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Oshoring, Innovation, and Imitation
Sebastian Benz∗
October 2011
Preliminary Version
Please do not cite
Abstract
JEL Classication: F12, F21, F23, F43, O31
Keywords: Oshoring, Innovation, Imitation, Information Leakage
∗
Ifo
Institute
for
Economic
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1
Introduction
The dynamic evolution of an economy is driven by investment in physical or - in the broadest
possible sense - knowledge capital.
Modern growth theory, as pioneered by Grossman &
Helpman (1991) and Aghion & Howitt (1992), emphasizes knowledge capital.
This means
that the accumulation of some type of capital stock draws on an activity that is separate from
production of goods. This can either be an R&D activity, or some form of education activity,
or else it may arise in the form of an externality associated with production of goods. In turn,
oshoring may aect these fundamental dynamic relationships in two dierent ways. First, it
may become an integral part the investment activity (R&D or education) itself, say through
oshore provision of relevant R&D services or entire research projects, or it may alter the
incentives for this activity for domestic individuals and, thus, also the equilibrium allocation
of domestic resources between such investment on the one hand, and the production of goods
and services on the other. In the following, we focus on the second channel.
This problem also concerns politicians worldwide. Accepting the fact of global production
sharing, especially in developed countries prevails the ambition to focus on jobs with a high
education requirement and high value added, such as in R&D. However, this raises concerns
that research is less ecient if conducted far away from the production sites.
Moreover,
if production is oshored to countries with weak institutions, property rights can easily be
violated and production imitated, so that the long-run earning potential of an economy is
disrupted, even with the oshoring decision is optimal in the short-run.
Currently, there is only little guidance for politicians in their decision making. In an early
paper, Glass & Saggi (2001) introduce oshoring into a growth model where rms engage in
quality-improving innovation. Oshoring plays no role in innovation as such, but successful
innovations may be adapted towards oshore provision of an early stage of production. Viewed
from a static perspective, such oshoring may be detrimental in lowering wages, but a novel
trade-o now emerges in that it may enhance the incentive to innovate and thus increase the
economy's long-run growth rate.
A similar tension arises in the multi-country Ricardian model proposed by Rodriguez-
1
Clare (2010). Abstracting from dynamics, oshoring from a rich to a poor country raises real
wages in the poor, but lowers them in the rich country; see above. Allowing for dynamics
in the form of a R&D-activity which an individual may choose instead of production, and
which enhances the country's absolute advantage through time, oshoring has the additional
eect of altering the equilibrium sorting of individuals into R&D and production, respectively.
More people in the rich country do R&D, leading to higher overall productivity level of the
economy.
In this dynamic model, the eects that have been identied in the static model
appear as the short-run outcome. In the long-run, the rich country now additionally benets
from enhanced productivity due to more R&D which is sparked o by oshoring.
An opposite relationship between oshoring and innovation is emphasized by Naghavi &
Ottaviano (2009). This comes about through a watering down of the learning eect required
to make an innovation bear out its full economic potential. Importantly, however, learning is
assumed more dicult if parts of the production activity are undertaken oshore, mainly due
to more dicult communication of experience. Then, if oshoring is taken solely based on
static minimization of cost according to comparative advantage, it may cause a long-run loss
in terms of a lower growth rate. And it seems very likely that the oshoring decision fails to
fully internalize the learning eect since learning often arises as an externality.
Glass (2004) introduces an imitation channel in the (Southern) host country of oshoring
which pretty much acts like an increase in the cost of adapting a certain innovation to foreign
sourcing. She assumes the imitation risk and the share of oshored tasks to be exogenously
given and nds that an increase in the imitation intensity increases the relative wage of the
Northern country, however at the cost of reducing the innovation rate.
Photchanaprasert (2011) further renes this model with an endogeneous imitation risk
driven by Southern free entry into imitation and, amongst others, determined by the level
of intellectual property rights (IPR) protection in the North. Strengthening IPR protection
decreases the rate of imitation and also the rate of innovation.
Furthermore, the relative
wage of Northern to Southern workers and the real wage in the North decreases. If Northern
politicians are free to optimally set the IPR protection level, this gives clear incentives to
completely abstain from any IPR protection.
2
We walk a similar path, however, considering oshoring as across-industry phenomenon
where the level of oshoring is determined by the oshoring cost of a marginal task
featuring a lower cost of international coordination than
I
I.
All tasks
are sourced from abroad, hence
yielding endogeneous savings on production costs that depend on the oshoring technology
cost parameter
β
and the endogenously determined marginal task, as shown by Grossman &
Rossi-Hansberg (2008). We nd that the introduction of such task-specic heterogeneity in
the oshoring costs yields novel results for the eect of IPR protection. More precisely, the
maximization of either the growth rate or the intertemporal welfare function via IPR protection depends on the oshoring technology, with high oshoring costs mandating high levels of
IPR protection, while IPR protection should be reduced as oshoring becomes technologically
easier.
2
The Model
The model economy is made up of two countries, North and South. Each country is endowed
with a xed and inelastically supplied amount of labor.
2.1
Manufacturing Sector
Firms produce dierent varieties of an otherwise identical consumption good. Production of
a variety requires a blueprint. Blueprints are developed by an innovative research sector in
the North. Innovation in the South is prohibitively costly. However, in the South exists a imitative research sector, that tries to copy existing Northern varieties. How exactly production
blueprints in the two countries are developed is described in more detail below.
Production of each variety requires the performance of a unit interval of identical tasks. As
is standard in the oshoring literature, we order tasks from
0 to 1 according to their oshoring
costs. This cost schedule is generally assumed to represent the diculty of coordination or
the content of tacit information of each task.
However, the concept is suciently general
to accomodate more features to the costs of unbundling. These may also include the more
dicult transmission of knowledge from production to the research sector when production
3
is performed abroad, such as in Naghavi & Ottaviano (2009).
represented by
βτ (i),
with
τ (i) ≥ 1, τ 0 (i) ≥ 0
and
β≥1
Oshoring costs are thus
as technological oshoring costs.
By assumption, wages in the South are lower than in the North
Northern rms to resort to oshore production of all tasks
w/w∗ > 1.
i ≤ I , where I
This allows
is the marginal task
implicitly dened by
βτ (I) =
w
.
w∗
(1)
Oshoring costs for the marginal task equal the wage of Northern workers relative to Southern
workers. As shown by Grossman & Rossi-Hansberg (2008), this implies per-unit production
costs of
wΘ(I),
where the oshoring saving factor is dened as
RI
Θ(I) ≡ 1 − I +
0
τ (i)di
τ (I)
(2)
The market is characterized by monopolistic competition with an elasticity of substitution
between varieties. This yealds markup pricing
p = wΘ(I)/α,
where
α = (σ − 1)/σ .
σ
Prots
for each Northern rm are thus given by
π = (p − wΘ(I))x =
1−α
wΘ(I)x.
α
Southern rms prefer domestic production, due to the wage dierence.
production costs are thus simply given by
above, necessarily
w∗ ≤ wΘ(I).
w∗ .
(3)
Their per-unit
With positive oshoring costs as described
With innovative research in the South being prohibitively
costly, Southern rms choose costly imitation to copy existing varieties from the North. In
their price setting they might be constrained from Northern competition.
If the dierence
in production costs is small Southern rms set prices just below Northern rms' production
costs and still gain positive prots. If the dierence in production costs is high they set the
optimal price according to the monopolistic competition demand structure. Thus, they earn
prots
π ∗ = (p∗ − w∗ )x∗
(4)
Given the preference structure, relative demand for varieties from the two countries only
4
depends on relative prices such that
x
p −σ
= ∗
∗
x
p
(5)
and the relative prots of the two types of rms are given by
π
=
π∗
2.2
1−α
σ−1
p
−
p∗
.
(6)
α
τ (I)
Research Sector
Research conducted during one time period yields a certain success. Successful research in the
North means a blueprint for a new variety and can be conducted at a cost
N
is the stock of all blueprints ever developed. The appearance of
N
C = wa/N ,
where
in this cost equation
is a spillover from present knowledge in line with Grossman & Helpman (1991). Successful
research in the South means the disclosure of a Northern production blueprint and can be
conducted at cost
C ∗ = w∗ a∗ /γnI ,
where
γ
is a parameter that characterizes protection of
intellectual property rights (IPR) in the North and
n
is the stock of Northern production
blueprints not already disclosed to Southern rms. Intuitively, imitation is less costly if IPR
protection is weak and if there exist lots of unrevealed varieties, since it reduces the time a
researcher has to look for a varietey he is able to imitate. Moreover, imitation is less costly
if the share of oshore provided tasks is high, since it increases the knowledge in the South
about Northern varieties. The growth rate of all Northern varieties
the growth rate of unrevealed Northern varieties
g ≡ Ṅ /N ,
which is also
g ≡ ṅ/n and the imitation rate is m ≡ ṅ∗ /n.
Entry into research is free in both countries.
This means that the level of research is
determined by a no arbitrage condition
π = rv + mv
(7)
for the North which implies that prots from successful innovation exactly compensate for
interest payments forgone and the risk of being imitated. The imitation risk drops out for the
Southern no arbitrage condition.
5
The nominal interest rate is given by the sum of the discount factor and the relative
increase in rm value, which is given by the negative of the growth rate of number of rms
r = ρ − v̇/v .
Using the fact that the value of a rm must equal the cost of research in
equilibrium we obtain
wa
π
=
N
g+ρ+m
w ∗ a∗
π∗
=
γnI
g+ρ
and
(8)
where we can solve for the relative prots of Northern and Southern rms as
m + ρ + g aγβτ (I) g
π
=
π∗
ρ+g
a∗
m+g
(9)
Combining with equation (6) from above we can implicitly solve for the resulting oshoring
volume as
βτ (I) =
2.3
p
p∗
1−σ α + (1 − α)
ρ + g a∗ m + g
m + ρ + g aγ g
.
(10)
Labor Markets
We assume that workers are free to move between the research sector and the production
sector. Moreover, Southern workers can work for domestic companys or can perform oshore
production for Northern rms. This means that wages for homogenous workers are equal in
all professions.
Northern workers only perform a fraction
1−I
of tasks domestically. The full employment
condition, thus, satises
aṅ
+ (1 − I)nx
N
(11)
1−I
g
α
ag 2
+
a(g + ρ + m)
.
g+m
Θ(I) (g + m)
(1 − α)
(12)
L=
and inserting from above we obtain
L=
6
Analogously, full employment in the South is given by
aṅ∗
+
γnI
L∗ =
I
Z
τ (i)dinx + n∗ x∗
(13)
0
which can be written as
∗
L =
1
a∗ m max Θ(I)τ (I); 1−α
+ a∗ ρm/g
Z
I
+
γI
τ (i)di
0
a(g + ρ + m) α
g
(g + m)
Θ(I)
(1 − α)
(14)
where the maximum function in the rst term on the right hand side is due to the fact that
Southern producers are constrained to limit pricing, if Northern production costs are lower
than their monopoly price, which increases the demand for their product.
2.4
Consumer Optimization
The intertemporal utility function of a representative consumer is given by
∞
Z
e−ρt U (t)dt
W =
(15)
0
where the utility in each period
U (t)
has the form
α1
N
Z
α
U (t) =
(t)x(j) dj
(16)
1
and
W
is maximized subject to an intertemporal budget constraint
Z
∞
−rt
e
Z
E(t) ≤
0
where
E(t)
∞
e−rt w(t) + A
(17)
0
is consumer expenditure and
A
are assets owned in period
This structure yields a demand function for variety
j
Ep(j)−σ
x(j) = R N (t)
p(j)1−σ dj
1
7
0.
of
(18)
and the optimal time path of expenditure is given by
Ė
=r−ρ=g
E
(19)
which yields as solution for the intertemporal utility
W =
3
U
ρ−g
(20)
Optimal IPR Protection
Above we showed how to solve the model for four remaining equations with four unknown
variables.
The three equations are (10), (12), and (14), together with an unequality that
governs Southern rms price setting, while the three unknowns are the growth rate
imitation rate
m,
the oshoring volume
I,
and the relative price
p/p∗ .
g,
the
Unfortunately, further
analytical simplication of this system is not possible. Thus we resort to methods of numerical
simulations in order to perform comparative statics.
Intuitively, the technological labor requirement in the absence of knowledge spillovers is
larger for innovation than for imitation. We further assume the South to be larger than the
North to obtain an oshoring volume in the interesting range given the other parameter values that we choose. However, these parameterizations only aects our results quantitatively,
not qualitatively. To restrict the oshoring volume to values between 0 and 1, we choose a
convex oshoring cost schedule
τ (i)
with very high oshoring costs for higher indexed tasks.
We further restrict the growth rate and imitation rate to be positive in equilibrium. With
these assumptions a unique equilibrium can be identied.
The core of our analysis is that technological oshoring costs cannot be inuenced by
politicians. Nor are they a parameter of interest in rms' optimization problem. Hence, it
is an exogeneously given cost parameter. Nevertheless it is interesting to analyze reactions
to changes in this parameter, since empirical evidence shows a tremendous decline in international communication and interaction cost, due to new technological inventions, which was
8
an important aspect in increasing the volumes of oshoring in the recent decades.
The shift parameter for Northern economic policy is the level of IPR protection.
protection parameter is normalized to values between
0
and
1.
This
A high value close to
1
indicates large spillover ows from North to South and, therefore, low levels of IPR protection.
Accordingly, a low value indicates low spillover ows and high protection.
In contrast to
standard trade policy, this policy instrument can not be reciprocated by Southern politicians,
since there are no spillovers from the South to the North. Hence, Northern politicians can set
this parameter unilaterally and do not have to consider reciprocative action.
Figure 1. Growth Rate
Independent Variables: L = 100, L∗ = 300, a = 300, a∗ = 120, σ = 2, ρ = 0.2
In a rst step we analyze the outcome for the overall growth rate
Remember that
g
g
of the economy.
is dened as the growth rate in the number of new varieties in each period.
We show these results in gure 1.
The white line in this gure indicates the level of IPR
protection which maximizes the growth rate. It becomes clear that for an archaic oshoring
9
technology with high technological oshoring costs, growth is maximized by high levels of
IPR protection. However, as the oshoring technology improves, IPR protection should be
reduced and nally completely abolished. Interestingly, there is a kink on this transition path
from protection to a liberal IPR policy.
A side aspect of the dilusion of IPR protection is
a convergence of wages and prices. It seems worthwile for Northern politicians to accelerate
this dilusion to make Southern producers hit the price constraint determined by the wage
dierence. A further improvement in oshoring costs allows for a tightening of IPR protection
while keeping producers in the South just marginally price constrained. Only if
β
is reduced
even more, a more liberal IPR strategy can increase the growth rate.
Figure 2. Imitation Rate
Independent Variables: L = 100, L∗ = 300, a = 300, a∗ = 120, σ = 2, ρ = 0.2
Moreover, we have a look at the resulting imitation rate. Intuitively, low levels of IPR
protection decrease the cost of imitation for Southern researchers and, thus, yield higher
imitation rates. However, this outcome is less striking for high levels of technological oshoring
costs. As above, the white line indicates the growth-rate-maximizing levels of IPR protection.
10
Note that an increase of the imitation rate relative to the innovation rate in the North yields
an increase in the share of Southern varieties in the whole set of consumed varieties.
Figure 3. Oshoring Volume
Independent Variables: L = 100, L∗ = 300, a = 300, a∗ = 120, σ = 2, ρ = 0.2
Considering the oshoring volume it becomes clear that oshoring and imitation stand
in a substitutive relationship to each other due to the full employment condition. High IPR
protection makes the production sector more attractive.
Moreover, low levels of imitation
imply a low share of Southern varieties. Therefore, even for a given workforce in the production
sector the oshoring volume rises. Necessarily, this shift is even larger considering the above
mentioned increase in the number of production workers.
Considering the growth-rate-maximizing IPR protection rate, again indicated by the white
line, we see that the oshoring volume seems to be a crucial factor in its determination. When
oshoring is technologically dicult, IPR protection is high to disrupt earnings prospectives
from imitation in the South. More Southern workers are thus willing to work in the production
11
sector for a given wage, which allows for a higher oshoring level. On the other hand, when
oshoring is costly, low IPR protection increases incentives for imitative research in the South.
Thereby the cost of oshoring is raised and the oshoring volume is kept on a low level
compared to the technological possibilities.
Summarizing, intermediate levels of oshoring
seem to be an optimal choice for the maximization of the economy-wide growth rate. This is
due to two opposing forces. On the one hand, a high share of oshored production increases
the leverage of a given research eort and thus leads to more innovative work. On the other
hand, a high share of oshored production increases the risk of imitation, which destroys
prots from Northern innovation and thus reduces incentives for innovation. Balancing these
two forces, the growth rate is maximized at intermediate levels of oshoring.
Somehow surprising, the growth-maximizing IPR protection with high oshoring costs
yields a higher oshoring volume than the optimal IPR protection with low oshoring costs.
However, this result must be seen in the light of a generally lower growth rate when oshoring
costs are high.
Driving down the imitation rate by the same proportion must lead to an
increased movement of Southern workers into oshore production. To make this possible in
light of increasing oshoring costs, incentives for imitation must be reduced overproportionally
which leads to further increases in the oshoring volume.
However, the maximization of the growth rate is not necessarily the policy makers' objective function, since wages and prices are also aected by their decision. Taking a purely
static perspective it is easy to see that the relative wage in the two countries must stand in a
strictly monotone positive relationship with the oshoring level. Given the rising oshoring
costs schedule
τ 0 (i) > 0,
higher levels of oshoring can only be supported by higher wage
dierences. On the other hand, due to the oshoring costs saving factor
Θ0 (I) < 0,
higher
levels of oshoring lead to higher savings on production costs and thus translate into lower
prices for Northern varieties. Given increased demand for Southern labor, prices in the South,
however, are likely to rise. Incentives for oshoring may further change these results.
We show the outcome for the intertemporal welfare in gure 4. Again indicated by a solid
white line is the IPR protection level that maximizes the growth rate.
Furthermore, by a
dashed line we indicate the IPR protection level that maximizes this intertemporal welfare
12
Figure 4. Intertemporal Welfare
Independent Variables: L = 100, L∗ = 300, a = 300, a∗ = 120, σ = 2, ρ = 0.2
function.
The arising pattern indicates that policy makers only focusing on the long-run
growth rate choose an excessively tight IPR protection. Considering the short-run outcome
on real wages reduces the optimal IPR protection, such that more spillovers irradiate on
imitative researchers in the South. In turn they produce cheap imitated products increasing
real wages in the North at the cost of a slight reduction in incentives for innovation in the
North and, hence, a reduction in the resulting growth rate.
4
More Comparative Statics
We perform comparative statics to analyze the eect of other exogeneous shocks to the optimal
growth rate. The shocks that we consider for this analysis are to research productivity in the
North and South and to labor endowment in North and South.
13
We nd that a positive shock that increases research productivity in the North, makes
policy makers choose a lower IPR protection. Nevertheless, even for constant IPR protection,
the eect on the growth rate is substantial.
A one-percent shock to research productivity
increases the growth rate by roughly two percent.
Whereas the absolute increase in the
growth rate depends a lot on the level of technological oshoring costs, the relative increase
in the growth rate is more or less constant over the complete range analyzed, with high
absolute changes being matched by high ex ante growth rates. On the other hand, a positive
shock to Southern imitation productivity makes policy makers choose a tigher IPR protection.
However, the eect of this shock on the resulting growth rate is negligible.
A shock to the labor endowment in the North reduces the growth-maximizing level of IPR
protection. However, contrary to above, the eect on the growth rate is quite heterogeneous
over the range of technological oshoring costs. When oshoring costs are very low, an increase
in the labor force of one percent increases the growth rate by roughly one percent. However,
when oshoring costs are very high, the eect is almost doubled, increasing the growth rate
by slightly less than two percent. Increasing the size of the Southern labor force also yields
a reduction in the growth-maximizing IPR production rate.
In addition, the eect on the
growth rate is positive again. However, now the heterogeneity is in the opposite way. When
oshoring costs are very low, a one percent increase of the Southern labor force leads to rise
in the growth rate by 0.3 percent. If oshoring costs are very high, this eect is reduced to
0.1 percent.
5
Conclusion
This paper develops a model that combines endogeneous choices of innovation, imitation, and
oshoring. There are several mechanisms that link these three variables within the model.
Incentives for innovation in the North lead to more oshoring over the full employment conditions. There are backward linkages to oshoring to innovation, over the increased leverage
of the research activity.
Furthermore, on the one hand oshoring facilitates the leakage of
knowledge to the South and thereby the imitation rate of Northern inventions but, on the
14
other hand, imitative research is reduced since the full employment conditions also hold in
the South.
With this model we obtain interesting and plausible results. We take the view of a Northern politician who uses the rate of intellectual property rights (IPR) protection as policy
instrument. To maximize the long-run growth rate of the economy intermediate levels of oshoring are prefered, trading o benets from increased leverage of innovation with the costs
of an increased imitation risk. This implies that the optimal IPR protection is sensitive to the
technological oshoring costs. With high oshoring costs that induce too little oshoring, IPR
protection is tight to reduce prots from imitation and induce Southern workers to move into
the oshoring production sector. With low oshoring costs, however, oshoring levels are too
high and the Northern policy maker wants to reduce them choosing less IPR protection and
making the oshore production sector relatively less attractive for Southern labor compared
to imitative activity. Considering not the long-run growth rate but an intertemporal welfare
function yields slightly less IPR protection, but an identical pattern.
Comparing our results to similar models we nd some dierences. In a model with exogenous imitation risk, Glass (2001) nds that an increase in the intensity of imitation reduces
the rate of innovation and the extent of outsourcing. In our model we nd that increased
imitation due to less IPR protection reduces the extent of oshoring, while the eect on the
innovation rate can be positive or negative. If increased imitation, however, is due to a lower
oshoring cost parameter, the extent of oshoring is increased, while the eect on innovation,
again, is ambiguous.
Photchanaprasert (2011) nds that innovation rate and imitation rate are both maximized
at the lowest possible level of IPR protection. In contrast, while in our model the imitation
rate is maximized when IPR protection is very low, the innovation rate can be maximized at
almost every possible IPR protection rate, depending on the level of technological oshoring
costs, as explained above.
15
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