Trade in Knowledge Services and Innovation
Bastian Krieger, Fabian Trottner
November 2023

We investigate how the ongoing globalization of services impacts firm innovation and aggregate welfare. Using firm-level data from Germany, we show that access to knowledge
service imports, such as R&D, leads to more succesful product and process innovation.
To confront this evidence, we develop a theory of innovation offshoring that conceptualizes services trade in terms of tasks. To reason about the aggregate welfare implicationsof services trade, we embed this theory into a model of multi-product firms with endogenous innovation, variable markups and free entry. Our model yields an analytic
decomposition of the welfare gains from services trade into an allocative and technicalefficiency effect, as well as into the contribution of product and process innovation. We
inform the key elasticities highlighted by our theory using our reduced-form estimatesand offer a quantitative exploration of our theoretical results.

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1.

Introduction

The ongoing globalization of services is shifting the international landscape of innovation and knowledge creation. Technological and regulatory advancements opportunities
for research and development world global 10 percent p.a., (WTO 2019) and now accountfor a sizeable share of 18 percent of total services imports in the U.S. and 13 percent inGermany in 2020.1 An now leverage services trade as a way to access foreign expertiseand know-how,In this paper, we investigate the impact of services trade for innovation both empirically and theoretically. Empirically, we show that services trade fosters innovationby providing firms with the opportunity to procure foreign knowledge and ideas touse as inputs into their innovation process. Theoretically, we propose a new theoryof innovation offshoring that rationalizes these empirical findings and outlines a newsource for the welfare gains from trade based on
Our empirical analysis brings to bear firm-level information on services imports andinnovation from Germany, which we obtain by merging the Statistics on International
Trade in Services (SITS) with the Mannheim Innovation Panel (MIP). We define knowledge services as payments made by firms related to research, development, and testing;patents, licenses, inventions, and processes; artistic copyrights; and other rights, suchas franchise fees or trademarks. Additionally, our data provide comprehensive information on firms’ innovation activities, encompassing product and process innovation, as
well as innovation input like R&D expenditures.
To estimate the causal effect of knowledge imports on innovation, we construct firmspecific export supply shocks, serving as a quasi-experimental shift-share design (Bartik
1991; Goldsmith-Pinkham et al. 2020; Borusyak et al. 2021). Our shocks leverage variationin i) countries’ aggregate knowledge service exports to Germany and ii) firms’ preestimation expenditures on knowledge service imports from different source countries.
For identification, we assume that our shift-share design combines plausibly exogenous
export supply shocks common to all firms with a potentially endogenous measure offirm-level shock exposure Borusyak et al. 2021.2
Our empirical results provide initial evidence that access to knowledge imports
1 Cross-border transactions related to R&D services are included in two categories: R&D activities, andlicenses for the use of outcomes of R&D (WTO 2019). R&D services import shares are calculated from theWTO Stats dashboard by dividing the sum of services imports related to “research and development” and“charges for the use of intellectual property” by a country’s total commercial service imports.
2 Following Borusyak et al. (2021), we show that the statistical properties of our knowledge service
export supply shocks corroborate the plausibility of these assumptions.

1fosters firm innovation. According to our estimates, services results in a 0.4 to 1.8
percentage point increase in its likelihood of introducing new or improved products orprocesses. These findings are consistent across various innovation outcomes, providing
initial evidence that access to knowledge service imports raises a firm’s returns to
product and process innovation. Our findings also indicate that imports of knowledge
services are associated with increased firm expenditures on domestic R&D. Further, wefind no evidence that rising opportunities for importing other types of services have apositive impact on firm innovation.
To rationalize these empirical findings and evaluate their aggregate implications,
we then develop a theory of innovation offshoring focused on tradable tasks. In themodel, profit-seeking firms produce multiple products under conditions of monopolisticcompetition with variable markups and free entry. Producers have the option to enhancetheir capacity to introduce new products or processes by investing in knowledge, which
involves performing various tasks designed to resolve requisite problems for innovation.
Each of these tasks can potentially be outsourced or offshored, provided that a firm
can locate an external partners capable of resolving a specific problem. Outsourcing
may be attractive, if external partners have a higher productivity or scale efficiency
for performing a task, but is also subject to search and - in the case of offshoring trade costs. In this environment, firms become more likely to outsource innovation
activities domestically or abroad as they become more innovative, where the prevalenceof offshoring depends on the associated trade costs.
We use the model to characterize the equilibrium response of a decline in services
trade costs for innovation and welfare terms of microeconomic statistics. Aggregate
shocks to service trade costs have unequal direct and indirect effects on importers
and non-importers of knowledge services, shifting the profile of product and process
innovation and, ultimately, employment across firms. We trace the associated welfare
implications, show how these can be summarized by a few aggregate statistics, anddecompose the change in welfare into various channels, isolating the role of process
and product innovation.
We then quantify our theoretical results, using our firm-level estimates to recover
the model’s key structural elasticities, such as pass-through rates of shocks to the costs
of innovation into product variety. Quantitatively, the model-implied welfare gains fromknowledge services trade are sizeable, suggesting that a one percent decline in trade
costs would lead to an increase of welfare of 0.06 percent. The bulk of the welfare gains
is due to the entry of new firms and the introduction of new products by existing firms,

2which respectively account for about 60 and 30 percent of the overall gains. In contrast,
falling prices for varieties available prior to the fall in trade costs contribute less than
10 percent to the overall welfare gain. Given that barriers to services trade remain
substantial, our results highlight that trade liberalizations in services may be crucial to
fully realizing the gains from globalization.
Related Literature. This paper is the first to systematically analyze the causal effectsof trade in services on firm innovation. We contribute to three strands of literatureaddressing the connections between international trade and innovation.
Trade and Innovation. Our work relates to a vast body of research studying the effects
of international trade on innovation (see Shu & Steinwender (2019), Melitz & Redding(2021), and Akcigit & Melitz (2022)). Empirically, much of this work provides evidence on
the connection between innovation and exporting (Lileeva & Trefler 2010; Aw et al. 2011;
Bustos 2011; Lim et al. 2022) or import competition (Bloom et al. 2015; Bombardini et al.
2017; Fieler & Harrison 2018; Fieler et al. 2018; Autor et al. 2020; Chen & Steinwender2021). empirical work examining how intermediate good imports affect productivity
and innovation, e.g., Goldberg et al. (2010), Topalova & Khandelwal (2011), Halpern
et al. (2015), Ariu et al. (2019), and Eppinger (2019). Our work is the first to document a
causal relationship between a rapidly growing subset of service types and firm-level
innovation outcomes.
Theoretically, we contribute to the literature studying the static gains from tradein models with product differentiation and imperfect competition described in, e.g.,
Krugman (1979), Helpman & Krugman (1987), Melitz (2003), Arkolakis et al. (2012),
and Arkolakis et al. (2019). Like other static models of endogenous innovation andcompetition (Dhingra 2013,Aghion et al. 2022) our work highlights the importance ofendogenous competition and entry for the welfare effects of trade.3
Trade in Services. Our paper adds to the growing literature on services trade (Francois& Hoekman 2010, Benz et al. 2020). One stream of research investigates the determinantsof services trade flows (Mattoo & Sauve 2007; Lipsey 2009; Breinlich & Criscuolo 2011;
Jensen 2011; Borchert et al. 2013; Miroudot et al. 2013; Ariu 2016, Christen et al. 2019;
Eaton & Kortum 2019), while another studies the effects of service trade on various
economic outcomes (Jensen 2011; Arnold et al. 2011; Ariu 2016; Lejarraga & Oberhofer
3 Our theory abstracts from dynamic gains from innovation in growth models, analyzed, e.g., by Romer(1990), Grossman & Helpman (1991), Aghion & Howitt (1992), Ventura (1997), Eaton & Kortum (1999),
Costantini & Melitz (2007), Atkeson & Burstein (2011), Sampson (2016), Buera & Oberfield (2020), Perlaet al. (2021), Impullitti et al. (2022), Akcigit et al. (2021).

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2015; Eppinger 2019; Hebous & Johannesen 2021; Bamieh et al. 2022). While the potential
importance of services trade as a catalyst of international knowledge transfers has been
discussed in previous literature, e.g., Francois & Hoekman (2010) and Ariu et al. (2019),
our paper is the first to provide direct evidence on this channel.
External Knowledge Management. Finally, we contribute to the literature studying thestrategic management of external knowledge (Cassiman & Veugelers 2006; Grimpe &Kaiser 2010; Hagedoorn & Wang 2012), and, in particular, innovation offshoring (Rosenbusch et al. 2019; Tojeiro-Rivero et al. 2019; Zhong et al. 2022). Innovation offshoring,the management practice of sourcing innovation inputs abroad, includes both internal offshoring to foreign subsidiaries and external offshoring to trade partners.4 Our
work contributes by exploiting trade in knowledge-related services to obtain systematic
insights into the effects of innovation offshoring through external partners.

2.
2.1.

Data, variable construction, and descriptive statistics

Data Sources

We merge data on firms’ innovation activities from the Mannheim Innovation Panel(MIP, Peters & Rammer 2013) with administrative data on exports and imports of services
by firms from the Statistics on International Trade in Services database (SITS, Biewen& Meinusch 2021). The merging took place at the Research and Data Service Centre of
the Bundesbank, the German central bank.
The MIP is an annual survey of a representative sample of manufacturing and service
sector firms conducted by the ZEW - Leibniz Centre for European Economic Research- as part of the European Community Innovation Surveys. The data provide detailed
firm-level information on the introduction of new or improved products, services, andprocesses, the degree of success achieved through product or process innovations, andexpenditures on innovation. Moreover, the data contain information on general firm
characteristics, such as size, age, industry, region, company group membership, andperformance (e.g., revenues, export sales, profitability).
The SITS database is collected and administered by the Deutsche Bundesbank tocompile Germany’s balance of payments statistics. The data contain the universe ofservice trade between German residents - firms, individuals, and government agencies
4 In meta-analysis of a large set of quantitative studies, Rosenbusch et al. (2019) document a positive

relationship between innovation offshoring and innovation performance, suggesting there is no statisticaldifference between the innovation impact of offshoring via subsidiaries and via external partners.

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- and non-residents for all transactions exceeding a total monthly value of €12,500. In
terms of coverage, we observe unit-level transaction values of services exports andimports by country and service type at a monthly frequency for the years 2001 to 2012.
The classification of service types follows the Balance of Payments Manuel, and covers
over 130 categories.5 Trade flows in our data cover the following three modes of service
trade defined in the WTO’s General Agreement on Trade in Services (GATS):a. Mode 1: Cross-Border trade - A service is provided from a member of country A to amember of country B across borders.
b. Mode 2: Consumption Abroad - A service is provided from a member of country A
to a member of country B (or its property) within country A.
c. Mode 4: Presence of Natural Persons - A natural person from country A provides aservice to a member of country B within country B.
2.2.

Variable Construction

2.2.1.

Firm Innovation

Th MIP data provide numerous measures of firm innovativeness. We use two yearly survey questions define our broadest measure of innovation: i) a question asking whether
firms introduced product innovations, defined as new or significantly improved products or services, within the last three years, and ii) a question asking whether a firm
introduced process innovations, defined as new or significantly improved cost-reducing
internal processes, during the last three years. Our broadest measure of innovation
success takes the form of a dummy variable equal to one if a firm answered yes to atleast one of the two questions and zero otherwise. To distinguish product from process
innovations, we construct two analogous indicators using, respectively, only one of thetwo question.
Capturing product innovation, we extract information on i) yearly revenue shares
attributable to new or significantly improved products or services and ii) yearly revenues from new or significantly improved products or services. Regarding process
innovation, we extract information on i) the percentage point reduction in yearly unit
costs attributable to new or improved processes and ii) the value of total yearly costsavings due to process innovations.6
5 See Biewen & Meinusch (2021) for a detailed overview of the service types covered in the data.
6 Revenue shares, total revenues, average cost reductions, and total cost reductions refer to the current

year. The total yearly revenues with new or significantly improved products or services are calculated bymultiplying firms’ revenue shares with new or significantly improved products or services with their total

5Regarding innovation inputs, we extract information from the MIP data on firms’
yearly R&D expenditures.
2.2.2.

Knowledge Services

Towe classify four types of services as potential knowledge catalysts. Using the mostdisaggregated classification in the 5th Balance of Payments Manuel, our definitionof “knowledge services” comprises transactions related to (i) research, development,
and testing (BPM5 code 511), (ii) patents, licenses, inventions, and processes (502), (iii)
artistic copyrights (501), and (iv) other rights, such as franchise fees, trademarks, andmarketing rights (503). All these service categories are commonly subject of policy
debates around the regulation of international knowledge and intellectual property
dissemination (WTO 2022). In Appendix C we provide a l examples of international
knowledge transfers captured by each of these service types, including, e.g., the recent
research collaboration between the U.S.-based firm Pfizer and the German company
BioNTech that led to the development of mRNA-based vaccines against COVID-19.
2.2.3.

Additional Firm Characteristics

In addition to the above f
Innovation Capacity. Firms that consistently devote resources to innovation activities
are more likely to introduce new or significantly improved products, services, andprocesses. They may also have a higher demand for foreign knowledge services due
to, e.g., lower sourcing costs resulting from a higher knowledge stock or potential
complementarities between domestic and foreign innovation inputs. To control fordifferences in innovation efforts across firms, we create dummy variables indicatinga firm’s involvement in i) occasional and ii) continuous engagement in internal R&D
activities.
Foreign Market Exposure. A large body of empirical evidence suggests that firmlevel innovation is linked to participation in international markets via, e.g., exports
or multinational activity. We use the MIP to extract information on firm exporter andmultinational status. Further, we use the SITS to control for potential unobserved
differences in innovation activities across firms related to particular countries fromrevenues.The value of cost reductions are proxied by multiplying the stated percentage cost reduction
resulting from process innovations by firms’ total revenues.

6which firms source knowledge services. To do so, we construct a separate "importcountry-combination" fixed effect for each unique combination of source countries.7
Size, age, and firm structure. A firm’s size and age affect its ability to incur potential
fixed costs related to innovation activities and trade participation. To account for firmsize, we construct a dummy variable indicating whether a firm has than 250 employees
and another indicating whether a firm is a member of a national company group. To
control for age, we add a dummy variable indicating if a firm is more than 21 years old.8
Industry and location. To control for unobserved differences in innovation activities
and demand for foreign knowledge services between industries and localities, weconstruct fixed effects for a firms’ industry at the three-digit level, and the federal state
where it is headquartered.
2.3.

Descriptive Statistics

Aggregate Statistics on Knowledge Services Trade. Aggregate statistics from the SITS
database indicate that Germany’s annual knowledge service imports, on average, grewby five percent annually between 2005 and 2012. Total annual expenditures on knowledge service imports average €13 billion, corresponding to roughly 10 percent of aggregate innovation and 21 percent of R&D expenditures. Table A1 lists the main source
countries and sourcing industries during our sample period. Major source countries,
each accounting for more than five percent of total knowledge service exports to Germany, are the United States, the United Kingdom, Switzerland, France, and Austria.
Industries accounting for more than five percent of total knowledge service imports
are “chemicals and chemical products,” “other business activities,” “motor vehicles,
trailers and semi-trailers,” “electrical machinery and apparatus,” “wholesale trade andcommission trade,” and “research and development.”9Among the four services types included in our definition of knowledge services,
7 For example, three firms that import from France, France and Spain, and France and Austria each areassigned a separate fixed effect. Our import-combination fixed effects cover over 3,600 unique country
combinations.
8 Similarly, our company group dummies control for the ownership structure of a firm. Firms’ ownership structure is linked to their governance and access to resources. Both are likely determinants ofinnovation outcomes and service import activities.
9 "Other business activities" includes market research and technical consulting services, potentiallyexplaining this sector’s high share in overall knowledge service imports. “Wholesale and commission
trade” contains several services that are likely to import knowledge-related services, such as the wholesaleof machinery, industrial equipment, ships, aircrafts, or chemical products. According to Eurostat, thewholesale trade and commission trade industries were among the largest within the EU-27’s non-financial
business economy (NACE Rev. 1.1. Sections C to I and K) in 2009.

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import expenditures on services pertaining to “Research, development, and testing”
were most substantial, accounting for 46 percent of total knowledge service imports.
By import expenditures, the second-largest category are payments related to “patents,
licenses, inventions, and processes” (35 percent), while expenditures on services related
to “Other rights” (19 percent) and “Artistic copyrights” ( 5 percent) are less substantial.10
Sample Statistics. Our regression sample covers 11,151 firms and 26,512 firm-year observations between the years 2005 and 2012. Table A2 displays descriptive statistics. Around
4 percent of firms in our sample import import knowledge services. Conditional on
importing, the average annual expenditures on knowledge service imports are equal to€0.62 million.
The importing of knowledge services is strongly associated with innovation success. At the extensive margin, importers report innovation success, the introductionof product innovations, or the introduction of process innovations more than twice
as frequently as non-importers. Among knowledge importers, new or significantly
improved products accounted for 19 percent of yearly revenues, compared to 8.2 percent among non-importers. Process innovations reduced unit costs, on average, by 2.6
percent among importers, compared to 1.2 percent among non-importers.
Two innovation-related outcomes foreshadow broader systematic differences between importers and other firms. First, importers appear to have a higher capacity forinvestment, given that 61 percent of knowledge service importers continuously engage
in internal R&D, compared to only 18 percent among non-importers. Second, the valueof their revenues from product innovations along with their cost savings from process
innovations is magnitudes higher, suggesting importers are substantially larger.
Looking directly at other firm characteristics reveals that importers are larger than
non-importers; among the former, over 40 percent have more than 250 employees,
compared to 7 percent among the latter. Importers are also more frequently part ofa multinational company, and their exporter share is about twice as high compared
to non-importers. However, other differences with regards to age, occasional internal
R&D activities, and memberships in a national company group are less pronounced.
10 See Eppinger (2019), Kelle & Kleinert (2010), Kelle et al. (2013), and Hebous & Johannesen (2021) for

other statistics on Germany’s services trade.

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3.

Acces to knowledge services and firm innovation

This section presents reduced-form evidence on how access to knowledge service
imports impacts firm innovation. We outline below our empirical strategy, and present
our estimated effects.
3.1.

Empirical Strategy

To investigate how access to foreign knowledge services impacts firm innovation, we
consider the following empirical specification,
Y f t = βS f t + γ0 X f t + α +  f ,t .

(1)Here, Y f t is an innovation outcome of a firm f at time t. S f t is a firm-level export
supply for knowledge services, which we describe in detail below, and β is our parameterof interest. X f t is a vector of time-varying firm controls and α a set of year, industry,
regions, and import-country-combination fixed effects.11  f t is an idiosyncratic errorterm.
To construct firm-level export supply shocks for knowledge services, we utilize aquasi-experimental shift-share design (Bartik 1991,Goldsmith-Pinkham et al. 2020,Borusyak
et al. 2021), exploiting variation in firm exposure to a set of common shock. Moreformally, we utilize information on the universe of services trades from the SITS toconstruct the following shift-share instrumental variable (SSIV)∑ ωn f nto ln Int,–i( f ) ,
Sft =
0

if f is a knowledge service importer in 2002-04,

if f is not a knowledge service importer in 2002-04.
(2)
Common Shocks. The shifters Int,–i( f ) reflect industry-country-specific shocks toknowledge service export supply. Int,–i( f ) is the sum knowledge service imports froma country n across all units in the SITS in a given year t, leaving out firm f 0 s industry,i( f ).12 If the the demand for service imports is uncorrelated across industries after con11 We omit firm fixed effects as country-combination fixed effects already absorb about 80 percent of thevariation in our export supply shocks. Thus, their inclusion already represents a restrictive specification.
12 That is, I
nt,–i( f ) = ∑ f 0 ∈SITS,i( f 0 )6=i( f ) In f 0 t , where In f 0 t denotes expenditures on knowledge services

from country n by firm f 0 in year t, and SITS denotes the set of all units that appear in the SITS data,
which is significantly larger than our estimation sample. The underlying idea is to purge a mechanicalsource of bias arising from the fact that unobserved shocks to firms’ import demand are mechanically9ditioning on observables, variation in these shocks capture changes in a given source
country’s export capacity for knowledge services.13
Firm Shock Exposure - The exposure weights ω f nt0 quantify firm f ’s exposure to achange in country n’s export supply for services, based on the firm’s share of import
expenditure knowledge services from country n during a pre-estimation period t0 thatspans the years from 2002 to 2004.14 We limit shock exposure to a pre-period t0 as
current import shares may be affected by lagged shocks in a way that is correlated withunobservables  f t .
SSIV - Following (2), we sum the product of ω f nt0 and ln Int,–i( f ) across all source
countries n for each firm f and year t. The variable takes the value zero for all firmsthat did not import knowledge services during the pre-estimation period t0 , effectively
assigning them to a placebo country that never exports knowledge services.
Identification . We assume that identification ofnour parameterof interest β follows
ofrom exogenous variation from common shocks Int,–i, i.e., that shocks are conn,t,iditionally quasi-randomly assigned, and provide sufficient identifying variation.15 To
corroborate these assumptions, we follow Borusyak et al. (2021) and investigate (i) theconcentration of exposure weights, (ii) the statistical properties of the shocks, and (iii)the predictive power of our export supply shocks for past dependend variables and theset of controls. It should be noted that our shift-share variable, due to the leave-one-out
correction, does not have a convenient shock-level representation.
Exposure Concentration. To calculate shifts Int,–i( f ) , we use 62 countries, 43 industries,and eight years. The largest value of average country exposure equals 0.19,16 and theinverse Herfindahl index (HHI) of country shares within industry equals 16.4; in an
equivalent shock-level regression, this would indicate an effective sample size of about
131.17
correlated with aggregate import volumes.
13 Shocks to export capacity capture, e.g., changes in trade barriers, quality, or factor costs.
14 Past import shares are a proxy for exposure if, e.g., knowledge services from different suppliers
are imperfectly substitutable for a firm due to search costs, fixed costs associated with establishingsupplier-buyer relationships, or unobserved preference shocks.
15 See D for a more detailed discussion of the threats to identification and their relationship with ourcommon shocks.
16 Specifically, we limit the estimation sample to firms with positive knowledge service imports during
the pre-estimation period, which increases the inverse HHI of exposure weights to 51.6, and decreases
the maximum average exposure across different shocks to 0.06.
17 Monte-Carlos simulations by Borusyak et al. (2021) suggest good performance of shock-level shiftshare instruments in finite samples at an effective samples size of 20, yielding false rejection rates of true
zero nulls of 7.3% at a 5% confidence level. For an effective sample size 50 shocks, the false rejection rate10

Shock Variation. The mean of our exposure-weighted country-industry shocks isaround 0.3, with a standard deviation of 1.98. Residualizing shocks on years leaves thestandard deviation unchanged.
Shock Correlation. The average significance level of all pariwise correlation coefficients between shocks equals 33 percent, while the first quartile equals 7 percent, thesecond equals 25 percent, and the third quartile equals 56 percent. Therefore, morethan 75 percent of common shock correlations represent only weakly significant or
insignificant correlations.18
Quasi-Random Assignment. Table A3 shows that our SSIV has no predictive powerover invidividual firm controls, corroborating the assumption of quasi-random shock
assignment.19
3.2.

Innovation Propensity

We begin our empirical analysis by assessing how access to foreign knowledge service
exports impacts a firm’s propsensity to introduce a new product, service, or production
processes. Table A4 reports SSIV estimates across parallel specifications.20 The firstcolumn reports the coefficient estimate for β obtained from a specification that includes
year fixed effects and no firm controls, with subsequent columns adding industry(column 2), state- (column 3), and import-country-level fixed effects (column 4). Column
5 adds a set of general firm controls, and column 6 includes innovation-related firm
controls.
Across all specifications, we find that an increase access to foreign knowledge services has a positive and statistically significant effect on a firm’s propensity to innovate.
The estimates imply that doubling a firm’s export supply is associated with an increasein the likelihood of introducing a new product or process of 0.6 to 1.8 percentage points.
Additional Checks . Before proceeding to presenting results on the response of other
innovation outcomes, we conduct a suite of additional checks to solidify the causal
decreases to 5.6%.
18 Restricting our estimation sample to the subsample of knowledge service importers also strengthens
the plausibility of the assumption that our shocks are only weakly correlated. The mean significance ofthe pairwise shock correlations in this subsample equals 43 percent, while the first quartile equals 14
percent, the second quartile 41 percent, and the third quartile 70 percent.
19 In an additional robustness test, we use lags of our control variables as alternative outcomes. We do
not find a statistically significant coefficient for our shift-share variable in these specifications.
20 Standard errors are robust and clustered at the firm and country-combination-level. The reported
levels of statistical significance are robust to implementing the standard error correction by Adao et al.
(2019) addressing the concern that firms with similar exposure shares may have similar residuals.

11

interpretation of our estimate.
Excluding Non-Importers. Our point estimate is not sensitive to estimating equation (1)on the subsample of firms with positive knowledge service imports in the pre-estimation
period.21 Removing non-importers strenghens the causal interpretion of our SSIV
estimate by reducing the inverse Herfindahl index of average shock exposures from
16.4 to 51.6 and maximum average exposure from 0.19 to 0.06. Table A5 shows that theresulting point estimate of β persists at 0.006 and remains statistically significant.
Excluding Multinationals. Table A6 shows that our SSIV estimate of a subsample
regression that excludes firms which are part of a multinational company group.22 Ourpoint estimate for β remains positive and statistically significant, and the point estimatefor β increases from 0.006 to 0.012.
Shift-share construction. We explore alternative approaches to constructing our export
supply shocks. First, as our baseline set of shocks effectively limits shock exposure
to firms founded before the year 2005, we re-define the reference period for shock
exposure, t0 , as the first year a firm is observed importing knowledge services in the
SITS data. Second, to investigate whether our results are driven by few, high-leverageshocks, we construct two alternative shift-share variables analogous to (2), but limiting
the set of source countries to include either only or all except for the major source
countries listed in Table A1.23 Table A5 displays the results of re-estimating specification(1) with these alternative shift-share variables.
Imports of other service types. Our estimates may reflect a broader relationship between service imports and innovation if, e.g., shocks to the supply of knowledge service
are highly correlated with shocks to the export supply of other types of services. To
address this concern, we to construct shocks analogous to (2) for all service types, excluding knowledge services.24 As shown by Table A5, re-estimation of specification (1)with these shock yields a small, statisticially insignficant, and negative point estimatefor β.
21 Removing non-importers also raises the effective size of our sample by further reducing the concen-

tration of exposure weights across shocks. All non-importers are exposed to the common placebo shockwith an exposure weight of one, which mechanically raises the maximum average exposure and reduces
the inverse Herfindahl index.
22 Due to the intangible nature of services,. multinationals may report de facto non-existing crossborder service transactions to minimize their global tax burden by strategically shifting profits fromhigh- to low-tax countries (Hebous & Johannesen 2021).
23 Sixty-eight percent of the total value of knowledge service exports to Germany stemmed from fivecountries between 2005 and 2012.
24 The shocks are constructed as in (2) using information on firm-level and economy-wide imports ofservice types not included in our definition of knowledge services.

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3.3.

Product and process innovation

To provide further insights on the implications of knowledge imports for firm innovation, we broaden our analysis to include a richer set of innovation outcomes.
Extensive Margin. To study whether access to knowledge service imports differentially
impacts a firm’s propensity to innovate on products or processes, we re-estimate specification (1) using two alternative outcome variables indicating the introduction of (i) newor significantly improved products or services and (ii) new or significantly improved
cost-reducing processes. Table A6 reports the results.
We find that greater access to knowledge service imports has similar effects on
a firm’s propensity for product and process innovation. Our estimates suggest that
doubling a firm’s export supply of knowledge services makes it 0.4 percentage points
more likely to introduce a new product. propensity for adopting a new production
process increase by 0.5 percentage points. Considering that product innovations occur,on average, twice as frequently as process innovations, this suggests that access toknowledge imports has a comparatively
Intensive Margin . To investigate how shocks to a firm’s export supply of knowledge
services impact its returns to innovation investments at the intensive margin, we reestimate specification (1) using sales from product and cost reductions from process
innovations as a dependent variable.
The estimates displayed in Table A6 show that firms with access to a larger export
supply of knowledge services attain higher revenues through new or improved products.
Our estimates suggest that a 1 point increase the supply of foreign knowledge services
implies a statistically significant 0.11 percent increase in firm revenues attributable tosales of new or significantly improved products. We also find a positive, but statisticallyinsignificant effect on a firm’s revenue share of new or improved products.
Turning to the returns from adopting new processes, our results show that access toforeign knowledge services implies more substantial cost savings. Our point estimates
imply that a 1 point export supply shock to knowledge services raises the percentage
reduction in unit costs attributable to new processes by 0.0001 percent; this translates
into an increase in total cost savings from process innovations of 0.08 percent.

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3.4.

Domestic R&D Expenditures

To shed light on potential complementarities between foreign- and domestically-sourced
innovation activities within firms, we assess how changes in access to foreign knowledge
services affect expenditures on domestically-sourced R&D services. To measure a firm’s
domestic R&D expenditures, we subtract the value of a firm’s yearly imports of R&Drelated services from its total annual R&D expenditures reported in the MIP.
Table A7 reports the results of re-estimating (1) using logged domestic R&D expenditures as a dependent variable across parallel specifications with varying controls
and fixed effects. None of the displayed point estimates for β indicate that access toforeign knowledge services leads to reduced expenditures on domestically sourced
R&D. In contrast, we find a positive and statistically significant effect on domestic
R&D expenditures in most specifications, where a 1 point increase in export supply
increases domestic R&D expenditures by 0.05 to 0.34 percent across specifications that
include year, industry, and region fixed effects, as well as all time-varying firm controls.
Adding import-country-combination fixed effects, we find a positive, albeit statisticallyinsignificant on domestic R&D expenditures with a coefficient estimate for β of 0.03.

4.

A Model of Innovation and Services Trade

A broad increase in the opportunities for importing knowledge services has threeimportant consequences at the level of firms and within industries: it (i) led to greater
cost reductions through process innovations, (ii) increased revenues from new products,and (iii) induced greater innovation expenditures. In this section, we develop a theoryof innovation offshoring that rationalizes this evidence qualitatively and quantitatively.
There are two countries, Home and Foreign. The home economy produces a homogeneous final good, an endogenous mass of differentiated consumer products andknowledge services. Before proceeding to describing the demand and market structure of the economy, we begin below by describing the innovation process of a single
producer in the differentiated goods industry.
4.1.

A Theory of Innovation Offshoring

Production of differentiated varieties requires labor, `, and intangible capital, k, which
we refer to as knowledge. Technology is represented by a labor cost function that,conditional on knowledge, exhibits constant marginal and a fixed overhead cost. Labor

14

used is thus linear in output y: `( y, k) = f (k) · 1( y > 0) + c(k) · y, where 1(·) is an indicatorfunction. We assume that overall labor used is decreasing in knowledge (`k (·, ·) < 0) but
at a diminishing rate (`kk (·, ·) < 0).
Innovation Process. We posit a research technology which builds on a firm’s existingknowledge capital through investment in innovation. More formally, if a firm with initialknowledge base k invests an amount ι in innovation, its knowledge becomes k0 = k + ι.
Innovation is the outcome of a process that involves synthesisizing new insights frommany distinct knowledge areas, indexed by a type ω ∈ [0, 1], according to:
ι=

Z 1

1/χ
χ
ι(ω) dω,(3)0where ι(ω) denotes insight quality, and χ ≤ 1 governs the elasticity of subsitution
between different types of insights.
In each knowledge area, there is a research task. This task yields a random numberof insights with random quality. that is drawn from a Poisson distribution with mean
one. If the task is performed a total number of N(ω) times, the number of insights,n(ω), that will be discovered then follows a Poisson distribution with mean N(ω). The
quality ιi (ω) of each of these insights i = 1, ..., n(ω) is drawn randomly from a Pareto
distribution with tail parameter ζ > 2 and scale parameter kγ , ιi (ω) ∼ G(ι) = 1 – (kγ /ι)ζ .
We assume that the best insight is selected for integration into the innovation process.
As shown in the Appendix, these assumptions imply the following innovation production
function:
Z 1
1/χ
γ/ζ
χ/ζ
ι=A·k ·
N(ω) dω,(4)0where A ≡ Γ (1 – χζ )1/χ is a constant that depends on the Gamma function Γ (·). Twopoints are worth noting. First, innovative investments face diminishing returns dueto the randomness of research success, captured by 1/ζ. Second, existing knowledge
may enhance innovation productivity due to “standing on shoulders” effects (γ > ζ) or
possibly lower it due to “fishing-out” effects (γ < ζ).
Each task can be performed in-house, using labor; or it can be outsourced to an
external supplier. In-house execution of tasks suffers from diminishing returns toscale due to limited span-of-control.25 Hence, outsourcing may be attractive if external
25 The substantive assumption is that in-house task performance is subject to disceconomies of scale.

E.g., we could have, alternatively, posited rent-sharing between workers and firms due to monopsony inthe labor market or efficiency wages to generate such disceconomies of scale.

15

suppliers can handle large volumes of tasks more efficiently, without the diminishingreturns that the firm experiences.
Formally, to perform a given task in-house N times requires hiring N α workers,
with α > 1 capturing span-of-control. To outsource, the firm procures a competitively
supplied knowledge service at Home (l = H) or in a foreign market (l = F) at a priceψ · wl . Here, the parameter ψ governs the costs of outsourcing. We follow Grossman& Rossi-Hansberg (2008) in assuming that the input requirement for foreign services,τ · t(ω), varies by task. The schedule t(ω) reflects heterogeneity in offshoring costs
across tasks, where we index tasks so that t 0 (ω) > 0.26 The factor τ represents broader
conditions affecting the costs of coordinating international innovation activities.
Optimal offshoring decisions. For a given innovation target, the firm chooses whether
to perform each task in-house or through outsourcing, and at which level of intensity,
to minimize the cost function κ(ι; ·). Let the cost share of tasks offshored be denoted byκ(ι;·)
ϕO ≡ ∂ ln
and that of tasks outsourced by 1 – ϕI . We characterize the features of∂ ln τ
these optimal choices below, with details on mathematical derivations relegated to the
Appendix.
Let ω∗ denote the marginal task that leaves the firm indifferent between either
outsourcing arrangement, defined by τ · t(ω∗ ) = wH /wF .27 The optimal choice for tasks
in [0, ω∗ ] is then to offshore if τ · t(ω) · ψ · wF < wH · N(ω)α–1 and integrate them,otherwise. Conversely, tasks in [ω∗ , 1] are outsourced domestically if ψ < N(ω)α–1 ;
else, they are integrated. Both domestic and foreign outsourcing of tasks, thus, is more
attractive when a firm’s desired task intensity is higher; this implies selection and a
non-homotheticity in outsourcing decision, as shown by the following Proposition.
PROPOSITION 1. For a firm with knowledge base k,a. there exist two cutoffs ιI (k, τ), ιO (k, τ) > 0 such that ϕI (ι; k) < 1 if, and only if, ι > ιI (k);and ϕO (ι, k) > 0 if, and only if, and ι > ιO (k).
b. the cost elasticity of innovation is given by:E(ι; k, τ)≡hi∂ ln κ(ι; k, τ)= ζ · ϕI · α + 1 – ϕI .
∂ ln ι

(5)

26 This heterogeneity may capture both institutional and technological barriers to innovation outsourc-

ing. An example of the former are the prevalent securiy-driven restrictions on international researchcollaborations in knowledge areas such as nuclear physics or bio-chemical engineering.
27 We restrict attention to empirically relevant cases where ω∗ ∈ (0, 1] throughout the main text. See
the Appendix for a complete characterization of all cases.

16

c. the response of marginal innovation costs to changes in offshoring costs τ is given by:
h 1 – ϕOi
∂ ln κ0 (ι; κ, τ)= ϕO · 1 +· ηO ,∂ ln τ
E
χ/ζ
O
α–1 > ∂ ln t(ω∗ ) R ω∗ ( t(ω) ) χ/ζ–1 dω.
where ηO ≡ ∂∂lnlnϕι > 0 ⇔ α–χ/ζo∂ω∗t(ω∗ )The intuition underlying Proposition 1 is that firms use outsourcing as a tool to mitigate scale inefficiencies from limited span-of-control: when the size of a firm’s desired
innovative investment increases, scale inefficiencies become more costly, making outsourcing as well as offshoring more attractive. As a result, firms select into outsourcing
based on their innovativeness (part a.), the innovation cost elasticity E decreases in thecost share of tasks performed in-house 1 – ϕI (part b.), and marginal innovation cost
exposure to trade shocks is depends on a firm’s offshoring cost share ϕO , reflecting
both a price and scale effect (part c.).
The empirical counterpart to Proposition 1 is a positive correlation between knowledge service imports and innovation expenditures within industries, as observed in ourdata. Further, Proposition 1 lends theoretical justification to the construction of our
SSIV variable (equation (2)).
Going forward, a key implication of Proposition 1 is that changes in the opportunities
for importing knowledge services differentially shift the innovation incentives of exante heterogeneous firms. To reason about the associated implications for innovation
outcomes and welfare, we now embed our theory of innovation offshoring into a modelof monopolistic competition between heterogeneous multi-product firms.
4.2.

Preferences and Demand

A unit mass of identical domestic households inelastically supplies one unit of labor at
the competitive wage wH . Households hold quasi-linear preferences over consumptionof a homogeneous, numeraire good, X, and an aggregate index of differentiated varieties,
Y , represented by,U(X, Y ) = X + ln Y + 1.
(6)
Let PY denote the utility-based price index of Y so that consumers optimally purchasedifferentiated products up to the point where Y = 1/PY , and devote the remainder of
their income to consumption of the homogeneous good.
The consumption index Y is an aggregate over real consumption, yθ , of composite
goods with types indexed by θ. A composite good of type θ comprises hθ varieties

17with two characteristics: one that differentiates them from other composite goods andanother that renders them pairwise CES-substitutes with an elasticity of substitution
ε > 1. Given this formulation of preferences, per-capita consumption expenditures on avariety j equal:pθ j y θ j =

pθ j
pθ

1–ε
pθ yθ ,

(7)

where yθ j is the consumption of the variety, pθ j is its price and pθ is the CES priceR hθ 1–εindex of the composite good: p1–ε
θ = 0 pθ j d j .
Following Matsuyama & Ushchev (2017), the preferences represented by PY belong
to a class termed Homothetic with a Single Aggregator (HSA). HSA preferences are definedin terms of a market share function s(·) and a common aggregator P such thatpd ln PY pθ yθ= Y = s( θ )d ln pθ
P
P Y
and

(8)

Z

p
s( θ )dF(θ) = 1,
P
Θ

(9)

where dF(θ) is the measure of composites with type θ and Θ the set of all possible
types.28 Equation (8) gives the demand for composite goods in explicit form; the substantive implication is that this demand only depends on its price relative to a common
aggregator, P. This aggregator mediates price competition between goods; this is reflected in the price elasticity of demand:pθ 0 pθs( )pθσθ ≡ σ( ) = 1 – P pθ P > 1.
Ps( P )(10)

In the special case where the preferences represented by PY are CES, where s(z) = z 1–σ ,the price elasticity of demand is constant, σθ = σ, and P aligns with the ideal price index
PY . Away from this special case, the price elasticity of demand varies endogenouslywith a good’s relative price. We adopt
ASSUMPTION 1. (i) Either σ(·) = σ or σ0 (·) > 0 and (ii) in the neighboorhood of any equilibp
rium, ε > σ( Pθ ).
28 We impose s0 (z) < 0 when s(z) > 0, lim
z→0 s(z) = ∞, limz→z̄ s(z) → 0 for z̄ = inf{z > 0|s(z) = 0}.
θMatsuyama & Ushchev (2017) show that these assumptions guarantee that the demand system in (7) and(9) can be rationalized by a monotone, convex, continuous and homothetic rational preference relation.

18

The first part of Assumption 1 implies that a good’s demand becomes less elastic whenits price decreases relative to the common aggregator. As an implication, a compositeθ ≤ 0. The
good’s price elasticity of demand is decreasing in its product scope: ∂σ∂hθsecond part posits negative cross-price demand effects within composite goods; thishas implications for innovation decisions that we describe next.
4.3.

Production

The numeraire good X is competitively produced under constant returns to scale andtraded freely. By choice of units and numeraire, this fixes the wage in the home andforeign economy at one in units of the homogeneous good.
Firms in the differentiated goods sector purchase a fixed quantity of Fe units ofhome labor to enter. Upon entry, each firm receives a draw θ from a distribution G(θ),
granting it monopoly rights over blueprints for many distinct products with a common
type θ. The blueprint for a particular product j consists of a knowledge base, kθ j ≡ kθ ,an innovation cost function, κ(i j ; kθ j , τ), and a production technology, Cθ ( y, ι j ) =c(kθ j + ι j ) · y + f (kθ j + ι j ). The innovation cost function summarizes a firm’s underlying
decision to outsourcing innovation tasks, following Proposition 1.
Each firm chooses a product range, hθ , alongside setting a price pθ j , and determining the level of its innovation investment ιθ j for each product so as to maximize thefollowing market value function:
vθ =

Z hθ
0

πθ j (hθ , pθ j , ιθ j )d j ,(11)where πθ j are the profits generated by product j , πθ j ≡ [ pθ j – c(kθ0 j ] yθ j – f (kθ0 j ) –κ(ιθ j , kθ j , τ),In this environment, firms will choose the same innvation investment and price foreach product; henceforth, product-firm subscripts will thus be suppressed. For eachgood that a firm chooses to supply, the profit-maximizing price equals a markup µθ
over its marginal costs,ppθ j ≡ pθ = µ( θ )cθ ,(12)P
where the optimal markup satsfies Lerner’s formula,σ( pP )pµ( ) = p.
Pσ( P ) – 1

19

(13)

Firm internalize the monopoly power they hold over its portfolio of products and,hence, apply a common markup to all products.29 Their choices of product range, inturn, balance the additional profit from a new product against the profit loss due toθ = 0.30 Combining this condition withdiminished sales of existing products, πθ + hθ ∂π∂hθthe above pricing rule yields,pθ y θ
ε – σθ pθ yθ
– f θ – κθ =
·
.
σθ
ε–1
σθ

(14)

The right-hand side of equation (14) captures cannibalization effects: a new productreduces the firm price index (pθ ), subsequently reducing the profits of existing varieties(following Assumption 1). A firm’s optimal choice of product range, then, ensures thatprofits from new products on the left offset the profit loss from cannibalization.
The first-order condition for a firm’s desired knowledge capital stock is – y∂cθ /∂kθ0 –∂ f θ /∂kθ0 = ∂κθ /∂ιθ . A firm invests in knowledge until savings from lower production
costs are driven to zero; integrating this optimality condition with a firm’s other choices
yields:31
"
#


kθ0
1
fθ
fθ
cθ
cθ yθ · –k0 –·  0 = κθ ·· Eθ + k0 ,(15)
ε – 1 kθιθθθgwhere x denotes the elasticity of a function g(x) with respect to a variable x.
Equation (15) summarizes the forces that shape firms’ innovation incentives. The
scope for innovation offshoring (τ) is reflected in the cost (κθ ) and scale efficiency (Eθ )of a firm’s innovative investments. The term cθ yθ reflects scale economies: as scale
per product rises, innovative investments become more profitable. Scope economies,fin turn, are reflected in the term k0θ : knowledge accumulation may streamline theθffintroduction of new products (k0θ < 0) or make them more complicated (k0θ > 0).32 Inθθtuitively, the importance of scope economies for the profitability of innovation depends
29 This is a well-known feature of nested demand systems and would also be true if marginal costs were

not symmetric within firms. See Hottman et al. (2016) for a more detailed discussion.
30 To simplify notation, we suppress the argument of functions whenever this dependence is clear fromp
the context (e.g., we write σθ and κθ instead of σ( Pθ ) and κθ (ι, τ)).
31 The decomposition follows from rewriting the FOC for h as as f = σθ –1 pθ yθ – κ = cθ yθ – κ tooθθθε–1 σθ
ε–1
substitute for f θ in the FOC for innovation.
32 This formulation flexibly encompasses different types of innovation. When innovative investments
reduce variable but raise fixed costs, knowledge capital captures intangibles, as in De Ridder (2022).
Alternatively, knowledge capital may catalyze “scalability innovations”, e.g., the adoption of businessmodels or technologies with higher upfront but lower unit costs, such as cloud-computing and IT services.
Finally, innovation may lower both fixed and variable cost, capturing, e.g., advanced automation androbotics in manufacturing.

20

the strength of cannibalization effects in demand, captured by ε.
4.4.

Equilibrium

As in Melitz (2003), producers of differentiated products face an exogenous exit probability ∆ in each period. In steady state, firms will enter until the expected value of entry
equals the entry cost:Z1·
v dG(θ) = Fe .
(16)
∆ Θ θ
Denoting the equilibrium mass of entrants by M, the measure of type θ firms active in
steady state is equal to dF(θ) = MdG(θ).
An equilibrium is defined by a number of entrants M and a vector of firm choices{pθ , hθ , ιθ }θ∈Θ , so that consumers maximize utility taking prices as given, firms maximize profits, and the free entry condition holds. An equilibrium satisfies equations (7),(9), (10), (11), (13), (14), (15), and (16).

5.

The Firm-level and Aggregate Effects of Services Trade
Liberalization

In this section we use the model developed in the previous section to study the firm-level
and aggregate implications of services trade liberalization.
5.1.

Concepts

We first introduce two elasticities related to the shape of demand curves that facilitate
the exposition of our theoretical results. The first is a firm’s price cost pass-through,which describes how changes in marginal production costs cθ impact the its desired
price. Formally, we define:p∂ ln pθ=ρθ ≡ ρ( θ ) ≡P∂ ln cθ1pθ 0 p„ .
µ( )1 – P pθ Pµ( P )(17)

Under CES preferences, markups are constant, µ0θ (·) = 0, and cost pass-throughs complete, ρθ (·) = 1. Away from this special case, assumption 1 implies incomplete passthrough of cost shocks into prices, ρθ (z) ∈ (0, 1).

21

The second demand elasticity relevant for welfare analysis is the consumer surpluspthat a firm create, denoted by (δθ – 1)sθ ( Pθ ). Here δθ is the ratio of the area under thedemand curve to sales:
R ∞ s(ξ)
R yθ
p(y
)d
y
pθ
p /P ξ dξθδθ ≡ δ( ) = 0 pθ
≥ 1,
= 1+ θ pPs( P )s( Pθ )

(18)

where p(·) is the inverse residual demand curve for the firm’s composite good. Underσ .
CES preferences, δθ captures love-of-variety and coincides with the markup, δθ = σ–1
For other HSA preferences, δθ varies with a firm’s position on its residual demand curve,pθ /P.
5.2.

Effect on Firm Output and Innovation

We begin our analysis by drawing out the forces that shape the allocational implicationsof changes in the opportunities for innovation offshoring, d ln τ. As firms select into a
direct and an indirect effect. The direct effect reflects
We show in the Appendix that this increase in competition satisfies
d ln P = µ̄ · ϕO · d ln τ.

(19)Here, the average markup µ̄ = Es [1/µθ ]–1 reflects the responsiveness of aggregate profits
to competition.
PROPOSITION 2. The change in a firm’s relative price caused by a change in services trade
costs is given byp
1 – σθ ρθd ln θ = ρθ · Γθc – Γθh · ϕO
· d ln τ – ρθ ·· µ̄ · ϕO · d ln τ,θP
ε – σθ ρθ

(20)

ln cθ
ln hθ
where Γθc ≡ ∂∂ ln
and Γθh ≡ ∂∂ ln
are the pass-throughs of shocks to innovation investmentκθkθ
costs into unit production costs (cθ ) and product variety (hθ ).

The first on the right-hand side of equation (20) gives the cross-sectional effects
of changes in services trade costs on firm competitiveness. Following Proposition 3,∂ ln cθcinnovation expenditures on imported knowledge services, ∂∂lnlnκτθ = ϕO
θ . Γθ = ∂ ln κθln hθand Γθh = ∂∂ ln. These elasticities describe the pass-through of shocks to the costs ofκθinnovation investments into unit production costs (cθ ) and product range (hθ ).

22

The indirect effect is mediated through changes in competition. Initially, a decline
h in tradei costs, on average, increases the profits of existing firms by –ϕd ln τ =κθ O–Es s ϕθ d ln τ. To re-establish the free entry condition in the market, there mustθ
subsequently be an increase in competition.
5.3.

Welfare Gains from Knowledge Service Imports

Per-capita welfare W in the home country comprises (exogenous) labor income, Ȳ ,R
x yθplus consumer surplus, U = Y – log PY . Letting Ex [ yθ ] ≡ Θ R xθ dG(θ)dG(θ) denoteΘ θ

the x–weighted average of yθ , given two variables xθ ≥ 0, and yθ , changes in welfare
associated with shocks satisfy:


h
i


1
Es d ln hθ – Es d ln pθ ,dU = δ – 1 d ln M +{zε – 1}|{z}|
Entry/exit of varieties(21)

Divisa Price Index

where δ = Es [δθ ] is the average consumer surplus.
Welfare changes dW incoporate the consumer surplus brought about by firm entry
or exit (d ln M) or created through product introductions of existing firms (d ln hθ ) via
the first two terms on the right-hand-side of (21). Intuitively, the marginal entrant raises
consumer surplus in proportion to, Es [δθ ]–1. Changes in welfare associated with productintroductions by existing firms, in turn, are governed by the within-firm elasticity of
1 .
substitution, ε–1
The last summand in (21) captures how changes in real GDP affect welfare. If themodel did not allow firm entry or product innovation, the first two terms of (21) would
be zero and changes in welfare would be captured by measured GDP.
Theorem 1. In response to a change in service trade barriers, d ln τ, the change in per-capita
welfare U is given by,dU =– µ̄Λd ln τ – Es
| {z }|∆Technical Gains



n

o
Es [δθ ] 
ε–1
c
h
1–
σθ ρθ · Γθ – Γθ ϕθ –µ̄Λ d ln τ,µθε – σθ ρθ{z}∆Allocative Gains∂ ln hθ∂ ln cθ–1 hc1where λ = Es κs θ · ϕO
θ , µ̄ = Es [ /µθ ] , Γθ ≡ ∂ ln κθ and Γθ ≡ ∂ ln θ .
θ

h

i

(22)

Welfare changes associated with services trade costs stem from two effects. The
term labeled technical efficiency captures the change in welfare when the distributionpof relative prices ( Aθ )θ∈Θ is held fixed. In an economy with symmetric CES preferences,23sθ (z) = aθ z 1–σ and aθ > 0, this is the only effecti implying that the import share ofservices in GDP and aggregate markup are sufficient statistics to summarize welfarechanges. Through this lense, the technical efficiency effect captures sources of gains
from trade analogous to Arkolakis et al. (2012).
The second term in equation Equation (22) captures how reallocations of economic
activity between firms contribute to welfare. This term equals zero in an economy withhomogeneous markups, reflecting that reallocations have no first-order effect on welfare
when the initial allocation is efficient. In contrast, heterogeneity in markups spells
allocative inefficiencies; in this case, trade-induced shifts in the profile of innovation
across firms have ramifications for welfare. Γθc and Γθh , only matter for the allocative
efficiency effect.
5.4.

Changes in other aggregates: Markups and real GDP

We finish this section by characterizing the response of other important aggregates to a
decline in the costs of innovation offshoring - the aggregate markup, µ̄, and real GDP.
PROPOSITION 3. In response to a change in service trade barriers, d ln τ, the change in theaggregate markup µ̄ = Es [1/µθ ]–1 , is given byd ln µ = Es

n

on

o

µ
ε–1
c
h
µ̄Λ d ln τ.
Γθ – Γθ ϕθ +1–σθ – 1 ρθ + µ(1 – ρθ )µθ
ε – ρθ σθ
The response of real GDP per capita, d ln Q ≡ –Es d ln pθ , is given by

h
 i
ε–1
– ρθ µΛd ln τ – Es Γθc + Γθh ϕθ d ln τd ln Q = –Es
ε – ρθ σθChanges in the aggregate markup reflect

6.

Quantification

In this section, we quantify the welfare formula provided in section 5.

24

6.1.

Calibration

6.1.1.

Innovation cost pass-throughs: Γθh , Γθc

We use our reduced-form estimates to inform the structural innovation cost passthroughs. For unit costs, we use our estimates of the effect of export supply shocks
on firms’ reductions in unit costs attributable to innovation, which our model maps
ln cθ
into the outcome – ∂∂ ln
d ln kθ = –d ln cθ . For product variety, in turn, we leveragekθ
our reduced-form estimates pertaining to firm firm revenues from new products,∂ ln sθθ ρθd ln hθ = 1–σ
1– d ln hθ .
∂ ln hθTo derive the structural analogue of our empirical shift-share instrument, we extend
the model to allow firms to source knowledge services from multiple source countriesn ∈ N at a fixed cost f I,n and variable cost τn . The (cross-sectional or time) variation ininnovation costs can then written as follows:– d ln κθ = –ϕθ

X

ωθn

n∈N

d ln PnId ln τn + α f + θd ln τ

(23)

where ωθn ≡ ∑τnτIθn1
is the import expenditure share of firm θ on knowledge
n n Iθn {ϕθ >0}services from country n, αF is a firm fixed effect and θ a structural residua.
Our empirical firm-level shocks rely on aggregete import volumes to proxy forchanges in structural trade costs. Γθc via the two-stage IV estimate of the effect of innoh i d ln c /d ln S
 
θ
f ,t
.
vation expenditures on unit costs, E Γ c = E Γbc =f

6.1.2.

fθθ

d ln κθ /d ln S f ,tOther statistics

We rely on external estimates to calibrate the cross-firm price elasticity of demandσθ , the perceived price elasticity of product demand ε, and price cost pass-throughsρθ . Hottman et al. (2016) find an average cannibalization rate, defined as the partial
elasticity of firm sales of old products with respect to the number of products, equal
to -0.5, implying that (1–ρ)+ερ
= 0.5. We set the average markup equal to µ̄ = 1.15, inσline with existing estimates in the literature.33 We choose price cost pass-through tobe equal to ρ = 0.7, following Amiti et al. (2019) and Arkolakis et al. (2019). Given thesechoices, we inform the elasticity of substitution σ by imposing a cannibalization rate
33 Using firm-level markup estimates for German firms by Ganglmair et al. (2021), we find an averagemarkup across the firms within our sample of 1.5. Since our sample is biased towards larger firms, thislikely overstates the economy-wide markup. Setting a lower markup is a conservative choice, given that
our estimated welfare gains increase in the size of the average markup.

25

of 0.5. Given the sparseness of estimates of the average brand-level consumer surplus σδθ – 1 in the literature, we choose a conservative value of Es [δθ ] = 1.05 for ourEs σ–1baseline analysis.
To calculate the ratio of knowledge service imports to sales, we divide the average
yearly imports of knowledge services during our sample period by the average yearlyrevenues reported as part of the core indicators of the Mannheim innovation panel. To
calculate the aggregate import share of knowledge services, we divide yearly averagesof the total yearly import volumes of knowledge services in the SITS by the total yearlyR&D expenditures reported in the MIP core indicators.
6.1.3.

Results [Needs Updating]We summarize our calibrated parameters in table A8. Following proposition 3, we findthat the elasticity of aggregate spending on knowledge service imports to trade costs 1–θequals –0.8. Given the estimate for the trade elasticity, our reduced-form estimates imply
that the average firm-level pass-through of knowledge cost shocks into unit costs andthe number of products, respectively, equals 0.004, and –0.95. Hence, while theoreticallyambigious, our results suggest that reductions in services trade costs cause importers
to adopt more cost-effective processes, and to engage in more product innovation.
6.2.

Quantitative Results [Still Needs Updating]Baseline
table A9 displays the gains from knowledge services trade following ?? and 1 under ourbaseline calibration. The results suggest that the welfare gains from services trade are
sizeable, implying that a 1 percent reduction in services trade costs raises consumer
welfare by 0.06 percent. The bulk of these welfare gains stems from increasing productvariety through the expansion of product lines and brands. In particular, changes in thenumber of products by existing firms account for 27 percent of the welfare gains, while
the entry of new firms accounts for 64 percent. In contrast, reductions in the prices ofold products offered by the initial set of firms account for less than 10 percent of theoverall welfare effect. These findings underscore the importance of product entry for
the welfare gains from trade, highlighting in particular the role of product innovation
by existing firms.
Our theoretical results further allow us to disentangle the importance of the direct
and indirect effects of trade shocks for aggregate welfare. According to our estimates,

26

rising aggregate competition discourages innovation, which counteracts the welfare
gains implied by the direct effects along three margins of welfare gains. In total, theinnovation-discouraging effects of rising competition lower welfare by 0.004 percent, or
5.7% percent of the overall gain. Rising competition primiarly impedes firms’ incentives
to invest in new product lines, lowering the gains materializing through this margin by
18 percent, which corresponds to a reduction in the total gains of 4.8%.
Discussion and robustness
We conclude by discussing the sensititivty of the quantitative results to our calibration
choices.
Cost pass-throughs and markups. Following Theorem 1, the cost pass-through ρ, ceterisparibus, affects the economy’s adjustment to trade shocks via two channels. On the
one hand, a lower cost pass-through ρ implies that firms’ perceived demand elasticity
responds more to changes in its product range, implying that prices of existing products
respond more to product innovation. Second, a lower cost pass-through tends to reduce
firm entry by raising the partial elasticity of firm-level prices to aggregate competition.
Intuitively, if competition has a larger impact on firms’ desired markups, less entry
is required to achieve a given increase in competition. The level of markups, on theother hand, affects both the rate of entry, as well as the consumer surplus generated byentrants.
In table we report how our welfare estimates change under alternative assumptions
on markups and pass-throughs. Throughout, we maintain that the cannibalization rateequals 0.5, and adjust the between-brand elasticity of substitution σ to be consistent
with alternative choices for markups and pass-throughs.

7.

Conclusion

In this paper, we used detailed data on the service imports and innovation activity ofGerman firms to analyze how supply shocks to foreign knowledge impact firm innovation and market-wide economic outcomes. To disentangle the direction of causality
between export supply of knowledge services and innovation, we utilized a shift-share
design to construct firm-level access shocks to foreign knowledge services.
We first showed that increasing a firm’s access to knowledge-related service imports
raises its innovativeness. On the extensive margin, greater access to foreign knowledge
makes a firm more likely to introduce new products and production processes. On the27intensive margin, it leads to greater revenues from product and greater cost reductions
from process innovation. Second, we showed the positive impact on innovation outputs
is accompanied by higher expenditures on domestically-sourced R&D, suggesting that
foreign- and indigeneously-sourced knowledge are complementary inputs into firms’
innovation process. Third, we traced the direct and indirect effects of knowledge services trade in a theoretical model with endogenous innovation and competition. Basedon our theoretical model, we quantified the gains from services trade via a small set of
sufficient statistics informed by our data and estimates, showing that
Moreover, our results show the potential for sizable economic gains resulting fromtrade in knowledge services for the German economy. As a result, our estimates provide
tentative policy advice. Policy makers should be aware of the importance of access toforeign knowledge services within their trade negotiations. First, foreign knowledge
leads to an improved innovation performance of their domestic firms. Second, firms’
domestic innovation efforts are complemented by foreign knowledge access. Therefore,
the effect of an increase in foreign knowledge access via service trades is not limited toraising knowledge imports but raises indigenous innovation efforts at the same time.
In addition, as a result of technological progress, it is reasonable to expect that tradein knowledge services is going to expand further. It might even be that the bulk ofinternational service trade still lies ahead (Eppinger 2019). Thus, policy makers should
aim at utilizing this potential opportunity for economic gains resulting from increasing
access to foreign knowledge. However, while trying to utilize the potential gains fromservice trade, it is necessary to consider the heterogeneous effects of different service
types, as access to foreign services unrelated to knowledge did not seem to foster
domestic firm innovation.
There are several starting points for future research. First, Germany was the focus
of our study. However, the effects of foreign knowledge services might differ between
more and less developed countries. At this point, the previous literature already showedthat countries differ with regard to their imports of intermediate goods (Shu & Steinwender (2019)). As a result, studies exploring the importance of country characteristics
for the effects of foreign knowledge service access would be promising additions to
the literature. Second, our model predicts a heterogeneous relevance of knowledge
service access between firms, whereas our analysis concentrates on the average firm.
Thus, similar to contributing by focusing on country characteristics, systematicallyinvestigating the heterogeneous effects of foreign knowledge access for firms withdifferent characteristics has the potential to provide valuable insights. Third, we cannot

28

investigate the separate effects of different knowledge service types because of sample
limitations. Thus, constructing a similar database for a larger sample, such as a large
sample of US or EU firms, and repeating our analysis could contribute to the literatureby shedding light on a potentially differing relevance of our covered knowledge service
types.

29

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34

Appendix
Appendix A.

TablesTable A1. Knowledge Service Exports to Germany: Major Source Countries and Sourcing
Industries

Share in Total Knowledge Service Imports (%)
Source Country
United States

36

United Kingdom

10

Switzerland

9

France8Austria5

Others32

Sourcing Industry
Chemicals and Chemical Products

22

Other Business Activities

17

Motor-Vehicles, Trailers, Semi-Trailers

15

Electrical Machinery and Apparatus

7

Wholesale and Commission Trade

5

Research and Development

5

Others27

Notes: Based on annual averages of total knowledge service imports of all German residents in the SITS database during the period
2005 to 2012. Where applicable, averages taken across industry or source country. Imports of knowledge services are defined as
total yearly imports of services related to (i) research, development, and testing (BPM5 code 511), (ii) patents, licenses, inventions,and processes (502), (iii) artistic copyrights (501), and (iv) other rights, such as franchise fees, trademarks, and marketing rights(503).

35

Table A2. Sample Descriptive Statistics

Knowledge Service Importers

Non-Importers

Unique Firm Observations

512

10,639Firm-Year Observations

1,334

25,718Innovation-related firm characteristics

Mean

Stand. Dev.

Mean

Stand. Dev.

Knowledge Service Imports (€millions)

0.64

0.75

0

0.0

Product or Process Innovation (%)

68.6

46.4

33.2

47.1

Product innovation (%)

64.5

47.9

29.8

45.7

Revenue share of product innovations (%)

18.6

25.5

8.2

18.6

Revenues of product Innovations (€millions)

60.0

79.5

3.1

5.4

Process Innovation (%)

30.3

45.9

12.1

32.5

Unit cost reduction from process innovation (%)

2.6

5.9

1.2

4.7

Cost savings from process innovations (€millions)

1.74

24.9

0.05

0.7

Occasional internal R&D (%)

11.1

31.5

10.1

32.9

Continuous internal R&D (%)

61.9

48.6

18.9

30.2

Older than 21 years (%)

53.1

49.9

42.2

49.4

More than 250 employees (%)

42.8

49.5

6.7

25.0

Domestic Company Group (%)

13.6

34.3

12.3

29.8

Exporter (%)

88.1

32.3

48.1

49.9

Multinational Company Group (%)

53.8

49.8

9.8

29.7

General firm characteristics

Notes: Descriptive statistics are based on unweighted averages taken across all firm-year observations during the sample period
from 2005 to 2012, and are calculated separately by firm-year importer status. Importers are firms with positive expenditures on
foreign knowledge services. Knowledge service imports are calculated from the SITS database, and defined as total yearly importsof services related to (i) research, development, and testing (BPM5 code 511), (ii) patents, licenses, inventions, and processes (502),(iii) artistic copyrights (501), and (iv) other rights, such as franchise fees, trademarks, and marketing rights (503). All other firm
characteristics are taken from the MIP database. Product innovation is defined as the introduction of one or many new or
improved products. Process innovation is defined as the introduction of new or improved production processes. Revenue share of
product innovations and unit cost reduction from process innovation are measured in percent and multiplied by 100. Averages ofall other variables measured in percent correspond to an average across dummy variables multiplied by 100.

36

37
0.23
X
X
X
X
26512

0.121∗∗∗(0.007)0.008∗∗∗(0.001)–0.046∗∗∗(0.004)–0.030∗∗∗(0.002)–0.042∗∗∗(0.003)–0.051∗∗∗(0.007)0.005(0.005)

Old

0.289
X
X
X
X
26512

–0.000(0.002)0.182∗∗∗(0.004)0.136∗∗∗(0.002)0.014∗∗∗(0.002)0.074∗∗∗(0.002)0.004(0.004)0.036∗∗∗(0.004)

Large

(2)

0.31
X
X
X
X
26512

0.157∗∗∗(0.008)0.041∗∗∗(0.002)0.157∗∗∗(0.002)0.258∗∗∗(0.005)–0.002(0.002)–0.008∗∗∗(0.001)–0.002(0.006)

Exporter

(3)

0.27
X
X
X
X
26512

–0.174∗∗∗(0.016)
0.036∗∗∗(0.003)0.089∗∗∗(0.008)0.007(0.005)–0.019∗∗∗(0.002)0.254∗∗∗(0.008)0.070∗∗∗(0.001)

Multin. Group

(4)

0.10
X
X
X
X
26512

0.027∗∗∗(0.001)
0.046∗∗∗(0.002)–0.004(0.003)–0.016∗∗∗(0.001)0.240∗∗∗(0.012)0.023∗∗∗(0.001)–0.220∗∗∗(0.001)Ger. Group

(5)

0.11
X
X
X
X
26512

–0.231∗∗∗(0.008)–0.000(0.002)–0.018∗∗∗(0.001)0.020∗∗∗(0.004)0.082∗∗∗(0.001)0.038∗∗∗(0.002)0.022∗∗∗(0.001)

Occ. R&D

(6)

0.36
X
X
X
X
26512

–0.001(0.003)–0.029∗∗∗(0.001)0.142∗∗∗(0.006)
0.159∗∗∗(0.003)0.123∗∗∗(0.014)–0.050∗∗∗(0.002)–0.302∗∗∗(0.015)Cont. R&D

(7)

0.43
X
X
X
X
11106

0.004
(0.005)–0.022∗∗∗(0.002)0.087∗∗∗(0.004)0.074∗∗∗(0.002)0.035∗∗∗(0.003)0.043∗∗∗(0.002)0.411∗∗∗(0.006)–0.570∗∗∗(0.007)(8)
Innovation indicator
1-yr lagNotes: The table presents the results of estimating (1) using firm controls and various lags of our innovation indicator as dependent variables. Estimates are based on OLS. Fixed effects
are included as indicated. Standard errors are displayed in parentheses and clustered at the firm- and import-country-combination-level. P-values correspond to * p < 0.1, ** p < 0.05,*** p < 0.01.

R2Year FE
Industry FE
State FE
Import-Origin FE
Observations

MultinationalGroup
GermanGroup
Occasional
R&D
Continuous
R&D

ExporterLarge Firm

Old Firm

Sft

Dep. Variable(1)

Table A3. Quasi-Random Assignment of Common Shocks: Falsification Tests

Table A4. Export Supply Shocks to Knowledge Services: Effect on Firm Innovation
Propensity
(1)

(2)

(3)

(4)

(5)

(6)

0.027∗∗∗

0.016∗∗∗

0.016∗∗∗

0.007∗∗∗

0.005∗∗

0.006∗∗∗(0.002)(0.002)(0.001)(0.002)(0.004)(0.002)–0.042∗∗∗–0.019∗∗∗(0.002)(0.002)0.163∗∗∗

0.079∗∗∗(0.004)(0.004)0.177∗∗∗

0.063∗∗∗(0.002)(0.002)Multinational Group

0.100∗∗∗

0.021∗∗∗(0.010)(0.002)German Group0.07∗∗∗

0.036∗∗∗(0.002)(0.002)

Export Supply Knowledge Services
Controls
Old Firm
Large Firm
Exporter

0.503∗∗∗

Occasional R&D(0.002)0.621∗∗∗

Continuous R&D(0.005)
R2

0.02

0.16

0.16

0.18

0.23

0.45

Year FE

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Industry FE
Federal State FE
Import Origin FE
Unique Firms

11151

11151

11151

11151

11151

11151

Observations

26512

26512

26512

26512

26512

26512

Notes: Coefficient estimates for specification (1) with a firm dummy indicating the introduction of new or significantly improved
products or processes as dependent variable. Shocks to firms’ export supply of knowledge services correspond to variable S f t
defined in (2). Fixed effects are included as indicated. Standard errors are displayed in parentheses and clustered at the firm- andimport-country-combination-level. P-values correspond to *p < 0.1, ** p < 0.05, ***p < 0.01. P-values are robust to implementing thestandard error correction proposed by Adao et al. (2019).

38

Table A5. Export Supply Shocks to Knowledge Services: Effect on Firm Innovation
Propensity, Robustness Checks

Knowledge Service Export Supply: Baseline

(1)

(2)

0.006∗∗∗

0.012∗∗∗(0.002)(0.003)

(3)

(4)

(5)

(6)

0.006∗∗∗

Alternative year t0 to measure exposure(0.000)
Only main importers

0.003(0.111)0.015∗

Excluding main importers(0.003)
Export Supply Other Services–0.000(0.096)

R2

0.63

0.42

0.44

0.44

0.44

0.44

Year FE

X

X

X

X

X

X

Industry FE

X

X

X

X

X

X

Federal State FE

X

X

X

X

X

X

Import Origin FE

X

X

X

X

X

X

Observations

1330

23308

26512

26512

26512

26512

Notes: Coefficient estimate for β in specification (1) with a dummy indicating product, service, or process innovation as dependent
variable. Shocks to firms’ export supply of knowledge services correspond to variable S f t defined in (2). Column 1 restricts theestimation sample to firms with positive imports of knowledge-related services during the pre-estimation years 2002-2004. Column
2 restricts the estimation sample to firms not part of a multinational company group. Column 3 constructs export supply shocks asin (2), but sets the reference year for shock exposure to to the first year a firm appears in the SITS database. Column 4 constructs
S f ,t as in (2), but only uses information on imports from the set of major source countries listed in table (A1) to construct shocks
and exposure weights. Column 5 constructs S f ,t as in (2), but excludes imports from all major source countries. to construct shocks
and exposure weights. Column 6 replaces S f ,t with shocks to the export supply of service types not included in the definition ofknowledge services, following (2) and using information on firm-level and economy-wide imports of all services types from theSITS. Estimates are based on a linear probability model, and fixed effects are included as indicated. Standard errors are displayedin parentheses and are clustered at the firm- and import-country-combination-level. P-values correspond to ∗ p < 0.1, ∗∗ p < 0.05,∗∗∗ p < 0.01.

39

40
0.18
26512

–0.006∗∗(0.002)0.111∗∗∗(0.005)0.015∗∗∗(0.002)0.055∗∗∗(0.005)0.036∗∗∗(0.002)
0.195∗∗∗(0.003)0.248∗∗∗(0.002)0.10
26512–0.002∗∗∗(0.000)0.003∗∗∗(0.047)0.002∗∗∗(0.000)0.002∗∗∗(0.000)0.003∗∗∗(0.000)0.017∗∗∗(0.000)0.025∗∗∗(0.039)0.001∗∗∗(0.000)0.005∗∗(0.002)

0.21
26512

–0.010(0.045)2.094∗∗∗(0.089)0.207∗∗∗(0.028)0.966∗∗∗(0.071)0.544∗∗∗(0.042)2.475∗∗∗(0.049)3.305∗∗∗(0.051)

0.096∗∗(0.039)log(total reduction)

0.45
26512

–0.017∗∗∗(0.002)0.064∗∗∗(0.006)
0.064∗∗∗(0.002)0.019∗∗∗(0.003)0.022∗∗∗(0.002)0.454∗∗∗(0.003)0.611∗∗∗(0.006)0.006∗∗(0.002)dummy (0/1)

0.32
26512

–0.019∗∗∗(0.001)–0.013∗∗∗(0.003)0.021∗∗∗(0.001)–0.004∗∗∗(0.001)0.000(0.001)9.809∗∗∗(0.101)0.188∗∗∗(0.003)0.001(0.001)

in % of revenue

0.49
26512

–0.106∗∗∗(0.033)
1.943∗∗∗(0.077)
0.946∗∗∗(0.024)0.849∗∗∗(0.053)0.560∗∗∗(0.035)5.892∗∗∗(0.024)8.464∗∗∗(0.054)0.113∗∗∗(0.044)log(total revenue)

Product/Service Innovation

Notes: Coefficient estimates for specification (1) using innovation outcomes capturing product and process innovation as dependent variables. Shocks to firms’ export supply ofknowledge services correspond to variable S f t defined in (2). Estimates are based on OLS, and include year, industry, federal state, and import-origin fixed effects. Standard errors are
displayed in parentheses and clustered at the firm- and import-origin-level. P-values correspond to * p < 0.1, ** p < 0.05, *** p < 0.01.

R2
Observations

Continuous internal R&D

Occasional internal R&D

Domestic Company GroupMultinational Company Group

ExporterLarge Firm

Old Firm

Controls

Export Supply Knowledge Services

in % of unit costs

dummy (0/1)

Cost Savings from Process Innvation

Table A6. Export Supply Shocks to Knowledge Services: Effect on Firm Product/Process Innovation

Table A7. Supply Shocks to Knowledge Service Exports: Effect on Firms’ Domestic R&D
Expenditures

Export supply knowledge services

(1)

(2)

(3)

(4)

(5)

(6)

0.509∗∗∗

0.337∗∗∗

0.334∗∗∗

0.164∗∗∗

0.070∗∗∗

0.038(0.038)(0.031)(0.031)(0.026)(0.016)(0.037)

Controls
Old Firm (0/1)
Large Firm (0/1)
Exporter (0/1)
Multinational Group
German Group–0.322∗∗∗

0.024

0.014

(0.054)(0.024)(0.014)2.857∗∗∗

1.052∗∗∗

0.983∗∗∗(0.105)(0.045)(0.049)2.292∗∗∗

0.300∗∗∗

0.292∗∗∗(0.050)(0.012)(0.008)1.944∗∗∗

0.502∗∗∗

0.292∗∗∗(0.084)(0.054)(0.008)0.830∗∗∗

0.204∗∗∗

0.444∗∗∗(0.036)
Occasional R&D
Continuous R&D(0.014)(0.026)8.455∗∗∗

8.456∗∗∗(0.056)(0.048)10.90∗∗∗

10.83∗∗∗(0.095)(0.041)

R2

0.05

0.27

0.27

0.35

0.86

0.865

Year FE

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Industry FE
Federal State FE

X

Import-Origin FE
Observations

26512

26512

26512

26512

26512

26512

Notes: Coefficient estimates of specification (1) with log(domestic R&D expenditures+1) as dependent variable. Domestic R&D
expenditures are measured as the difference between firms’ total R&D expenditures reported in the MIP and expenditures on R&D
service imports from the SITS. Shocks to firms’ export supply of knowledge services correspond to variable S f t defined in (2).
Estimates are based on OLS. Fixed effects are included as indicated. Standard errors are displayed in parentheses and clustered at
the firm- and import-country-combination-level. P-values correspond to * p < 0.1, ** p < 0.05, *** p < 0.01.

41

Table A8. Calibrated Moments

Parameter/StatistichiEs pτqθ Iθh ,Es [ϕθ ]θ θ θKnowledge import ratios

Estimate

Source/Target

0.002, 0.19

Author’s calculations

Cannibalization rate

1–ρθ +εθ ρθ
σ0.5

Hottman et al. (2016)

Product level surplus

δ

1.05

n.a.

Perceived demand elasticictyε7.6µ = 1.15

Price cost pass-throughρ

0.7

Amiti et al. (2019)

EoS across firms

σ

11.1

Authors’ calculations

Aggregate trade elasticity

τI– ∂∂ln
ln τ
γc

0.8

Authors’ estimates

0.004

Authors’ estimates

γh

–0.95

Author’s estimates

Innovation cost pass-throughs

Table A9. Calibrated Welfare Gains from Services Tradeln U–∂∂ ln τ

Welfare Gain

0.06

Decomposition
New Products

27%

New Firms

64%

GDP

9%

Notes: This table presents estimates of the elasticity of welfare with respect to variable trade costs of knowledge service imports
following Theorem 1 under the assumption that firms are homogeneous and using the estimates in table A8.

Table A10. Welfare Gains: Robustness

ρ = 0.9µ = 1.25µ = 1.25,ρ = 0.9

0.10

0.17

0.13

New Products

29%

32%

33%

New Firms

67%

58%

62%

GDP

5%

10%

5%

Welfare Gain
Decomposition

Notes: This table presents estimates of the elasticity of welfare with respect to the relative costs of service imports in Theorem 1,
using the estimates in Table A8.

42

Appendix B.

ProofsB.1.

Derivation of the knowledge production function
Define G(ι) = Pr ι(ω) > ι̃ . For a given number of ideas, the probability of a firm acquires
less than ι̃ units of additional expertise in knowledge area ω equals:
"
Pr

#
max

i=0,1,...,n(ω)–1

ι(ω) ≤ ι̃ = (1 – G(ι̃))n(ω) .

(A1)

Given that the arrival rate of new ideas is distributed Possion with mean N(ω), n(ω) ∼Poisson(N(ω)):
 ∞ e–N(ω) N(ω)nPr ι(ω) ≤ ι̃ = ∑(1 – G(ι̃))nn!
n=0∞ (N(1 – G(ι̃))n(A2)= e–N(ω) ∑n!
n=0= e–N(ω)G(ι̃)
For a general distribution G(·), this last equation describes the distribution of expertise inknowledge area ω for a given number of activities completed N(ω). When the quality ofγ
ideas is drawn from a Pareto distribution, Pr[ιi (ω) > ι̃] = G(ι̃) = k j ι̃–ζ , then Pr ι(ω) ≤ ι̃ =e–N(ω)kγj (ι̃)–ζ, whereE(ι(ω))χ =Z ∞(z)χ d(1 – e–N(ω)kγj (z)–ζ

)dz

0

Z ∞
=
Z0
=
0

γ

(z)χ (N(ω)k j ζ(z)ζ–1 )e∞h–N(ω)kζ–γ
z –ζ
j

dz

γ χ/ζ 1– χu ζ –1 e–u duN(ω)k j

i

h
iχ/ζ
γχ/ζ
=Γ (1 – χ/ζ) N(ω)
kj ,γwhere we changed the variable of integration in the third line to u = N(ω)k j z –ζ so thatγ/ζγ

z = N(ω)1/ζ k j u–1/ζ and du = –ζN(ω)k j z –ζ–1 dz. Here, Γ (·) denotes the Gamma function.
Since 2χ < 2 < ζ by assumption, the expectation above is well defined, 1 – χ/ζ > 0.
To derive the knowledge production function, let the set of feasible input combina-

43

tions that, in expectation, yield innovation output ι be defined as:γ/ζN(ι j ) ≡ {N(ω)ω∈Ω : k j Γ (1 – χ/ζ)1/χZ hiχ/ζ N(ω)
dω = ιχ }ω

Undernthe parametric restriction
2κ ≤ ζ, the following term has a finite variance foro∀N ∈ N(dki ) : dk j ≥ 0 ,
Z

h

Ωj

i

γ h
ζ

Var z(ω) N j (ω) dω = k j

Γ (1– 2 · χ/ζ) – Γ 2(1 – χ/ζ)iZΩi

N(ω)2χ/ζ dω < ∞,We impose that there exist an an extension of the Kolmogorov measure which ensuresthat all paths N(·) are measurable. The strong law of large numbers for independently
distributed random variables then gives the innovation production function:a.s.
ι j = kγ/ζ A1/χ
j

!1/χ

Z


χ/ζ
N(ω)
dω

,

Ωj

where A ≡ Γ (1 – χ/ζ) . The knowledge production function, then, satisfies
k0j – k j
kj
B.2.

γ/ζ–1

= ι j /k j = A1/χ k j

Z
Ωj

!1/χ

χ/ζ
dω
.
N(ω)

Derivation of the Innovation Cost Functionq

Let the offshoring cutoff ω∗ be implicitly defined by qFHτ = t(ω∗ ) so that tasks inω ∈ [0, ω∗ ] are either performed in-house, using labor; or offshored, using a foreign
contractor. The monotonicity of t(·), then, implies that tasks up to a cutoff ω∗o ≤ ω∗ areoffshored, with this cutoff being implicitly defined by:N(ω∗o ) =ατt(ω∗o )qF 1/(α–1).
wH

The remaining tasks ω ∈ [ω∗o , ω∗ ] will be produced in-house.
Cost-symmetry between tasks that are outsourced domestically implies that all
tasks in the set [ω∗ , 1] must be performed in-house if wH N(ω∗ )α–1 < qH ; else, they are
optimally outsourced to domestic contractors.
These considerations imply that the firm’s cost-minimization problem can be written

44

as:
Z ω∗

Z 1

κ(ι, τ) =minqH
Nd (ω)dω + τqFoω∗i
Nd (ω), N(ω), Ni (ω)

o

Z ω∗
i

N(ω)t(ω)dω + qH
Ni (ω)α dωω∗oω∗ , ω∗o , ω∗iχ/ζ+ λ ι – kγ/ζ (1 – ω∗i )Nd

Z ω∗
0

+
0

!1/χ "#∗ )q 1/(α–1)
ατt(ω
o F
+ λO
– N(ω∗o )wH+ λI t(ω∗ )τqF – qH
+ λD wH N(ω∗ )α – qH N(ω∗i )α .
The optimal intensity Ni (ω) ≡ Ni for tasks performed in-house satisfies the following
FOC:
χ/ζ 1
,
wH Niα α = λι1–χ Niζ
∂ ln κ(ι,τ)τ ∂κ
By the envelope theorem, ∂κ∂ι = λ, κ ∂τ = ϕo . Defining E ≡ ∂ ln ι , we can then express
the cost share of tasks performed in-house, ϕI ≡ (ω∗i – ω∗o )wH NIα as:
χ/ζ
Ni 1
I
∗
∗
ϕ α ≡ (ωi – ωo )E χ .
ι ζ

Following similar steps, the FOCs determining the intensity of outsourced tasks can be
written as:


R ω∗o
∗ N χ/ζ
χ/ζ
1
–
ω
γ/ζ
N(ω) kD 1
iϕO = E 0, ϕD = E
.
χ
χ
ι
ζ
ι
ζ
Rearranging and substituting into the constraint, we obtain:hi
E = ζ ϕI α + 1 – ϕ .
2O∂ ln ι
Noting that ∂∂E= ∂ ln= ∂∂ϕ, the cross-elasticity of the cost elasticity E withln ττ∂ ln ιln ιrespect to the cost parameter τ equals:∂ ln E(1 – ϕO )= ϕo ×× ηO ,∂ ln τ
E

45

χ/ζ

N(ω)χ/ζ dω + (ω∗i – ω∗o )NiO

where we defined the output elasticity of the offshoring share as ηO ≡ ∂ ln∂ϕln (ι,τ). Givenι∂κκthat marginal cost are equal to: ∂ι = ι × E, we can then express the elasticity of marginal
cost with respect to innovation scale and offshoring cost as:
"
#


O
∂κ
1
–
ϕ
∂ ln EOO
d ln= ϕ × 1+
· η × d ln τ + E +× d ln ι.
∂ιE∂ ln ι
Differentiating the optimal input demands, we can further show thatϕO (1 – ϕO )

1–  Iζ ϕ α + 1 – ϕI

R ω∗

!

o N(ω∗ )χ/ζ dω∂ ln ω∗o,oN(ω)χ/ζ dω ∂ ln ι· ηO = –χ + Roω∗
0

o

α–χ/ζ

and, since (t(ω∗o )qH τ) α–1 = ικ×E
χ ×ζ ,∂ ln ω∗0
α – 1 ∂ ln ω∗o=·∂ ln ι
α – χ/ζ ∂ ln t(ω∗o )E–χ+which impliesζ ϕI α + 1 – ϕI

ϕO (1 – ϕO )
E+  Iζ ϕ α + 1 – ϕI

1 – T(ω∗o )ηO > 0 ⇔ χ<T(ω∗o )
whereϕO (1 – ϕO )

!
,

!

R ω∗
∗
o N(ω∗ )χ/ζ dω
α
–
1
∂
ln
ω
o
o
∗
o
T(ωo ) ≡
.
∗
R
∗
ω
o
α – χ/ζ ∂ ln t(ωo )N(ω)χ/ζ dω
0



t(ω)
Since N(ω) = t(ω∗)
o1/χ/ζ–1

N(ω∗o ), a sufficient condition for ηO > 0 is hence given by:1

α–1t(ω̄) 1–χ/ζ∂t(ω̄)>.
χ/ζα – χ/ζ R ω∗o∂ω̄χ/ζ–1 dωo t(ω)
To derive the threshold innovation investment for offshoring, note that no tasks will beoffshored if α–1E/ζ α–χ/ζ∗t(ωo ) =(τqF ) –1 < t(0)ιχ
 α–1Since 1 ≤ E/ζ ≤ α, ∃ιo s.t. ∀ι < ιO , t(0) > ιαχ α–χ/ζ (τqF ) –1 and hence ω∗o = 0. Similarly,∃ιD , s.t. ∀ι < ιD , 1 – ω∗I = 0 and no domestic offshoring occurs.

46

B.3.

Problem of the Firm

A firm of type θ can build k0 units of knowledge capital for a particular product j at a
total innovation cost of κθ (k0 ) ≡ κ(k0 – kθ ). The derivations in the text, then, imply that∂ ln κ
∂κ∂ ln κ k0 ∂ ln κ k0
×
=
=
×
=
0
∂ ln k∂ ln ιθ ιθ∂ιθκθ ∂ιθ
This section provides detailed derivations of optimal firm decisions. Conditional on
an importing regime 1I , the problem of a firm θ can be written:(oR hn–ε pε–1 s ( p ) – η (ι) – κκ d jΠθ (1I ) = maxh, p ,k,p,λ
[
p
–
c
(k)]
p
θ
θ P
θ
j
0
θ
j
j
)
,
R

h 1–ε
1/(1–ε)+λ ( 0 p j d j )–p
In the following, we establish the existence and uniqueness of a solution to thisproblem. Throughout, we treat a firm’s product range h as a continuous variable.
S
Prices and product range range . The firm chooses ( p j ) ∈ P ≡ j ∈[0,h] P[0,h] where P[0,h]denotes all smooth, strictly positive price allocations on [0, h]. The FOC with respect to
p j is given by,[(1 – ε) p j + εc j ]which implies:

pj yj
pεθ

+ λ p1–ε
j = 0,

(A3)

Z h
0

[(1 – ε) p j + εc j ] p j y j d j = λpθGiven h, k and p, it is easy to verify that the second-order condition is satisfied globally
pj ∂yjsince p1 λpε p–ε
+
(1–
ε)
y
j < 0, which establishes a global maximum p j (h, p, k),j y ∂pjjj

Next, the FOC with respect to h is given by
Z h
ε
1
1–ε
d j ) 1–ε = 0.
[ pi – ci ] yi – f i – κi +λ pi (p1–εj
1–ε0∂[ p –c ] y(A4)i θ i = –λ p1–ε pε < 0. Evoking the
Applying the envelope theorem, we obtain∂ piiimplicit function theorem and Assumption 1, we can show that47∂ p j (h, p, k)∂hε – σθ 1=·
1–ε p 1– yσθλpε p–ε
j ε–σ

θ

1
j pj




pj ∂yj–εε
λp p j y ∂ p + (1 – ε) y j
j
j

< 0,

which implies that the left-hand-side of (A4) is strictly decreasing sinceε
λ p1–εi ph 1 ∂p

i +

pi ∂h

Z
1 1 1–ε 1 h ∂ p j i
p +d j < 0.
1–εp ip 0 ∂hHence, there exist global maxima for any given p and ι, p j (p, ι) and h(p, ι).
The FOC for p is given by
Z h[ pi – ci ] yi di = pθ λ.

(ε – σθ )0(A5)∂h[ pi –cθ ] yθ∂h[ pi –cθ ] yθ
1 λ p1–ε pε ,and
= –λ p1–εpε h < 0,
= σ–1
∂ pi
i
i
∂h
∂
y
∂
p
j
∂h
i
∂p ∝ ∂p < 0,implying that, ∂p > 0. It is then easy to check that the left-hand-side of

By the envelope theorem,(A5) is strictly decreasing. Hence, there exists a unique product range and price thatsolves the firm’s problem at a given level of innovation investment.
Combining these first-order conditions, we obtain the characterization of prices andquantities stated in the main text.
Z h
0

Z h
[(σθ – 1) p j + σθ c j ] p j y j d j = (ε – σθ )σθpθ j =c ,σθ – 1 θ j

p1–ε
θ = µθ

i

Z hθ 

Z hθ00[ pi – ci ] yi di

cθ1–ε
j dj.

This implies:
Z hθ h0( p θ j – cθ j ) y θ j – f θ j d j =01
c y – f θj d jσθ – 1 θ j θ jFrom the FOC for hθ :Z hθ 
0
Z hθ h1ε – σθ ip y – f θ j̄ – κθ j̄ d j =pθ j y θ jdjσθ θ j̄ θ j̄
ε–1
0

48

Knowledge .

The FOC with respect to innovation is given by"#kθ0 c0 (kθ0 )kθ0 f 0 (kθ0 )∂ ln κθ–f θ – κθy θ cθ –
= 0.
cθ
fθ
∂ιθ

(A6)

Further below, we derive the determinant of the Hessian of the firm’s market valuefunction, given by:
1 ∂ ln f θ )/Ehi n ∂ ln(– ∂ ln cθ – ε–1oθ ∂ ln( f θ + κθ )∂ ln ιθ∂ ln ιθdet Hvθ =+– Eθ .
∂ ln ιθ∂ ln ιθ

where Eθ is the innovation scale elasticity defined in Proposition 1. The following,
then, gives a sufficient condition that guarantees the existence and uniqueness of awell-defined solution to the firm’s problem:∂ ln f∂ ln cθ1θ∂ ln f θfθ∂ ln Eθ ∂ ln(– ∂ ln ιθ – εθ –1 ∂ ln ιθ ).
<+(– Eθ ) ·∂ ln ιθ∂ ln ιθ∂ ln ιθf θ + κθ

B.4.

Log-linearized model

In this part, we log-linearize the model. We expand all equilibrium conditions to theln yθyθ
first order in shocks. We repeatedly use the following elasticities: – ∂∂ ln= σθ , – ∂∂ ln
=
p
ln h
θ

θ

σθ
∂ ln yθεθ –1 , and ∂ ln P = σθ – 1. As in the main text, we suppress product subscripts throughout

the derivations, yθ ≡ yθ j .
Markups
1 d ln h , changes markups are given by
Noting that d ln pθ = d ln pθ + 1–εθ
d ln µθθ= ρρθ –1 d ln pPθ = 1–ρ
ρθ
θ



1
ε–1 d ln hθ + d ln P – d ln pθ


.

(A7)

Prices and Quantities
The changes in product-level and firm-level prices equald ln pθ = d ln θ + d ln cθ.
1= (1 – ρθ ) d ln P + ε–1 d ln hθ + ρθ d ln cθ

(A8)

ρθ
d ln hθ ,(A9)
ε–1
Given these changes in prices, the corresponding changes in product quantity and firmd ln pθ = (1 – ρθ )d ln P + ρθ d ln cθ –49

market share equal,–εθd ln hθ – σθ ρθ d ln cθ + (σθ ρθ – 1)d ln P .
d ln yθ = σθερθ–1

(A10)



1
p
d ln sθ = (1 – σθ )d ln θ = (σθ – 1)ρθ d ln P +d ln hθ – d ln cθPεθ – 1(A11)

θ

Innovation
To differentiate the first-order conditions for innovation, we first evoke Proposition
1 to show tht


f
ιθ


∂ ln κθ k + Eθ k0
1 – ϕo(A12)θ=ϕθ · 1 + Ω̃θ· ηo · d ln τ∂ ln τ
E
k0
where Ω̃ = ι θ Eθ /θf
k + Eθ kιθ0θ
. The total derivative of the FOC for innovation invest-

ments then equals:"γcc
θ d ln cθ = ϕθ · 1 + Ω̃

1 – ϕOθ#d ln hθ
η
d
ln
τ
+
(1
–
σ
ρ
)d
ln
P
+
(ε
–
σ
ρ
)
,
o
θ
θ
θ
θ
θ
εθ – 1
EO
θ

(A13)

where
f
∂ ln(–cθ – ε 1–1 θ )kθ0∂ ln c–1 (k0 )∂ ln E
cc
θ

–
(E
+
Ω̃
)
×
–
1
.
γθ = 1 – σθ ρθ + θθ∂ ln ιθιθ∂ ln cθ∂ ln kθ0Differentiating the FOC for hθ , we can show that:
γhc
d ln hθ1 – σθ ρθ
1 – Ωθ Oθ=d ln P +d ln cθ +d ln τ
εθ – 1ρθ σθ – εθρθ σθ – εθρθ σθ – εθ
where γhcθ ≡ σθ ρθ – 1+

(A14)

∂ ln( f θ +κθ ) ∂ ln c–1 (kθ )fθand Ωθ ≡ f +κdenotes the share of product∂ ln cθ∂ ln kθ jθ θ

sunk costs attributable to innovation investment.
Substituting for εhθ–1 in the total derivative of the FOC for knowledge, we obtain:θ

1–ϕOΩθ – Ω̃θ E θ · ηocd ln cθ = ϕO·d ln τ ≡ ϕOθ
θ · Γθ · d ln τcchcγθ + γθ50Γθc · γhc
1 – σθ ρθd ln hθOθ + Ωθ d ln τ=d ln P + ϕθ ·εθ – 1ρθ σθ – εθρθ σθ – εθFree Entry
We denote a firm’s total expenditures on imported knowledge services by τIθ ≡R1
hθ 0 1{O(ω) = 1}τwF ψt(ω)N(ω)dω ≡ hθ κθ ϕθ . Applying the envelope theorem to differentiate the free entry condition, we then obtain:
i
R h
P∂ yθ
h
(
p
–
c
)
y
d
ln
P
–
h
κ
ϕ
d
ln
τ
dG(θ) = 0θ θ θθ θ y ∂P
Θ θ θ

(A15)

θ

Budget constraint
Differentiating the budget constraint, we find:hp i
0 = d ln M + Es (1 – σθ )d ln θ
P

(A16)

WelfareBy virtue of the envelope theorem, changes in consumer surplus are given by– d ln PY = dW = Es [δθ – 1] d ln M + Es d ln pθ
B.5.

(A17)

Derivation of firm-level effects of Services Trade costs∂y

To derive the change in the common aggregator, note that ( pθ – cθ ) · hθ · yθ · yP · ∂Pθ =σθ –1
1σθ · pθ · y θ · hθ = µθ sθ to rewrite equation A15 as:

θ


Z 
P∂ yθ
h θ ( p θ – cθ ) y θ
d ln P – hθ κθ ϕθ d ln τ dG(θ) = 0
yθ ∂P
Θ
 


1
hθ κθ
⇔Es
ϕθ d ln τ = 0
d ln P – Esµθsθ
⇔d ln P = µ × ϕ × d ln τ,–1where we denoted the average markup
h by µ ≡ E
i s [1/µθ ] , and the cost share of imported
services in aggregate sales by ϕ ≡ Es hθs κθ ϕθ .
θTo derive the direct effect, we begin by solving for changes in marginal costs d ln cθ
and product variety d ln hθ as functions of changes in trade costs d ln τ and competitiond ln P. Using equations (A14) and (A13) we obtain:d ln cθ = Γθc ϕO
θ d ln τ,

51

(A18)

1
1 – σθ ρθd ln hθ = Γθh ϕO
d ln τ +d ln P.
θεθ – 1ρθ σθ – εθ(A19)

The structural pass-through of knowledge cost shocks into unit costs, Γθc , is given by∂ ln cθ=Γθc ≡∂ ln κθθ ηOΩθ – Ω̃θ 1–ϕ
θ
h Eθi
.
det Hvθ

Here,Hvθ is the Hessian of the firm’s logged market value function, which is negative
i n ∂ ln(– ∂ ln cθ – ε 1–1 ∂ ln f θ )/Eθ ∂ ln( f + κ )ho∂ ln ιθ∂ ln ιθθθθ
det Hvθ =+– Eθ
∂ ln ιθ∂ ln ιθ< 0.

θHence, Γθc > 0 if, and only if, ∂c∂ι < 0.
θ

Proof. The pass-through of knowledge cost shocks into a firm’s product range, in turn,equals:Γθc + (1 – Ωθ )∂ ln hθ γhc
h
θ
,
(A20)
Γθ ≡
≡
∂ ln κθρθ σθ – εwhereγhc
θ = 1 – σθ ρθ –∂ ln f θΩθ+ (1 – Ωθ )Eθ∂ ln ιθ∂ ln c–1 (kθ )∂ ln cθ

(A21)

f +κ

c
θ θ
Rising innovation cost induce less product innovation if γhc> 0. Restrictingθ Γθ + ωκθcattention to the empirically relevant case where Γθ > 0, this implies that the pass-throughof cost shocks into product scope Γθh is negative if

f θ ∂ ln f θ∂ ln c–1 (ιθ )1 pθ y θ1κθ· Eθ · (–)>,(σθ ρθ – 1) – c –κθ + f θ∂ ln cθε – 1 µθΓθ κθ + εθ ∂ ln ιθand positive otherwise. The left-hand-side is unambigiously positive since Γθc > 0 implies
that unit costs are decreasing in knowledge. The sign and magnitude of the term on
the right depends on structural elasticities related to demand (markups, pass-through),technology and innovation.
p
Finally, to characterize the change in a firm’s normalized price d ln Pθ in terms ofchanges in trade costs, we can substitute the above expressions for d ln P, d ln cθ andd ln hθ into equation (A9),pρθd ln θ = ρθ d ln cθ – ρθ d ln P –d ln hθPεθ – 1

52

= ρθ

B.6.



Γθc – Γθhεθ – 1ϕθ –µ̄Λ d ln τ.
εθ – ρθ σθ

Proof of Theorem 1

Proof. Using equation (A16) to substitute for d ln M in equation (A17), we obtain:
h


p i
dW = (Es [δθ ] – 1) Es (σθ – 1)d ln θ – Es d ln pθPp= –d ln P + Es (σθ – 1)Es [δθ ] – σθ d ln θPEs [δθ ]pθ= –d ln P – Es 1 –,σθ d ln
µθ
P




Es [δθ ] εθ – 1chµ̄Λ d ln τ,= –µ̄Λd ln τ – Es 1 –σθ ρθ Γθ – Γθ ϕθ –µθεθ – ρθ σθ
pwhere we evoked Lemma ?? to solve for d ln P and d ln Pθ and go from the third to thefourth line.
Using Lemma ??, we can then change in real GDP:d ln Q ≡ –Es d ln pθ
1= –Es [1 – ρθ ] d ln P – Es
d ln hθ + ρθ d ln cθεθ – 1h i
1 – ρθ σθch= Es –– 1 + ρθ d ln P – Es Γθ + Γθ ϕθ d ln τρθ σθ – εθ


h
 i
εθ – 1= –Es– ρθ µΛd ln τ – Es Γθc + Γθh ϕθ d ln τεθ – ρθ σθ
h i–1
To characterize changes in the aggregate markup, we totally differentiate µ = Es µ1
θto obtainµd ln µ = –Es(d ln Msθ – d ln µθ ) .
µθ
We use firm-level markups are given byρ –1
pd ln µθ = θ
d ln θ .
ρθP

53The change in total sales of firms of type θ, in turn, is given byhpp id ln Msθ = Es (σθ – 1)d ln θ – (σθ – 1)d ln θ .
PP
Putting this together, we obtain:


h
pθ i
1
ρθ – 1pθ
d ln µ = – Es (σθ – 1)d ln– µ̄Es
(1 – σθ –
)d ln
P
µθ
ρθ
P


 


µ
εθ – 1ch=Es
1–Γθ – Γθ ϕθ +µ̄Λ d ln τ(σθ – 1) ρθ + µ(1 – ρθ ) ·µθεθ – ρθ σθ

B.7.

General equilibrium formulation

To frame our analysis in general equilibrium, we fully specify the problem of contractor
firms and assume that H is a small open economy.
Knowledge services sector
We fully specify the problem of contractors in the services sector. Contractors have thesame span-of-control for performing innovation tasks as firms in the heterogeneous
good sector. More formally, if a contractor wants to supply N units of knowledge services
it must hire ` = ψ1 ×N α workers. We assume that knowledge services Here, the parameterψ governs the relative cost-efficieny of contractors.
We assume that contractors place bids for the right to supply knowledge services toa final good producer at a competitive price ql . A bid takes the form of a binding offer
to supply services at a discount d. The profits of a contractor that submits a bid to win
the auction to supply N knowledge services are given byπN
c (N) = ql N –1 α
N wl – d(N).
ψ

Equilibrium bids ensure that profits are independent of N, which implies that d(N)solves the following differential equation∂d(N)α= ql – N α–1 wl .
∂Nψ
Equilibrium profits are equal to zero, which implies that ql = ψ1 N α–1 wl – d(N)N

54

Under perfect competition and free entry, the aggregate supply curve for knowledge
services in location l equals:Sql , Mls = Mls × N = Mls

Hence, the knowledge services industry

55




ψql 1/(α–1)αwkAppendix C.

Examples of Knowledge Service Trades

Research, Development, and Testing Services. From BioNTech (Germany) to Pfizer (US)
Pfizer and BioNTech entered a detailed research collaboration and license agreement todevelop mRNA-based vaccines for the prevention of influenca in 2018. The agreement
covered the eligibility of BioNTech to receive up to USD 305 million in potential development, regulatory and commercial milestone payments as well as up to double-digit
royalties (BioNTech & Pfizer 2018a). The amounts of potential development payments
are censored in the published agreement (BioNTech & Pfizer 2018b). However, the listof development milestones provides an example of the import of foreign development
services by Pfizer. The milestones covered, inter alia, payments for the initiation of thefirst, second, and third phase of the vaccine’s clinical trials.
Patents, Licences, Inventions, and Processes. From Ballard Power Systems (Canada) to Audi (Germany)
Audi bought a package of patents from Ballard Power Systems in 2015. The trade covereda purchase of fuel cell technology patents from Ballard Power Systems worth EUR 40
million by Audi (dpa 2015), and demonstrated an example of patent services imports by
Audi.
Artistic Copyrights. From Rodd Industrial Design (United Kingdom) to Motorola (United States), Philips(Netherlands), and Panasonic (Japan)
Rodd Industrial Designs is a design studio founded in the United Kingdom in 2000.
It delivers design directions to a variety of foreign companies. Examples are designs
for phones, monitors, electric razors, and shower heads. Customers listed on theirwebsite are, for example, Motorola, Philips, and Panasonic. Rodd Industrial Designs
usually retains the copyrights to their design until the payment of their final invoice(UKIPO 2012). After the payment the copyright is transferred to their customer. Theinternational transfer of copyrights for designs developed by Rodd Industrial Designs
represents an import of copyright services by their the customers.
Other Rights, such as Franchise Fees, Trademarks, and Marketing Rights. From Novartis (Switzerland) to Eris Lifesciences (India)

56

Eris Lifesciences acquired the trademarks Zomelis from Novartis for the Indian market
in 2019. Zomelis is used in the treatment of type two diabetes, whereas it belongs to aclass of drugs relying on the novel DPP4 inhibitors technology. The acquisition of Eris
Lifesciences valued around USD 13 million and represent a trademark service import.
It enabled Eris Lifesciences to introduce Novartis in its product portfolio and to sell iton the Indian market starting December 2019. (Vinay 2019)57

Appendix D.

Endogeneity of Access to Foreign Knowledge Services

Potential sources of endogeneity for access to foreign knowledge services are:a. Reverse Causality: Access to foreign knowledge services might trigger firm innovations due to reducing firms’ cost of innovations, and firm innovations might trigger
access to foreign knowledge services due to a firm’s increasing knowledge sourcing
ability.
b. Self-Selection: More innovative firms might actively improve their access to foreign knowledge services as they potentially benefit more from the access than lessinnovative firms due to its complementarity with existing innovation efforts.
c. Omitted Variable Bias: Firms might be more innovative and have easier accessto foreign knowledge services as a result of unobserved firm characteristics, forinstance, being a member of a multinational company group.
Borusyak et al. (2021) provide conditions under which identification in quasi-experimental
shift-share designs is achieved under endogenous exposure of statistical units to presumably exogenous common shocks. In our case, exposure corresponds to the preestimation period country import shares of firms, while common shocks are capturedby the aggregate knowledge service exports to Germany by country, year, and industry.
More precisely, with regard to industry, we exclude knowledge service exports from afirm’s own industry when constructing our common shocks. To achieve identification,
we assume that the set of common shocks is exogenous to the threats to identification
listed above.
We consider our assumption of the exogeneity of our common shocks as plausible.
First, our common shocks are most likely not structurally influenced by the innovation
activities or the selection of individual firms as an individual firm’s industry is removed
during shock construction. Moreover, the simultaneous correlation of unobserved
characteristics with our aggregated common shocks and firm outcomes is unlikely.
Again, firm characteristics are unlikely to influence our common shocks due to the
exclusion of a firm’s industry. In addition, the fixed effects included in our regressions
cover more aggregate characteristics related to both variables, such as German regions,
import countries, industries, and time trends.

58Appendix E.

Theoretical Extensions

59