Discussion Paper No. 1055

INNOVATION OFFSHORING
WITH FULLY ENDOGENOUS GROWTH

Colin Davis
Ken-ichi Hashimoto

May 2019

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Innovation Offshoring with Fully Endogenous GrowthColin Davis
Doshisha University∗

Ken-ichi Hashimoto
Kobe University†

May 2019

Abstract
In recent years firms have started to offshore their innovation activities to emerging economies. This paper investigates the implications of innovation offshoring for
productivity growth in a two-country framework that features a tension between accessto technical knowledge and low-cost high-skilled labor in the innovation location decision. Industry and innovation tend to concentrate in the asset-wealthy country when
trade costs are relatively high. A positive relationship between innovation costs andindustry concentration then ensures that improved international knowledge diffusion
coincides with an increase in net offshoring flows in innovation from the asset-wealthy
country to the asset-poor country, and potentially with faster productivity growth.
JEL Classifications: F12, F43, R11
Keywords: innovation offshoring, international knowledge diffusion, endogenous productivity growth, process innovation, industry location, international trade∗

The Institute for the Liberal Arts, Doshisha University, Karasuma-Higashi-iru, Imadegawa-dori, Kamigyo, Kyoto, Japan, 602-8580, cdavis@mail.doshisha.ac.jp.
†
Graduate School of Economics, Kobe University, 2-1 Rokkodai, Nada, Kobe, Japan, 657-8501,
hashimoto@econ.kobe-u.ac.jp.
Acknowledgements: We are grateful for helpful comments from Lisa Anouliès, José de Sousa, Dimitris
Doulos, Hirokazu Ishise, Tadashi Morita, Yoshiyasu Ono, and Takayuki Tsuruga, and from participants of
the ISER Seminar at Osaka University, the Rokkodai Macroeconomics Seminar at Kobe University, the International Economics Seminar at Kyoto University, the RITM Lunch Seminar at Université Paris-Sud, ETSG
2016, the JSIE Kansai Seminar, and the International Atlantic Economic Conference London 2018. This work
was completed in part while Davis was visiting RITM at the Université Paris-Sud. He is thankful for theirgenerous hospitality and support. We acknowledge financial support from JSPS through Grants-in-Aid for
Scientific Research (A), (C) and (S): grant numbers 15H05728, 16H02016, 16K03624, and 19K01638.

1

Introduction

Although research and development (R&D) has traditionally been concentrated in advanced
countries, in recent years firms have begun to offshore their innovation activities towards
emerging economies. For example, despite the steady position of the U.S. as the largest
producer of R&D services in terms of gross domestic expenditure (NSF 2016), over the past
decade it has experienced growing trade deficits in R&D services with a number of emerging
economies. In particular, U.S. trade deficits with China and India grew at average annual
rates of 22% and 17% over the period from 2006 through 2015 to become US$2.4 billion
and US$3.4 billion in 2016 (BEA 2018). More generally, the main hosts for R&D offshoringoutside the U.S. and the European Union are now Brazil, China, India, Russia, Singapore,
and Taiwan (Hausmann et al. 2007; Puga and Trefler 2010; Santos-Paulino et al. 2014).
The rise in the offshoring of R&D services has attracted the attention of policymakers whoare concerned about the implications for economic growth and who hope to attract firms
offering the high wages associated with R&D employment (UNCTAD 2005).
Beginning to address these concerns, there is an emerging empirical literature investigating the links between R&D offshoring, innovation performance, and economic growth.
At the firm level, Nieto and Rodrı́guez (2011) and Bertrand and Mol (2013) find that offshoring R&D leads to a higher propensity for the introduction of new products. Similarly,
Rodrı́guez and Nieto (2016) document a positive relationship between innovation offshoringand sales growth. At the aggregate level, D’Agostino et al. (2013) show that OECD regionswith firms that offshore innovation to emerging economies have more patent applications,and Castellani and Pieri (2013) report that European regions with a greater number of outward oriented R&D investment projects exhibit higher rates of labor productivity growth.
While the empirical literature suggests a positive relationship between R&D offshoring andinnovation-based economic growth, to the best of our knowledge this relationship has notbeen formally modeled within an endogenous growth framework.
This paper develops an endogenous market structure and endogenous growth framework2(Peretto 1996; Aghion and Howitt 1998; Peretto and Connolly 2007; Etro 2009) to study
the relationship between offshoring patterns in innovation and manufacturing and long-run
productivity growth. In particular, we extend the two-country trade model of Davis andHashimoto (2015) to include an occupational choice for skill-differentiated workers between
low-skilled employment in production and high-skilled employment in R&D. Firms create
new differentiated products for supply to a monopolistically competitive market, while investing in process innovation to reduce future production costs. Geographic patterns of industry and R&D activity are determined endogenously, as the free movement of investment
allows firms to shift product development, production, and process innovation separately
between countries with the aim of minimizing costs (Martin and Ottaviano 1999, 2001).
The model captures two key factors that have been emphasized in the business literaturewhen considering the attractiveness of a location for R&D: access to technical knowledge
and the supply of low-cost high-skilled labor (see, for example, Chung and Yeaple 2008;
Manning et al. 2008; Lewin et al. 2009; Demirbag and Glaister 2010). On the one hand,knowledge spillovers from production to innovation are local in nature, leading to higher
labor productivity in R&D in the country hosting the greater share of industry. On theother hand, the concentration of industry generates greater demand for high-skilled labor ininnovation, pushing up high-skilled wages. These factors generate a tension in the firm-level
location decision for R&D activity.
At the aggregate level, market size is determined endogenously through a circular causality between production and innovation location patterns that is generated by two mechanisms. The first is a knowledge spillover effect whereby increases in a country’s investment
income and labor income expand the national market, attracting manufacturing and strengthening knowledge spillovers. Increased R&D activity in turn raises labor income, expands
market size, and further attracts manufacturing. The second mechanism is a wage effectwhich regulates how fast high-skilled wages can rise as the market expands without inducing firms to relocate innovation internationally in search of lower cost high-skilled labor. We

3

show that the wage effect dominates and thus economic activity concentrates in the assetwealthy country for high trade costs, while the knowledge spillover effect dominates andeconomic activity therefore concentrates in the asset-poor country for low trade costs.
We then study the direction of net offshoring flows in production and innovation at themacro-level using the difference between the value of world output owned by a country andthe value of output located in the country. There are three cases. First, for high trade costs,
the market of the asset-wealthy country is not large enough to support the production andinnovation of all domestically-owned firms, and net offshoring flows towards the asset-poor
country. Second, for intermediate trade costs, the larger market of the asset-wealthy country
attracts the production and innovation activities of all domestically-owned firms, and theasset-wealthy country therefore receives net offshoring inflows from the asset-poor country.
Third, for low trade costs, net offshoring flows from the asset-wealthy country towards thelarger labor-income-based market of the asset-poor country.
Long-run growth is driven by firm-level investment in process innovation, which is inturn closely linked with industry location patterns both directly through changes in innovation costs and indirectly through the inverse relationship between firm scale and the numberof firms in the market. In particular, increased industry concentration leads to higher innovation costs, as rising high-skilled wages more than offset the benefit of improved knowledge spillovers, with two effects on market entry. The first is a product development effectwhereby the level of market entry falls as the cost of creating new product designs rises.
The second is a process innovation effect with rising innovation costs reducing firm-level
employment in process innovation, raising firm-level profits, and inducing a greater level ofmarket entry. Combining these effects, we find that there is a negative relationship between
industry concentration and productivity growth when the process innovation effect dominates, and a convex relationship when the product development effect dominates. Although
there is no general consensus in the empirical literature on the relationship between industry concentration and economic growth, the negative relationship that arises for most cases

4within our framework is consistent with several of the empirical results of Bosker (2007)
and Gardiner et al. (2011).
Focusing on the case for which the asset-wealthy country has the larger market, we study
the effects of greater economic integration. First, a decrease in trade costs increases the concentration of industry and R&D in the asset-wealthy country, causing net offshoring flows
out of the asset-wealthy country to fall. Consequently, the unit cost of process innovation
rises, potentially dampening productivity growth. Second, an improvement in knowledge
diffusion increases net offshoring flows out of the asset-wealthy country as firms shift innovation to the asset-poor country to take advantage of lower high-skilled wages. As a result,the increased dispersion of production and innovation away from the asset-wealthy country leads to lower innovation costs and potentially a higher rate of productivity growth. In
this manner, our framework yields a positive relationship between net innovation offshoringflows and productivity growth, which in consistent with the results of the empirical literature
introduced above (Castellani and Pieri 2013; D’Agostino et al. 2013).
There is a well-developed international trade literature studying the determinants andeffects of multinational production patterns within quantitative general equilibrium frameworks (Burstein and Monge-Naranjo 2009; Ramondo 2009; Ramondo and Rodriguez-Claire
2013; Grumpert et al. 2017; Tintelnot 2017). Importantly, Ekholm and Hakkala (2007)
introduce a two-country model which allows for the geographic separation of R&D andhigh-tech production, with imperfect technology spillovers and trade costs generating agglomeration forces in each activity. A home market effect in the high-tech industry andcompeting demands for skilled labor across sectors generate higher skilled wages in thelarge country, potentially inducing firms to offshore innovation to the small country with
its cheaper skilled labor. More recently, Arkolakis et al. (2018) construct a multi-country
model with heterogenous production technologies and skilled differentiated workers, andshow that home market effects interact with comparative advantage to produce a patternof specialization with some countries specializing in innovation while others specialize in5

production. While these frameworks allow for a study of the welfare gains associated withmultinational production patterns, they do not consider the implications for long-run growth.
Our analysis builds on antecedents in the endogenous growth literature that extend thevariety-expansion model of Grossman and Helpman (1991) to consider the effects of manufacturing offshoring on innovation-based growth (Martin and Ottaviano 1999, 2001; Gao
2005, 2007; Naghavi and Ottaviano 2009a, 2009b).1 In this literature, it is common for
innovation to agglomerate fully in the advanced country either by assumption or because of
localized knowledge spillovers. As a consequence, these models are not viable for the studyof how R&D offshoring from developed countries to emerging economies affects economic
growth. Davis (2013) investigates the trade-off between localized knowledge spillovers andhigh-skilled wage costs in the R&D location choice for firms by including an occupational
choice for skill-differentiated workers, but the link between industry location and economic
growth is cut, leaving no relationship between offshoring patterns and economic growth.
The key contribution of our paper is the introduction of a framework that allows for a theoretical study of the positive link between R&D offshoring and innovation-based economic
growth that has been documented in the empirical literature.
The paper proceeds as follows. Section 2 introduces the model. Section 3 characterizes
industry and innovation location patterns and derives the direction of offshoring flows. We
then outline the effects of economic integration on market entry and productivity growth,and study the link between net offshoring flows and long-run growth. Section 4 concludes.

2

The Model

We propose a model of international trade with two countries indexed by i and j. The
countries potentially employ labor in four activities: traditional production, manufacturing,process innovation, and product development. Firms are free to separate their production
1

McGrattan and Prescott (2009) extend the neoclassical growth model to include investment in technology
capital and show that openness to foreign direct investment promotes improvements in productivity.

6and innovation activities geographically. Labor is the sole factor of production with symmetric endowments across countries. There is no international migration, but labor is mobile
between sectors with national supplies of low-skilled and high-skilled labor determined endogenously through an occupational choice made by skill-differentiated workers.

2.1 Household Preferences
Dynastic households in each country select optimal expenditure-saving paths to maximize
utility over an infinite time horizon. The lifetime utility of the representative household incountry i is

Ui (t) =Z ∞e−ρ(τ −t) (α ln CXi (τ ) + (1 − α) ln CY i (τ )) dτ,(1)t

where the consumptions of a composite of manufacturing goods and a traditional good attime t are CXi (t) and CY i (t), the subjective discount rate is ρ, and α ∈ (0, 1). The manufacturing composite isCXi (t) =Z Ni (t)xii (ω, t)

σ−1
σ

dω +

Z Nj (t)xij (ω, t)

0

0

σ−1
σ

dω

σ
! σ−1

,

(2)

where xii (t) and xij (t) are the country i household demands for each of the Ni (t) andNj (t) manufacturing varieties produced in countries i and j, and σ > 1 is the elasticity of
substitution. Lifetime utility is maximized subject to a national flow budget constraint:Ḃi (t) = r(t)Bi (t) + Ii (t) − Ei (t),(3)

where Bi (t) is asset wealth, Ii (t) is labor income, Ei (t) is household expenditure, r(t) is
the interest rate, and a dot over a variable denotes time differentiation. The solution to thehousehold’s utility maximization problem is the optimal expenditure-saving path describedby the Euler condition: Ėi (t)/Ei (t) = Ėj (t)/Ej (t) = r(t) − ρ, where with equal access to7

an international financial market, the households of both countries face a common interest
rate and have common motions for expenditure.
At each moment in time, households allocate constant expenditure shares to the manufacturing composite and the traditional good: PXi (t)CXi (t) = αEi (t) and PY i (t)CY i (t) =(1 − α)Ei (t), where PXi (t) is the price index over manufacturing goods and PY i (t) is the
traditional good price. In particular, the price index over manufacturing goods is

PXi (t) =Z Ni (t)pXi (t, ω)1−σ dω +0

Z Nj (t)(ζpXj (t, ω))1−σ dω

0

1
! 1−σ

,

(4)

where pXi (t) and pXj (t) are the prices associated with manufacturing varieties produced incountries i and j. Iceberg costs are incurred on international trade in manufacturing goods
with a shipment of ζ > 1 units required for every unit sold in an export market. Viewing (4)as the unit expenditure function over manufacturing goods, Shephard’s Lemma yields thecountry i demands for varieties produced in countries i and j:xii (t) = αpXi (t)−σ PXi (t)σ−1 Ei (t),xij (t) = α(ζpXj (t))−σ PXi (t)σ−1 Ei (t).

(5)

2.2 Occupational Choice
Each country has a population of workers Z with heterogeneous skill levels z that follow a
continuous uniform distribution with support [0, 1]. At each moment in time, workers choose
between low-skilled employment in production and high-skilled employment in innovation.
Workers employed in production in country i each supply one unit of low-skilled labor,regardless of skill level, earning the low-skilled wage rate wLi (t). In contrast, workers
employed in innovation supply high-skilled labor according to their skill levels. Specifically,a worker with skill level z supplies z units of high-skilled labor, and earns income zwHi (t),where wHi (t) is the high-skilled wage rate.
Competitive national labor markets ensure that all firms offer the same low-skilled and8high-skilled wages. Thus, with active production and innovation sectors, each country
has a marginal worker who can earn equal incomes from low-skilled and high-skilled employment, and is indifferent between employment type. The skill level of this marginal
worker equals the relative wage rate z = wLi (t)/wHi (t). We separate the labor force into
those workers z ∈ [0, 1/wi (t)] who choose employment in production, and those workers z ∈ [1/wi (t), 1] who select employment in innovation, where wi (t) ≡ wHi (t)/wLi (t)denotes the relative high-skilled wage rate in country i.
The occupational choice results in the following effective low-skilled and high-skilledlabor supplies for country i:

Li (t) =Z,wi (t)Hi (t) =(wi (t)2 − 1)Z.
2wi (t)2(6)

As such, expected national labor income, conditional on employment levels, becomes Ii (t) ≡wLi (t)Li (t) + wHi (t)Hi (t) = wLi (t)(1 + wi (t)2 )Z/(2wi (t)).
2.3 Traditional Production
Traditional firms employ one unit of low-skilled labor with a constant returns to scale technology to produce one unit of output for supply to an international market characterized
by free trade. Setting the traditional good as the model numeraire, we suppose that demand is sufficiently large that both countries continue to produce traditional goods at all
moments in time. The traditional good price and low-skilled wage rates then equal one(PY i (t) = PY j (t) = wLi (t) = wLj (t) = 1), and the combined demands of households incountries i and j determine the world demand for low-skilled labor in traditional production:

LY i (t) + LY j (t) = (1 − α)E(t),with E(t) ≡ Ei (t) + Ej (t).

9(7)

2.4 Manufacturing
The manufacturing sector is monopolistically competitive (Dixit and Stiglitz 1977), witheach firm producing a single unique product in one location for supply to both domestic
and export markets. Following Peretto and Connolly (2007), the technology of a firm withproduction located in country i is

xi (t) = θ(t)γ (lXi (t) − ψ),(8)where xi (t) is firm-level output, lXi (t) is low-skilled employment in production, θ(t) is
firm-level productivity, ψ > 0 is a fixed operating cost, and γ ∈ (0, 1) is the productivity
elasticity of output. Although each firm employs a unique production technology, in order tosimplify the analysis, we assume that initial productivity levels are symmetric across firms(θ(t) ≡ θi (t) = θj (t)) operating in both countries.
Firms maximize operating profit (πi (t) = pXi (t)xi (t) − lXi (t)) by setting price equal toa constant markup over unit cost: pXi (t) = pXj (t) = σθ(t)−γ /(σ − 1). Equating supply
with the combined demands from households in both countries (5), xi (t) = xii (t) + ζxij (t),the optimal operating profit of a firm with production located in country i is
αpXi (t)1−σπi (t) =σEi (t)
ϕEj (t)+1−σPXi (t)PXj (t)1−σ



− ψ,

(9)

where ϕ ≡ ζ 1−σ ∈ (0, 1) describes the freeness of trade between countries with ϕ = 0
indicating prohibitively high trade costs and ϕ = 1 indicating perfectly free trade.
Firms are free to shift production between countries, with the objective of maximizing
operating profit (Martin and Ottaviano 1999, 2001). Therefore, when there are active manufacturing sectors in both countries, operating profit is the same for all firms, regardless of
the location of production; that is, πi (t) = πj (t).2 Combining the price indices (4) with2
In order to keep the model tractable, we assume that there are no additional fixed costs associated withthe separation of production and innovation activities across countries. See Tintelnot (2017) for a quantitative
general equilibrium framework that examines how the tension between trade costs and the fixed costs of10

operating profit (9), and recalling that the prices of differentiated varieties are equal acrossfirms and locations, we solve for the equilibrium share of firms with production located incountry i as follows:sXi (t) ≡Ni (t)Ei (t) − ϕEj (t)=,N(t)(1 − ϕ)E(t)(10)

where N(t) ≡ Ni (t) + Nj (t). Note that a common motion for household expenditures(Ėi (t)/Ei (t) = Ėj (t)/Ej (t)) results in constant production shares over time (ṡXi (t) = 0).
Substituting the manufacturing shares of each country back into operating profit yields firmlevel employment in production for all locations:lXi (t) = lXj (t) =α(σ − 1)E(t)
+ ψ,
σN(t)

(11)

where we have used the production function (8).

2.5 Process Innovation
Firms invest in process innovation with the aim of lowering unit production costs. In particular, the evolution of productivity for a firm with process innovation located in country i
followsθ̇i (t) = ki (t)θi (t)hIi (t),(12)

where hIi (t) is firm-level high-skilled employment and ki (t)θi (t) is labor productivity inprocess innovation. Following the in-house process innovation literature (Smulders and vande Klundert 1995; Peretto 1996; Peretto and Connolly 2007), firm-level R&D exhibits an intertemporal knowledge spillover through which the technical knowledge created by current
innovation activity improves the labor productivity of future innovation efforts. Specifiestablishing foreign production generates various multinational production patterns in a multi-country model.

11cally, the productivity coefficient θi (t) represents the current stock of technical knowledge,
and ki (t) determines the strength of intertemporal knowledge spillovers from the stock ofknowledge into current innovation activity. As the stock of technical knowledge expands
over time, innovation costs fall, creating the potential for perpetual productivity growth inlong-run equilibrium.
There is a large body of empirical research documenting both the localized nature ofknowledge spillovers and the international scope for knowledge diffusion (Bottazi and Peri
2007; Mancusi 2008; Coe et al. 2009; Ang and Madsen 2013).3 Adapting the setup of
Baldwin and Forslid (2000), we capture the geographic nature of knowledge diffusion withthe following specification for the strength of knowledge spillovers from production into
process innovation located in country i:ki (t) = sXi (t) + δsXj (t),(13)

where the localized nature of knowledge spillovers is regulated by the degree of knowledge
diffusion δ ∈ (0, 1). Under this specification, the labor productivity of high-skilled workers
in process innovation is determined as the weighted-average productivity of the observablestock of knowledge, with a stronger weighting for production technologies employed in
proximity to the innovation department of the firm.
Total per-period profit is Πi (t) = πj (t)−wi (t)hIi (t), with the high-skilled wage rate now
denoted by wi (t) = wHi (t). Firm value equals the presented discounted value of expected
profits:

Vi (t) =

Z ∞

Rτ

′

′

e− t (r(τ )+λ)dτ Πi (τ )dτ,

(14)

t

where λ > 0 is an instantaneous default rate which indicates the probability that a firmspecific shock forces the firm to exit the market (Baldwin 1999).
3

See Keller (2004) for a survey of the various channels through which knowledge spillovers arise.

12Each firm sets its level of high-skilled employment in process innovation to maximize
firm value (14) subject to (12). We solve this optimization problem with the following
current-value Hamiltonian function: Fi (t) = Πi (t) + pIi (t)ki (t)θi (t)hIi (t), where pIi (t) can
be conceived as the cost of a unit mass of new process innovations developed by a firm incountry i over the time interval dt. The first order conditions for optimization provide thefollowing static and dynamic efficiency conditions:pIi (t) =wi (t),ki (t)θ(t)pIi (t)(r(t) + λ) − ṗIi (t) =∂πj (t)α(σ − 1)γE(t)
=
,
∂θ(t)
σθ(t)N(t)(15)

where we have used (9) and (11). Note that under monopolistic competition, each firm
perceives the price indices (PXi (t)) and knowledge spillovers (ki (t)θ(t)) as constant whenmaximizing firm value, given its atomistic market share.4
Firms are free to shift their innovation activities between countries, ensuring a common
cost for new process innovations when there is innovation located in both countries; that is,pIi (t) = pIj (t). We use this condition to obtain the country i production share that equates
the cost of process innovations across countries:sXi (t) =wi (t) − δwj (t),(1 − δ)(wi (t) + wj (t))(16)

where we have used (13) and (15). Note that constant production shares (ṡXi (t) = 0)
lead to common motions for high-skilled wages (ẇi (t)/wi (t) = ẇj (t)/wj (t)). In addition,
similar to the framework of Ekholm and Hakkala (2007), the degree of knowledge diffusion
regulates the range of relative high-skilled wages over which dispersed location patterns arefeasible; that is, wi (t)/wj (t) ∈ (δ, 1/δ) is required for sXi (t) ∈ (0, 1).
In order to emphasize the role of high-skilled wages and knowledge spillovers, we set
the regional cost component of unit innovation costs as ci (t) ≡ wi (t)/ki (t) such that the4

Using (11), (12), and (15), steady-state firm-level employment in process innovation becomes hIi =(lXi − ψ)/wi − (ρ + λ)/ki . Accordingly, firm-level investment in process innovation (hIi ) increases with thescale of production, as in Rubini (2014) and Piguillem and Rubini (2019).

13

price of new innovations is pIi (t) = ci (t)/θ(t) in country i. Then, substituting (16) backinto (13) yields the regional component of the unit cost for process innovation asc(t) =wi (t)
wj (t)wi (t) + wj (t)==.
ki (t)
kj (t)
1+δ

(17)This unit cost component captures two key factors in the location decision for R&D thathave been emphasized in the literature: the observable stock of technical knowledge and thecost of employing high-skilled labor (Chung and Yeaple 2008; Manning et al. 2008; Lewin
et al. 2009; Demirbag and Glaister 2010).

2.6 Product Development
New firms employ high-skilled labor in product development as they prepare to enter the
manufacturing industry. The creation of a new product design requires αE(t)/(Ni (t) +δNj (t)) units of high-skilled labor in country i, where the numerator captures the overall
size of the market for manufacturing varieties, generating a positive relationship between
entry costs and market size (Etro 2004, Peretto and Connelly 2007, Peretto and Valente2015). The denominator captures the benefit of knowledge spillovers into the product development process, where we assume that the national stock of knowledge associated withproduct design is measured by the number of product varieties currently being produced in
the country. Then, because knowledge spillovers diminish with distance, δ ∈ (0, 1), there
are greater knowledge spillovers into product development in the country with the larger
share of production (Baldwin et al. 2001).
Free entry into the manufacturing industry drives firm value (14) down to the cost ofdesigning a new product, and when both countries have active R&D sectors, the cost of
product development equalizes across locations. Using (14), we therefore have

Vi (t) = Vj (t) =

αE(t)
αE(t)
αE(t)
wi (t) =wj (t) =c(t).
ki (t)N(t)kj (t)N(t)
N(t)

14

(18)

The time derivative of (14) yields the following no-arbitrage condition for investment in a
new product design (Grossman and Helpman 1991):(r(t) + λ)Vi (t) − V̇i (t) = πi (t) − wj (t)hIj (t).

(19)

Together the investment conditions (15) and (19) imply that c(t) = wi (t)/ki (t) = wj (t)/kj (t),wi (t)hIi (t) = wj (t)hIj (t), and ki (t)hIi (t) = kj (t)hIj (t), when both countries host innovation activity.
Aggregating the high-skilled labor employed in product development across countries,and subtracting the number of firms (λN(t)) that default at each moment of time yields a
differential equation for the evolution of market entry and exit:ki (t)HN i (t) + kj (t)HN j (t)Ṅ (t)
=
− λ,
N(t)
αE(t)

(20)

where HN i (t) and HN j (t) are the levels of high-skilled labor employed in the product development sectors of each country.

2.7 Labor Market Clearing
In this section, we derive the market clearing conditions associated with low-skilled andhigh-skilled labor. First, combining the low-skilled labor supply (6) with the labor demands
from the traditional sector (7) and the manufacturing sector (11) yields the world market
clearing condition for low-skilled labor as follows:

L(t) ≡ Li (t) + Lj (t) = µE(t) + ψN(t),(21)

with µ ≡ (σ − α)/σ ∈ (0, 1).
Second, utilizing the high-skilled labor supply (6) with the labor demands from process
innovation (12) and product development (20) we obtain the world market clearing condition15

for high-skilled labor aswi (t)Hi (t) + wj (t)Hj (t) =

!
θ̇(t)
Ṅ(t)
N(t)
+ αE(t)+ αE(t)λ c(t),
θ(t)
N(t)

(22)

where we have used c(t) = wi (t)/ki (t) = wj (t)/kj (t) and wi (t)hIi (t) = wj (t)hIj (t).
Finally, denoting the number of firms with process innovation located in country i by
Mi (t), we show that the total value of country i’s R&D output (process innovation and product development combined) is equal to high-skilled labor income; that is, Mi (t)pIi (t)θ̇(t) +Vi (t)Ṅi (t) = Mi (t)wi (t)hIi (t) + wi (t)HN i (t) = wi (t)Hi (t). As such, we derive country i’sshare of the total value of world R&D output as follows:sIi (t) ≡wi (t)Hi (t).
wi (t)Hi (t) + wj (t)Hj (t)(23)

Thus, we find that national shares of innovation activity are determined proportionately withshares of high-skilled labor income.

3Long-run Location and Trade Patterns

We derive the long-run industry and innovation location patterns consistent with equilibriumin the investment and labor markets. To simplify the analysis, we focus on the level ofmarket entry relative to overall market size for the manufacturing sector: n ≡ N/(αE),
where we henceforth suppress time arguments to simplify notation. Steady-state equilibrium
is characterized by constant values for household expenditure (Ė = Ėi = Ėj = 0), highskilled wages (ẇi = ẇj = 0), market entry (ṅ = 0), and asset wealth (Ḃ = Ḃi = Ḃj = 0).
The number of new product designs introduced each period matches the number of firms
exiting the market, ensuring a constant steady-state number of incumbent firms (Ṅ = 0).
We set country i as the asset wealthy country and country j as the asset poor country tosimplify the exposition; that is, we assume Bi > Bj .

16

3.1 National Labor Allocations
Long-run equilibrium is fully characterized through two conditions that determine highskilled wages and hence the division of national labor forces into low-skilled and highskilled labor. The first condition is an investment locus that describes the high-skilled wage
combinations for which investment levels in process innovation and product development
are optimal. Denoting total asset wealth by B ≡ Bi + Bj and total labor income by I =Ii + Ij , we have B = NVi = αEc from (18), and Ḃ/B = r + (I − E)/B from (3).
Combining these expressions with (15), (18), (19), and (21), we obtain the investment locusasν − (ρ + λ)c(1 − αρc)Lµ=−,ψ − (ρ + λ)c
αψI
αψ

(24)

where we have used Ė = ẇi = ẇj = 0, and the marginal profit associated with an increasein the size of the firm’s market segment provides a measure of firm-level market power:ν ≡ ∂Π/∂(1/n) = (1 − (σ − 1)γ)/σ ∈ (0, 1).5 Noting that 1 > αρc is necessary for apositive level of expenditure given world labor income, E = I/(1 − αρc), the investment
locus has a strictly negative slope in (wi , wj ) space, as depicted by the Φ-curve in Figure 1.
The second condition is a share locus that indicates the high-skilled wage combinations
which are consistent with national production shares that equalize operating profits, process
innovation costs, and product development costs across countries. We use Ḃ = ρB +I − E = 0 together with the household flow budget constraint (3) to obtain Ei = Ii +bi αρcI/(1 − αρc), where bi ≡ Bi /B is country i’s share of asset wealth. Substituting
household expenditure into (10) and equating the result with (16) then yields the share locus
5

Substitution of (8), (11), (12), and (15) into Πi = πj − wi hIi gives per-period profit as Π = (1 − (σ −1)γ)/(σn) + (ρ + λ)c − ψ.

17Figure 1: Equilibrium Labor Allocations
wj

Φ

wj

wj /wi = 1/δ

wj /wi = 1/δ

Φ

Ω
b

e

e
b

wj /wi = δ

wj /wi = δ

Ω
wi

1

wi

1

(b) ϕ > ϕB(a) ϕ < ϕB

These stylized labor allocation patterns can be reproduced numerically using α = 0.85, σ = 3.5,
γ = 0.35, ρ = 0.01, λ = 0.01, ψ = 0.2, b = 0.65, δ = 0.8, Z = 1, and ϕB = 0.96, for both panels, andwith ϕ = 0.6 for Panel (a) and ϕ = 0.97 for Panel (b).

as follows (see Appendix B):(bi − ϕbj )αρc (Ii − ϕIj )(1 − αρc)wi − δwj+=.
1−ϕ(1 − ϕ)I(1 − δ)(wi + wj )(25)This expression has lower and upper hyperbolic branches, as illustrated by the Ω-curves
in Figures 1a and 1b, with asymptotes implicitly defined by wi = wj and 1 − δϕ + (δ −ϕ)wi wj + αρ(1 − δ)(1 + ϕ)(bj wi wj − bi )c = 0, and a vertical transverse axis for bi > bj .6
Long-run equilibrium is determined at point e where the investment locus and the sharelocus intersect. We investigate the local dynamics around this steady state and obtain thefollowing stability conditions for a long-run equilibrium with positive high-skilled employment levels in both countries.
Lemma 1 A long-run equilibrium with dispersed industry and innovation is saddle-path
6

Using the expressions introduced in Appendix B, the share locus can be rewritten as follows:(1 − δ)(1 + ϕ)(bi − bj )(1 + wi wj )wj αρc= 1.
(1 − δϕ + (δ − ϕ)wi wj + (1 − δ)(1 + ϕ)(bj wi wj − bi )αρc)(wi − wj )The denominator describes the asymptotes that arise for bi > bj .

18

stable for ψ > (ρ + λ)c.
Proof: See Appendix A.
We focus our analysis on long-run equilibria that satisfy the stability condition outlined
in Lemma 1. In addition, we consider cases for which the share locus (25) crosses theinvestment locus (24) once from below to ensure the uniqueness of equilibrium.

3.2 Production and Innovation Location Patterns
In this section, we study the long-run location patterns that arise for different levels of trade
costs. In particular, while each firm selects independent, and potentially different, locations
for product development, production, and process innovation, we show that aggregate location patterns are linked through a circular causality driven by two mechanisms: a knowledge
spillover effect and a wage effect.
The knowledge spillover effect is described by the LHS of the share locus (25), withincreases in a country’s share of investment income (first term) or labor income (secondterm) expanding the national market, attracting manufacturing, and strengthening knowledge spillovers from production to innovation. In turn, stronger knowledge spillovers invite
more innovation, raising labor income as high-skilled employment increases and further expanding the national market. In this manner, national shares of production and innovation
are linked with market size through a home market effect (Krugman 1980), and thus thestrength of the knowledge spillover effect is increasing in the freeness of trade.
The wage effect is captured by the RHS of the share locus (25), and regulates the rate at
which a country’s high-skilled wages can rise as its market expands without inducing firms
to relocate their innovation activities internationally to reduce the cost of employing highskilled labor. The wage effect is increasing in the degree of knowledge diffusion: greater
knowledge diffusion facilitates a faster rise in high-skilled wages as a country’s market
expands.
The tension between market expansion and rising high-skilled wages generates two po19

tential cases for location patterns. We identify these patterns by observing the direction of
the labor market adjustments that occur after an increase in country i’s share of investment
income (bi ). In particular, through the share locus (25), we show that an increase in bi raises
country i’s shares of production (sXi ) and innovation (sIi ) when ϕ < ϕB , but lowers themwhen ϕ > ϕB , whereϕB ≡1 + δwi wj − (1 − δ)(bi − wi wj bj )αρc,
δ + wi wj + (1 − δ)(bi − wi wj bj )αρcwith positive values for both the numerator and denominator since 1 > αρc.
First, when ϕ < ϕB , the wage effect dominates the knowledge spillover effect, andthe increase in bi initially raises sXi causing relative innovation costs to fall for country i;that is, ci < cj . Firms then relocate innovation and production to country i, with wi /wj
rising at a faster rate than ki /kj until innovation costs are again equal. In this first case, theasset wealthy country i has a larger market with greater high-skilled employment, and larger
shares of production (sXi > 1/2) and innovation (sIi > 1/2).
Second, when ϕ > ϕB , the knowledge spillover effect dominates, and the initial shift inlocation patterns resulting from an increase in bi leads to higher innovation costs for countryi; that is, ci > cj . Accordingly, firms shift innovation and production to country j with ki /kj
falling at a faster rate than wi /wj until innovation costs are again equal across countries.
In this second case, the asset-poor country j has a larger market with greater high-skilledemployment, and higher production (sXi < 1/2) and innovation shares (sIi < 1/2).
Changes in trade costs have opposing effects on the location patterns described for thetwo cases outlined above. For the first case (ϕ < ϕB ) shown in Figure 1a, a decrease intrade costs moves point e rightward along the investment locus, with country i’s shares of
production and innovation expanding as the knowledge spillover effect is magnified. Production concentrates fully in asset-wealthy country i where the investment locus crosses thewj /wi = δ dashed line (sXi = 1). We denote the threshold for the freeness of trade asso-

20

Figure 2: Trade Costs and Location PatternssIi ∈ (1/2, 1)

z

0

|

}|

{z

sIi = 1

}|

ϕIi

ϕXi

{z

}|

sXi ∈ (1/2, 1)

sIi ∈ (1/2, 1)

z

ϕXi

0

|

}|

{z

}|

sXi ∈ (1/2, 1)

sIi = 0

{z

ϕB

{z

sXi = 1

}|

ϕIi

{z

sXi = 1

}|

ϕXj

{z

sXi = 0(a) δ < δ

sIi = 1

{z

}|

}|

ϕB

}|

(b) δ ≥ δ

}|

ϕIj

{z

}|

sXi ∈ (0, 1/2)

{

ϕ

{

ϕ

1

}

sIi ∈ (0, 1/2)

sIi = 0{zsIi ∈ (0, 1/2)

{z

{z

}|

ϕIj

ϕXj

{z

}|

sXi = 01{z}sXi ∈ (0, 1/2)

ciated with this point by ϕXi . Similarly, innovation concentrates fully in country i at theintersection of the investment locus and the horizontal axis (sIi = 1). The threshold for thefreeness of trade linked with this point is ϕIi .
In contrast, in the second case illustrated for ϕ > ϕB in Figure 1b, an increase in trade
costs moves point e leftward along the investment locus until either production is fully
concentrated in asset-poor country j where the investment locus crosses the wj /wi = 1/δ
dashed line (sXi = 0), or innovation is fully concentrated in country j at the intersectionof the investment locus with the vertical axis (sIi = 0). We use ϕXj and ϕIj to denote thethreshold values for the freeness of trade associated with the full concentration of production
and innovation in country j.
The long-run location patterns associated with various trade costs levels are summarized
in the following proposition:
Proposition 1 (i) For ϕ < ϕB , the asset-wealthy country has larger shares of industry andinnovation, with the full concentration of industry for ϕ ∈ (ϕXi , ϕB ) and the full concentration of innovation for ϕ ∈ (ϕIi , ϕB ). (ii) For ϕ > ϕB , the asset-poor country has larger
shares of industry and innovation, with the full concentration of industry for ϕ ∈ (ϕB , ϕXj )and the full concentration of innovation for ϕ ∈ (ϕB , ϕIj ). There exists a threshold δ such21

that ϕIi < ϕXi and ϕIj > ϕXj for δ < δ, but ϕIi ≥ ϕXi and ϕIj ≤ ϕXj for δ ≥ δ.
Proof: See Appendix C.
Figure 2 summarizes the location patterns associated with various ranges for the freeness of trade, with the shaded sections matching with the shaded areas in Figure 1 where
production is fully concentrated and the regional component of innovation costs is not equalized across countries (ci 6= cj ). The degree of knowledge diffusion determines whether thefull concentration of manufacturing coincides with the full concentration of innovation. As
shown in Figure 2a, if δ < δ, the knowledge spillover advantage of the larger national market
discourages firms from locating innovation in the smaller country, and innovation concentrates fully before manufacturing; that is, ϕXi > ϕIi and ϕXj < ϕIj . As depicted in Figure
2b, however, if δ > δ, a high degree of knowledge diffusion reduces the localized benefitsof knowledge spillovers, allowing the smaller country to attract innovation with its low-costhigh-skilled labor, even with manufacturing fully concentrated in the larger country; that is,
ϕXi < ϕIi and ϕXj > ϕIj . In Appendix C, we show that a sufficient improvement in the
degree of knowledge diffusion reduces high-skilled employment in country i, but expands
it in country j, decreasing country i’s shares of manufacturing and innovation.

3.3 Net Offshoring Patterns
Net offshoring flows in the manufacturing sector are measured at the macro-level using thedifference between the value of world output owned by country i and the value of production
located in country i at each moment in time:

SX ≡ (bi N − Ni )pXi xi = (bi − sXi )αE,

(26)

where we have used (8), (10), and (11). Net offshoring flows depend on nationals shares ofasset wealth and production (bi − sXi ), and overall market size (αE). Thus, net offshoringflows from the asset-wealthy country i to the asset-poor country j when SX > 0, and from22

country j to country i when SX < 0. Characterizing the direction of net offshoring patterns
in production using the freeness of trade, we obtain the following:
Proposition 2 Net offshoring in manufacturing flows from the asset-wealthy country to theasset-poor country for ϕ 6∈ (ϕXO , ϕB ), and from the asset-poor country to the asset-wealthy
country for ϕ ∈ (ϕXO , ϕB ), where ϕXO ∈ (0, ϕX ).
Proof: See Appendix D.
Net offshoring flows for the manufacturing sector are illustrated by the SX curve in Figure 3, where the vertical axis shows SX over the range ϕ ∈ (0, 1) measured on the horizontal
axis. After all fall in trade costs, country i’s share of production increases (dsXi /dϕ > 0),
while total expenditure increases (dE/dϕ > 0) for ϕ < ϕB , but decreases (dE/dϕ < 0)for ϕ > ϕB . In Appendix D, we show that the SX curve crosses the horizontal axis oncewith a negative slope for ϕ < ϕB , and that it has a strictly negative slope for ϕ > ϕB .
There are therefore three potential cases for the direction of net offshoring. Starting from ahigh level of trade costs over the range ϕ ∈ (0, ϕXO ), the market of asset-wealthy country i
is not sufficiently large to support the production of all country i owned firms, resulting in
net offshoring flows from country i to country j (SX > 0). For a mid-level of trade costsϕ ∈ (ϕXO , ϕB ), the country i market is sufficiently large to attract the production of a larger
share of firms, including the production of firms with country j owners, and net offshoring
therefore flows from country j to country i (SX < 0). For a low level of trade costs over
the range ϕ ∈ (ϕB , 1), the larger market of country j attracts the greatest share of production, with a share of country i owned firms also locating production in country j, thereby
generating net offshoring flows from country i to country j (SX > 0).
Net offshoring flows in innovation are similarly calculated at the macro-level using thedifference between the value of world R&D output owned by country i and the value of
R&D output produced in country i at each moment in time. Recalling that the total valueof country i’s R&D output is equal to high-skilled labor income, we obtain net offshoring

23

Figure 3: Equilibrium Offshoring Patterns
SI , SX

SI , SXϕXj ϕIj

ϕXj

SX

SI
SX

SI
0

SI
SI

SX

SX

ϕXO

0

ϕIO

0

ϕIi ϕXi ϕB

ϕXO

ϕ
0

1

(a) δ < δ < δ

ϕXi

ϕB

ϕ
1

(b) δ > δ > δ

These stylized labor allocation patterns can be reproduced numerically using α = 0.85, σ = 3.5,
γ = 0.35, ρ = 0.01, λ = 0.01, ψ = 0.2, b = 0.65, and Z = 1 for both panels, and with δ = 0.4 and
ϕB = 0.85 for Panel (a), and δ = 0.8 and ϕB = 0.96 for Panel (b).

flows for country i as follows:SI ≡ bi (wi Hi + wj Hj ) − wi Hi = (bi − sIi )(wi Hi + wj Hj ),(27)

where we have used (23). Net offshoring flows are determined by national shares of asset wealth and innovation activity (bi − sIi ) and the aggregate scale of innovation activity(wi Hi + wj Hj ). Thus, net offshoring in innovation flows from the asset-wealthy country ito the asset-poor country j when SI > 0, and from country j to country i when SI < 0. We
use the freeness of trade to characterize net offshoring patterns in innovation as follows:
Proposition 3 When δ < δ, net offshoring in innovation flows from the asset-wealthy country to the asset-poor country for ϕ 6∈ (ϕIO , ϕB ) and from the asset-poor country to theasset-wealthy country for ϕ ∈ (ϕIO , ϕB ), where δ < δ and ϕIO ∈ (0, ϕI ). When δ > δ,
net offshoring in innovation always flows from the asset-wealthy country to the asset-poor
country.
Proof: See Appendix D.
24

The pattern of innovation offshoring depends on the degree of knowledge diffusion. As
shown in Figure 3a, where net offshoring flows for innovation are measured on the verticalaxis (SI ), when knowledge diffusion is relatively low (δ < δ), there are three cases. The firstcase occurs over the range ϕ ∈ (0, ϕIO ) where country i’s greater share of industry provides
it with a knowledge spillover advantage that allows it to attract a larger share of innovation.
The knowledge spillover advantage is not sufficient, however, to prevent a share of country
i owned firms from locating innovation in country j with the aim of taking advantage oflower high-skilled wages. As a result, net offshoring in innovation flows from country i tocountry j (SI > 0). The second case occurs for intermediate trade costs ϕ ∈ (ϕIO , ϕB )where country i’s share of industry generates a knowledge spillover advantage that is great
enough to ensure that all country i owned firms, and a share of country j owned firms,
locate innovation in the country i country, despite higher high-skilled wages. In this casenet offshoring flows from country j to country i (SI < 0). The third case arises for low
trade costs ϕ ∈ (ϕB , 1) when country j has a larger share of industry, and all country j
firms and a share of country i firms locate innovation in country j to take advantage ofgreater knowledge spillovers, generating net offshoring flows from country i to country j(SI > 0).
In general, marginal improvements in knowledge diffusion have ambiguous effects onnational labor allocations. In Appendix C, we show, however, that for ϕ < ϕB , we havesXi > 1/2, and sIi > 1/2, and a sufficient increase in the degree of knowledge diffusion reduces country i’s shares of production and innovation causing the SX and SI curves
to shift upwards in Figure 3. In particular, as shown in Figure 3b, for sufficiently highdegree of knowledge diffusion, the knowledge spillover advantage associated with industry concentration is relatively weak, creating an incentive for firms to focus on minimizing the cost of employing high-skilled labor when choosing where to locate innovation.
As such, innovation never concentrates fully in one country. Indeed, with perfect knowledge diffusion (δ = 1), exactly half of all innovation activity is located in each country:

25

SI = (bi − 1/2)(wi Hi + wj Hj ) > 0. Therefore, in the case for δ > δ, net offshoring
in innovation always flows from the asset-wealthy country i to the asset-poor country j(SI > 0).
3.4 Market Entry and Productivity Growth
We now consider how changes in location patterns affect long-run market entry and productivity growth. Combining (9), (11), (12), (15), and (19) yields the level of market entryn=ν − (ρ + λ)c,
ψ − (ρ + λ)c(28)

as a function of the regional unit innovation cost (c), where ν > (ρ + λ)c is necessary fora positive level of market entry, as ψ > (ρ + λ)c is required for the saddle-path stability oflong-run equilibrium (Lemma 1). Using (28), we obtain the following lemma.
Lemma 2 The level of market entry is increasing in the regional component of unit innovation costs (c) for ν > ψ, and decreasing in c for ν < ψ.
Proof: See Appendix E.
Following Davis and Hashimoto (2015), a rise in the regional component of unit innovation costs has two effects on the level of market entry. The first is a product development
effect under which higher innovation costs dampen investment in product development, lowering the level of market entry. The second is a process innovation effect whereby higher
innovation costs reduce the optimal level of investment in process innovation, leading tohigher per-period profits, inducing investment in product development, and putting upward
pressure on the level of market entry. The overall balance of these effects depends on thelevel of market power (ν) relative to the per-period fixed cost (ψ). When ν < ψ, the product development effect dominates and market entry falls. Alternatively, when ν > ψ, theprocess innovation effect dominates and market entry rises.

26

The long-run rate of productivity growth is derived as a function of the regional component of unit innovation costs (c) from (12), (15), and (28):g≡θ̇(σ − 1)γ(ψ − (ρ + λ)c)=− ρ − λ.
θσ(ν − (ρ + λ)c)c(29)

Note that long-run productivity growth is not biased by a scale effect as changes in overall
population size (2Z) are fully absorbed by adjustments in the number of firms in the market(N), leaving the level of market entry (n) and the rate of productivity growth unchanged.7
We use (29) to obtain the following lemma.
Lemma 3 The productivity growth rate is decreasing in the regional unit innovation costp(c) for ν > ψ, and convex in c with a minimum at c = (ψ − ψ(ψ − ν))/(ρ + λ) for ν < ψ.
Proof: See Appendix E.

An increase in the regional component of unit innovation costs (c) affects long-run productivity growth through two mechanisms (Davis and Hashimoto 2015). The first is the
direct negative effect of higher innovation costs on investment in process innovation. The
second is the effect of adjustments in the level of market entry. From Lemma 2, whenν > ψ the level of market entry increases and the overall result is a slower rate of productivity growth. Alternatively, when ν < ψ productivity growth decelerates if c < c as thenegative process innovation effect dominates, but productivity growth accelerates if c > cas the positive effect of lower market entry dominates.
Improved economic integration resulting from either a fall in trade costs or a rise inknowledge diffusion affects market entry and productivity growth through adjustments in
the regional component of innovation costs. Beginning with an investigation of the effects
of adjustments in trade costs, we obtain the following result.
7

There is now a large empirical literature concluding that there is no significant relationship between economic growth and population size (Dinopoulos and Thompson 1999; Barro and Sala-i-Martin 2004; andLaincz and Peretto 2006). The framework presented in this paper corrects for scale effects by focusing on
the innovation associated with the production technologies of individual product lines, rather than considering
R&D at the national level.

27

Proposition 4 If ϕ < ϕB , a fall in trade costs expands market entry and slows productivity
growth for ν > ψ, but reduces market entry and initially slows (c < c) but then hastens(c > c) productivity growth for ν < ψ. Alternatively, if ϕ > ϕB , a fall in trade costs reduces
market entry and hastens productivity growth for ν > ψ, but expands market entry andinitially slows (c > c) but then hastens (c < c) productivity growth for ν < ψ.
Proof: See Appendix E.
Greater economic integration through a reduction in trade costs affects market entry andproductivity growth through adjustments in national shares of production (sXi ). Importantly,
an increase in the concentration of manufacturing raises the regional component of innovation costs (dc/dsXi > 0) because the negative effect of increased high-skilled wages always
dominates the positive effect of improved knowledge spillovers.8 Thus, as we have seen in
Proposition 1, a rise in the freeness of trade increases the concentration of manufacturingin country i for ϕ < ϕB , raising innovation costs, but decreases the concentration of manufacturing in country j, lowering innovation costs for ϕ > ϕB . Combining the effects ofchanges in trade costs on innovation costs with the results of Lemmas 2 and 3 generates thecases outlined in Proposition 4.
Investigating the effects of an adjustment in the degree of knowledge diffusion, we obtainthe following proposition.
Proposition 5 When ϕ < ϕB , a rise in the degree of knowledge diffusion reduces market
entry and hastens productivity growth for ν > ψ, but expands market entry and initiallyslows (c > c) but then hastens (c < c) productivity growth for ν < ψ. In contrast, whenφ > ϕB , a rise in the degree of knowledge diffusion has ambiguous effects on both market
entry and productivity growth.
Proof: See Appendix E.
8In general the empirical literature reports mixed results for the effect of industry concentration on economic growth. See Gardiner et al. (2011) for a literature survey and for evidence supporting a negative
relationship between a number of measures of industry concentration and GDP growth.

28

As discussed in the previous section, the relationship between the degree of knowledge
diffusion and national labor market allocations is generally ambiguous. However, whenϕ < ϕB and production and innovation are concentrated in the asset-wealthy country i, asufficient rise in the degree of knowledge diffusion decreases the concentration of industry
causing innovation costs to fall (dc/dsXi > 0). As a result, for ν > ψ the level of market
entry falls and productivity growth accelerates. For ν < ψ, however, market entry rises,and productivity growth either decelerates or accelerates depending on whether the positive
process innovation effect or the negative market entry effect dominates, according to thecurrent level of regional innovation costs. When ϕ > ϕB , the effect of a rise in the degree ofknowledge diffusion on national labor allocations, and thus on innovation costs, is generally
ambiguous.

3.5 Innovation Offshoring and Long-run Productivity Growth
In this final section we tie together the results of the previous sections with the aim ofclarify the relationships between net offshoring flows and the rate of productivity growth.
Focusing on the case for which the asset-wealthy country has greater shares of production
and innovation (ϕ < ϕB ), we summarize the effects of improved economic integration in
the following proposition.
Proposition 6 When ϕ < ϕB , improved economic integration, through a fall in trade costs
or a rise in the degree of knowledge diffusion, generates a positive relationship between net
offshoring flows in innovation from the asset-wealthy country to the asset-poor country andthe long-run rate of productivity growth both for ν > ψ and for ν < ψ with c < c.
As we have seen, a dispersed location pattern for industry and innovation reduces innovation costs (dc/dsXi > 0) as the positive effect of lower high-skilled wages dominates
the negative effect of reduced knowledge spillovers. In addition, because innovation activity
shifts out of the asset-wealthy country, less concentrated location patterns also coincide with
29

Table 1: Improvements of Knowledge Diffusion
ν−ψ
0.1
0.1
0.1
−0.1
−0.1
−0.1

δ
0.05
0.1
0.15
0.05
0.1
0.15

sXi
0.513
0.512
0.511
0.514
0.513
0.512

sIi
0.81
0.703
0.638
0.707
0.639
0.596

SXi
0.468
0.469
0.469
0.467
0.468
0.469

SIi
−0.005
0.004
0.011
0.005
0.015
0.023

c
1.981
1.818
1.68
2.026
1.862
1.722

n
1.471
1.464
1.459
0.574
0.576
0.578

g
0.014
0.017
0.021
0.059
0.069
0.079

Base parameters values are α = 0.95, γ = 0.19, ρ = 0.02, ψ = 0.25, b = 0.75, ϕ = 0.15, and Z = 1.
In the upper half of the table, σ = 2.203 and λ = 0.001, and in the lower half σ = 3.5 and λ = 0.0125.

greater net offshoring flows in innovation from the asset-wealthy country to the asset-poor
country. Therefore, turning to improvements in economic integration, a fall in trade costs
lowers net offshoring flows out of the asset-wealthy country and raises innovation costs,
while a rise in the degree of knowledge diffusion increases net offshoring flows out of theasset-wealthy country and lowers innovation costs. As such, economic integration generates a positive relationship between net innovation offshoring flows out of the asset-wealthy
country and long-run productivity growth when ν > ψ and when ν < ψ with c < c, following from Proposition 5. Table 1 provides numerical examples for the effects of improved
knowledge diffusion on net offshoring flows in manufacturing (SX ) and innovation (SI ), thelevel of market entry (n), and the rate of productivity growth (g). The examples suggestthat improved knowledge diffusion may be a key factor in the recent pattern of innovation
offshoring from advanced to emerging economies, and that this pattern may have a positive
influence on long-run productivity growth.

4Concluding Remarks

This paper has introduced a two-country model of trade to examine the relationship between
net offshoring patterns in innovation and manufacturing and fully endogenous productivity
growth. Central to the model, monopolistically competitive firms invest in process innovation that lowers production costs and drives aggregate productivity growth. The occupational choice of skill-differentiated workers into low-skilled employment in production30

and high-skilled employment in innovation determines national labor allocations, while thefree movement of investment allows firms to shift their production and innovation activities
freely and separately between countries. These two mechanisms create a tension between
accessing the technical knowledge contained in production processes and sourcing low-costhigh-skilled labor as firms independently select the optimal locations for production andinnovation. A key feature of the model is a positive relationship between the unit cost ofprocess innovation and the geographic concentration of industry and innovation as the benefit of greater knowledge spillovers is offset by the cost of rising high-skilled wages.
We characterize location patterns according to the level of trade costs. Specifically, whilehigh trade costs lead to a larger market and the concentration of production and innovation in
the asset-wealthy country, when trade costs are low production and innovation concentrate
in proximity to the larger market of the asset-poor country. Given these location patterns,
we use the level of trade costs to identify three cases for the directions of net offshoring
in innovation and manufacturing. For high trade costs, although the asset-wealthy country
has greater shares industry and innovation, the domestic market is not sufficiently large toattract the production and innovation activities of all firms with domestic owners, and net
offshoring thus flows towards the asset-poor country. For intermediate trade costs, however,net offshoring flows from the asset-poor country towards the larger market of the assetwealthy country. Finally, for low trade costs, net offshoring flows towards the asset-poor
country as it maintains greater concentrations of industry and innovation.
Focusing on the case for which the asset-wealthy country has greater shares of industry
and innovation activity, we investigate the effects of an improvement in knowledge diffusion between countries, and find that net offshoring flows in innovation and manufacturingfrom the asset-wealthy country to the asset-poor country increase as firms offshore innovation to the asset-poor country to take advantage of lower wages for high-skilled workers.
The resulting increased dispersion of industry and innovation activity away from the assetwealthy country results in a lower unit cost for process innovation and therefore potentially31

accelerates productivity growth.

Appendix A: Saddle-Path Stability
This appendix derives the necessary conditions for the saddle-path stability of long-run equilibrium. For this purpose, we reduce the dynamic system to two differential equations in wi
and n, and use the fact that common motions for high-skilled wages (ẇi /wi = ẇj /wj )ensure a constant international high-skilled wage differential: wj /wi = ki /kj ≡ κ.
First, combining (6) and (21) with B = αEc, Ḃ = rB + I − E, and Ė = (r − ρ)Eyields the following differential equation for high-skilled wages:(n − nI )ψI
ẇi
=
,
wi
cL

nI =

(1 − αρc)L
µ
−
,
αψI
αψ

(A1)

where nI is the steady-state level of market entry consistent with optimal investment inprocess innovation.
Next, substituting (15), (18), and (21) into (19) leads to the following differential equation for the level of market entry:ṅψ − (ρ + λ)cẇi (µ + αψn)ν − (ρ + λ)c= (nN − n)
+ 2(1 − n),n=
, (A2)Nnc
wi (µ + αψn2 )ψ − (ρ + λ)cwhere nN is the steady-state level of market entry consistent with optimal investment inproduct development. Setting nI = nN gives the steady-state investment locus (24).
We evaluate the local dynamics around the steady-state described by (24) and (25) using
a Taylor expansion of (A1) and (A2) with wj = κwi . The determinant of the Jacobianmatrix (J1 ) for the linearized system is(ψ − (ρ + λ)c)(µ + αψn)ψnwi I ∂Φ
|J1 | = −(µ + αψn2 )c2 L
∂wj




wj
dwj
.
−
wj
dwi Φ=0As the high-skilled wage rate (wi ) is a control variable and the level of market entry (n) is a32state variable, we require one positive and one negative eigenvalue for saddle-path stability.
Accordingly, we consider long-run equilibria that satisfy |J1 | < 0. In Appendix C, we showthat ∂Φ/∂wj > 0 and dwj /dwi |Φ=0 < 0. Thus, ψ > (ρ + λ)c is a sufficient condition forsaddle-path stability as outlined in Lemma 1.

Appendix B: Derivation of the Share Locus
First, we use Ė = (r − ρ)E, Ḃi = rBi + Ii − Ei and Ḃ = rB + I − E to obtain
Ei = Ii − bi (I − E). Then, substituting Ei into (10) and equating with (16) we have(bi − ϕbj )1−ϕ(µ + αψn)I(Ii − ϕIj )(µ + αψn)wi − δwj
1−+=,L(1 − ϕ)L(1 − δ)(wi + wj )(B1)

where we have assumed common growth rates for asset wealth (Ḃi /Bi = Ḃj /Bj ), ensuringthat ḃi = 0 at all moments in time. Substituting nL from (A1) into (B1) yields the steadystate share locus (25).

Appendix C: Proposition 1
Using L = (wi + wj )Z/(wi wj ) and I = (wi + wj )(1 + wi wj )Z/(2wi wj ), the investment
locus (24) and the share locus (25) are rewritten asν − (ρ + λ)c2(1 − αρc)
µ
−
+
= 0,
ψ − (ρ + λ)c αψ(1 + wi wj ) αψ
1 − δϕ + (δ − ϕ)wi wj + (1 − δ)(1 + ϕ)(bi wi wj − bj )αρc
wi
−
= 0.
Ω=
wj
1 − δϕ + (δ − ϕ)wi wj + (1 − δ)(1 + ϕ)(bj wi wj − bi )αρc
Φ=

33

(C1)
(C2)

The slopes of (24) and (25) are then (dwj /dwi )|Φ = −(∂Φ/∂wj )/(∂Φ/∂wi ) < 0 and(dwj /dwi )|Ω = −(∂Ω/∂wi )/(∂Ω/∂wj ), where∂Φ(ν − ψ)(ρ + λ)2(1 − αρc)wj
2ρ
=
+
+
> 0,
∂wi
(1 + δ)(ψ − (ρ + λ)c)2 αψ(1 + wi wj )2 (1 + δ)ψ(1 + wi wj )(ν − ψ)(ρ + λ)2(1 − αρc)wi
2ρ
∂Φ
=
+
+
> 0,
2
2
∂wj
(1 + δ)(ψ − (ρ + λ)c)αψ(1 + wi wj )(1 + δ)ψ(1 + wi wj )∂Ω
1(1 − δφ + (δ − ϕ)wi wj )(1 + wi wj ) + (1 − δ 2 )(1 + ϕ)(1 − αρc)wj c
=
−
,
∂wi
wj
αρ(1 − δ 2 )(1 + ϕ)(bi − bj )(1 + wi wj )2 wj2(wi − wj )−2 c2∂Ω(1 − δφ + (δ − ϕ)wi wj )(1 + wi wj ) + (1 − δ 2 )(1 + ϕ)(1 − αρc)wi c
wi=− 2 −,∂wj
wj
αρ(1 − δ 2 )(1 + ϕ)(bi − bj )(1 + wi wj )2 wj2(wi − wj )−2 c2
and we have used the share locus: (wi − wj )/wj = αρ(1 − δ)(1 + ϕ)(bi − bj )(1 +wi wj )c/ (1 − δϕ + (δ − ϕ)wi wj + αρ(1 − δ)(1 + ϕ)(bj wiwj − bi )c). Because 1 > αρc,
we have ∂Φ/∂wi > 0 and ∂Φ/∂wj > 0 for ν > ψ. Furthermore, since ∂ 2 Φ/(∂wi ∂ψ) < 0,
∂ 2 Φ/(∂wj ∂ψ) < 0, and limψ→∞ ∂Φ/∂wi = limψ→∞ ∂Φ/∂wj = 0, we have ∂Φ/∂wi > 0
and ∂Φ/∂wj > 0 for all values of ψ. The investment locus (24) thus has a negative slope.
The slope of the share locus (25) may be positive or negative. We limit the analysis tocases for which the share locus cuts the investment locus once from below to ensure theuniqueness of equilibrium.
We now derive the threshold value ϕB . Using (C1) and (C2), we obtaindwi
1 ∂Φ ∂Ω=,
dbi|J2 | ∂wj ∂bi

dwj
1 ∂Φ ∂Ω=−,
dbi|J2 | ∂wi ∂biwhere |J2 | = (∂Ω/∂wj )(∂Φ/∂wj )((dwj /dwi )|Ω=0 − (dwj /dwi )|Φ=0 ) < 0 under the assumption of uniqueness for long-run equilibrium, and(1 − δ)(1 + ϕ)(wi + wj )(1 + wi wj )αρc
∂Ω
=−
.
∂bi
(1 − δϕ + (δ − ϕ)wi wj + (1 − δ)(1 + ϕ)(bj wi wj − bi )αρc)wj
Setting the denominator of this partial derivative to zero and solving for ϕB , we have∂Ω/∂bi < 0, dwi /dbi > 0, and dwj /dbi < 0 when ϕ < ϕB , but ∂Ω/∂bi > 0, dwi /dbi < 0,34and dwj /dbi > 0 when ϕ > ϕB . From (16) we have ∂sXi /∂wi > 0 and ∂sXi /∂wj < 0,and from (23) we have ∂sIi /∂wi > 0 and ∂sIi /∂wj < 0. Thus, wi > wj , sXi > 1/2, andsIi > 1/2 for ϕ < ϕB , and wi < wj , sXi < 1/2, and sIi < 1/2 for ϕ > ϕB .
Next, we derive the threshold values ϕXi , ϕIi , ϕXj , and ϕIj . From (C1) and (C2),1 ∂Φ ∂Ω
dwi
=
> 0,
dϕ
|J2 | ∂wj ∂ϕdwj
1 ∂Φ ∂Ω=−< 0,dϕ|J2 | ∂wi ∂ϕ(C3)

where ∂Ω/∂ϕ = −(1 + δ)(wi − wj)2/((1 − δ)(1 + ϕ)2 (bi − bj )wj2 αρc) < 0. Therefore,
dsXi /dϕ > 0 and dsIi /dϕ > 0 ensure the existence of the following threshold values:
ϕXi ∈ (0, ϕB ) for sXi = 1, ϕIi ∈ (0, ϕB ) for sIi = 1, ϕXj ∈ (ϕB , 1) for sXi = 0, andϕIj ∈ (ϕB , 1) for sIi = 0.
The effects of changes in the degree of knowledge diffusion for large values of δ are
obtained from (C1) and (C2) as follows:
2(1 − αρc)wi ∂Ω
1
∂Ω ∂Φ
1 ∂Ω
dwi
< 0,
=
−
+
dδ
|J2 | αψ(1 + wiwj )2 ∂δc ∂δ∂ωj ∂δ
2(1 − αρc)wi ∂Ω
1
∂Ω ∂Φ
dwj
1 ∂Ω
> 0,
=−
−
+
dδ
|J2 | αψ(1 + wiwj )2 ∂δc ∂δ∂ωi ∂δ
where∂Φ(ν − ψ)(ρ + λ)c
2ρc
=−
−
< 0,
2
∂δ
(1 + δ)(ψ − (ρ + λ)c)
(1 + δ)ψ(1 + wi wj )∂Ω2(1 − δϕ + (δ − ϕ)wi wj ) + (1 − δ 2 )(wi wj − ϕ)
=
> 0,
∂δ
αρ(1 − δ)2 (1 + δ)(1 + ϕ)(bi − bj )(1 + wi wj )wj2 (wi − wj )−2 c
1 ∂Ω∂Ω(1 − ϕ)(wi − wj )2(1 − αρc)(wi − wj )2
1
+
=
−
+ ,
2
2
2
2
c ∂δ
∂ωi
(1 − δ) (1 + ϕ)(bi − bj )wj αρc(bi − bj )(1 + wi wj ) wj αρc wj(1 − ϕ)(wi − wj )2∂Ω(1 − αρc)wi (wi − wj )2
wi
1 ∂Ω
=
+
−
− 2,
2
2
2
2
2
c ∂δ
∂ωi
(1 − δ) (1 + ϕ)(bi − bj )wj αρc(bi − bj )(1 + wi wj ) wj αρc wj
and 2(1 − δϕ + (δ − ϕ)wi wj ) + (1 − δ 2 )(wi wj − ϕ) > 0 for all δ, ϕ ∈ (0, 1). Focusing
on the horizontal axis in Figure 1, since dwi /dδ|Φ=0;wj =1 = −(∂Φ/∂δ)/(∂Φ/∂wi ) > 0, arise in δ shifts the investment locus to the right, while the wj /wi = δ dashed line shifts to35

the left. Thus, we can define the threshold value δ = δ at which ϕXi = ϕIi , and we have
ϕXi > ϕIi for δ < δ and ϕXi ≤ ϕIi for δ ≥ δ. Similarly, given the symmetric natureof the investment locus, we have ϕXj < ϕIj for δ < δ and ϕXj ≥ ϕIj for δ ≥ δ. This
completes the derivation of the thresholds values shown in Figure 2. Finally, for sufficiently
large values of δ, dwi /dδ < 0 and dwj /dδ > 0 imply dsXi /dδ < 0 and dsIi /dδ < 0.
Appendix D: Propositions 2 and 3
First, from (26) and E = I/(1 − αρc) we havedSX
dsXi
α(bi − sXi )
=−
αE +
dϕ
dϕ
(1 − αρc)



dI
dc
+ αρE
dϕ
dϕ



,

where the first term on the righthand side is negative, while the second term is positive for
ϕ < ϕB and negative for ϕ > ϕB . Since dSX /dϕ < 0 at bi − sXi = 0, however, the SX
curve has a single point and a negative slope at SX = 0. Thus, we derive the threshold value
ϕXO ∈ (0, ϕB ), for which SX = 0. As wj /wi < 1 for ϕ < ϕB , evaluating (C2) at ϕ = 0
yields1>

1 + δwi wj + (1 − δ)(bj wi wj − bi )αρc
wj
bj + δbi=> δ,>
wi Ω=0; ϕ=0 1 + δwi wj + (1 − δ)(bi wi wj − bj )αρcbi + δbj

for bi > bj . We have SX ≥ 0 for wj /wi ≥ (bj + δbi )/(bi + δbj ), and SX ≡ −(1 − bi )αE < 0
for wj /wi = δ. Thus, since d(wj /wi )/dϕ < 0 from (C3), there exists a threshold value
ϕXO ∈ (0, ϕB ), with SX < 0 for ϕ ∈ (ϕXO , ϕB ) and SX > 0 for ϕ 6∈ (ϕXO , ϕB ).
Second, from (27) we havedSI
Ij dwjIi dwi
= bi
− bj
< 0.
dϕ
wj dϕ
wi dϕ
We derive the threshold value ϕIO ∈ (0, ϕB ), for which SI = 0. From (27), we have SI = 0
when bi /bj = wi Hi /(wj Hj ), which requires wj /wi < 1 for bi > bj . This condition has

36

a positive slope, dwj /dwi = wj 2 (1 + wi )bj /(wi (1 + wj 2 )bi ) > 0, and thus intersects theinvestment locus once in (wi , wj ) space at ϕIO ∈ (0, ϕB ). Then, because d(wj /wi )/dϕ < 0from (C3), we have SI < 0 for ϕ ∈ (ϕIO , ϕB ) and SI > 0 for ϕ 6∈ (ϕIO , ϕB ).
Third, because dwi /dδ < 0 and dwj /dδ > 0 for large values of δ, sufficient increases inδ shift the SX and SI curves upwards in Figure 3, as dsXi /dδ < 0 and dsIi /dδ < 0.
Appendix E: Propositions 4 and 5First, the effects of changes in regional unit innovation costs on market entry and productivity growth are(ν − ψ)(ρ + λ)
dn
=
,
dc
(ψ − (ρ + λ)c)2

dg
g+ρ+λ
(g + ρ + λ)(ρ + λ)(ν − ψ)
=−
−
,
dc
c
(v − (ρ + λ)c)(ψ − (ρ + λ)c)with d2 g/dc2 = (2(g+ρ+λ)/c)(1/c+(ν −ψ)ψ(ρ+λ)/((ν −(ρ+λ)c)(ψ−(ρ+λ)c)2 )) > 0.
Thus, as outlined in Lemma 2, we have dn/dc > 0 when ν > ψ, and dn/dc < 0 when
ν < ψ. And, as summarized in Lemma 3, we have dg/dc < 0 when ν > ψ, but dg/dc > 0pfor c < c and dg/dc ≤ 0 for c ≥ c when ν < ψ, where c = (ψ − (ψ − ν)ψ)/(ρ + λ).

Lastly, the following are used with |J2 | < 0 to obtain Propositions 4 and 5:

dc
2(1 − αρc)(wi − wj )3
=− 2
,
dϕ
α ψρc(1 − δ)(1 + ϕ)2 (bi − bj )(1 + wi wj )2 wj2 |J2 |
 


dc
∂Ω
∂Ω
2(1 − αρc)∂Ωc wi
+ (wi − wj )
,
=
− wj
dδ
αψ(1 + δ)(1 + wi wj )2 |J2 |
∂wi
∂wi
∂δ
where wi ∂Ω/∂wi −wj ∂Ω/∂wi = 2wi /wj +(1−αρc)(wi −wj )3 /((bi −bj )(1+wi wj )2 wj2 αρc)and |J2 | < 0. Hence, for ϕ < ϕB we have dc/dϕ > 0 and dc/dδ < 0, and for ϕ > ϕB wehave dc/dϕ < 0 and dc/dδ ≶ 0. Combining these results yields Propositions 4 and 5.

References[1] Aghion, P., Howitt, P. (1998). Endogenous Growth Theory. Cambridge: MIT Press.

37[2] Ang, J., Madsen, J. (2013). International R&D spillovers and productivity trends in
the Asian miracle economies. Economic Inquiry 51, 1523-1541.
[3] Arkolakis, C., Ramondo, N., Rodriguez-Clare, A., Yeaple, S. (2018). Innovation andproduction in the global economy. American Economic Review 108, 2128-2173.
[4] Baldwin, R. (1999). Agglomeration and endogenous capital. European Economic
Review 43, 253-280.
[5] Baldwin, R., Forslid R. (2000). The core-periphery model and endogenous growth:
Stabilizing and destabilizing integration. Economica 67, 307-324.
[6] Baldwin, R., Martin, P., Ottaviano G. (2001). Global income divergence, trade, andindustrialization: The geography of growth take-offs. Journal of Economic Growth 6,
5-37.
[7] Barro, R., Sala-i-Martin, X. (2004). Economic Growth. Cambridge: MIT Press.
[8] BEA (2018). International services accounts: Research and development services,
Bureau of Economic Analysis, http://www.bea.gov.
[9] Bertrand, O., Mol, M. (2013). The antecedents and innovation effects of domestic
and offshore R&D outsourcing: The contingent impact of cognitive distance andabsorptive capacity. Strategic Management Journal 34, 751-760.
[10] Bosker, M. (2007). Growth, agglomeration and convergence: A space-time analysis
for European regions. Spatial Economic Analysis 2, 91-100.
[11] Bottazzi, L., Peri, G. (2007). The international dynamics of R&D and innovation in
the long run and in the short run. The Economic Journal 117, 486-511.
[12] Burstein, A., Monge-Naranjo, A. (2009). Foreign know-how, firm control, and theincome of developing countries. Quarterly Journal of Economics 124, 149-195.
[13] Castellani, D., Pieri, F. (2013). R&D offshoring and the productivity growth ofEuropean regions. Research Policy 42, 1581-1594.
[14] Chung, W., Yeaple, S. (2008). International knowledge sourcing: Evidence from U.S.
firms expanding abroad. Strategic Management Journal 29, 1207-1224.
[15] Coe, D., Helpman, E., Hoffmaister, A. (2009). International R&D spillovers andinstitutions. European Economic Review 53, 723-741.
[16] D’Agostino, L., Laursen, K., Santangelo, G. (2013). The impact of R&D offshoringon the home knowledge production of OECD investing regions. Journal of Economic
Geography 13, 145-175.
[17] Davis, C. (2013). Regional integration and innovation offshoring with occupational
choice and endogenous growth. Journal of Economics 180, 59-79.
[18] Davis, C., Hashimoto, K. (2015). Industry concentration, knowledge diffusion andeconomic growth without scale effects. Economica 82, 769-789.
[19] Demirbag, M., Glaister, K. (2010). Factors determining offshore location choice for
R&D projects: A comparative study of developed and emerging regions. Journal ofManagement Studies 47, 1534-1560.
38

[20] Dinopoulos E., Thompson, P. (1999). Scale effects in Schumpeterian models of
economic growth. Journal of Evolutionary Economics 9, 157-185.
[21] Dixit, A., Stiglitz, J. E. (1977). Monopolistic competition and optimum productdiversity. American Economic Review 67, 297-308.
[22] Ekholm, K., Hakkala, K. (2007). Location of R&D and high-tech production byvertically integrated multinationals. The Economic Journal 117, 512-543.
[23] Etro, F. (2004). Innovation by Leaders. The Economic Journal 114, 281-303.
[24] Etro, F. (2009). Endogenous Market Structures and the Macroeconomy. Berlin:
Springer.
[25] Gao, T. (2005). Foreign direct investment and growth under economic integration.
Journal of International Economics 67, 157-174.
[26] Gao, T. (2007). Trade costs, international production shifting, and growth. European
Economic Review 51, 317-335.
[27] Gardiner, B., Martin, R., Tyler, P. (2011). Does spatial agglomeration increase national
growth? Some evidence from Europe. Journal of Economic Geography 11, 979-1006.
[28] Grossman, G., Helpman, E. (1991). Innovation and Growth in the Global Economy.
Cambridge: MIT Press.
[29] Gumpert, A., Moxnes, A., Ramondo, N. Tintelnot, F. (2017). The life-cycle dynamics
of exporters and multinational firms. National Bureau of Economic Research, Working
Paper 24013.
[30] Hausmann, R., Hwang, J., Rodrik, D. (2007). What you export matters. Journal of
Economic Growth 12, 1-25.
[31] Keller, W. (2004). International technology diffusion. Journal of Economic Literature
42, 752-782.
[32] Krugman, P. (1980). Scale economies, product differentiation, and the pattern of trade.
American Economic Review 70, 950-959.
[33] Laincz C., Peretto, P. (2006). Scale effects in endogenous growth theory: An error of
aggregation not specification. Journal of Economic Growth 11, 263-288.
[34] Lewin, A., Massini, S., Peeters, C. (2009). Why are companies offshoring innovation?
The emerging global race for talent. Journal of International Business Studies 40,
901-925.
[35] Mancusi, M. (2008). International spillovers and absorptive capacity: A cross-region
cross-sector analysis based on patents and citations. Journal of International Economics 76, 155-165.
[36] Manning, S., Massini, S., Lewin, A. (2008). A dynamic perspective on next-generation
offshoring: The global sourcing of science and engineering talent. Academy of Management Perspectives 22, 35-54.
[37] Martin, P., Ottaviano, G. (1999). Growing locations: Industry location in a model ofendogenous growth. European Economic Review 43, 281-302.
39

[38] Martin, P., Ottaviano, G. (2001). Growth and agglomeration. International Economic
Review 42, 947-968.
[39] McGrattan, E., Prescott, E. (2009). Openness, technology capital, and development.
Journal of Economic Theory 144, 2454-2476.
[40] Naghavi, A., Ottaviano, G. (2009a). Offshoring and product innovation. Economic
Theory 38, 517-532.
[41] Naghavi, A., Ottaviano, G. (2009b). Firm heterogeneity, contract enforcement, and theindustry dynamics of offshoring. Scandinavian Journal of Economics 111, 629-653.
[42] Nieto, M., Rodrı́guez, A. (2011). Offshoring of R&D: Looking abroad to improve
innovation performance. Journal of International Business Studies 42, 345-361.
[43] NSF (2016). Science and engineering indicators 2016. National Science Foundation,
National Center for Science and Engineering Statistics.
[44] Peretto, P. (1996). Sunk costs, market structure, and growth. International Economic
Review 37, 895-923.
[45] Peretto, P., Connolly, M. (2007). The manhattan metaphor. Journal of Economic
Growth 12, 329-350.
[46] Peretto, P., Valente, S. (2015). Growth on a finite planet: Resources, technology andpopulation in the long run. Journal of Economic Growth 20, 305-331.
[47] Piguillem, F., Rubini, L. (2019). Barriers to firm growth in open economies. The B.E.
Journal of Macroeconomics 19. 1-36.
[48] Puga, D., Trefler, D. (2010). Wake up and smell the ginseng: International trade andthe rise of incremental innovation in low-wage countries. Journal of Development
Economics 91, 64-76.
[49] Ramondo, N., (2009). Foreign plants and industry productivity: Evidence from Chile.
Scandinavian Journal of Economics 111, 789-809.
[50] Ramondo, N., Rodriguez-Clair, A. (2013). Trade, multinational production, and thegains from openness. Journal of Political Economy 121, 273-322.
[51] Rodrı́guez, A., Nieto, M. (2016). Does R&D offshoring lead to SME growth? Different governance modes and the mediating role of innovation. Strategic Management
Journal 37, 1734-1753.
[52] Rubini, L. (2014). Innovation and trade elasticity. Journal of Monetary Economics 66,
32-46.
[53] Santos-Paulino, A., Squicciarini, M., Fan, P. (2014). Foreign direct investment, R&D
mobility and the new economic geography: A survey. World Economy 37, 1692-1715.
[54] Smulders, S., van de Klundert, T. (1995). Imperfect competition, concentration, andgrowth with firm-specific R&D. European Economic Review 39, 139-160.
[55] Tintelnot, F. (2017). Global production with export platforms. Quarterly Journal of
Economics 132, 157-209.
[56] UNCTAD (2005). World Investment Report: Transnational Corporations and theInternationalization of R&D. New York and Geneva: United Nations.
40