Intellectual Property Rights and Diaspora Knowledge
Networks: Can Patent Protection Generate Brain Gain from
Skilled Migration?

Alireza Naghavi University of Bologna
Chiara Strozzi University of Modena and Reggio Emilia and IZA

Abstract. This paper studies the mechanism through which intellectual property rights (IPR) protection can in‡uence the impact of skilled migration on innovation activities in developing countries.
We argue that knowledge acquired by emigrants abroad can ‡ow back to their country of origin
through diaspora networks. IPR protection in the sending country facilitates this channel by increasing returns to skills and encouraging workers to move into the innovation sector. An expansionof the innovation sector allows diaspora knowledge to be absorbed by a larger range of workers.
Strong IPR enforcement therefore makes it more likely for brain drain to be transformed into brain
gain.
JEL classi…cation: O30, F22, J24
Corresponding author: Alireza Naghavi, alireza.naghavi@unibo.it

We are grateful to Andrés Carvajal and two anonymous referees for their valuable comments and insights which
greatly helped us to improve the paper. We would also like to thank Olena Ivus, Peter Kuhn, Elisabetta Lodigiani,
Arsen Palestini, Hillel Rapoport, Gilles Saint-Paul, as well as the seminar participants at University of Lille 1,
the University of Bologna, EEA 2011 Oslo, GLOBELICS 2010 Kuala Lumpur, GLOBELICS 2011 Buenos Aires,International Workshop on Economics of Global Interactions 2011 Bari, ITSG 2011 Milan, PRIN Workshop 2013
Bologna, RES 2012 Cambridge, and the WIPO Experts’Meeting on Intellectual Property, the International Mobilityof Knowledge Workers and the Brain Drain 2013 Geneva for very helpful remarks. We would like to acknowledge theEuropean Commission for …nancial support through the 7th Framework Programme Project INGINEUS. Financial
support from Fondazione Cassa Risparmio di Modena and from MIUR through the PRIN project "Institutions, Social
Dynamics, and Economic Development" is also acknowledged.

1

1.

Introduction

International trade and foreign direct investment (FDI) have often been identi…ed as the main
determinants of innovation and growth in developing countries (South) (Saggi 2002; Keller 2004).
Skilled migration is a third factor that has been gaining importance due to its remarkable growthalong with trade and FDI since the 1990’s (Docquier and Rapoport 2012). The resulting surge
in the outward transfer of the human capital has created controversial debates about the threats
and opportunities that skilled emigration may pose to the South. On the one hand, the traditional
literature on migration and brain drain presents mechanisms through which skilled emigration could
be detrimental to growth.1 On the other hand, a growing branch of contributions argues that skilled
emigration needs not harm the South and may even increase its potential for development througha brain gain.
The so-called brain gain e¤ect derives from an incentive channel that works through increased
expected returns to education brought about by migration prospects (Mountford 1997; Stark, Helmenstein and Prskawetz 1997; Beine, Docquier and Rapoport 2001, 2008; BDR).2 An additional
channel is return migration, which can induce innovation through the knowledge possessed by migrants returning from more advanced economies (Domingues Dos Santos and Postel-Vinay 2003;
Mayr and Peri 2009; Dustmann, Fadlon and Weiss 2011). Finally, cross-border diaspora networks
among skilled emigrants and natives may also promote access to foreign-produced knowledge andfoster innovation by encouraging trade, investments, and the recirculation of information back tothe sending countries (Agrawal, Kapur and McHale 2011; AKM; Kerr 2008). Student/scholarly
networks, local associations of skilled expatriates, short-term consultancies by high-skilled expatriates in their country of origins, and other unestablished intellectual/scienti…c diaspora networks area few examples of such networks (Meyer and Brown 1999).3 Sociological studies, such as Meyer(2001), suggest that such informal networks are crucial in turning brain drain into a brain gain.
Nevertheless, AKM (2011) did not …nd a strong case for the Indian diaspora of inventors in the US
and the transfer of their knowledge back to their homeland. Breschi, Lissoni and Miguelez (2015;
BLM) add that while inventors in India do not bene…t from their expatriates abroad, other countries
such as China and Russia seem to experience substantial advantages that stem from their diasporas.
They argue that these di¤erent …ndings across sending countries may have a lot to do with theirabsorptive capacity.
This research contributes to the literature by exploring the channel through which the knowledge
acquired by emigrants after interacting with superior skills in developed countries (North) can ‡owback to the South. We refer to this channel as an "intellectual diaspora", that is, the remotemobilization of intellectuals and professionals abroad and their connection to scienti…c, technologicaland cultural programs at home.4 This can be thought of as a scientist from the South being moreproductive in the North due to better facilities and more resources, with some of the bene…ts of his
innovation ‡owing back to his home country. We provide a framework to show how the bene…ciale¤ect of diaspora networks through the cross-border sharing of ideas is heterogeneous, and that it
depends on the absorptive capacity of the sending country. The paper aims to assess the role ofintellectual property rights (IPR) protection in the South in determining its absorptive capacity,and in turn, the impact of emigration on innovation activities in the home (sending) country. In
a companion study, Naghavi and Strozzi (2015), we show evidence that knowledge acquired byemigrants abroad could be exploited in their home countries under sound IPR institutions. Motivatedby these …ndings, we build a model to propose a mechanism through which an appropriate level of
IPR protection could help reverse the brain drain caused by skilled emigration. In sum, we argue
1 Seminal works include those of Berry and Soligo (1969), Bhagwati and Hamada (1974) and Miyagiwa (1991). For
a recent complete survey of the literature on brain drain and development, see Docquier and Rapoport (2011).
2 The possibilities of such gains from emigration were …rst referred to by Bhagwati and Rodrigues (1975).
3 Williams (2007) and Oettl and Agrawal (2008) focus on the externalities of international migration to emphasize
their role in knowledge and technology transfer. More recently, BDR (2011) show the in‡uence of diasporas on theevolution of migration ‡ows and their composition in terms of skills.
4 In this framework, the capacity of innovation of Southern innovators, who remain in their origin countries, isrelated to their access to valuable technological knowledge that is partially accumulated abroad (i.e., brain banks).
For more on this issue, see AKM (2011).

2

that although emigration may directly result in a brain drain, it also generates a ‡ow of ideas
and inventions back to the sending country, the extent of which depends on the strength of IPR
protection. The results complement the …ndings of BLM (2015) in that the diaspora channel is
only operational when the source region is in possession of a su¢ cient level of absorptive capacity toenable interaction opportunities between inventors abroad and those residing in their home countries.
While the trade-o¤ faced by an emerging economy between imitation and the provision of incentives for domestic innovation through IPRs are well-understood (Maskus 2000), the interrelationshipbetween skilled migration and IPR policy in determining innovation remains unexplored. Our work…lls this gap and contributes to the above-mentioned strand of research by capturing the diaspora
dimension of migration and revealing how IPR protection in the sending country may in‡uence thee¤ect of skilled migration on innovation there.5 On this basis, we shed light on the net impactof emigration on innovation and determine whether a strong IPR regime at home can eventuallyturn the initial brain drain into a brain gain. Our theoretical framework is a variant of the Yeaple(2005) and Ohnsorge and Tre‡er (2007) models of heterogeneous workers, in which we introduce aninnovation sector, migration, and IPR protection. Emigration reduces e¤ective innovation activities
due to the loss of the most skilled (the extensive margin). Migration, however, also opens a diaspora channel through which the knowledge acquired abroad can ‡ow back to the home economy
and enhance skills of the remaining workers in the innovation sector (the intensive margi n). To
investigate whether the bene…cial e¤ect of diasporas could outweigh the direct negative e¤ect of theout‡ow of skilled workers, we look at the absorptive capacity of the sending country. A strong levelof IPR protection increases absorptive capacity by raising returns to skills, encouraging workers to
shift from production to innovation activities. An enlarged innovation sector allows diaspora gains
to reach out to a larger range of workers actively using their skills in the economy. As a consequence,a strong level of IPR protection in the sending country increases the magnitude of potential bene…ts
from diasporas, making it more likely for the gains to outweigh the negative e¤ects of brain drainon innovation, and thus facilitating a potential net brain gain.6

2.

The model

2.1. The basic framework
Suppose there are two regions: a developing economy referred to as the South and an alternative
North with better economic opportunities and employment possibilities, where skills and wages are
assumed to be higher. Because the focus of our study is the southern market, we concentrate ouranalysis on goods invented, produced and consumed locally in the South.7
Following a Dixit and Stiglitz (1977) monopolistic competition framework with CES (constantelasticity of substitution) preferences, consumers have the following utility function:
2N
31
Z
Ui = Ci = 4 cj dj 5 ;(1)0where individual aggregate consumption index Ci is divided between a continuum of N invented
5 Among the vast literature on intellectual property rights, Chen and Puttinan (2005) and Parello (2008) areperhaps most closely related to our work, as they speci…cally focus on domestic skill accumulation and innovation.
While the former positively relates IPR protection to innovation, the latter deems it to be ine¤ective for innovationin less-developed countries.
6 These results are in contrast to the theoretical conclusion obtained by McAusland and Kuhn (2011), who claim
IPRs to be an obstacle to the international ‡ow of brains. In short, they argue that if brains are emigrating, a country
may as well lower its IPRs to free-ride on brains that have moved elsewhere. While their study is to our knowledge
the …rst contribution that explicitly investigates the link between IPRs and brain circulation, it does not take into
account any channels through which the skills acquired abroad can be transferred back into the country of origin.
7 Using a reduced form model that abstracts from trade and FDI related issues allows us to single out the impactof South-North migration, but clearly does not provide de…nitive answers to how IPRs and diasporas interact. See
Iranzo and Peri (2009) for a study of trade and migration and Davis and Naghavi (2011) for the e¤ects of trade ando¤shoring on innovation within the same occupational choice setting. These papers however do not deal with theissue of IPRs.

3

goods subscripted by j 2 (0; N ), and 2 (0; 1) represents the inverse measure of product di¤erentiation.
There are two sectors in the economy: a production and an innovation sector. Labor is the only
factor of production and innovation, and is mobile between sectors. In the spirit of Roy (1951)
occupational choice model with heterogeneous labor, workers are spread over a continuum of skillsz 2 [0; 1), distributed with density g(z) and cumulative distribution G(z). We normalize the massof workers to one. De…ne z1 as the skills of a threshold worker indi¤erent between working in the
production or the innovation sector and z2 as the threshold above which workers choose to migrate.
While production does not require skills, a worker i with skills zi in the innovation sector has
productivity hi such thathi = zi + Z;
(2)
where zi represents own skill endowment and Z (de…ned below) is the international spillover ofknowledge learned by emigrants abroad through what we call the diaspora channel. We are interested
in observing the initial skill endowment of each individual (their innate ability) used in the innovation
sector and how the assumed superior knowledge from the North can ‡ow back to upgrade workers’
productivity.
The timing of the model is as follows. Given the IPR regime, which is assumed to be exogenous
to our model, emigration takes place in period 0, activating the diaspora channel. Innovation is thencarried out in the …rst period, and production occurs in the second.
Emigration in period 0 is modeled as a movement of labor from the South to the North at a
cost F , which allows only the highest skilled to move. Potential diaspora is then realized by meansof skilled emigrants transferring their newly acquired knowledge back to the South. We de…ne thepositive externalities from diaspora networks as
Z = b (z2 );(3)

where the skills endowment of those who migrate to the North is
Z1(z2 ) = zg(z)dz:

(4)

z2

Parameter b
0 measures the intensity of diaspora gains, which is in‡uenced by factors such as
the level of academic and professional interactions and the amount of skills learned in the North,or the successful transmission of knowledge to the South. This measure can also be thought of as
to how much innovations undertaken by emigrants abroad are still suitable to serve the southerneconomy, a concept referred to as a negative "expatriate brains" e¤ect in McAusland and Kuhn
(2011). Note that b = 0 implies no international knowledge transfer, b = 1 the return of only
original (pre-migration) skills of emigrants, and b > 1 the di¤usion of their improved skills to theSouth.
In period 1, N goods are invented. Each good needs units of skills. The total amount of humancapital in the economy can be written as
Zz2
H(z1 ; z2 ) = hi g(z)dz:

(5)

z1

The total number of inventions available for consumption are in turnN = H(z1 ; z2 )= :(6)

To work in the innovation sector, each worker must obtain education at a cost e, which is paid in
the second period. The wage per unit of skill for the high-skilled in the innovation sector is !H andis paid in period 2, giving each individual with skills zi a wage equivalent to hi !H .
In period 2, the production sector absorbs all workers who have not worked in the innovation4

sector in the …rst period. The production function is CRS in labor and has a productivity equal to
1 so that there is a one-to-one relationship between output and labor. Individual wage is identicalfor all workers in this sector and equals !L .

2.2. Patents and consumption
We use the basic framework presented in Saint-Paul (2003, 2004) as our benchmark, modeling IPR
protection as the probability that an innovator can obtain monopoly power over his invention.8 The
probability of being granted a patent is q, which captures the degree of IPR protection.9 We assume
a numéraire sector producing generic goods whose patents have expired with a price normalized to1, which also determines wages in the production sector, !L = 1.10 A non-patented good can be
imitated driving its price (pN ) down to the marginal cost of production.
If a patent is granted, a …rm charges monopoly price (pP ) which given preferences includes a markup over marginal cost. The extent of the mark-up depends on the level of product di¤erentiation
among the varieties available in the market ( ). Prices pN and pP are given by
pN = !L = 1;
pP = !L = = 1= :A higher degree of product di¤erentiation (lower ) implies more monopoly power and therefore
a higher price. When IPRs are fully protected, the model falls under a standard monopolisticcompetition model. Similarly, no IPR protection represents the case of perfect competition.
Next, consumption is divided between patented and non-patented goods, cP and cN , respectively. Consumers allocate their income y (net of education cost) between the two types of goods by
maximizing (1) or equivalently
M ax NP cP + NN cN ;(7)
cN ;cP

under the budget constraint
y = NP cP + NN cN ;(8)

where NP + NN = N , and NP = N q and NN = N (1 q) are the total number of patented and nonpatented goods respectively, determined by the IPR regime. The solution to the above maximization
problem is:y ( 1 1)y;(9)cN = ; cP =
where
= Nq

(

+ N (1

1)

q)

(10)

captures the love of variety e¤ect as @ =@N > 0 and the disutility caused by monopoly pricing as@ =@q < 0. Consumers do not care whether the commodities they buy are patent-protected, but
are inclined to consume more non-patented goods because they are cheaper.
Using (1), (7), (9) and (10), aggregate consumption index is therefore
C=

y
;
P

where P is the aggregate price index,
(

P =

1)

;
(

that originates from the standard Dixit-Stiglitz index of all varieties’prices, P = NP pP(

1)(+ N N pN

8 Saint-Paul (2004) uses this setting to explore the implications of IPRs and redistribution on occupational choice
and welfare.
9 Grossman and Lai (2004) also model patent protection in a similar manner.
1 0 For clarity of exposition, here we implicitly consider a homogeneous numéraire good that takes the form of j = 0,
as in Melitz and Redding (2014). The results remain identical using a separable utility function with an additive
numéraireire good, a, as demonstrated in Appendix A.6.

5

1)

1)

.

The value of a patent, which is equal to monopoly pro…ts, is equal to
=(

1)

1

Y

(

1)

;

(11)

where Y is aggregate income (net of education cost). In the above expression, the …rst term on theright-hand side (RHS) is the mark-up over marginal cost (pP !L ), whereas the second is total
demand for the patented good.
Under a competitive innovation sector, expected operating pro…t from inventing a new good must
equal to its cost of creation in terms of skills such thatq = !H :Using (11), this gives!H = q(Replacing for from (10) and recalling thatwages in the innovation sector !H as
(
@!H
=
@q

1

1)Y

(

1)

=

:

(12)

> 1, stronger patent protection (higher q) increases

1)Y

1
(

1)

N

2 2

>0

(13)

for a given level of aggregate income. More stringent IPR enforcement protects inventors against
imitation making it more attractive to work in the innovation sector.

2.3. Migration
To determine the migration threshold skill level z2 , suppose a worker migrates to the North if his
gains from doing so, net of migration costs, exceed what he would earn in the innovation sector athome:
F + !H Z! M zi e F > ! H h i e ) ! M z2 F = ! H z2 + ! H Z ) z2 =
;
(14)
!M !H
where we consider an exogenous wage in the innovation sector of the North higher than that in
the South: !M > !H . Note that this assumption allows the paper to focus on South-North skilledmigration, where returns to skills are assumed to be determined by the protection of the output ofskills, i.e. patents, and therefore higher in the North.11
Suppose a positive level of migration is triggered by a reduction in F . We can state
Lemma1. A reduction in the …xed cost of migration encourages emigration of skills to the North@ (z2 )
@z2 < 0 .

@z2
@F > 0 , but opens a channel for potential diaspora gains

Proof. Follows directly from (4) and (14).
It follows from Lemmas 1 that a reduction in migration costs F spurs the brain drain syndrome,decreasing the size of the innovation sector by a movement of workers from the upper tail of the
distribution of skills out of the country. At the same time migration creates an opportunity for new
knowledge to ‡ow into the country through an increased number of skilled migrants abroad, (z2 ).12
1 1 There are other cases not dealt with in this model, where for example the least-skilled migrate because returns to
education are assumed to be higher in the South due to the scarcity of skills (Borjas 1987). Including heterogeneous
migration costs that are decreasing in skills to this framework generates a further possibility of non-monotonic migration patterns and self-selection into migration by those with an intermediate level of schooling (Chiquiar and Hanson2005).
1 2 In addition, higher prospective wages abroad !
M encourage the ‡ow of skills away from the country, whereas
higher wages in the innovation sector at home !H reduce skilled emigration. Higher potential gains from diaspora
Z similarly discourage migration as individuals are aware that they can partially enjoy the knowledge acquired byothers who emigrate without bearing the costs of migration themselves.

62.4. Intellectual property rights protection
To pin down the threshold skill level z1 above which individuals choose to obtain education andwork in the innovation sector, consider a worker with productivity hi , who can either work in theinnovation sector and earn !H hi e, where !H > 1, or become a production worker with wage
!L = 1. Choosing the option that generates a higher income, a worker self-selects to work in theinnovation sector if! H hie > 1 ) ! H zi + ! H Z

e > 1 ) z1 =1 + e !H Z
:
!H

(15)

@!H
@q > 0by blocking imita-

Lemma 2. IPR protection increases returns to skills in the Southtion, shifting workers from the production to the innovation sector@z1@!H < 0.

Proof. Follows directly from (13) and (15).
It follows from Lemmas 2 that better IPR enforcement q attracts production workers to theinnovation sector by reducing imitation, thereby increasing the returns to working in that sector(!H ).13 The impact of IPR enforcement on the southern labor market in the absence of migration
is illustrated in Figure 1.
[FIGURE 1 ABOUT HERE]
We concentrate the analysis on the interior equilibria, so that z1 > 0. At the limit when z1 = 0,
the economy ceases to produce the invented varieties regardless of a fully operational innovation
sector. Likewise, to assure the existence of a home innovation sector, z2 > z1 must be true. Formally,+!H Z
1+e !H Z
looking at (14) and (15), this holds when !FM. Using the most demanding scenario for!H >!H
the inequality to be satis…ed (i.e. setting Z and !H to their minimum level of 0 and 1 respectively),
the condition reduces to F=(1 + e) > (!M 1). This means that for an innovator sector to exist,
the relative …xed cost of migration with respect to education should be greater than the gains from
migration (where a lower F increases z2 and a higher e increases z1 ).14 Under this condition, thelower skilled population cannot a¤ord to cover migration costs. Therefore, there does not exist
a level of zi which makes a worker indi¤erent between migrating and working in the production
sector. Instead, we can be certain that an innovation sector exists, in which a worker with skills z2
is indi¤erent about staying or migrating. At the limit when z1 = z2 , there is no longer an innovation
sector in the South, as all those who obtain education migrate.15
Next we look at the e¤ect of IPR protection on the migration decision of innovation workers. A@z2
look back at (14) shows that the threshold skill level z2 increases in wages !H as @!
> 0, that is,Hhigher skilled wages in the South discourage emigration to the North. It follows:
Lemma 3. Higher returns to skills obtained through IPR protection retain skilled workers in the@z2home innovation sector @!
> 0 and reduce the size of diasporas @ @z(z22 ) < 0 .
H
Proof. Follows directly from (4), (13) and (14).
Lemma 3 suggests that IPR protection works as a force against brain drain by preserving skills in
the South. An improvement in the IPR protection level q partially prevents migration by recognizing
the rights of inventors and discouraging imitation. A change in z2 also changes the composition of
1 3 In addition, higher training costs e prevent entry by the low-skilled, whereas higher wages in the innovation sector
at home !H and higher potential diaspora gains Z increase returns to working in the innovation sector, thereby
shifting workers there.
1 4 See Appendix A.1 for the feasibility of the assumption.
1 5 In case z > z , thresholds z and z simply do not exist. In such a scenario, there is again no innovation sector in
12
1
2
the South. The unique relevant threshold becomes a new z3 , which is derived by comparing earnings from migration
with earnings from working in the production sector: using !M zi
e F = 1, z3 = (1 + e + f )=!M . Workers
with skills lower than z3 stay in the production sector while workers with skills higher than z3 obtain education andmigrate. Note that z3 only depends on the exogenous parameters of the model and is therefore independent from IPR
protection.

7

international spillovers that a¤ect workers’ productivity. Namely, reduced migration induced by
IPRs limits potential gains from diaspora by encouraging more skilled workers to remain in thehome economy.

2.5. General equilibrium
The economy is in equilibrium when the allocation of workers across sectors is compatible withthe labor and product market clearing conditions. In this section, we will see that wages adjust
endogenously together with z1 and z2 to reach equilibrium, thereby determining also the amountof human capital being utilized in the economy H(z1 ; z2 ), the number of inventions N , and theaggregate price index P .
The total number of workers in the production sector in terms of the threshold skill level z1 is
Zz1
L(z1 ) = g(z)dz = G(z1 );

(16)

0

and total skills in the innovation sector in terms of z1 and z2 is expressed by
Zz2
H(z1 ; z2 ) = hi g(z)dz:

(17)

z1

Market clearing implies that total output Y is equal to total factor income:16
Y = !H H(z1 ; z2 ) + L(z1 ):(18)

This equilibrium condition can equivalently be written through the labor market clearing condition1
Y ( 1)Y;(19)
L(z1 ) = [N (1 q)] + N q
where the …rst and the second term on the RHS derive from total consumer demand for non-patented
and patented goods, respectively.
We can close the model by using equations (6), (10), (12), (18), and (19) to solve for the equilibrium wage in terms of z1 and z2 :!H = !H (z1 ; z2 ) =q(

1)

H(z1 ; z2 )[1

1
(

1)

L(z1 )

:

1

q(1

(

1)

(20)

)]

An increase in q on the RHS of (20) is always compensated by a fall in z1 (as @L(z1 )=@z1 >0 in the numerator and @H(z1 ; z2 )=@z1 < 0 in the denominator) and an upward shift in z2 (as@H(z1 ; z2 )=@z2 > 0) to maintain equilibrium. Using (20) together with (15), (14), we obtain thefollowing two-equation system:!H (z1 ; z2 )(z1 + Z) = 1 + e;
!H (z1 ; z2 )(z2 + Z) = !M z2

(21)
F:

Using (20) to rewrite the equilibrium condition (21) and dividing each side of the two equations, it
is easy to see that thresholds z1 and z2 must move in opposite directions:! M z2 F
1+e=
z2 + Zz1 + Z(22)

The RHS of (22) is clearly decreasing in z1 and increasing in z2 as @Z=@z2 < 0. The LHS is also
1 6 We assume education cost e to be embedded in Y , which simpli…es the notation but does not in‡uence the results.

8strictly increasing in z2 as@Z!M Z + F + @z
(F
dLHS
2
=
dz2
(z2 + Z)2

! M z2 )

> 0,

(23)

@Z
where @z
< 0 and F !M z2 < 0 from (14). Thresholds z1 and z2 must therefore move in opposite
2
directions to maintain equilibrium. We can state that in general equilibrium, the reallocation ofworkers in the economy caused by migration or IPR protection either reduces or increases the sizeof the innovation sector from both sides of the distribution. It will be seen below how this generalequilibrium e¤ect reinforces our key results. We can now calculate the dynamics of z1 and z2 withrespect to changes in the IPR regime, q, and subsequently analyze how skilled emigration could
promote innovation in the South. We then explore the conditions under which the bene…cial e¤ects
of cross-border diaspora are likely to outweigh the negative brain drain e¤ect of emigration andtransform it into brain gain.

3.

Diasporas and innovation

This section studies the combined e¤ect of IPRs and migration on innovation in the sending country
through the diaspora channel, i.e. the spillover of superior knowledge learned by migrants back totheir country of origin. Such potential gains from skilled migration are denoted by Z in equation(3) and illustrated in Figure 2. The aim is to show that although a reduction in migration costs F
hurts innovation in the South via brain drain by inducing the marginal emigrant to leave (Lemma1), it also helps the southern inframarginal innovators via diaspora feedbacks. The extent to whichsuch feedbacks create gains for the sending country depends on the size of the innovation sector,
itself determined by the level of IPR enforcement.
[FIGURE 2 ABOUT HERE]
To start, observing Lemmas 2-3 reveals that IPR protection increases the size of the innovation
sector by attracting less skilled workers into the innovation sector and discouraging more skilledworkers from migration:
Proposition 1. IPRs fosters potential gains from diaspora by expanding the size of the innodz2
1
vation sector from both sides of the spectrum ( dzdq < 0, dq > 0), thereby increasing the absorptive
capacity of the home economy.
Proof. Follows directly from Lemmas 2-3 with the formal proof in the Appendix A.2.
Proposition 1 states that for any given F that yields a positive level of migration, more stringent
IPR protection allows potential gains from diaspora, Z, to fall on a larger range of workers active in
the innovation sector. It will be seen below that this e¤ect of IPRs can create net gains from diasporas
despite of reducing the number of migrants, as long as the intensity of international knowledge ‡ows
is su¢ ciently high (large b). The change in the magnitude of the diaspora mechanism caused bystronger IPRs is depicted in Figure 3.
[FIGURE 3 ABOUT HERE]
We can also directly derive the consequences of strengthening IPR enforcement on innovation in
the South by calculating the e¤ect of a change in the IPR regime on the number of inventions, N .
Corollary 1. IPR protection increases the number of innovations by driving more workers
into the home innovation sector, but also decreases it by limiting migration and hence reducing the1 ;z2 ;q)70 .
amount of diaspora knowledge spillovers. The total e¤ ect is therefore ambiguous dN (zdq
Proof. See Appendix A.3.
We are now in the position to make some conclusions about how IPR protection in‡uences thee¤ect of migration on innovation activities in the sending country. Recall from (6) that the number
9

of innovations in the South is proportional to H(z1 ; z2 ), which according to Equations (2) and (5)depends both on the size of the innovation sector and the potential gains from diaspora. To measure
the net e¤ect of migration on innovation in the South, we must weigh the magnitude of the negative
brain drain e¤ect against gains brought about by the diaspora channel. To make the point, let us…rst consider a shift from a no-migration scenario to one with a positive level of migration. Brain
drain can be summarized as the direct loss of skills embedded in workers who migrate abroad, i.e., theextensive margin. This is, in other words, the amount of skills initially available prior to migration
minus the basic skills of the remaining workers post-migration:
Z1
BD = zg(z)dz
z1

Z1
Zz2
zg(z)dz = zg(z)dz:

(24)

z2

z1

Next, we rewrite the aggregate supply of skills as
Zz2
Zz2
Zz2
H(z1 ; z2 ) = (z + Z)g(z)dz = zg(z)dz + b (z2 ) g(z)dz:

(25)

z1

z1

z1

The …rst term on the RHS represents the amount of skills that workers in the innovation sector are
originally endowed with, and the second term represents the aggregate diaspora e¤ect on the same
workers still residing in the South, i.e., the intensive margin.17 The second term on the RHS of (25)denotes the virtual return of upgraded skills through diasporas and can be rewritten to de…ne brain
gain as
Zz2
Z1
BG = b (z2 ) g(z)dz = b[G(z2 ) G(z1 )] zg(z)dz;
(26)
z1

z2

The term in the brackets [G(z2 ) G(z1 )] represents the size of the innovation sector, which multipliedby the diaspora term b (z2 ) accounts for the total e¤ect of the latter on innovation in the home
economy. Recall that an improvement in the IPR regime increases returns to skills (working in
the innovation sector) by increasing wages !H . This results in an expansion of the innovation
sector by reducing z1 and increasing z2 . The RHS of Equation (26) reveals that protecting IPRs
increases the number of workers in the innovation sector who can bene…t from diaspora by enlarging[G(z2 ) G(z1 )]. However, it also reduces the size of diasporas (number of migrants) and hence theamount of potential knowledge they can send back.
To determine whether the brain gain e¤ects caused by a diaspora channel could dominate the‡ight of skills caused by brain drain, we must calculate the net e¤ect of migration on total humancapital in the sending country and test whether

Z1zg(z)dzz2

b[G(z2 )BD BG ? 0
Z1
G(z1 )] zg(z)dz ? 0

(27)

z2

b[G(z2 )G(z1 )]? 1:

As seen above, the termb[G(z2 ) G(z1 )] can take a value greater or less than one. Braingains through diaspora dominate when > 1, which is more likely for high levels of IPR protection
@z2
@
@
0
0
1
because @z@q < 0 ) G (z1 ) > 0 ) @z1 < 0 and @q > 0 ) G (z2 ) > 0 ) @z2 > 0. As a result, in linewith the positive interaction e¤ect between IPR protection and emigration in the empirical …ndingsof Naghavi and Strozzi (2015), IPRs makes it more likely for skilled migration to generate brain
gains by increasing the size of the innovation sector and absorptive capacity in the South. Also theintensity of international spillovers (b) must be large enough to compensate for the negative diaspora
1 7 Note that emigrants are excluded when summing up local skills in the South.

10e¤ect of IPRs through the reduced stock of knowledge that can potentially be sent back, (z2 ).
Proposition 2. Gains from diaspora could outweigh the direct loss of skills caused by migration
if the IPR level in the South and intensity of knowledge spillovers are su¢ ciently high such thatb[G(z2 ) G(z1 )]> 1. IPRs furnish the conditions for knowledge from diasporas to reach out toa larger number of workers in the innovation sectord[G(z2 ) G(z1 )]
>0
dq

.

Proof. Derives from Lemma 1 and Proposition 1 together with (27).
An alternative approach to measure diaspora spillovers would be to consider the average skill level
Z1
1~
of migrants abroad, = 1 G(z2 ) zdg(z), as opposed to the absolute sum in equation (3). This canz2

be attractive because the quality of knowledge transmitted home through diasporas would be fallingwith increased migration as every additional skilled migrant has lower skills than the previous one
and therefore reduces the average contribution to the home economy through a reduction in G(z2 ).
As a result, what would matter is the composition of the emigrants, and not the scale. Nevertheless,for any given any level of migration, better IPR protection allows the diaspora spillovers to fall over alarger range of innovation workers at home increasing their skills on the intensive margin. Using this1
, on the RHS of (26), which in fact strengthens
approach only results in an additional term, 1 G(z2)
our original argument.
Looking at the problem from a broader perspective, we can also calculate the e¤ect of an exogenous reduction in migration costs F on the number of innovations in the South and how the sign ofthe change depends on the IPR regime.
Corollary 2. Migration induced by a lower F results in a drain of existing skills utilizable
in the innovation sector, but increases the possibility for superior knowledge to be learned and sent
back from diasporas. Stronger IPR protection in the South makes it more likely for the latter positive
1 ;z2 ;q)e¤ ect to dominate so that dN (zdF
<0 .
Proof. See Appendix A.4.
Interestingly, the results produced by the model are compatible with the alternative explanations
provided in BDR (2001) and Mayr and Peri (2009) on human capital development and return
migration respectively. To compare, IPRs work as an intermediary channel to extract (brain) gains
from skilled migration by encouraging education in the home country. Similarly, IPRs induce return
migration of workers with enhanced skills back into the innovation workers. We can therefore
conclude that when skilled migration generates positive knowledge ‡ows, IPR protection createsthe conditions for the southern innovation sector to absorb bene…ts from diasporas by stimulating
human capital development, return migration, or intellectual diaspora networks.

4.

Extension: local spillovers

In our model, the size of the innovation sector is proportional to the number of inventions, N , which
is itself directly determined by the amount of human capital in the innovation sector, H(z1 ; z2 ). This
allows us to focus the analysis on the initial skill endowment of each individual (their innate ability)
used in the innovation sector and how the assumed superior knowledge from the North can ‡owback to upgrade workers’productivity in proportion to their skills. Using such framework, however,
abstracts from local spillovers caused by interaction among Southern co-workers in the innovation
sector.
In an alternative framework, average skills in the innovation sector can also play a role in the
productivity of innovation workers, hi . This concept is for example used in the production functionof Helpman, Itskhoki and Redding (2009, 2010, 2013) to show how the productivity of a worker
may depend on the average productivity of his team. Introducing this feature creates a secondary(direct) negative e¤ect of IPR enforcement on innovation because average skills and hence research
productivity is reduced as less talented workers become researchers. This view is also is in line with
Glass and Saggi (1998) and Vandenbussche, Aghion and Meghir (2006), who argue that a shift of11

less skilled workers away from less skill-intensive activities could have adverse e¤ects for countries
far from the technological frontier.
We now study the impact of IPR protection, directly and through emigration, and the combination of the two by means of diaspora knowledge networks on local externalities that occur within
the southern innovation sector.
De…ne local spillovers as a direct product of average level of skills in the innovation sector, or
the amount of e¤ective innovation activities that lead to the creation of new patents:
z~ =

1

1
G(z1 )

Z1
zdg(z):(28)

z1

We …rst use the amount of skills workers are endowed with to study the direct e¤ect of IPRs andmigration on innovation (~z ) keeping Z …xed. We then investigate how the productivity of eachworker (hi ) increases in the intensive margin through diasporas in proportion to their initial level ofskills.
As in the main analysis, better IPR enforcement q changes average skill level and thereforee¤ective innovation activities by increasing the returns to working in the innovation sector. IPR
protection increases !H as demonstrated in (13), encouraging less skilled workers to move into theinnovation sector. As a consequence, local spillovers measured by the average level of skills in (28)d~z
> 0.18
fall due to an expansion of that sector towards the less skilled mass of workers, i.e. dz
1Di¤erentiating (28) with respect to z1 re‡ects the basic results from the occupational choice modeld~zof Roy (1951). Because dz> 0, the entry of less-skilled workers in the innovation sector reduces
1
average skills. We interpret this as a direct negative e¤ect of IPRs on innovation caused by amisallocation of the low-skilled to the innovation sector.
To account for migration, lets rede…ne average skills in (28) asz~ =1
G(z2 )

G(z1 )

Zz2
zdg(z):(29)z1Here, we see that a higher !H also discourages the most skilled from emigrating, thereby increasd~z
ing the local spillovers presented in (29), i.e. dz> 0.19 Addition of workers with higher skills than2
those in the innovation sector increases average skills. We can conclude that an increase in the IPR
protection also has a positive e¤ect on local spillovers by preserving workers from the upper tail ofthe distribution of skills in the South. The total e¤ect of IPR on z~ hence depends on the distributionof skills in the country: when the distribution is skewed towards the low-skilled the negative e¤ect of
IPR dominates (more likely for developing countries), whereas the positive e¤ect through migration
would prevail for societies with a skill distribution skewed towards the high end.
The results in the previous sections can be replicated by bringing together IPR protection andmigration to study their combined e¤ect on innovation in the sending country through diaspora
externalities, Z in equation (3). This …nal e¤ect of IPRs via migration is independent of local
spillovers and directly depends on the size of the innovation sector, which increases from both
spectrums. This allows potential gains from diaspora to fall on a larger range of workers active in
the innovation sector to work against the negative impact of IPRs on local spillovers. Therefore,
our main argument that IPRs creates the conditions for new knowledge from diasporas to bene…t alarger number of innovation workers in the intensive margin remains valid. This is an important point
because in Naghavi and Strozzi (2015) we also show that in emerging and developing countries IPR
protection by itself has a negative impact on domestic innovation, whereas it works as a moderating
factor to exploit gains from international migration by enhancing the absorptive capacity of thehome country.
In sum, the IPR regime a¤ects innovation in two ways. On the one hand, it a¤ects the size
1 8 See Appendix A.5 for the proof.
1 9 See the Appendix A.5 for proof.

12

of the innovation sector. On the other hand, it endogenously in‡uences the skill composition in
the innovation sector. Both are caused by a ‡ow of low-skilled workers from the production to theinnovation sector (i.e., z1 falls) and reduced emigration (i.e., z2 rises). Although the presence ofthe low skilled in the innovation sector may directly reduce local spillovers (~z ), the potential forabsorption of the newly acquired skills from the North (b ) is higher regardless because the diaspora
e¤ect in‡uences a larger range of workers.

5.

Conclusion

In this paper, we have explored the link between cross-border diaspora networks and innovation
capacity in migrants’countries of origin. The perspective we adopt is that of a developing country.
We argue that although skilled emigration out of a developing country may directly result in thewell-known concept of brain drain, it can also cause an indirect brain gain e¤ect, the extent of which
depends on the level of intellectual property rights protection in the country of origin. While theliterature on brain gain and development highlights that the brain gain channel is realized throughan increase in the incentives for human capital formation in the sending countries, in our framework
the brain gain channel is realized through an increase in the size of the innovation sector. Bothinterpretations, however, lead to the same conclusion: under certain conditions, skilled emigration
could be bene…cial for growth in the sending countries.
We investigate under what circumstances skilled emigration may be bene…cial for development.
We show that this occurs in the presence of a strong IPR regime, which may turn a brain drain
into a brain gain. IPR protection in‡uences a country’s potential for innovation by changing thesize of the innovation sector. This could increase the absorptive capacity of the emigrants’countryof origin, thus leading to more bene…cial e¤ects from cross-border diaspora networks.
The mechanism at work is as follows. Emigration has two e¤ects. On the one hand, it decreases
the amount of skills in the innovation sector by losing the most skilled through a lower z2 (theextensive margin). On the other hand, it can increase the skills of the remaining workers in theinnovation sector through the positive externalities of the diaspora channel Z (the intensive margin).
The IPR regime in turn in‡uences innovation by changing the size of the innovation sector. An
increase in IPR protection enhances the attractiveness of working in the innovation sector, thusincreasing its size from both ends of the spectrum: this causes a ‡ow of low-skilled workers from theproduction to the innovation sector (i.e., z1 falls) and reduces emigration (i.e., z2 rises). Although
IPRs reduce the size of the diaspora by limiting migration, the potential for absorption of the newly
acquired skills from the North is higher because the diaspora e¤ect in‡uences a larger range ofworkers.
Our theory draws upon the realistic assumption that emigration may give origin to cross-borderdiaspora networks between skilled emigrants and natives. It turns out that in the presence of astrong IPR regime the gains in human capital deriving from the diaspora channel of knowledge are
more likely to outweigh the direct drain of skills caused by emigration. As a consequence, whenpatents are su¢ ciently protected, informal networks of emigrants and people remaining at home are
crucial in turning a brain drain into a brain gain. The simple setting introduced is a …rst step tohighlight the joint role of institutions and migration in promoting growth and aims to encourage
further research on the issue. It can be extended to incorporate a wider range of topics into theframework such as trade, FDI, and imitation (versus innovation) in developing countries.

13

A.

Appendix

A.1. Feasibility of the assumption on thresholds
Inequality z1 < z2 must hold so that not everyone in the innovation sector migrates. This requires
1 + e !H Z
F + !H Z
<
!H
!M !H
(!M
)F >

!H ) (1 + e
!H

!H Z)

!H Z:

For a z2 < 1 to exist so that someone would …nd it optimal to migrate, we must have a worker
with skills zi < 1 such that! M zie

F > ! H zi + ! H Z e) F < (!M !H )zi!H Z:

Putting the two inequalities together, we prove the existence of a feasible range of F along which
both conditions are valid. That is, z1 < z2 < 1 is viable if and only if(!M(!M!H )zi(!M!H Z >!H ) (1 + e
!H

!H Z)

!H Z

!H ) (1 + e !H Z)< (!M !H ) zi
!H
1 + e !H Z
< zi
!H
1 + e < !H (zi + Z);

which is true for all zi > z1 (see (15)).We can therefore conclude that the two conditions cancontemporaneously be satis…ed for the entire range of skill distribution.

A.2. Derivations of the equilibrium
We have a system of two equations:!H (z1 + Z)
!H

z

q(

1)

H(z1 ; z2 )[1

}|
(

1
1)

L(z1 )

q(1

(

1)

{

)]

(z1 + Z)

! M z2! M z2zq(

1)

H(z1 ; z2 )[1

(

1
1)

L(z1 )

q(1

(

e=0

1

e=0

!H (z2 + Z)

!H

}|

1

1)

{

)]

(z2 + Z)

F =0

F =0

given
@H(z1 ; z2 )@H(z1 ; z2 )@L(z1 )
> 0;
< 0;
>0
@z1
@z1
@z2
which implies
@!H
@!H
@!H
> 0;
> 0;
< 0:
@q
@z1
@z2
14

We would like to establish whether
dz1
dz2
? 0;
? 0:
dq
dq
Considering !H as a function of z1 , z2 , and q, we have the two conditions given by two functionsi (z1 ; z2 ; q) = 0 for i = 1; 2:(

1 (z1 ; z2 ; q) =(z1 + Z)!H (z1 ; z2 ; q) + 1 + e = 0
z2 ! M = 0
2 (z1 ; z2 ; q) = (z2 + Z)!H (z1 ; z2 ; q) + F:

Subsequently, we calculate the total di¤erentials d 1 and d 2 and equate them:d 1 = d 2 ()

@ 1
@ 1
@ 1
@ 1
@ 2
@ 2
@ 2
@ 1
dz1 +
dz2 +
dq +
dZ =
dz1 +
dz2 +
dq +
dZ:
@z1
@z2
@q
@Z
@z1
@z2
@q
@Z

Then, we consider the plane (z1 ; q) to evaluate the slope of the function z1 (q), so we impose dz2 = 0,dZ = 0, and after calculating the …rst-order partial derivatives we obtain:!H ( ) + (z1 + Z)

@!H
@z1

dz1

(z1 + Z)

@!H
@!H
@!H
dq = (z2 + Z)dq:
dz1 + (z2 + Z)
@q
@z1
@q

Subsequently, we collect terms and identify the ratio of the di¤erentials:
dz1
=
dq

@!H
@q
:
@!H
!H ( ) + (z1 + z2 + 2Z)@z1(z1 + z2 + 2Z)(A1)

From the investigation of (A1) we can deduce that
@!H
dz1
@!H
< 0 as> 0:> 0 and
dq
@z1
@q

(A2)

We can repeat the same procedure by setting dz1 = 0 and dZ = 0 in the relation d 1 = d 2 toestablish a relationship between the di¤erentials dz2 and dq:(z1 + Z)=

!H ( )

@!H
dz2
@z2

@Z
@!H
dq
dz2 (z1 + Z)
@z2
@q
@!H
@Z
@!H
!M + (z2 + Z)
+ !H
dz2 dz2 + (z2 + Z)
dq:
@z2
@z2
@q
!H

The slope will amount to the following:
dz2
=
dq

@!H
@q
@!H
@Z
!M + (z1 + z2 + 2Z)
+ 2!H
@z2
@z2
(z1 + z2 + 2Z)!H ( )(A3)(A3) has a form that is analogous to (A1), so we can carry out a similar investigation:dz2> 0 as !Hdq!M < 0,

@!H
@Z
@!H
< 0,
< 0, and
> 0:
@z2
@z2
@q

We have therefore proved that
dz1
dz2
< 0;
> 0:
dq
dq
That is, stronger IPR protection expands the size of the innovation sector from both sides of thespectrum of skills by decreasing z1 and increasing z2 .
15

Finally, to account for the general equilibrium e¤ect, we must also derive the sign of(A3) by (A1) we obtaindz2. Dividing
dz1

@!H
@z1
@!H
@Z
!M + (z2 + z1 + 2Z)
+ 2!H
@z2
@z2
!H ( ) + (z1 + z2 + 2Z)

dz2 =dq
dz2==
dz1 =dqdz1!H ( )(A4)

Using the same argument as that for (A1) and (A3), we can deduce from (A4) that
dz2
< 0:
dz1
This is because, given (A2), the numerator of (A4) is positive while the denominator is negative.
We have therefore proved that stronger IPR protection expands the size of the innovation sector
from both sides of the spectrum of skills by decreasing z1 and increasing z2 . Furthermore, thresholds
z1 and z2 always move in opposite directions.

A.3. Proof of Corollary 1
According to (6), the sign of a change in N (z1 ; z2 ; q) is equivalent to that in H(z1 ; z2 ; q). We therefore
proceed by taking the total derivative of H(z1 ; z2 ; q) with respect to q.
Zz2
d hi g(z)dzdH(z1 ; z2 ; q)
=
dq

=

Zz2
d zi g(z)dz
z1

dq

+

z
z

z1

dq

=

Zz2
d [zi + b (z2 )]g(z)dz
z1

Zz2 Z1d [b zdg(z)dz]g(z)dz
z1

z2

dq

=

Zz2
d zi g(z)dz
z1

dq

+

}|

{z
}|
{ z
}|
{
+
z}|{
z}|{
dz2
dz1
= z2 G0 (z2 )z1 G0 (z1 )
dq
dq
|
{z
}
+

m ore skills enter innovation sector

z

z1

0

+

z2

dq

d @b[G(z2 )

}|
+
}|

bz2 G0 (z2 )[G(z2 )
|
{z

1
Z1
G(z1 )] zdg(z)dz A
z2

dq

{
+
z}|{
dz2
G(z1 )]
dq}{

change in spillover am ount on current workers(-) as IPRs reduce diasp ora

+

z

=

dq

Zz2
Z1
d [zi + b zg(z)dz]g(z)dz

}|
{
z
}|
{ z
}|
{
+
z}|{
z}|{
dz2
dz1
+ G0 (z2 )b (z2 )G0 (z1 )b (z2 )
dq
dq
|
{z
}
+

b ene…ts from diasp ora for new innovation workers= G0 (z2 )dz2[z2 + b (z2 )]dq

G0 (z1 )dz1[z1 + b (z2 )]dq

16

bz2 G0 (z2 )[G(z2 )G(z1 )]dz2
dq

= G0 (z2 )dz2h(z2 )dq

G0 (z1 )dz1
h(z1 )dq

G0 (z2 )dz2z2 b[G(z2 )dq

G(z1 )]The …rst two terms represent the positive e¤ect of IPRs due to entry of more workers into theinnovation sector and the last term is the negative diaspora e¤ect caused by reduced migration.

A.4. Proof of Corollary 2
According to (6), the sign of a change in N (z1 ; z2 ; q) is equivalent to that in H(z1 ; z2 ; q). We therefore
proceed by taking the total derivative of H(z1 ; z2 ; q) with respect to F .

dH(z1 ; z2 ; q)
=
dF

=
z
=

Zz2
d zi g(z)dz
z1

dF
+

}|
+
}|

{
+
z}|{
dz2
z2 G0 (z2 )|{z dF}z+Zz2
d hi g(z)dz
z1

dF

=

Zz2
d [zi + b (z2 )]g(z)dz
z1

Zz2 Z1d [b zg(z)dz]g(z)dz
z1

z2

dF
{z

brain drain: skills leaving

z

=

}|
+
}|

bz2 G0 (z2 )[G(z2 )
|
{z

Zz2
d zi g(z)dz
z1

dF
{
+
z}|{
dz2
G(z1 )]dF}

dz2
fz2 (1dF

b[G(z2 )

z2

z1

dF
0

+

d @b[G(z2 )1
Z1
G(z1 )] zg(z)dz A
z2

dF

+

{z

change in spillover am ount on current workers(-) as m igration generates m ore diasp oras

= G0 (z2 )

=

dF

Z1
Zz2
d [zi + b zg(z)dz]g(z)dz

+

}|
+
}|

{
+
z}|{
dz2
G0 (z2 )b (z2 )
dF}
|
{z
z

{

brain drain: diasp oras b ene…ts no longer used

G(z1 )]) + b (z2 )g

1 ;z2 ;q)We obtain dH(zdF< 0 if and only if z2 b[G(z2 ) G(z1 )] > z2 + b (z2 ), which can be simpli…ed
to z2 > h(z2 ). Note the extra term on the RHS with respect to Proposition 1 that appears here as
we are calculating the number of inventions as opposed to a pure brain drain. That is, when talking
in terms of total productivity per workers, those who leave take with them not only their innate
abilities but also what they learn from diasporas. Rewriting the new condition as>1+

b (z2 );
z2

it is more likely to be satis…ed under strong IPR enforcement as an increase in q increases the RHS
through a higher z2 and a lower z1 (expanding the innovation sector), and decreases the LHS througha higher z2 (less brain drain and more remaining workers to bene…t from diasporas). Setting theinitial (pre-existing) level of diaspora knowledge ‡ow equal to zero, the condition simpli…es to thatobtained in Proposition 1.

A.5. Proof of the results in Section 4
To …nd out the direct e¤ect of IPR protection on local spillovers we have to calculate d~z =dz1 > 0.
To prove the e¤ect of variations in z1 on average skills we derive
i
h
Rz
R1
R1
1 zG0 (z )dz ]d[ 111
zdG(z)
d 1 G(z[1 G(z1 )] [ G0 (z1 )] z1 zdG(z)
z1
1)
dz1
=
2
dz1
[1 G(z1 )]G0 (z1 )[ez z1 ]=>0[1 G(z1 )]17This implies that if z1 goes down as a consequence of a rise in IPR protection q, then z~ also
falls due to the Roy e¤ect, and the misallocation of workers, i.e. less skilled labor moving into theinnovation sector.
To calculate the e¤ect of IPRs on local spillovers through migration we have to calculate d~z =dz2 .
To prove the e¤ect of variations in z2 on average skills we derivedh1
G(z2 ) G(z1 )izdG(z)
z1

R z2

dz2

i
hR
d zz2 zG0 (z2 )dz
1

=
=

dz2

[G(z2 )Rz
[G0 (z2 )] z12 zdG(z)G(z1 )]2[G(z2 )

G(z1 )]G0 (z2 )[z2 ze]>0[G(z2 ) G(z1 )]This implies that if z2 goes increases as a consequence of reduced migration (due to better IPRs),
then z~ also increases due to the Roy e¤ect, and by keeping the most skilled in the home innovation
sector.

A.6. Introducing a separable numéraire good
Consider utility

2N
31
Z
Ui = Ci = 4 cj dj 5 + a;0

where individual aggregate consumption index Ci is divided between a continuum of N invented
goods subscripted by j 2 (0; N ), plus a numéraire homogenous good labeled a, with
2 (0; 1)
representing the inverse measure of product di¤erentiation.
Using a monotonic transformation to utility function Ui , which would yield the same optimization solution, consumers maximize
M ax NP cP + NN cN + a ;cN ;cP

under the budget constrainty = pP NP cP + pN NN cN + a;
Normalizing the price of the numéraire to one also determines wages in the production sector,!L = 1. A non-patented good can be imitated driving its price down to the marginal cost of
production, pN = 1. Consequently, given pP = , NP + NN = N , NP = N q and NN = N (1 q),
the solution to the above maximization problem is:a = cN =y; cP =

y

1
(

1)

;

where
= Nq

(

1)

+ N (1q) + 1;(A5)

leading to an aggregate price index of((

P = N P pP

1)(

+ N N pN

1)

1)

+1

:

The labor market clearing condition turns toL(z1 ) = [N (1q) + 1]

18

Y

+ Nq

Y

1
(

1)

;

which together with (6), (12), (18), and now (A5) give the equilibrium wage in the innovation sector:!H = !H (z1 ; z2 ) =q(

1)+ H(z1 ; z2 )[1

1
(

1)

L(z1 )

q(1

:

1
(

1)

(A6)

)]

It is easy to see that the rest of the analysis and the results obtained in the paper remain identicalusing (A6).

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Figure 1.
Stronger IPRs Enforcement

Figure 2.
Diaspora Gains

Figure 3.
The Impact of IPRs on Diaspora