which can be re-written as

ÃX 6=

!¡1− Λ

¢+ [1− (2 + )Λ]

=

*X 6=

(

£1− ¡1− Λ

¢

¤P 6=¡−1

¢ ¡

¢+

)+

[1− (1− Λ)]P 6=¡−1

¢ ¡

¢+

+(where ≡ Ω ) for = 1 2

The left-hand side (LHS) of equation (12) is, in fact, the marginal cost per consumer in

country i of strengthening IPR there. The first term is the loss in consumer surplus attributed

to inventions from firms outside country i (note that while patent protection is in force in

country i, each consumer only enjoys consumer surplus of from each foreign-developed

product, but when patent protection ceases, domestic firms can imitate the good at no cost, and

so each consumer obtains consumer surplus of from the good); the second term is the loss of

16

consumer surplus attributed to inventions from country i; and the third term is the offsetting

of the losses of consumer surplus by gains in profits of firms in country i. The right-hand side

(RHS) or the third line of (12) is the marginal benefit per consumer in country i. The first term

is the increase in consumer welfare in country i due to increases in flows of innovations from

firms outside country i; the second term is the increase in consumer welfare in country i due

to the increase in flow of innovation from country i. If We define the left-hand side of (12) as

() and the right-hand side of (12) as, then1

()

Ω=−(), where ()

is the Government i’s objective function. (Hereinafter, we put an argument ‘’ after the name

of a function if profit-bias affects the value of the function.)

In order to solve the above system of equations, we need the following additional equations:

= ¡

¢ 1−+ + (1− )

¡

¢ 1−+ for = 1 2

¡

¢−( −1 ) =

¡

¢−( −1 ) for = 2 (assume that k=1 for the US)

¡

¢−( −1 ) =

¡

¢−( −1 ) for = 2 (assume that k=1 for the US)

= 015 and = 003

where the superscript denotes the country with the largest market outside of the US. It turns

out that is Japan.

As discussed above, −1 should be larger than one but very close to one according to Axtell

(2001). The case with −1 = 1 is given byÃX

!(1− Λ)− (1 + )Λ =

(P

) [1− (1− Λ)]P

for = 1 2

Amazingly, this is mathematically equivalent to assuming that there is neither variable nor

fixed trade costs. Therefore, the general case collapses back to the free-trade case when −1 = 1.

As the free-trade case (with linear equations in unknowns for = 1 2 ) is much

easier to compute than the more general case (where −1 1 and there are 4−2 equations and

4−2 unknowns), we start our analysis by assuming −1 = 1, which provides a good benchmark

and a good approximation of the central case of analysis, as we shall adopt a value of −1 greater

than but close to one in the central case, a value adopted by many in the literature.

Global Optimum

17

Next, we want to compare the Nash equilibrium with the global optimum. It can be easily

shown that the first-order condition for global welfare maximization with respect to the choice

of Ω is given by

"() + −

ÃX 6=

!#

= × +X 6=

ÃX 6=

Ω

0

!+X 6=

Ω

= × +X 6=

"

µ

0

¶+

ÃX 6=

!

0

#+X 6=

µ

¶(13)

The LHS is the marginal global cost of strengthening IPR protection in that country. The

second term inside the squared brackets is the welfare that will not be taken into account

when IPR protection in country i is chosen to maximize global welfare instead of to maximize

government i’s profit-biased objective (therefore it is an addition to marginal cost); the third

term inside the squared brackets reduces the global marginal cost as it takes into account the

increases in profits of firms outside of country i. The RHS represents the marginal global benefit

of strengthening IPR in country i. The second term and the third term are both increases in

welfare of consumers outside of country i. The second term is due to faster foreign innovations,

while the third term is due to faster domestic innovations (“foreign” and “domestic” here are

relative to each country outside of country i). The cross-border externalities of IPR protection

are captured by the third term inside the squared brackets on the LHS plus the second and

third terms on the RHS. It is apparent that since an increase in the variable trade cost (a

decrease in ) leads to less international spillovers, the likelihood of under-protection of IPR

in equilibrium is lower. Likewise, an increase in profit-bias (an increase in ) reduces the gap

between marginal global benefit and marginal national benefit, making under-protection of IPR

less likely.

Let us define the of the first order condition above as and the

as . It follows that

1

Ω=

− , where

is world welfare (without bias

towards firm profits).

18

4.1 Is there global under-protection of IPR?

We define under-protection as a situation when, starting from Nash equilibrium, global welfare

increases as a result of some positive changes in all Ω∈N (where the magnitudes of increaseare not necessarily equal). The point of the analysis is to come up with a sufficient condition

under which, starting from Nash equilibrium©Ω

ª∈N , some simultaneous (but not necessarily

equal) increases in IPR protection of all countries is globally welfare-improving. Note that

an increase in the strength of protection in all countries raises the values of all patents. This

increases the global deadweight losses, but gives a boost to the rate of innovation. To simplify

the analysis, we focus on changes in Ω∈N such that Ω = Ω for all i. We want to find

a sufficient condition under which such changes lead to an increase in global welfare. In other

words, we seek a condition under which the marginal global benefit outweighs the marginal

global cost.

First We prove the following lemma:

Lemma 1. A sufficient condition for under-protection of IPR in Nash equilibrium isX

1

Ω

0 for all Ω∈N such thatX

1

()

Ω= 0.

Proof. A sufficient condition for under-protection isX

1

Ω

0 in Nash equilibrium©Ω

ª∈N .

This is true becauseP

1

Ω 0 implies that if we increase each Ω in

©Ω

ª∈N such that

Ω = Ω ∀, then =³P

ΩΩ

´=³P

1

Ω

´Ω 0. That is, global welfare

increases as each Ω increases slightly such thatΩΩ

=

for all 6= . This clearly indicates

under-protection at Nash equilibrium. Moreover, since()

Ω= 0 for all in Nash equilibrium,P

1

()

Ω= 0 includes the Nash equilibrium as a special case. ¥

To understand Lemma 1 better, let us consider a two-country case. First refer to Figure 1

for an idea of the relationship between Nash equilibrium and global optimum. In that diagram,

point E is the Nash equilibrium while point G is the global optimum. BRF-S and BRF-N are

the best response functions of South and North respectively. Point G is at the intersection of the

curves

Ω= 0 and

Ω= 0, which are not shown.11 It is not hard to see that starting from

11Note that the slopes of the iso-global-welfare lines = are always equal to

at their intersection

19

any point on the iso-global-welfare line to the left of GG (defined by 1

Ω+ 1

Ω= 0), any

small increase in Ω and Ω such thatΩΩ

=

would increase . In the context of Figure

1, a necessary and sufficient condition for there to be under-protection in Nash equilibrium is

that point E is to the left of the curve GG.12

Figure 1 and 2 about here

Figure 2 shows the relationship between the curves GG and EE (defined by 1

()

Ω+

1

()

Ω= 0). The curves FOC-S and FOC-N are the first order conditions for maximization

of global welfare with respect to the choice of Ω and Ω respectively. In the context of Figure

2, a sufficient condition for point E to be on the left of GG is that EE is to the left of curve GG.

And this is exactly the condition stated in Lemma 1. If this condition is satisfied, at any point

that lies on EE (including the Nash equilibrium point E), any small change in Ω and Ω such

thatΩ =Ω would increase global welfare, since1

Ω+ 1

Ω 0. Proposition

2 below provides a sufficient condition for the EE to be on the left of GG. Therefore, our next

step is to prove the following proposition:

Proposition 2 A sufficient condition for under-protection of IPR in Nash equilibrium when

there are trade barriers and profit-bias is

−X6=max

0 (14)

where max is the largest among all countries.

Proof. See the appendix. ¥

To check that −¡P − max

¢ 0 is a reasonable condition, note that in the special case of

the basic model where there is neither trade barrier nor profit-bias, when there are two countries

( = 2), = 1, = 1 for = 1 2 and = 0, the condition is satisfied. Moreover, it accords

with the intuition that the free-rider problem gets more serious when there are more countries

playing the patent-setting game, for a larger leads to higher chance of under-protection. It

with the line 1

Ω+ 1

Ω= 0. This is because, along = , Ω

Ω= −

³

Ω

Ω

´. But at any

point on the curve 1

Ω+ 1

Ω= 0, we have −

³

Ω

Ω

´=

.

12Note that if point E is to the right of GG, then any simultaneous small decrease of Ω and Ω such that

ΩΩ

=

would increase .

20

also is consistent with the notions that trade barriers weaken the cross-border externality of

IPR protection, because a smaller for each leads to lower chance of under-protection, and

that stronger government bias towards patent-holding firms tends to strengthen patents, for a

larger leads to lower chance of under-protection. In what follow, we shall explain a calibration

exercise to find out whether the above sufficient condition is satisfied.

What is a reasonable value for ? In the political-economy literature (Grossman and Help-

man 1994; Maggi and Goldberg 1999), researchers have tried to estimate the weight the U.S.

government puts on campaign contributions when it puts a weight of unity on welfare. They

rarely come up with a number more than 0.5. Since this is a preference parameter, it should be

the same in the context of patent protection. Suppose there is a patent lobby, and suppose there

is no consumer lobby, nor is there lobbying from other sectors of the economy. Based on these

suppositions, it is easy to show that the value the government puts on campaign contributions

is exactly the same as in our model.13 To make it more likely to be over-protection, we set

= 1.

What is a reasonable value for ? This is the number of independent government decision-

makers in the patent-setting game. Thus, it is the number of countries in the world that consume

and trade patent-sensitive goods, and that adopt neither zero nor full patent protection. Ginarte

and Park (1997) construct a patent rights index for a large number of countries, and none of

the fifty most innovative of them is reported to have zero protection or full protection. From

the data set in the World Intellectual Property Organization (WIPO) website, we find that

residents of 39 countries obtained patents from the US Patent Office in the years 1996-1999,

and residents of 41 countries obtained patents from the European Patent Office during this

period.14 In Table 1, we list the thirty most innovative countries (as measured by the average

number of patents they obtained from the US Patent Office in 1996-1999) with their patent

counts and market sizes. As inequality (14) indicates, the more countries that are included

in the game, the more likely the inequality is satisfied. Therefore, it suffices to prove under-

protection if we find that the inequality holds for the twenty countries with the largest market

for patent-sensitive goods. Therefore, we use these countries for our empirical analysis. Thus,

= 20.

What are reasonable values for the probabilities that firms export and produce and sell in

13A proof is available from the author upon request.14For the WIPO website, refer to http://www.wipo.int/ipstats/en/statistics/patents/

21

foreign countries? Eaton, Kortum and Kramarz (2004) report that in 1986 only 17.4% of French

manufacturing firms exported, and of those who exported, only 19.7% exported to ten or more

countries. Moreover, in 1987, only 14.6 % of US manufacturing firms exported. Bernard, Eaton,

Jensen and Kortum (2003) report that 79% of US manufacturing plants did not export at all in

1992. To summarize, the most accepted figures for the manufacturing sector of the US are that

15-20% of firms sell to foreign markets, of which about 1/5 produce in the foreign market in

which they sell. (See, for example, Bernard, Jensen and Schott 2009.) To be conservative, we

assume that 15% of American firms in the patent-sensitive industries sell to foreign markets,

while 3% produce in the foreign countries in which they sell their goods. In other words, we

set = 015 and

= 003, as Japan is the largest foreign market for US firms.

From Lai, Wong and Yan (2007), we obtain the average estimate of elasticity of demand

of patent-sensitive goods out of thirty studies / countries as 5.63. So, we assume = 5. For

robustness, we also try = 15.

We estimate the value of based on previous work of Boldrin and Levine (2009). We

conclude that the best point estimate of is 4. It turns out that changing (say to 1) does not

affect the results very much. So, we do not present any results corresponding to the alternative

values for .

What is a reasonable value for ? To answer this question, we instead ask what is a reason-

able value for (− 1). We discussed above that it is reasonable to assume that (− 1) isgreater than one but very close to one. Therefore, we try the cases of (− 1) = 1 and 105.For the variable trade cost, we try = 0 and 05 respectively. As it is unlikely that the

iceberg trade cost is more than 0.5, there is really no need to try any greater than 0.5.

In the case (− 1) = 1, it does not matter what value takes. Therefore, we have

altogether six cases to consider for the different combinations of (− 1), , and .

We proxy by the natural logarithm of the dollar value of the consumption of patent-

sensitive goods by each country and proxy by the number of patents granted to residents of

each country by the U.S. patent office (adjusted for home bias of American patentees). Data on

for 1996-1999 are obtained from Lai, Wong and Yan (2007), and data on for 1996-1999

are from the website of WIPO. We use data for the twenty countries with the largest except

Russia (for lack of market size data).

The results of our calibration is listed in the Tables 2A-2F. We find that for all twenty

countries, is greater than 0.7 in all six cases. It follows that condition (14) is satisfied in all

22

six cases we tried. Therefore, we conclude that there is under-protection of patent rights when

there is no international coordination. This is because of the free-rider problem in protection

of patents. When a country determines its strength of patent protection, it does not take into

account the positive externality on other countries, leading it to protect less than the optimal

amount from the global welfare point of view.

As a final note in this subsection, we recognize that some people may argue that the globally

optimal combination of strengths of national patent protection should take into account the

politically-augmented objective function of each national government, as these functions reflect

the preferences of each government, which represents each country in international negotiations.

If maximizing the sum of the politically-augmented objective functions is the goal of interna-

tional coordination, then one simply remove the term + inside the squared brackets on the

LHS of equation (13). In this case, it is clear that there is always under-protection of patents

in each country, as the marginal global cost is lower than the marginal national cost while the

marginal global benefit is higher than the marginal national benefit. There are unambiguous

positive cross-border externalities as the increases in profits of foreign firms and consumer sur-

plus of foreign consumers due to induced innovations are not taken into account as Ω increases,

just like in the basic model. The spillovers are smaller in this case, as there are trade barriers.

4.2 Harmonization with the most protective country

We have concluded that global patent protection would be too weak without international co-

ordination. But would it be too strong with the current international coordination, namely

TRIPS? One way to characterize TRIPS in the context of our model is that TRIPS requires

all other countries to harmonize their IPR standards with the pre-TRIPS standards of the

most protective country. A similar view has been expressed by a few observers, such as Re-

ichman (1995), and the assumption has been used to analyze multi-issue negotiations in the

GATT/WTO by Lai and Qiu (2003).15 Under this assumption, is such a harmonization scheme

15If one examines the Ginarte-Park patent rights index for the periods 1960-1990, 1995, 2000 and 2005 (refer

to Park 2005), one sees that the most protective country before TRIPS (i.e. 1960-1990) was the US, whose

index was 4.14. By 2005, all developed or newly industrialized economies would have already adopted the patent

standard required by TRIPS. What is the patent right index for countries that adopt the minimum requirement

mandated by TRIPS? It turned out that it is about 4.1 (e.g. Israel 4.13, Australia 4.17, New Zealand 4.01,

Norway 4.17). So harmonization with the pre-TRIPS standard of the US is more or less what the TRIPS

mandated.

23

going to be over-protective from a global welfare point of view?

Suppose best response function (12) is applied to country k where Ω = maxΩ

∈N .Suppose we sum up all the J first order conditions (13) and impose the restriction Ω = Ω∗

∀ ∈ N on this equation. As Ω∗ is the globally efficient harmonized patent strength, Ω Ω∗

is the necessary and sufficient condition that there is no over-protection of patent rights even

if all countries harmonize their IPR standards with the most protective country in the world.

As national patent strengths are strategic substitutes, we can pin down the upper bound of

Ω by finding the best response of country k, call itΩ, if all other countries do not protect at all.

Then, Ω Ω∗ is a sufficient condition for there to be no over-protection under harmonization.

Applying Ω = Ω and Ω = 0 ∀ 6= to equation (12), and manipulating the resulting equation,

we get ÃX 6=

!¡ −

¢+ ( − )− (1 + )

=

nP 6=

£ −

¡ −

¢Ω

¤o+

£ − ( − )Ω

¤Ω

Simplifying, multiplying both sides byP

∈N and shifting a term to the left hand side,

we have

(P

)¡P

¢ ¡

−

¢− (1 + ) (P

)¡1−

¢ − (

P) (1 + )

= (P

)¡P

¢

Ω

− (P

)¡P

¢ ¡

−

¢(15)

where we have simplified notation by definingP

≡P

∈N andP

≡P

∈N .

Summing up all J first order conditions (13) and applying Ω = Ω∗ ∀ ∈ N , we haveX∈N

n

h³P 6=

´ ¡ − −

¢+ ( − − )

io

=X∈N

nP 6=

£ −

¡ −

¢Ω∗¤+

£ − ( − )Ω

∗¤oΩ∗

As Axtell (2001) indicates, the literature found that for a large sample of US firms, 1−

is very close to 1. It can be shown that when 1− = 1, = 1 = for all . Let us make

the approximation that = for all , and continue to leave the term in all equations.

Returning to the above equation, simplifying and shifting a term to the left hand side, we have

(P

)¡P

¢ ¡

− − ¢− (1 + )

¡1−

¢ ¡P

¢ −

¡1−

¢ ¡P

¢

= (P

)¡P

¢

Ω∗− (

P)

¡P¢ ¡

−

¢(16)

24

whereP

≡P

∈N .

A sufficient condition for Ω Ω∗ is therefore 15 − 16 0, which is equivalent to£(P

)¡P

¢− ¡P

¢¤ − (1 + )

¡1−

¢ £ (

P)−

¡P

¢¤

− £ (P)−¡P

¢¤ − (

P) 0

(17)

Recalling ≡ P

and defining ∆ ≡¡P

¢£(P

)¡P

¢¤, we get

Proposition 3 A sufficient condition for there to be no over-protection of global IPR by requir-

ing all countries to harmonize their patent standard with that of the most innovative country in

Nash equilibrium is

−∆ + 2 +

1−−∆ + 2 +

, (18)

assuming each consumer is faced with a constant elasticity demand curve and that = for

all .

Proof. Assuming constant elasticity demand = − faced by each consumer, it can be easily

shown that = (see Appendix D). Substituting into inequality (17) and manipulating, we

obtain (18). ¥

Let us make the (realistic) assumption that the most protective country before TRIPS is

also the most innovative, i.e. = max∈N . Assume further that is greater than the

average market size, i.e. P

, which is realistic. A few observations are in order.

First, if = 1 for all and = 0, then the condition (18) is clearly satisfied. This confirms

the result in subsection 4.2. Second, the condition is more likely satisfied if is smaller or

is larger. This makes sense as they tend to make global under-protection more likely in

Nash equilibrium. Third, as gets closer toP

, it makes and −∆ both smaller,

which in turn makes the right hand side of (18) smaller, making the condition more likely to be

satisfied.16 In other words, it is less likely for there to be over-protection when the distribution

16First, as gets further away fromP

, it makes larger. But it also makes −∆ larger. This canbe seen from the fact that −∆ increases from 0 to 1−

P as increases from

P to 1 (i.e. as

the distribution of changes from totally even to totally skewed). Second, we need 1, which means that

1 − . Once this is established, we see that an increase in keeping −∆ constant, or an increase

in −∆ keeping constant both lead to an increase in the right hand side of (18). Applying the chain rule,we can conclude that the right hand side of (18) increases with .

25

of innovative capability among countries is not too skewed. This makes sense as harmonization

with the standard of the most innovative (and protective) country becomes more onerous for

the other countries if the most protective country is a lot more protective than the rest of the

countries. In general, a condition more stringent than stated in Proposition 2 is required, as it

requires not only that patent rights are under-protected in Nash equilibrium, but sufficiently

so.

Therefore, we need to know the distributions of and among the countries. From the

data, we obtain = 0491 and ∆ = 00545, and therefore −∆ = 0437.17 With these data

inserted into (18), we find that for = 1, (18) is reduced to

3124 +

3165 + = 0994 when = 4.

The sufficient condition is satisfied or very close to being satisfied, as is close to one.

Numerical calculation actually shows that based on the analysis of the twenty largest markets,

we get Ω Ω∗ when = 4, = 1, = 15 or 5, = 0 or 05, (− 1) = 1 or 105. (Refer

to Table 2A-2F.) Therefore, we conclude that the distribution of innovative capability among

countries is not too skewed so that requiring all countries to harmonize their patent standards

with that of the most protective (and most innovative) country in Nash equilibrium (i.e. the

US) does not lead to over-protection of patent rights from the global welfare point of view.

This result implies that while TRIPS increases the welfare of the countries that are most

protective before TRIPS but hurts the countries that are least protective before TRIPS, the

gains of the former group of countries outweigh the losses of the latter group of countries, as

global welfare increases. The situation in a two-country case is shown in Figure 1. It shows

that global harmonization with the North’s pre-TRIPS standard is a movement from point E

to point E’. As E’ is still inside the frontier GG, global welfare increases from E to E’. Many

commentators (e.g. Reichman 1995) believe that TRIPS is a quid pro quo between the North

(the more protective countries before TRIPS) and the South (the less protective countries before

TRIPS) in which the former opens their market to the exports of traditional goods from the

latter while the latter agrees to harmonize its IPR standards with the pre-TRIPS standards of

the former. This observation supports our result here: As the North gains more than the South

17 ranges from 011 to 1 as the distribution of changes from totally even to totally skewed, while −∆ranges from 0 to 064 as changes from totally even to totally skewed. Therefore, the current distribution of

is somewhere in the middle.

26

loses in this global IPR harmonization scheme, the North has incentives to “bribe” the South

to harmonize IPR. A detailed analysis of this sort is found in Lai and Qiu (2003).

5 Conclusion

We extend the basic model of Grossman and Lai (2004) by introducing profit-biased government

preferences and trade barriers. We make use of the estimates of a parameter from the political

economy literature to proxy for the degree of governments’ profit-bias. Then we calculate that

the sufficient condition for under-protection of patents in the global system in Nash equilibrium

is satisfied for all the reasonable values of trade barriers we can think of. Therefore, we conclude

that there would be under-protection of patent rights without international policy coordination

in IPR protection. It means that the free-rider problem with a large number of independent

players overrides the effects of profit-bias and trade barriers, giving rise to too low a rate of

innovation in the world.

Does requiring all countries to harmonize their patent standards with the equilibrium stan-

dard of the most innovative country lead to global over-protection of patent rights? To answer

this question requires us to know the distribution of innovative capability among countries as

well as the distribution of the domestic market size among countries. Drawing on estimates of

these variables for twenty countries, and applying them to our model, we conclude that such

harmonization quite likely still does not lead to global over-protection of patent rights. There-

fore, there is no evidence that there will be global over-protection of patent rights when the

TRIPS agreement is fully enforced.

We have only considered expanding-variety type of innovation in our model. Other types

of innovation, such as quality-improvement type of innovation, have not been considered. If

innovation takes the form of improvement of the quality of state of the art technology, then

as a country strengthens patent protection, such as by increasing the patent breadth, it is not

clear if foreign innovators can benefit from it, as it is harder for an innovation to be patented,

though once patented its monopoly position lasts longer. It is also not clear if foreign consumers

benefit from it as the rate of innovation may not be made faster by such a policy. Therefore,

we are not sure of the nature and the signs of the resulting cross-border externalities and their

net effect. This is left for future work.

27

References

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2001, vol. 293, pp. 1818-1820.

[2] Bernard, Andrew B, J. Bradford Jensen and Peter K. Schott (2009) “Importers, Exporters,

and Multinationals: A Portrait of Firms in the U.S. that Trade Goods” in Producer dy-

namics: New Evidence from Micro Data, T Dunne, J.B. Jensen and M.J. Roberts (eds.),

University of Chicago Press

[3] Bernard, Andrew B.; Jonathan Eaton, J. Bradford Jensen and Samuel Kortum (2003),

“Plants and Productivity in International Trade,” American Economic Review, 93(4):

pp.1268-1290.

[4] Boldrin, Michele and Levine David (2009), MARKET SIZE AND INTELLECTUAL

PROPERTY PROTECTION,” International Economic Review, 50: pp. 855—881.

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1992, 59 (issue 233), pp. 35-51.

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May 2004.

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Study.” Research Policy, October 1997, 26(3), pp. 283-301.

[8] Grossman, G. M. and E. Helpman (1994). Protection for sale. American Economic Re-

view 84, 833—850.

[9] Grossman, Gene M. and Lai, Edwin L.-C. (2004), “International Protection of Intellectual

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[10] Helpman, Elhanan “Innovation, Imitation, and Intellectual Property Rights.” Economet-

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Heterogeneous Firms,” American Economic Review, 2004.

28

[12] Hummels, David, “Towards a Geography of Trade Costs,” manuscript, University of

Chicago, September 2001.

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in Keith E. Maskus (ed.) Intellectual Property, Growth and Trade, vol. 2 of the series

Frontiers of Economics and Globalization, Elsevier, 2008.

[14] Lai, Edwin L.-C. and Qiu, Larry D. “The North’s Intellectual Property Rights Standard

for the South?” Journal of International Economics, January 2003, 59(1), pp. 183-209.

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Property: An Empirical Investigation,” manuscript, November 2007.

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[17] Maskus, Keith E. Intellectual Property Rights in the Global Economy, Washington D.C.:

The Institute for International Economics, 2000a.

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1269-1284

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161-185.

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29

Appendix

A Mean values of profit and consumer surplus

Define the unconditional means of the monopoly profit, the competitive consumer surplus and

consumer surplus under monopoly are, respectively,

=

Z e () () =

Z e () ()

=

Z e () ()

where is unit cost of production. Define productivity = 1. We assume that has a Pareto

distribution. e (), e () and e () are monopoly profit, the competitive consumer surplus

and consumer surplus under monopoly, respectively, expressed as functions of .

It can be easily shown that

e =

µ1

− 1¶−+1 where Pr( ≤ ) = ()

.

Therefore, the unconditional mean of the competitive consumer surplus is given by:

=

Z e () () where () = ()

=

Z 1

0

µ1

− 1¶−+1−1

=

µ1

− 1¶

µ1

1− +

¶−1.

Similarly,

e =

µ1

− 1¶Λ−+1

and the unconditional mean of the consumer surplus is equal to:

=

Z e () ()

=

µ1

− 1¶Λ

µ

1− +

¶−1.

30

Finally, e =

µ1

− 1¶Λ−+1.

The unconditional mean of the profit of a firm is equal to:

=

Z e () ()=

µ1

− 1¶Λ

µ

1− +

¶−1.

B Distribution of firm profits

As Axtell (Science, 2001 ) and other emperical work suggest, firm size follows a Pareto Distri-

bution ( ), where is very close to 1.

Therefore, it is natural to assume that firm productivity follows a Pareto Distribution

( ) :

Pr(1

) = 1− (

) where ∈ [∞)

which is equivalent to Pr( ) = Pr(1 1

) = (), where ∈ [0 1

].

As e = ¡1

−1¢Λ−+1 in the model, then ∀

Pr(e ) = Pr

∙

µΛ

− 1¶−+1

¸= Pr

µ1−

(− 1) Λ

¶= Pr

"1

µ(− 1) Λ

¶ 1−1#

= 1−

⎡⎢⎣ ³(−1)Λ

´ 1−1

⎤⎥⎦

= 1−µΛ−1

− 1¶

−1· −

−1

This implies that, e follows a Pareto Distribution (min −1), where min =

Λ−1−1 , represents

the minimum firm profit per consmer.

According to Axtell (2001), the index −1 should be very close to 1 for several methods

of estimation. Using US Census Bureau data, the number is 1.059, and this number is also

adopted by other researchers.

31

C Fixed cost of exporting and probability of exporting

A firm will carry out FDI in country k iff

e ()Ω − ≥ ()Ω − for a firm with unit cost

⇐⇒ −

1− ≤ e ()Ω

⇐⇒ = (1− ) e ¡

¢Ω + where is the critical for FDI to k.

A firm will export to country k iff

e ()Ω − ≥ 0 for a firm with unit cost

⇐⇒

≤ e ()Ω

⇐⇒ = e ¡¢Ω where is the critical for exporting to k.

From the previous equation, we have

= (1− ) e ¡

¢Ω +

= (1− ) e ¡

¢Ω + e ¡¢Ω .

We assume that

so that the firm that carries out FDI in a country always has the option of exporting to that

country but chooses not to do so. In other words, the cutoff market-size-adjusted profit for car-

rying out FDI is always higher than that for exporting to a country. See diagram_export_mode.

We further assume that if a good is not sold in a foreign market, the innovator still obtains

a patent there. Therefore, the good cannot be legally imitated in that market until the patent

expires.

Pr(e ) = 1−µΛ−1

− 1¶

−1· −

−1

⇐⇒ Pr(¡e e ¡¢¢ = µΛ−1− 1

¶ −1· £e ¡¢¤−

−1 =

"Λ−1e ¡¢ (− 1)

# −1

⇐⇒ =

"Λ−1e ¡¢ (− 1)

# −1

where is the probability of exporting to k

⇐⇒ ¡

¢ −1=

Λ−1e ¡¢ (− 1)⇐⇒ e ¡¢ = Λ−1

− 1¡

¢ 1− .

32

Similarly, we have e ¡

¢=

Λ−1

− 1¡

¢ 1− .

Therefore,

= ¡

¢Ω

= Ω

Λ−1

− 1¡

¢ 1−

= ΓΩΛ¡

¢ 1− where Γ ≡ −1

− 1

and

= (1− )Ω

µΛ

− 1¶−1

¡

¢ 1− + Ω

µΛ

− 1¶−1

¡

¢ 1−

= ΓΩΛh(1− )

¡

¢ 1− +

¡

¢ 1−

i.

D Value of A Patent

Following the equations in the last section, firm profit e = ¡

Λ−1¢−+1 follows a Pareto

Distribution ³Λ−1−1

−1

´.

And the cutoff cost of exporting to and doing FDI in country , and are determined

by

= e()Ω

− = (1− )e()Ω

where e() =

µΛ

− 1¶−+1.

After solving for and , it is clear that

1) All firms ∈ £0 1

¤will produce and sell domestically

2) Firms with ∈ £

¤will also export (but not FDI) to country , and get a profit

()

3) Firms with ∈ £0

¤will also do FDI in (but not export to) country , and get a

profit e()Then, a firm in country does not only sell domestically and get a expected profit of

=R 1

0e() () =

µ1

− 1¶Λ

µ

1− +

¶−1, where () = () ,

33

but also exports to (but not do FDI in) country (6= ), and get expected exporting profit of

¡

¢=R

() () =

µ

− + 1

¶µΛ

− 1¶h¡

¢−+1 − ¡

¢−+1i,

or do FDI in (but not export to) country (6= ), and get expected FDI profit of

¡

¢=R 0

e() () = µ

− + 1

¶µΛ

− 1¶¡

¢−+1.

Then, we can get the expected value of a patent for a firm in country :

= Ω +P 6=

Ω −P 6=

£¡ −

¢ +

¤,

where

= ¡

¢+

¡

¢=

µ

− + 1

¶µΛ

− 1¶n

h¡

¢−+1 − ¡

¢−+1i+¡

¢−+1o=

µ

− + 1

¶µΛ−1

− 1¶½

∙¡

¢−+1 − ¡

¢−+1

¸+¡

¢−+1

¾=

and

=

¡

¢+

¡

¢=

µ

− + 1

¶µΛ−1

− 1¶½

∙¡

¢−+1 − ¡

¢−+1

¸+¡

¢−+1

¾=

where

=

∙¡

¢−+1 − ¡

¢−+1

¸+¡

¢−+1 .

Moreover,

= Pr¡

¢=¡ ·

¢

= Pr¡

¢=¡ ·

¢

Therefore,

34

= Ω +P 6=

Ω −P 6=

£¡ −

¢ +

¤= Ω +

P 6=

Ω

−P 6=

n¡ −

¢ΓΩΛ

¡

¢ 1− +ΓΩΛ

h(1− )

¡

¢ 1− +

¡

¢ 1−

io=

"Ω +

µ− 1

¶P 6=

Ω

#

E Proof of Proposition 2

Recall that equation (12) is equivalent to 1

()

Ω= 0 while (13) is equivalent to 1

Ω= 0.

We have established in Lemma 1 that a sufficient condition for under-protection is³P

1

Ω

´

0 for all combinations of Ω∈N that satisfyP

1

()

Ω= 0. From equation (13), we know

this condition is equivalent to

X

" −

ÃX 6=

!#

X

"X 6=

Ã

0 +

X 6=

0

!+X 6=

#(19)

for all combinations of Ω∈N that satisfyP

1

()

Ω= 0.

But the RHS of (19) is greater than zero, as there are positive cross-border externalities as

a country strengthens its patent protection. Therefore, a sufficient condition for (19) to hold is

X

" −

ÃX 6=

!# 0

a sufficient condition of which is

−X6=max

0

which is (14). ¥

35

F Globally Optimal Harmonized Patent Protection

The following equation is to be solved for the globally optimal harmonized e (where Λ ≡ ¡ −1

¢,

= number of countries)

en³X

´( − 2Λ)− 2Λ

h³X

´³Xe´−X³e´io

= X

⎧⎨⎩X 6=

*e

h1−

³1− Λe´ eiP

6=

h¡−1

¢e

i+

++

(1− (1− Λ) e)P 6=

h¡−1

¢e

i+

⎫⎬⎭+X

⎧⎨⎩X 6=

*

h1−

³1− Λe´ eiP

6=h¡

−1

¢e

i+

+X 6=

e

h1−

³1− Λe´ eiP

6=h¡

−1

¢e

i+

+

+X 6=

⎛⎝ e [1− (1− Λ) e]P6=

h¡−1

¢e

i+

⎞⎠⎫⎬⎭Moreover, e =

³e´ 1−+

+ (1− )³e

´ 1−+

for = 1 2

·³e´−( −1 ) = ·

³e´−( −1 ) for = 2 (assume that k=1 for the US)

·³e

´−( −1 )= ·

³e

´−( −1 )for = 2 (assume that k=1 for the US)

and e = 015

e = 003

The above equations form a system of 3 + 1 equations and 3 + 1 unknowns.

When −1= 1, we have e = 1 for all , and we can easily show that

e =

(1− 2Λ) + (1− Λ)

G Data for and

The variable is proxied by the natural logarithm of the average dollar value of consumption

(or use) of patent-sensitive goods per year by country i over the years 1996-1999 (estimated by

Lai, Wong and Yan 2007). The variable is proxied by the average number of patents granted

to the resident of country i by the US patent office per year over the years 1996-1999 (obtained

36

from the WIPO website). However, to adjust for home-bias of the US data, we calculate the

US innovative capability as the mean of an upper bound and a lower bound. The upper bound

is the yearly average of the actual number of patents granted to US residents by the US patent

office, , where

denotes the number of patents granted to residents of country i by country

j. This is an upper bound because it probably over-states the innovative capability of the US

because even relatively trivial inventions might be patented in the US by US residents as the

cost of patenting and subsequent working of the patents by domestic residents is relatively low.

This is the home bias effect. The lower bound estimate is obtained by the formula

g =

× .

The idea is that American capability to obtain patents relative to that of Japan in Europe

is approximately equal to American capability to obtain patents relative to that of Japan in

the US. Comparison with Japan is chosen because its innovative capability is comparable to

that of the US while other countries are much further behind. The reason for choosing patents

awarded in Europe is because European countries have a longer tradition of patent protection

and have been having patent systems similar to that of the US. Japan, on the other hand, has a

more liberal patent system with narrower protection than in the US and in Europe. Therefore,

calibration with the Japanese patent counts is not done. The estimate g is considered a

lower bound of US innovative capability as some useful American innovations are not patented

overseas perhaps because they are relatively less significant (but may be still useful). This is

just the opposite of the home bias effect.

The estimated innovative capability of the US is therefore calculated as

d = g +

2

After taking the above into account, we obtain Table 1, which shows the patent counts

and market sizes of the thirty most innovative countries. It can be easily calculated that

¡P

¢= 048,

¡P

¢ (P

)¡P

¢= 019. Table 1 about here ¥

37

E’

Figure 1

0

S

S

N

N

GG

E

G

0S

S

W a

BRF-S

0N

N

W a

BRF-N

45 degrees

S

N

1 1 0w w

S S N N

W WM M

wW W

Slope = NS MM /

Slope = NS MM /

Figure 2

EE

GG

E

G

0w

N

W

FOC-N

0w

S

W

FOC-S

0S

S

W a

BRF-S

0N

N

W a

BRF-N

45 degrees

S

N

1 1 0S N

S S N N

W a W aM M

1 1 0w w

S S N N

W WM M

Slope =1

Slope = y

kkM

Net profit FDIkk FM

EXkk FMy

Domestic Export FDI

0

- EXF

- FDIF

Figure 3.

US phi M ln(M) phi*ln(M) Japan 51510 1772986841 9.25 476400.8209 Germany 27044 1170193555 9.07 245241.9613 France 8065 562757898.1 8.75 70571.34369 UK 3310 367990558.4 8.57 28352.9194 China 3042 284028686.2 8.45 25715.12783 Italy 68 281883387.7 8.45 574.6047248 Brazil 1379 267299074.1 8.43 11620.82949 Spain 73 202314883.7 8.31 606.3400319 Canada 201 153705026.3 8.19 1645.524302 India 2703 148452725 8.17 22087.80283 South Korea 70 142688343.3 8.15 570.8071947 Netherlands 2551 134158352.1 8.13 20733.55279 Australia 1020 103945394.5 8.02 8177.141357 Mexico 594 97579663.7 7.99 4745.679434 Argentina 54 92621183.25 7.97 430.2023575 Switzerland 38 76182172.99 7.88 299.5104275 Belgium 1190 70095671.69 7.85 9336.37253 Sweden 586 67683862.59 7.83 4588.664289 Austria 1087 58760190.1 7.77 8444.99343 Sum 104585 6055327470 157.21 940144.1983

Table 1: Data on M and phi

M is the average value of consumption (or absorption) per year in US dollars of patent-sensitive goods in the country in the year 1996-1999

phi is the average number of patents granted to residents of the country per year by the US Patent Office in the years 1996-1999

*US figure for phi is adjusted for home-bias effect as discussed in the text

t lam/(ep-1) a gamma epsilon phi ln(M) omega theta_ex theta_fdi theta US 0 1 1 4 1.5 51510 9.249 0.519 1 Japan 0 1 1 4 1.5 27044 9.068 0.398 1 Germany 0 1 1 4 1.5 8065 8.750 0.282 1 France 0 1 1 4 1.5 3310 8.566 0.240 1 UK 0 1 1 4 1.5 3042 8.453 0.225 1 China 0 1 1 4 1.5 68 8.450 0.211 1 Italy 0 1 1 4 1.5 1379 8.427 0.214 1 Brazil 0 1 1 4 1.5 73 8.306 0.193 1 Spain 0 1 1 4 1.5 201 8.187 0.179 1 Canada 0 1 1 4 1.5 2703 8.172 0.189 1 India 0 1 1 4 1.5 70 8.154 0.174 1 South Korea 0 1 1 4 1.5 2551 8.128 0.182 1 Netherlands 0 1 1 4 1.5 1020 8.017 0.160 1 Australia 0 1 1 4 1.5 594 7.989 0.154 1 Mexico 0 1 1 4 1.5 54 7.967 0.149 1 Argentina 0 1 1 4 1.5 38 7.882 0.137 1 Switzerland 0 1 1 4 1.5 1190 7.846 0.137 1 Belgium 0 1 1 4 1.5 586 7.830 0.132 1 Sweden 0 1 1 4 1.5 1087 7.769 0.126 1 Austria 0 1 1 4 1.5 401 7.757 0.121 1

Table 2A. Globally optimal harmonized omega = 1 t lam/(ep-1) a gamma epsilon phi ln(M) omega theta_ex theta_fdi theta US 0 1 1 4 5 51510 9.249 0.886 1 Japan 0 1 1 4 5 27044 9.068 0.607 1 Germany 0 1 1 4 5 8065 8.750 0.361 1 France 0 1 1 4 5 3310 8.566 0.282 1 UK 0 1 1 4 5 3042 8.453 0.262 1 China 0 1 1 4 5 68 8.450 0.227 1 Italy 0 1 1 4 5 1379 8.427 0.239 1 Brazil 0 1 1 4 5 73 8.306 0.205 1 Spain 0 1 1 4 5 201 8.187 0.188 1 Canada 0 1 1 4 5 2703 8.172 0.216 1 India 0 1 1 4 5 70 8.154 0.181 1 South Korea 0 1 1 4 5 2551 8.128 0.207 1 Netherlands 0 1 1 4 5 1020 8.017 0.171 1 Australia 0 1 1 4 5 594 7.989 0.161 1 Mexico 0 1 1 4 5 54 7.967 0.150 1 Argentina 0 1 1 4 5 38 7.882 0.136 1 Switzerland 0 1 1 4 5 1190 7.846 0.144 1 Belgium 0 1 1 4 5 586 7.830 0.134 1 Sweden 0 1 1 4 5 1087 7.769 0.130 1 Austria 0 1 1 4 5 401 7.757 0.119 1

Table 2B. Globally optimal harmonized omega = 1

t lam/(ep-1) a gamma epsilon phi ln(M) omega theta_ex theta_fdi theta US 0 1.05 1 4 1.5 51510 9.249 0.601 0.199 0.0398 0.926 Japan 0 1.05 1 4 1.5 27044 9.068 0.468 0.150 0.0300 0.914 Germany 0 1.05 1 4 1.5 8065 8.750 0.326 0.099 0.0198 0.896 France 0 1.05 1 4 1.5 3310 8.566 0.269 0.079 0.0158 0.886 UK 0 1.05 1 4 1.5 3042 8.453 0.249 0.072 0.0144 0.882 China 0 1.05 1 4 1.5 68 8.450 0.225 0.065 0.0129 0.878 Italy 0 1.05 1 4 1.5 1379 8.427 0.232 0.066 0.0133 0.879 Brazil 0 1.05 1 4 1.5 73 8.306 0.200 0.056 0.0112 0.872 Spain 0 1.05 1 4 1.5 201 8.187 0.178 0.049 0.0097 0.866 Canada 0 1.05 1 4 1.5 2703 8.172 0.198 0.055 0.0109 0.871 India 0 1.05 1 4 1.5 70 8.154 0.170 0.046 0.0092 0.864 South Korea 0 1.05 1 4 1.5 2551 8.128 0.189 0.051 0.0103 0.868 Netherlands 0 1.05 1 4 1.5 1020 8.017 0.149 0.039 0.0079 0.857 Australia 0 1.05 1 4 1.5 594 7.989 0.136 0.036 0.0072 0.853 Mexico 0 1.05 1 4 1.5 54 7.967 0.122 0.032 0.0064 0.849 Argentina 0 1.05 1 4 1.5 38 7.882 0.043 0.011 0.0021 0.805 Switzerland 0 1.05 1 4 1.5 1190 7.846 0.038 0.009 0.0018 0.800 Belgium 0 1.05 1 4 1.5 586 7.830 0.049 0.012 0.0024 0.810 Sweden 0 1.05 1 4 1.5 1087 7.769 0.058 0.014 0.0028 0.816 Austria 0 1.05 1 4 1.5 401 7.757 0.063 0.015 0.0031 0.820

Table 2C. Globally optimal harmonized omega = 1 t lam/(ep-1) a gamma epsilon phi ln(M) omega theta_ex theta_fdi theta US 0 1.05 1 4 5 51510 9.249 0.959 0.216 0.0433 0.930 Japan 0 1.05 1 4 5 27044 9.068 0.690 0.150 0.0300 0.914 Germany 0 1.05 1 4 5 8065 8.750 0.422 0.086 0.0172 0.890 France 0 1.05 1 4 5 3310 8.566 0.321 0.063 0.0126 0.877 UK 0 1.05 1 4 5 3042 8.453 0.295 0.057 0.0114 0.873 China 0 1.05 1 4 5 68 8.450 0.239 0.046 0.0092 0.863 Italy 0 1.05 1 4 5 1379 8.427 0.260 0.050 0.0099 0.867 Brazil 0 1.05 1 4 5 73 8.306 0.202 0.038 0.0075 0.855 Spain 0 1.05 1 4 5 201 8.187 0.165 0.030 0.0060 0.846 Canada 0 1.05 1 4 5 2703 8.172 0.226 0.042 0.0083 0.860 India 0 1.05 1 4 5 70 8.154 0.032 0.005 0.0011 0.779 South Korea 0 1.05 1 4 5 2551 8.128 0.211 0.039 0.0077 0.856 Netherlands 0 1.05 1 4 5 1020 8.017 0.037 0.006 0.0012 0.784 Australia 0 1.05 1 4 5 594 7.989 0.044 0.007 0.0015 0.792 Mexico 0 1.05 1 4 5 54 7.967 0.055 0.009 0.0018 0.800 Argentina 0 1.05 1 4 5 38 7.882 0.067 0.011 0.0022 0.807 Switzerland 0 1.05 1 4 5 1190 7.846 0.058 0.009 0.0019 0.801 Belgium 0 1.05 1 4 5 586 7.830 0.067 0.011 0.0022 0.807 Sweden 0 1.05 1 4 5 1087 7.769 0.068 0.011 0.0022 0.808 Austria 0 1.05 1 4 5 401 7.757 0.074 0.012 0.0024 0.811

Table 2D. Globally optimal harmonized omega = 1

t lam/(ep-1) a gamma epsilon phi ln(M) omega theta_ex theta_fdi theta US 0.5 1.05 1 4 1.5 51510 9.249 0.605 0.200 0.0399 0.914 Japan 0.5 1.05 1 4 1.5 27044 9.068 0.470 0.150 0.0300 0.901 Germany 0.5 1.05 1 4 1.5 8065 8.750 0.325 0.098 0.0196 0.883 France 0.5 1.05 1 4 1.5 3310 8.566 0.267 0.078 0.0156 0.874 UK 0.5 1.05 1 4 1.5 3042 8.453 0.248 0.071 0.0142 0.870 China 0.5 1.05 1 4 1.5 68 8.450 0.223 0.064 0.0128 0.865 Italy 0.5 1.05 1 4 1.5 1379 8.427 0.230 0.066 0.0131 0.867 Brazil 0.5 1.05 1 4 1.5 73 8.306 0.198 0.055 0.0110 0.859 Spain 0.5 1.05 1 4 1.5 201 8.187 0.176 0.048 0.0096 0.854 Canada 0.5 1.05 1 4 1.5 2703 8.172 0.197 0.054 0.0108 0.858 India 0.5 1.05 1 4 1.5 70 8.154 0.167 0.045 0.0091 0.851 South Korea 0.5 1.05 1 4 1.5 2551 8.128 0.187 0.051 0.0102 0.856 Netherlands 0.5 1.05 1 4 1.5 1020 8.017 0.147 0.039 0.0078 0.845 Australia 0.5 1.05 1 4 1.5 594 7.989 0.134 0.035 0.0070 0.841 Mexico 0.5 1.05 1 4 1.5 54 7.967 0.119 0.031 0.0062 0.836 Argentina 0.5 1.05 1 4 1.5 38 7.882 0.044 0.011 0.0021 0.795 Switzerland 0.5 1.05 1 4 1.5 1190 7.846 0.038 0.009 0.0018 0.789 Belgium 0.5 1.05 1 4 1.5 586 7.830 0.049 0.012 0.0024 0.799 Sweden 0.5 1.05 1 4 1.5 1087 7.769 0.057 0.014 0.0028 0.805 Austria 0.5 1.05 1 4 1.5 401 7.757 0.062 0.015 0.0031 0.808

Table 2E. Globally optimal harmonized omega = 0.941 t lam/(ep-1) a gamma epsilon phi ln(M) omega theta_ex theta_fdi theta US 0.5 1.05 1 4 5 51510 9.249 0.963 0.217 0.0434 0.875 Japan 0.5 1.05 1 4 5 27044 9.068 0.692 0.150 0.0300 0.860 Germany 0.5 1.05 1 4 5 8065 8.750 0.420 0.085 0.0171 0.837 France 0.5 1.05 1 4 5 3310 8.566 0.318 0.062 0.0125 0.824 UK 0.5 1.05 1 4 5 3042 8.453 0.293 0.057 0.0113 0.821 China 0.5 1.05 1 4 5 68 8.450 0.236 0.045 0.0090 0.812 Italy 0.5 1.05 1 4 5 1379 8.427 0.257 0.049 0.0098 0.815 Brazil 0.5 1.05 1 4 5 73 8.306 0.201 0.037 0.0075 0.804 Spain 0.5 1.05 1 4 5 201 8.187 0.025 0.004 0.0008 0.724 Canada 0.5 1.05 1 4 5 2703 8.172 0.228 0.042 0.0084 0.809 India 0.5 1.05 1 4 5 70 8.154 0.028 0.005 0.0009 0.729 South Korea 0.5 1.05 1 4 5 2551 8.128 0.214 0.039 0.0078 0.806 Netherlands 0.5 1.05 1 4 5 1020 8.017 0.032 0.005 0.0010 0.732 Australia 0.5 1.05 1 4 5 594 7.989 0.039 0.006 0.0013 0.740 Mexico 0.5 1.05 1 4 5 54 7.967 0.049 0.008 0.0016 0.748 Argentina 0.5 1.05 1 4 5 38 7.882 0.061 0.010 0.0020 0.756 Switzerland 0.5 1.05 1 4 5 1190 7.846 0.051 0.008 0.0017 0.749 Belgium 0.5 1.05 1 4 5 586 7.830 0.061 0.010 0.0020 0.756 Sweden 0.5 1.05 1 4 5 1087 7.769 0.062 0.010 0.0020 0.756 Austria 0.5 1.05 1 4 5 401 7.757 0.069 0.011 0.0023 0.760

Table 2F. Globally optimal harmonized omega = 1