O�shoring, Innovation, and Imitation

Sebastian Benz∗

October 2011

Preliminary Version

Please do not cite

Abstract

JEL Classi�cation: F12, F21, F23, F43, O31

Keywords: O�shoring, Innovation, Imitation, Information Leakage

∗Ifo Institute for Economic Research, Poschingerstr. 5, 81679 München, Germany, Phone:+49 (0) 89 9224-1695, Benz@ifo.de

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,

o�shoring may a�ect these fundamental dynamic relationships in two di�erent ways. First, it

may become an integral part the investment activity (R&D or education) itself, say through

o�shore 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 e�cient if conducted far away from the production sites. Moreover,

if production is o�shored 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 o�shoring 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 o�shoring into a growth model where �rms engage in

quality-improving innovation. O�shoring plays no role in innovation as such, but successful

innovations may be adapted towards o�shore provision of an early stage of production. Viewed

from a static perspective, such o�shoring 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, o�shoring 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, o�shoring has the additional

e�ect 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 e�ects that have been identi�ed in the static model

appear as the short-run outcome. In the long-run, the rich country now additionally bene�ts

from enhanced productivity due to more R&D which is sparked o� by o�shoring.

An opposite relationship between o�shoring and innovation is emphasized by Naghavi &

Ottaviano (2009). This comes about through a �watering down� of the learning e�ect required

to make an innovation bear out its full economic potential. Importantly, however, learning is

assumed more di�cult if parts of the production activity are undertaken o�shore, mainly due

to more di�cult communication of experience. Then, if o�shoring 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 o�shoring decision fails to

fully internalize the learning e�ect since learning often arises as an externality.

Glass (2004) introduces an imitation channel in the (Southern) host country of o�shoring

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 o�shored 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 re�nes 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.

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We walk a similar path, however, considering o�shoring as across-industry phenomenon

where the level of o�shoring is determined by the o�shoring cost of a marginal task I. All tasks

featuring a lower cost of international coordination than I are sourced from abroad, hence

yielding endogeneous savings on production costs that depend on the o�shoring 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-speci�c heterogeneity in

the o�shoring costs yields novel results for the e�ect of IPR protection. More precisely, the

maximization of either the growth rate or the intertemporal welfare function via IPR protec-

tion depends on the o�shoring technology, with high o�shoring costs mandating high levels of

IPR protection, while IPR protection should be reduced as o�shoring 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 di�erent 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 im-

itative 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 o�shoring literature, we order tasks from 0 to 1 according to their o�shoring

costs. This cost schedule is generally assumed to represent the di�culty of coordination or

the content of tacit information of each task. However, the concept is su�ciently general

to accomodate more features to the costs of unbundling. These may also include the more

di�cult transmission of knowledge from production to the research sector when production

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is performed abroad, such as in Naghavi & Ottaviano (2009). O�shoring costs are thus

represented by βτ(i), with τ(i) ≥ 1, τ ′(i) ≥ 0 and β ≥ 1 as technological o�shoring costs.

By assumption, wages in the South are lower than in the North w/w∗ > 1. This allows

Northern �rms to resort to o�shore production of all tasks i ≤ I, where I is the marginal task

implicitly de�ned by

βτ(I) =w

w∗. (1)

O�shoring 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 o�shoring saving factor is de�ned as

Θ(I) ≡ 1− I +

∫ I0 τ(i)diτ(I)

(2)

The market is characterized by monopolistic competition with an elasticity of substitution σ

between varieties. This yealds markup pricing p = wΘ(I)/α, where α = (σ − 1)/σ. Pro�ts

for each Northern �rm are thus given by

π = (p− wΘ(I))x =1− α

αwΘ(I)x. (3)

Southern �rms prefer domestic production, due to the wage di�erence. Their per-unit

production costs are thus simply given by w∗. With positive o�shoring costs as described

above, necessarily w∗ ≤ wΘ(I). 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 di�erence

in production costs is small Southern �rms set prices just below Northern �rms' production

costs and still gain positive pro�ts. If the di�erence in production costs is high they set the

optimal price according to the monopolistic competition demand structure. Thus, they earn

pro�ts

π∗ = (p∗ − w∗)x∗ (4)

Given the preference structure, relative demand for varieties from the two countries only

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depends on relative prices such that

x

x∗=

p

p∗−σ

(5)

and the relative pro�ts of the two types of �rms are given by

π

π∗=

1− α(pp∗

)σ−1− α

τ(I)

. (6)

2.2 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 C = wa/N , where

N is the stock of all blueprints ever developed. The appearance of N 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 o�shore provided tasks is high, since it increases the knowledge in the South

about Northern varieties. The growth rate of all Northern varieties g ≡ N/N , which is also

the growth rate of unrevealed Northern varieties g ≡ n/n and the imitation rate is m ≡ n∗/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 pro�ts 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 − v/v. Using the fact that the value of a �rm must equal the cost of research in

equilibrium we obtain

wa

N=

π

g + ρ+mand

w∗a∗

γnI=

π∗

g + ρ(8)

where we can solve for the relative pro�ts of Northern and Southern �rms as

π

π∗=m+ ρ+ g

ρ+ g

aγβτ(I)a∗

g

m+ g(9)

Combining with equation (6) from above we can implicitly solve for the resulting o�shoring

volume as

βτ(I) =(p

p∗

)1−σ (α+ (1− α)

(ρ+ g

m+ ρ+ g

a∗

aγ

m+ g

g

)). (10)

2.3 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 o�shore

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, satis�es

L =an

N+ (1− I)nx (11)

and inserting from above we obtain

L =ag2

g +m+

1− I

Θ(I)g

(g +m)a(g + ρ+m)

α

(1− α). (12)

6

Analogously, full employment in the South is given by

L∗ =an∗

γnI+∫ I

0τ(i)dinx+ n∗x∗ (13)

which can be written as

L∗ =a∗mmax

(Θ(I)τ(I); 1

1−α

)+ a∗ρm/g

γI+∫ I

0τ(i)di

g

(g +m)a(g + ρ+m)

Θ(I)α

(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

W =∫ ∞

0e−ρtU(t)dt (15)

where the utility in each period U(t) has the form

U(t) =(∫ N

1(t)x(j)αdj

) 1α

(16)

and W is maximized subject to an intertemporal budget constraint

∫ ∞0

e−rtE(t) ≤∫ ∞

0e−rtw(t) +A (17)

where E(t) is consumer expenditure and A are assets owned in period 0.

This structure yields a demand function for variety j of

x(j) =Ep(j)−σ∫ N(t)

1 p(j)1−σdj(18)

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and the optimal time path of expenditure is given by

E

E= r − ρ = g (19)

which yields as solution for the intertemporal utility

W =U

ρ− g(20)

3 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 g, the

imitation rate m, the o�shoring volume I, and the relative price p/p∗. Unfortunately, further

analytical simpli�cation 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 o�shoring volume in the �interesting� range given the other parameter val-

ues that we choose. However, these parameterizations only a�ects our results quantitatively,

not qualitatively. To restrict the o�shoring volume to values between 0 and 1, we choose a

convex o�shoring cost schedule τ(i) with very high o�shoring 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 identi�ed.

The core of our analysis is that technological o�shoring costs cannot be in�uenced 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 inter-

national communication and interaction cost, due to new technological inventions, which was

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an important aspect in increasing the volumes of o�shoring in the recent decades.

The shift parameter for Northern economic policy is the level of IPR protection. This

protection parameter is normalized to values between 0 and 1. 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 g of the economy.

Remember that g is de�ned 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 o�shoring

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technology with high technological o�shoring costs, growth is maximized by high levels of

IPR protection. However, as the o�shoring 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

di�erence. A further improvement in o�shoring 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 o�shoring

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. O�shoring Volume

Independent Variables: L = 100, L∗ = 300, a = 300, a∗ = 120, σ = 2, ρ = 0.2

Considering the o�shoring volume it becomes clear that o�shoring 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 o�shoring 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 o�shoring volume seems to be a crucial factor in its determination. When

o�shoring is technologically di�cult, IPR protection is high to disrupt earnings prospectives

from imitation in the South. More Southern workers are thus willing to work in the production

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sector for a given wage, which allows for a higher o�shoring level. On the other hand, when

o�shoring is costly, low IPR protection increases incentives for imitative research in the South.

Thereby the cost of o�shoring is raised and the o�shoring volume is kept on a low level

compared to the technological possibilities. Summarizing, intermediate levels of o�shoring

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 o�shored production increases

the leverage of a given research e�ort and thus leads to more innovative work. On the other

hand, a high share of o�shored production increases the risk of imitation, which destroys

pro�ts from Northern innovation and thus reduces incentives for innovation. Balancing these

two forces, the growth rate is maximized at intermediate levels of o�shoring.

Somehow surprising, the growth-maximizing IPR protection with high o�shoring costs

yields a higher o�shoring volume than the optimal IPR protection with low o�shoring costs.

However, this result must be seen in the light of a generally lower growth rate when o�shoring

costs are high. Driving down the imitation rate by the same proportion must lead to an

increased movement of Southern workers into o�shore production. To make this possible in

light of increasing o�shoring costs, incentives for imitation must be reduced overproportionally

which leads to further increases in the o�shoring volume.

However, the maximization of the growth rate is not necessarily the policy makers' ob-

jective function, since wages and prices are also a�ected 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 o�shoring level. Given the rising o�shoring

costs schedule τ ′(i) > 0, higher levels of o�shoring can only be supported by higher wage

di�erences. On the other hand, due to the o�shoring costs saving factor Θ′(I) < 0, higher

levels of o�shoring 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 o�shoring 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

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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 e�ect 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.

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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 e�ect 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 o�shoring 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 e�ect 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 e�ect on the growth rate is quite heterogeneous

over the range of technological o�shoring costs. When o�shoring costs are very low, an increase

in the labor force of one percent increases the growth rate by roughly one percent. However,

when o�shoring costs are very high, the e�ect 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 e�ect on the

growth rate is positive again. However, now the heterogeneity is in the opposite way. When

o�shoring 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 o�shoring costs are very high, this e�ect is reduced to

0.1 percent.

5 Conclusion

This paper develops a model that combines endogeneous choices of innovation, imitation, and

o�shoring. There are several mechanisms that link these three variables within the model.

Incentives for innovation in the North lead to more o�shoring over the full employment con-

ditions. There are backward linkages to o�shoring to innovation, over the increased leverage

of the research activity. Furthermore, on the one hand o�shoring 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 North-

ern 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 o�-

shoring are prefered, trading o� bene�ts 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 o�shoring costs. With high o�shoring costs that induce too little o�shoring, IPR

protection is tight to reduce pro�ts from imitation and induce Southern workers to move into

the o�shoring production sector. With low o�shoring costs, however, o�shoring levels are too

high and the Northern policy maker wants to reduce them choosing less IPR protection and

making the o�shore 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 di�erences. In a model with exoge-

nous 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 o�shoring, while the e�ect on the

innovation rate can be positive or negative. If increased imitation, however, is due to a lower

o�shoring cost parameter, the extent of o�shoring is increased, while the e�ect 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 o�shoring

costs, as explained above.

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