Transcript Knowledge Worker Emigration and the National

"The International
Migration of Knowledge
Workers: When is Brain
Drain Beneficial?"
Peter J. Kuhn, UC Santa Barbara
Carol McAusland, U Maryland
The Idea behind the Product:
Quiksilver Hooligan S/S T-Shirt
Price $24.50
1 5280 Hanes 5.5 oz Heavyweight Cotton Tee
100% ComfortSoft ™ cotton • 5.5-oz….
Type in the quantity for each color and size that
you want, and click the "add to cart" button White:
S: $1.54 M: $1.79 L: $1.79 XL: $1.79 XXL: $2.79
Other ‘ideas’ reproducible at very
low marginal cost:






Movies, books, music, video games
A sports performance
A formula for a drug or vaccine
Software
A scientific discovery
A better or more appealing/marketable design
for any product
Some features of “knowledge goods”:


Market size matters
Many knowledge goods suffer “losses in
translation” if produced and consumed in
different places:
Close to zero for orchestral music, Stata, AIDS
vaccine?
 Close to one for income tax software, comedy?

What are the implications of this for
international labor mobility?


Unless translation costs are zero, “Knowledge
Producers” (Brains?) will want to live in large
markets.
Lots of knowledge producers have migrated to
the U.S.:
Jim Carrey
Alanis Morissette
Alexander Graham Bell
Igor I. Sikorsky
Paul Anka
Diana Krall
David Frum
Celine Dion
Dan Aykroyd
Vladimir Kosma
Zworykin
Mike Myers
Peter Jennings
John Roebling
Plus of course:









Prof Yongmiao Hong
Visiting Tan Chin
Tuan Professor
23 April - 18 May
2007
Prof Hong is Professor of
Economics and of
Statistical Science at Cornell
University. He
has served on the editorial boards
of several
major journals in econometrics….
Questions in this paper:


Who gains/loses from knowledge worker
mobility (sending country, receiving country,
brains)?
How does this depend on:
Relative market sizes
 “Translation costs”
 Intellectual Property Rights (IPR) Policy

Our answer:




Brain Drain may be Pareto-Improving.
Why? Since knowledge workers produce a
public good, consumers in their native countries
can still benefit from their efforts.
The net gain depends on the balance between
knowledge creation and knowledge diffusion
caused by emigration.
Neither of these effects are captured in any
existing models of the “brain drain”.
Brain Drain Literature

Survey: Commander, Kangasniemi, Winters
(2004)
Earliest literature



Modelled “brain drain” as just another international
factor flow (e.g. Berry and Soligo 1969, Jones, Coelho
and Easton 1986).
In the simplest model (small, undistorted economy),
any factor outflow that doesn’t exactly mirror the
existing factor endowment ratio hurts remaining
residents.
Exceptions do exist:


large economies (when terms of trade are affected)
when there are at least as many traded goods as factors of
production (then the effect is zero).
Factors that accentuate harm from
draining brains


Fiscal externalities: with publicly-financed
education and progressive taxation, skilled
emigrants create a fiscal loss (Bhagwati and
Hamada 1974).
Education and Endogenous Growth: If
skilled workers raise the sending country’s
growth rate, very large long-term losses can
result (Miyagawa 1991, Wong and Yip 1999).
Factors that might create “Beneficial
Brain Drain (BBD)





“Social safety valve” for unemployed skilled workers
(Bhagwati and Rodriguez 1975)
Remittances (Ozden and Schiff 2006)
Return migration (DeVoretz 2005)
Education incentives provided by an “emigration
lottery” (Stark, Helmenstein and Prskawetz 1997, 1998;
Mountford 1997)
Discipline on sending countries’ tax authority (Haupt
and Janeba 2004, Bucovetsky 2003)
Note:
None of these papers model consumer utility
explicitly, and certainly not product quality.
Yet quality is precisely how ‘knowledge work’
affects production and utility.
As a result, existing work has missed an important
potential benefit to all consumers from brain
drain.
Our Paper



“Brains” produce knowledge goods that can
have a “public good” aspect
Inventors produce higher quality when the
returns are higher
Demand for knowledge goods exhibits “Home
Bias”
Model
Production


Focus on representative “artist,” a.k.a.
researcher, inventor, knowledge worker
Artist produces a prototype of quality ρ at cost
c(ρ)


c’(ρ)>0, c’’(ρ)>0
Reproductions are costless
Demand



q=per capita consumption
Individual inverse demand = tρp(q)
p(q) = base demand

with ε = elasticity of “base” demand
1
   dp( q )
dq



p(q)
q
assume ε decreasing in q
ρ=quality
t=“relevance”
“Relevance”





Armington (1969): goods differentiated by
country of origin
Trefler (1995): Home Bias
Some knowledge goods don’t survive translation
well at all: political writing
Others are universal: laws of physics
Most goods are in between: cultural goods
(literature, movies, pop music), medicine,
product design
Lost in translation




τ=fraction of value surviving translation
1-τ=iceberg translation cost
Suppose a prototype is produced in market j
Relevance of this product to consumer living in
market i is tij
 tij=1
if i=j
 tij=τ ≤ 0 if i≠j
Artist’s Decisions

Where to live/work?
Source country S
 Recipient country R



Which quality to produce?
What price to charge?
Pricing



Assume markets are segmented
Full intellectual property rights protection*—
artist has monopoly power
πi≡max pi(q)q
=maximum base profits in market i


Note: ε=1 at profit maximizing base
price/quantity
Total profits from market i = Niρtijπi
Total profits




Definitions
Xi=Niπi — effective size of market i
Mj=tSjXS+tRjXR — the artist’s global effective
market when she lives/works in country j.
Total global operating profits when artist
lives/works in country i
=NSρtSjπS +NRρtRjπR
=ρMj
Which quality to produce?

At a price, artist can raise the quality of her
prototype/reproductions
hire complementary inputs
 acquire additional training/skills
 work longer hours


Assume quality cost function is identical
regardless of production location




Suppose Artist lives/works in country j.
She chooses quality ρ to maximize ρMj-c(ρ)
First order condition:
Mj=c’(ρ)
(1)
Equation (1) implicitly defines equilibrium
quality — ρ(Mj) — as a function of effective
market size, and hence, of residency
with dρ/dMj=1/c’’>0
Where to live/work?

Assume relocation is costless.

Lemma 0 (not in paper): Absent translation
costs (i.e. τ=1) the artist is indifferent about
where she lives.

Lemma 1: If translation costs are non-zero (i.e.
τ<1), the artist emigrates if and only if XS<XR.
Restrict attention to cases where
XR<XS

Just focus on cases where voluntary emigration
would occur if allowed
Knowledge Creation

Define any increase in prototype quality as
“knowledge creation” (more, or better,
songs/theorems/vaccines)
Proposition 1

Voluntary emigration induces knowledge
creation

Proof: by Lemma 1, artist emigrates iff XR>XS
and τ<1, i.e. iff MR>MS. Because
dρ/dM=1/c’’>0 , ρ(MR)>ρ(MS).
Who benefits from Brain Drain?



Artist—revealed preference
Consumers in Recipient country?
Consumers in Source country?
qi
 i   p(q)dq  p(q i )q i
0
Consumer Surplus

Define CSij=NitijρФi where
qi
   p(q)dq  p(q )q
i
0
is “base” consumer surplus when
qi=argmax pi(q)q
i
i
Lemma 2

Consumers in country i are better off when the
artist voluntarily migrates iff
tiSρ(MS)<tiRρ(MR).
(2)
Proof: Because Ni and Фi are independent of ρ,
CSiR>CSij iff (2) holds.
Proposition 2 (a)

Recipient consumers are always made better off
by the artist’s voluntary migration

Proof: Because tRS=τ<tSS=1 and ρ(MS)<ρ(MR),
(2) always holds.
Source Consumers?

“Knowledge diversion” hurts Source consumers:
Absent emigration, Artist’s product is fully relevant
to Source consumers
 Once Artist moves/lives abroad, only fraction τ of
product survives translation.

r(MR)-r(MS)
r(MR)
1
S S
1- r(N p )
r(NRpR)
r(MR)-r(MS) =rate of knowledge creation
r(MR)
0
1
t = translation/survival rate
Figure 1: knowledge creation versus knowledge diversion
r(MR)-r(MS)
r(MR)
1
1t =rate of knowledge diversion (translation loss)
S S
1- r(N p )
r(NRpR)
r(MR)-r(MS) =rate of knowledge creation
r(MR)
0
1
t = translation/survival rate
Figure 1: knowledge creation versus knowledge diversion
r(MR)-r(MS)
r(MR)
1
1t =rate of knowledge diversion (translation loss)
S S
1- r(N p )
r(NRpR)
r(MR)-r(MS) =rate of knowledge creation
r(MR)
0
t
1
t = translation/survival rate
Beneficial Brain Drain
Figure 1: knowledge creation versus knowledge diversion
' ( rS )
d X R cRX
S

 (rt)r(RM )S r (M )
(r )r
dt X c' 'X



 r (M R )1  (M R )

t 1
Proposition 2(b)

If
ΛΨ(ρ(XR+XS))>1,
(3)
— where
measures the difference in
R
S
X X


relative marketX Rsize
equals
the
Sand
X
c' ( r )
elasticity of quality with respect
 ( rto
)  market size
c' ' ( r ) r
— then Source consumers gain from the artist’s
voluntary migration if τ is not too small.

Sketch of proof:
Look at the graph: if
knowledge diversion
line is flatter than
knowledge creation
curve at τ=1 then
clearly BD is
beneficial for some
τ<1.
_
tc  r
 1

Proposition 2(c)


A1. c  r
constant*.
 1

so Ψ is a
If A1 and (3) each
hold
_
there exists a t such
_
that Brain Drain is
neutral for τ=1 or τ= t,
Brain Drain is beneficial
to Source Consumers_
 (t ,1)
for τ
, and harmful
_
if τ< .
t
*Paper contains typo on p. 5
Observations
emigration definitely hurts Source’s consumers
when τ=0: if τ sufficiently low then BD lowers
Source welfare.
-> If translation costs are sufficiently high, BD
hurts Home consumers.

Ψ is one over the elasticity of marginal quality
costs, or, equivalently, the elasticity of quality
with respect to market size.
 Ψ > 1 is a necessary condition for (3).
-> If quality inelastic to market size, i.e. Ψ < 1,
BD harmful even for high knowledge survival
rates.

Proposition 3: the interval of survival rates
_
( t , 1) at which BD benefits Source consumers is
larger the bigger the gap between effective
market sizes.
->BBD more likely when Source is small relative
to recipient.

Recap
If
marginal investment costs don’t rise too quickly with
quality,
 translation costs aren’t prohibitive,
 and overseas market sufficiently bigger than sending
market,

then Brain Drain benefits consumers in Source
country.
Endogenous Intellectual Property
Rights


Effective market size depends on population
size, income level, and strength of IPRs
Emigration may change governments IPR
calculus
Pirates




Introduce a competitive fringe also capable of
reproducing artist’s prototype at zero cost.
Assume expected penalty for distributing pirated
goods is proportional to the price premium tρ.
Generates (expected) marginal cost dij=βitijρ
where βi is increasing in the strength of country
i’s IPRs.
β also equals the base price of pirated goods
Define β-dependent equivalent of
variables
β*≡p(qi), i.e. β* is price uncontested monopolist
would charge
 π*≡π(β*) (uncontested monopoly profits)
 p-1(β) (contested per capita output)
 Xi(β)≡Niπi(βi) (effective market size)
p(q)dq  p (  ) (base consumer surplus)
 (  )  
 CSSj(β)=NStSj(β)=NStSjρФS(βS)
(7)

p 1 (  )
0
1

Lemma 3: Under A1, CSSj is strictly (locally)
concave in β.
Government’s IPR policy choice



A2. XS(β*)<XR, i.e. Artist emigrates if allowed
Government can permit or prohibit emigration
exit (Open vs. Closed door)
Define
βO=argmax CSSR
 βC=argmax CSSS

N S [1   (0)](0)
1
tN Rp R
Proposition 4
Under A1 and A2
(a) if Source offers any IPR protection at all, it
offers weaker policy when its exits are open than
closed. Specifically, βO<βC iff
N S [1   (0)](0)
;
(10)
1

tN Rp R
if (10) fails then βO=βC=0.
(b) Source never offers full IPR protection:
βO≤βC<β*.
(Sketch of) Proof of Part (b)



If artist’s residency is fixed, then Source Gov’t
only worries about impact of weak IPRs on CSSj
via lower domestic prices and weaker quality.
Under A2, residency depends only on exit
policy.
At βS=β* (full IPRs), dCSSj/dβ<0, so always set
βS<β*.
Intuition

at β*, weakening IPRs lowers consumer prices
but has negligible effect on quality
Part (a) - Intuition

Lowering βS impacts CSS through two channels:
direct: lower prices for Source consumers
 indirect: shrink global market, reducing
Artist’s incentives to invest in high quality


Indirect effect is smaller when doors open
because, after Artist emigrates, Source market’s
contribution to Artist’s effective global market is
relatively smaller.
Implication
When the artist emigrates, link between Source
market size and investment decisions weakened.
This liberates Source government to set weaker
policy.
-> Open exit policy in small countries weakens IPR
discipline

t(X)r ( X SX(  )(  tX) R) 1
 r (RtX ( 
S
C 
 X  X () X)  )
_
R
S
S
C
R
Proposition 5; BBD with endogenous
IPRs


Suppose Source’s IPRs are set optimally given
exit policy, i.e. β=βO and β=βC when Source’s
exits are open and closed respectively.
Define
r ( X S (  )  tX R )
t
R τ at which
as the non-unity
r (tX Svalue
(  )  Xof
)
.
_
t ( )
_
t ( C )
Under A1 and A2,
(a)
(11)
 X R  X S ( C ) 
 R
1
S
C 
 X  X ( ) 
is a sufficient condition for Source to prefer an open-exit
policy i lieu of closed-exits for some non-empty range
(τ1,1) of translation costs
_
1
(b) if condition (10) holds then τ < t (.C )
Intuition

With endogenous IPRs, Source can redirect
some of the benefits from Knowledge Creation
to consumers via lower base prices
Conclusions

In the late 20th century:
Knowledge goods production concentrated in a
single country (US) with large domestic market
 A significant share of those goods was produced by
immigrants
 IPR protection was stronger in the US than in the
“brain-sending” countries

All the above features could be in the mutual
interests of the host country, the
Sending countries, and the “brains”
In particular:

Brain Drain may benefit sending country if:
Emigrants produce knowledge/public goods
 quality responsive to market size
 source market is sufficiently small relative to
recipient market
 translation costs are low (but not zero)


BBD even more likely if IPRs endogenous

Free emigration has negative “disciplining” effect on
IPRs
Noteworthy Model Features:




BBD is compatible with full IPR protection.
The model incorporates the declining cultural
relevance of knowledge produced for the
foreign market.
Sending country places no welfare weight on the
utility of its expatriates.
As translation costs fall, the model predicts that
“gains from drain” will first rise, then fall.
Caveats & Extensions


Extra “effort” is probably not the main reason
brains produce higher quality abroad. An
expanded treatment would incorporate
dynamically-created agglomeration economies.
An expanded model would also have multiple
knowledge producers, and competition among
them.
In case you ask...
How important are skilled
immigrants to the U.S.?


“Nearly a quarter of all active U.S. physicians are
international medical graduates (IMGs)—
physicians trained outside the United States and
Canada.” (Hart et al 2007, p.1159)
Foreign born Scientists and Engineers (S&E)
make up 16.6% of US S&E labor force (approx
7 million) and 23% of US S&E academics. (NSF
Science and Engineering Indicators 2006)
Does the U.S. produce the most
“knowledge”?

In 2000, more patents taken out by US residents than
by residents of any other country
(In 2000, 34.3% of Triadic Patent Families (defined by the
OECD as “patents taken out at the European Patent Office
(EPO), the Japanese Patent Office (JPO) and the US Patent
& Trademark Office ( USPTO) that share one or more
priorities”) were taken out by American residents. The
comparable proportions for residents of Japan and the EU
are 26.9 and 31.4 (Source: OECD, Patent Database,
September 2004.)
Does skilled emigration vary with
country size?
Carrington & Detragiache (1999)

Use 1990 data to show out-migration rates (to USA)
of skilled workers tends to be higher for small
countries
77% for Guyana
 67% for Jamaica
 1.1% for India
 1.4% for China

Are IPRs weaker outside the U.S.?


“borrowing a musical tape from a friend to copy
onto a blank tape for private use” (Canadian
Intellectual Property Office 2005, p.6) is not
considered copyright infringement.
Pharmaceutical pricing