High-Skill Immigration, Offshore R&D, and Firm
Dynamics*
Jingting Fan†

Eunhee Lee‡

Valerie Smeets§

This Draft: December 2021

Abstract
We study firms’ decision to use foreign R&D inputs—immigrant researchers and imported
R&D services—and the implications of this use for firm performance and aggregate productivity. Using Danish data, we document that firms with immigrant researchers are more likely
to source foreign R&D services and that using either foreign input increases R&D efficiency
and firm performance. We develop and estimate a model of firm dynamics that rationalizes
these patterns. Counterfactual experiments show that the two foreign inputs play crucial
yet complementary roles in R&D. Without access to these inputs, R&D participation and theaggregate return to R&D both would decrease substantially.

* We thank Treb Allen, Costas Arkolakis, Lorenzo Caliendo, Davin Chor, Swati Dhingra, Xintong Han, Toshiaki

Komatsu, Fernando Leibovici, Kevin Lim, Nina Pavcnik, Natalia Ramondo, Mark Roberts, Ana Maria Santacreu, Peter
Schott, Chong Xiang, Daniel Xu, and participants at CAED 2019, DIEW 2019, SAET 2021, SED 2021, IIOC 2021, EIIT
2021, NOITS 2021, the University of Virginia, Fudan University, Shanghai University of Finance and Economics, Dartmouth College, the University of Auckland, Hanyang University, UC Davis, Seoul National University, Copenhagen
Business School, Copenhagen University, the London School of Economics, Mannheim University, the virtual ITM
seminar series, and the KAEA Virtual Seminar Series for helpful comments. Frank Zhang provided excellent research
assistance. Any error is our own.
† Department of Economics, The Pennsylvania State University (e-mail: jxf524@psu.edu)‡ Department of Economics, University of Maryland, College Park (e-mail: eunhee11@umd.edu)§ Department of Economics and Business Economics, Aarhus University and CEPR (e-mail: vas@econ.au.dk)

1

Introduction

Reductions in trade barriers and advances in communication technologies over the past half century have made it easier for firms to source inputs globally. Recent studies suggest an important
two-way relationship between the use of foreign intermediate inputs and firm productivity: on
the one hand, productive firms self-select into importing foreign inputs; on the other hand, access to foreign intermediate inputs improves firm performance, indirectly through its interaction
with R&D as well as directly.1 In modeling and quantifying these channels, the literature has focused almost exclusively on the role of imported production inputs. Yet increasingly, firms acrossthe globe also adopt foreign R&D inputs, either by sourcing R&D services from abroad or byrecruiting immigrant researchers to the firm. Figure 1 shows the empirical relevance of these
two global R&D sourcing strategies for firms in Denmark, the country of focus in this paper.
The left panel is immigrants’ share of total R&D-related wage bill. The right panel is the shareof foreign sourced R&D services in total R&D expenditures. Both panels show a clear upward
trend, indicating growing dependence of Danish firms on foreign R&D inputs.2
In this paper, we develop and estimate a dynamic model to analyze firms’ decision to use
foreign R&D inputs and the implications of this decision for firm-level and aggregate outcomes.
We find that these two foreign inputs, immigrant researchers and offshore R&D, play crucial yet
complementary roles in overall R&D. Alternative models that omit these inputs or the interaction
between them would result in biased assessments of the effectiveness of innovation policies, e.g.,
R&D subsidies, as well as immigration and offshoring policies.
Our model is a model of firm dynamics with endogenous R&D as in Aw, Roberts and Xu(2011) and Doraszelski and Jaumandreu (2013), but features two important new mechanisms.
First, we posit that three R&D inputs—domestic researchers, immigrant researchers, and imported R&D services—are imperfect substitutes, so the marginal return from R&D investment
is higher when firms can flexibly combine these inputs. We label this mechanism as the love forvariety of ideas. Second, recruiting immigrant researchers and sourcing R&D services globally
both require upfront investments, so only a small fraction of firms take advantage of these options. However, as immigrants are able to provide information and knowhow about foreign R&D
suppliers, firms with immigrant researchers might face a lower barrier in sourcing R&D services
from abroad. We call this additional interaction between the two forms of foreign R&D inputs
the information channel.
Using the estimated model, we show that the benefit from foreign R&D inputs is an important
motive for firms to carry out R&D. Without access to these inputs, the R&D participation ratewould decrease by 60% and the effect of R&D on aggregate productivity would shrink by 80%.
1 Contributions to this literature include Amiti and Konings (2007), Goldberg, Khandelwal, Pavcnik and Topalova(2010), Halpern, Koren and Szeidl (2015), and Bøler, Moxnes and Ulltveit-Moe (2015), among others.
2 These trends are equally prominent in other countries. According to the Patent Cooperation Treaty data, between
2000 and 2010, around 10-15% of inventors in developed countries are foreign nationals. Relatedly, many global
firms source R&D services from abroad by establishing overseas R&D centers. Both phenomena have become moreprevalent over the past decades. See, e.g., Miguelez and Fink (2013), and Fan (2020) for details.

1Figure 1: Increasingly Globalized R&D Patterns of Firms Operating in Denmark(a) Immigrants among Researchers.1

Share of Offshore R&D
.15
.2
.25

.3

Share of R&D immigrants in R&D wagebill
.05
.06
.07
.08
.09

(b) Offshore Share of R&D Expenditures

2000

2005

Year

2010

2015

2000

Aggregate share of R&D immigrants

2005

Year

2010

2015

Aggregate share of offshore R&D

Notes: Plotted in the left panel is immigrants’ share in the total research wage bill, calculated as the ratio of the wage bill of
immigrants in R&D-related occupations over the wage bill of all workers in R&D-related occupations. Plotted in the right panel isthe ratio between offshore R&D expenditures and total R&D expenditures, domestic and offshore combined, for firms operating in
Denmark. In this definition, offshore R&D expenditures have two components: the R&D services purchased from abroad througharms’ length contracts, and the R&D carried out by foreign entities within the same business group of a firm operating in Denmark
for the use of that firm. See Section 2 for the definition of R&D-related occupations and additional details of the data.

Hence, omitting foreign inputs would lead researchers to substantially underestimate the effect ofan R&D subsidy on aggregate productivity. Moreover, as we estimate important complementarity
between the two foreign inputs, policies that change the cost of hiring immigrants have a large
impact on firms’ offshore R&D decision, and vice versa. Not accounting for such interconnection
underestimates the impacts of these policies on aggregate productivity by 30-50%.
Our model is grounded in the new facts we document using administrative data from Statistics Denmark between 2001 and 2015. We link the matched employer-employee data, which allows us to identify the occupation and immigration status of individuals, to a number of surveys
and administrative datasets at the firm level, covering firms’ location, accounting information,
R&D status, import and export, and participation in offshore R&D. With rich characteristics on
both firms and workers, we are able to identify whether a firm hires immigrant researchers andassess how this decision correlates with the characteristics and other decisions of the firm.
We document three facts on firms’ use of foreign R&D inputs. First, firms employing immigrant researchers are more likely to engage in offshore R&D. This correlation is robust when various firm and industry characteristics are controlled for; when we focus on the firm-destinationregion-level, i.e., firms recruiting immigrants from Eastern Europe, for example, are more likely
to source R&D services from Eastern Europe; when we employ a shift-share design that exploits
the increase in the supply of immigrants to rule out reverse causality. We interpret this finding as
capturing the possibility that immigrant researchers bring knowledge about their home countries
to the firm, which reduces the frictions in sourcing R&D from these countries.
The second and third facts highlight a two-way relationship between the use of foreign R&D
inputs and productivity. On the one hand, firms with immigrant researchers and firms engaging
2

in offshore R&D are more productive than firms doing R&D using domestic inputs only, whichis consistent with selection on productivity in these activities. On the other hand, controlling fortheir productivity and R&D expenditures, firms using foreign R&D inputs tend to have higher
future productivity than the ones doing R&D exclusively with domestic inputs. This correlationis robust when we control for industry-time fixed effects and firms’ participation in international
markets through import and export of physical goods. This effect is also present when weuse production function estimation techniques to address the simultaneity bias in measuring
productivity arising from firms’ endogenous choice of inputs.
We develop and estimate a structural model to identify the mechanisms behind these facts andconduct policy experiments. In the model, heterogeneous firms choose whether to conduct R&D,
and if so, how much to invest and whether to use immigrant researchers and/or imported R&D
services. Investment in R&D increases future productivity stochastically. Adopting multiple R&D
inputs at the same time is costly, but it enhances the efficiency of R&D investment. We interpret
this mechanism analogously to the love for variety assumption dating back to Ethier (1982): byusing R&D inputs from a diverse source, firms gain access to different, potentially better ideas,
thus achieving higher R&D efficiency. In addition to giving firms an incentive to use foreign
R&D inputs, this mechanism also leads to an interaction between these inputs. For example,
the availability of imported R&D services increases the overall return to R&D, which encourages
more firms to participate in R&D and, in turn, increases the use of immigrant researchers. To
further account for the information value of immigrants, we allow for a possibility of reduced
fixed and sunk costs when offshore R&D is done in the presence of immigrant researchers. Boththe existence and the size of the information value will be disciplined by the data.
We estimate the model through indirect inference. We uncover the importance of the lovefor variety of ideas by matching the estimated impact of foreign R&D inputs on firm performance. In the data, conditioning on doing R&D, firms using foreign R&D inputs see on averagean additional 2.3% productivity increase. Assuming a constant elasticity of substitution between
the three types of inputs in R&D—domestic researchers, immigrant researchers, and imported
R&D services—, this 2.3% productivity premium translates into a constant elasticity of 1.33. We
estimate the fixed and sunk R&D cost parameters that govern the strength of the information
channel using two sources of information: first, the patterns of firms’ transition between different R&D modes; second, firms’ response to a natural experiment, an R&D subsidy program
introduced in Denmark in 2011, which reduced the user cost of R&D by 25% for eligible firms.
Our estimation finds that the switch from doing R&D with only domestic researchers to using
also imported R&D services incurs an average startup cost of about 1.1 million USD and a fixed
operation cost of 0.75 million USD. The presence of immigrant researchers in a firm reduces thestartup cost by 16% and the fixed cost by 25%. This result suggests that the love for variety
of ideas alone cannot account for the higher propensity of offshoring R&D among firms withimmigrant researchers in the data. The information channel also plays an important role.
Our counterfactual experiments highlight the quantitative importance of foreign inputs in3

R&D. We shut down the love for variety of ideas by making different R&D inputs perfect substitutes, which eliminates firms’ incentive to either hire immigrant researchers or offshore R&D.3
The R&D participation rate decreases from the baseline level of 40.3 percentage points (p.p.) to
15.7 p.p., and the economy retains only 20% of the effect of R&D on aggregate productivity computed in the benchmark equilibrium. This result has important implications for the effectivenessof innovation policies. For example, in the absence of the love for variety of ideas, the effect of adecrease in the sunk cost of R&D on aggregate productivity would be 85% smaller than the effectin the benchmark model. The omission of foreign inputs leads to a significant underestimation of
the effect precisely because these inputs are an important reason why firms participate in R&D
to begin with.
We also examine the interaction of the two foreign inputs via the information channel. As
expected, the elimination of this channel from the benchmark reduces the fraction of firms carrying out R&D with imported R&D services. As a sizable part of firms’ return from hiring
immigrant researchers materializes through their complementarity with imported R&D services,
the fraction of firms hiring immigrant researchers also decreases substantially. In total, the R&D
participation rate decreases by 13.6 p.p., or a third of its baseline level. Accounting for the complementarity between offshore R&D and immigrant researchers is important for the evaluation ofpolicies that target either of them. For example, in evaluating a policy that reduces the sunk costof offshore R&D, an alternative model without the information channel would infer an aggregate
productivity increase that is only half as large as the increase in the benchmark model.
This paper is related to four strands of the literature. First, it contributes to the literaturethat estimates the impact of imported intermediate inputs on firm performance (e.g., Amiti andKonings, 2007; Kasahara and Rodrigue, 2008; Goldberg, Khandelwal, Pavcnik and Topalova,
2010; Halpern, Koren and Szeidl, 2015; Antras, Fort and Tintelnot, 2017; Fieler, Eslava and Xu,
2018). While this literature also emphasizes the ‘love for variety’ in input use, their focus is on
imported inputs for production. In contrast, we focus on foreign R&D inputs such as immigrant
researchers and offshore R&D, which are ever more important as global integration expands
beyond the exchange of goods to the exchange of ideas and movement of high-skill workers.
We show that the use of foreign talent or imported R&D services has an independent effect onfirm productivity, above and beyond that of imported production inputs. Since R&D investment
contributes to firms’ knowledge capital, which is persistent, improvement in R&D efficiency is
accumulated and amplified over time. This dynamic effect of R&D inputs sets this paper further
apart from most papers from the literature on imported production inputs, which focuses on
static effects.
Second, our model of firm dynamics with endogenous R&D and our estimation methodology
build on the work of Doraszelski and Jaumandreu (2013), Aw, Roberts and Xu (2011), and Bøler,Moxnes and Ulltveit-Moe (2015). Most closely related, Bøler, Moxnes and Ulltveit-Moe (2015)
3 More precisely, this change shuts down the systematic component in firms’ incentive to use foreign R&D inputs.
We allow for idiosyncratic components in their R&D decisions as well.

4

argue that R&D and intermediate inputs are complements and jointly enhance firm performance.
Enabled by rich administrative data from Denmark, we contribute to this literature by looking
inside the black box of R&D and by examining the interaction between different inputs inside thisbox. We show that incorporating different R&D inputs not only matters for evaluating various
policies on offshoring or immigration, but also matters for understanding the impacts of genericR&D subsidies that are actively used in many countries.
By focusing on firms’ decision to conduct offshore R&D, this paper is also related to a nascent
literature studying the impacts of R&D within multinational corporations (MNCs). For example,
Bilir and Morales (2020) estimate how R&D in the headquarters and foreign affiliates of MNCs
affects production in the same or nearby affiliates; Fan (2020) examines how MNCs optimally
allocate R&D and production among their affiliates around the world. Instead of developing amodel of affiliate production within MNCs, we develop a model of R&D sourcing. This model
speaks to a key feature of our data—that our measure of offshore R&D captures the R&D services
that a firm operating in Denmark sources from abroad for itself and excludes the R&D done inforeign headquarters/affiliates exclusively for local use at those foreign locations.4
Finally, this paper is related to a broad literature on the consequences of high-skill immigration. The literature has documented two general patterns: that high-skill immigrants increase
firm and regional economic performance, and that immigrants generate trade and other businesslinkages between the origin and destination countries.5 Our first contribution to this literature
is to document both patterns in a unified setting for a specific yet important activity, R&D. Thisfinding suggests that one mechanism through which immigrants increase firm performance isexactly by helping the firm establish business connection at their home country. Our second
contribution is to develop and estimate a dynamic heterogeneous firm model of R&D with immigrants, which allows us to quantify this mechanism. Compared to most existing works that
estimate the impacts of immigrants using structural models (e.g., Burstein, Hanson, Tian andVogel, 2020; Caliendo, Parro, Opromolla and Sforza, 2021), our model incorporates two salientfeatures of the data, both of which are important for the evaluation of immigration policies: first,
only the most productive firms recruit immigrants; second, immigrants and offshoring interact
with each other. A few recent works have developed models with the second feature. In particular, Morales (2020) shows that foreign MNCs in the U.S. tend to recruit high-skill workers fromthe headquarter countries, which suggests that foreign employees working at a U.S. affiliate may
act as a bridge facilitating the communication between the U.S. affiliate and foreign headquarters. Distinct from and complimentary to Morales (2020), the information channel in our paper
4 To the extent that the R&D reported in our measure has spillover effects on the activities of the overseas head-quarters or affiliates of the firms operating in Denmark, our results underestimate the impact of offshore R&D.
5 Examples of research focusing on the first result include Peri (2012), Ottaviano, Peri and Wright (2018), Beerli,
Ruffner, Siegenthaler and Peri (Forthcoming), Burchardi, Chaney, Hassan, Tarquinio and Terry (2020). Examples ofresearch on the second result include Head and Ries (1998), Rauch and Trindade (2002), Burchardi, Chaney andHassan (2019), Olney and Pozzoli (2018), Ramanarayanan and Cardoso (2019), among many others. While moststudies find complementarity between immigration and economic linkages, some have documented a substitutable
relationship (Glennon, 2020).

5

is best viewed as the one between the headquarters in Denmark and the home countries of theseimmigrants. This channel is similar in spirit as the one proposed in Yeaple (2018), but we areable to estimate the strength of the channel, which Yeaple (2018) was not able to do due to thedata constraint.
The rest of the paper is organized as follows. In Section 2, we introduce the data and describe
the salient features of the data. In Sections 3 and 4, we develop and estimate the model. Section
5 reports results from counterfactual experiments. Section 6 concludes.

2

Data and Facts

In this section, we first describe the data used in this paper. We then document new facts on
the relationship between offshore R&D, the employment of immigrant researchers, and firm
performance. These facts motivate the key ingredients of the structural model.
2.1

Data Sources

We merge several datasets from Statistics Denmark on firms and workers over the period 2001
to 2015. Below we summarize the key pieces of information from these datasets; Appendix A.1
provides additional details.
Workers. The information on workers comes from the Integrated Data for Labor Market Research (IDA, hereafter), an annual snapshot in each November covering all working-age individuals in the labor force. Supplementing IDA with additional administrative datasets, we identify
workers’ birth country and other demographic information, the firm and the establishment at
which they work, and their occupation and wage. This information allows us to construct anindicator of whether a firm hires immigrants in R&D-related roles, in which immigration status
is defined by a worker’s birth country and R&D-relatedness is determined by their occupation.
Following Bernard et al. (2020), we deem an occupation as R&D-related if, according to thejob description, it involves creative and/or technical components such as design, testing, andexperimentation. This classification of R&D related occupations is broader than the definition of
R&D as activities carried out by scientists or university researchers that are pushing the boundaryof human knowledge, but it captures the fact that for many firms, some form of experimentationand innovation is needed to develop a new product.6 Slightly abusing language, we will callworkers in R&D-related occupations as R&D workers or researchers, and those in R&D-related
occupations not born in Denmark as immigrant R&D workers or immigrant researchers.
Firms. The information on the characteristics and activities of firms comes primarily fromtwo sources. The first source is the Regnskabsstatistik (FIRE, hereafter), an annual panel on
6 Examples of R&D-related occupations include software developers, mechanical engineers, and technicians inchemical sciences. An advantage of our classification is that because it is based on occupation, it includes only the
personnel directly involved in R&D-related activities. Supporting staffs in R&D units, e.g., accountants, do not countas researchers.

6firms’ accounting information derived from the value-added tax administrative data. FIRE covers
almost all private-sector firms above a certain size determined by the firm’s ownership structure.7
The information we extract from FIRE includes firm sales, value added, material use, wage bill,
and fixed capital investment. We use fixed capital investment to construct capital stock using
the perpetual inventory method. We deflate the wage bill using the consumer price index anddeflate all other accounting variables using their own industry-level deflators. We supplement
this dataset with firm-level trade data to control for firms’ import and export status in goods.
The second source is the Danish equivalent of the European Community Innovation Survey(the R&D Survey, hereafter), which provides information on firms’ R&D activities. Aiming togather as complete information on R&D-active firms as possible, the survey samples all firms
satisfying one of the following criteria: 1) have over 250 employees; 2) have more than 1 billion
Danish krone (DKK) in revenue; 3) spend at least 5 million DKK in R&D activities; or 4) operatein R&D industries (NACE Rev.2 industry 72).8 It also includes a stratified sample of all remaining
firms, resulting in an unbalanced panel of around 4,000 firms per year.
A unique and crucial feature of the R&D Survey is that it contains information on not only
firms’ R&D expenditures within Denmark, but also their R&D expenditures overseas—i.e., theiroffshore R&D. The questionnaire specifically requests that the offshore R&D expenditures reported should be for the use of the reporting entity in Denmark, so R&D done by the foreign
affiliates/headquarters of a Danish firm for the affiliates/headquarters themselves, such as thedevelopment of a product to be produced in a foreign country, is not included.9 The reported
offshore R&D, in turn, is most appropriately viewed as R&D services imported by the reporting
entity.10 Correspondingly, the model we develop focuses on the R&D sourcing and production
decisions of the firms operating in Denmark.
For corroborative evidence on the offshore R&D measure, we also leverage the Offshoring
Survey, which is part of a large European collaboration through Eurostat. The main purpose ofthis survey is to gather information about global value chains and international sourcing. The
survey samples all firms with 50 or more employees and a representative set of firms with 1049 employees. It reports whether a firm conducts R&D activities abroad in 2011, in house or
through arms’ length contracts, without requiring the reported R&D to be carried out solely for
7 Reporting to FIRE is mandatory for private corporations with an annual turnover above 500,000 and for individually owned companies with an annual turnover above 300,000 DKK. When matched to IDA, firms in FIRE account for
about 86% of total private-sector employment in Denmark. Some firms in FIRE cannot be matched with IDA because
the latter covers only the labor market information of each November.
8 Our analysis focuses on for-profit firms, so universities and research institutions will not be in our sample.
9 Offshore R&D includes both the R&D expenditures incurred by a foreign related party and those outsourced
through arm’s length contracts. The exact wording of the questionnaire for R&D in a related party is ‘FoU udført af
andre dele af koncernen i udlandet og anvendt internt i virksomheden,’ which means ‘R&D performed by other partsof the business group abroad and used internally in the company.’ Examples of offshore R&D include: the test of a
new drug in an overseas lab; the design of new toy sets by designers in a foreign location for the parent firm.
10 This feature differentiates the survey from other available datasets on affiliate R&D, such as the one from the U.S.
Bureau of Economic Analysis in which R&D reported in a foreign location could be carried out for the use of any
entities within the organization. To model the decisions that generate such data, researchers would have to jointly
consider the domestic and overseas production of firms (see, e.g., Bilir and Morales, 2020).

7

Table 1: Descriptive Statistics
Panel A: Worker Characteristics
Immigrant R&D
Immigrant non-R&D
Native R&D
Native non R&D% of obs
1.20
6.97
15.75
76.09

% College+
73.33
22.45
62.46
17.10

% Master +
33.90
6.90
22.98
5.35

Mean hourly wage (US$)
46.5
32.5
47.1
35.4

Mean VA/L (US$)
111,892
120,024
126,534
117,072% R&D firms
19.88
23.98
37.69
23.87

Mean R&D/Sales (%)
35.23
16.01
5.72
21.37

% Immi. R&D
7.74
14.29
33.08
13.70

% Offshore R&D
2.60
4.08
11.28
4.34

% Immi. R&D and Offshore R&D
1.08
3.15
10.51
3.15

% Immi. R&D
12.84
14.85
33.25
18.12

% Offshore R&D
5.05
5.45
15.97
7.49

% Immi. R&D and Offshore R&D
2.52
3.85
15.18
5.84

Panel B: Firm Characteristics
Number of employees
10-49
50-249≥ 250
All% of obs
46.90
39.88
13.22
100

10-49
50-249≥ 250
All
Panel C: Offshoring Survey
Number of employees
10-49
50-249≥ 250
All% of obs
23.17
56.54
20.30
100

Notes: Panels A and B are based on the matched sample between IDA, FIRE, and the R&D Survey, restricted to private sector
firms with at least 10 employees. Panel C further restricts the aforementioned sample to firms included in the Offshoring Survey.
Immigrants are identified based on their birth country. In Panel B, a reporting firm in Denmark is classified as doing offshore R&D
if it uses R&D services sourced from abroad. In Panel C, a reporting firm is classified as doing offshore R&D if it conducts R&D
activities abroad in 2011, i.e., according to the definition from the Offshoring Survey. Monetary values are in U.S. dollar. All statistics
are based on 2011. The number of firms in Panels B and C are 2,949 and 1,882 respectively.

the benefit of the reporting entity in Denmark. While this notion of offshore R&D is broader
than our baseline measure based on the R&D Survey and is available only for 2011, it provides
an alternative measure that we can use for validation.
Finally, both the R&D Survey and the Offshoring Survey include the information about theforeign region in which a firm conducts R&D. In Appendix A.2, we use this information toprovide further evidence on the connection between offshore R&D and firms’ employment ofimmigrant R&D workers.
2.2

Descriptive Statistics

Our baseline sample includes all for-profit private-sector firms that have more than 10 employees
and are in both FIRE and the R&D Survey. To validate the measure for offshore R&D, we will also
use the Offshoring Survey, in which case firms need to be in all three surveys. Table 1 presents
the descriptive statistics of our sample. Since the Offshoring Survey is available only for 2011, we
calculate all statistics based on that year.

8Panel A of Table 1 reports the characteristics of the workers at the sample firms, summarized by workers’ immigrant status and occupation. Approximately 17% of the workers are inoccupations related to R&D, as defined previously. Among them, about 7% are immigrants.
Not surprisingly, both immigrant and native R&D workers are more educated than non-R&D
workers. They make on average $47 per hour, significantly above the average hourly wage of
non-R&D workers.
Panel B of the table reports the characteristics of the firms in the sample by their size group.
About 24% of firms in the sample participate in R&D. The R&D participation rate is higher
among larger firms than small firms. Conditional on doing R&D, however, it is the smallerfirms that devote a larger fraction of revenues to R&D, which is suggestive of large fixed costs
associated with R&D activities.
The lower panel of Panel B reports firms’ employment of immigrant R&D workers and participation in offshore R&D. About 14% of the firms in the sample, or 57% of R&D active firms,
conduct R&D with immigrant researchers. The share of firms engaging in offshore R&D issmaller, at around 4% of the sample. Both activities are more common among larger firms. An
overwhelming majority of firms doing offshore R&D—3.15% out of 4.34% overall, 10.51% out of
11.28% among firms with more than 250 employees—employ immigrant R&D workers, whichsuggests that the two activities are likely interconnected. On the other hand, less than a quarterof the firms employing immigrant R&D workers conduct offshore R&D.
Panel C of Table 1 reports statistics on firms’ mode of R&D, focusing on firms in the Offshoring Survey and using the measure of offshore R&D from this survey. Two patterns emerge
from the reported statistics. First, across all firm size groups, a larger fraction of firms than reported in Panel B conducts offshore R&D, consistent with the R&D measure in the Offshoring
Survey being broader than the one in the R&D Survey. Second, like the one in the R&D Survey,
this measure also shows a higher conditional probability of employing immigrant R&D workers
among the firms doing offshore R&D than the conditional probability of offshoring R&D among
the firms employing immigrant R&D workers.
2.3

Relationship between Immigrant Researchers, Offshore R&D, and Firm Performance

To understand the asymmetric patterns in conditional probabilities between the use of immigrant
workers and offshore services in R&D, we look into the frequency of firms’ transition between
different R&D modes. In particular, we split firms into the following five R&D modes: R&D inactive (denoted by 0), R&D with only domestic inputs but no imported services or immigrant
researchers (N), R&D with domestic inputs and immigration researchers (N I), R&D with domestic inputs and imported R&D services (NF), and R&D with all three types of inputs (N IF).
Panel A of Table 2 reports the five-by-five transition matrix between these modes. Eachrow sums up to one. The entry in row m and column n of the matrix shows the fraction offirms in mode m in year t moving to mode n in year t + 1. The table shows that among firms
employing immigrant R&D workers (the N I row), about 12% adopt offshore R&D (the N IF or
9

Table 2: R&D Mode Choice and Firm Productivity
Panel At

Transition probability between R&D modes
t+1
0

N

NI

NF

N IF

0
N
NI
NF
N IF

0.933
0.330
0.154
0.219
0.062

0.034
0.527
0.055
0.342
0.010

0.024
0.092
0.675
0.041
0.277

0.004
0.041
0.007
0.338
0.026

0.006
0.010
0.110
0.059
0.625

Panel B

Frequency distribution and average productivity
0
N
NI
NF
N IF
112,999 115,987 136,164 132,113
160,225
77.80
7.95
9.14
1.48
3.63

mean VA/L (US$)% of sample

Notes: Panel A of the table reports the fraction of private firms (with at least 10 employees) in a mode in period t (indicated by therows) moving into a different mode in period t + 1 (indicated by columns). Each period is defined as a year and the reported values
are the average of year-to-year transition over the sample period. The statistics for Panel B are for 2011, based on the same sample
as Panel B of Table 1. Mean value added per labor is reported in US$.

NF column) in the next year. This is twice as large as the 5% probability that firms doing R&D
without immigrant researchers in year t start using offshore R&D services in year t + 1 (from N
to either N IF or NF). On the other hand, among firms doing offshore R&D, the fraction thatstarts employing immigrant R&D workers is around 10% (from NF to either N I or N IF), which
is about the same as the share of firms in mode N that switch to either N I or N IF modes.11
These findings support the idea that the presence of immigrant researchers at a firm encourages offshore R&D, which can explain why the majority of firms doing offshore R&D also employ
immigrant researchers. This effect could be due to either the enhanced benefit or the reduced
cost of offshore R&D from the presence of immigrant researchers. More specifically, as immigrants may bring diverse ideas, having immigrant researchers can increase the marginal returnfrom offshore R&D for a given level of R&D investment. Alternatively, immigrant researchers
may act as a bridge between the headquarters and the foreign R&D suppliers, thereby reducing
information frictions in offshore R&D. We will incorporate both mechanisms in the structuralmodel developed in the next section and let the data discipline the existence and the strength ofthese mechanisms.
In Appendix A.2, we supplement the above findings with regression-based evidence on therelationship between offshore R&D and a firm’s employment of immigrants. First, we show that
this relationship is robust when productivity and other firm characteristics, including their size,
industry affiliation, and importing/exporting status, are controlled for. This analysis rules out
the possibility that the higher propensity among firms with immigrants to start offshore R&D
is simply due to large and productive firms being more active in both decisions. Second, the11 The fraction of firms dropping out of R&D ranges between 6% for firms in the N IF mode to 33% for firms in the

N mode, and the average probability of dropping out of R&D is around 21% in our sample. As a comparison, theodds of quitting R&D are between 20% and 50% in Bøler et al. (2015) and around 35% Aw et al. (2011).

10

relationship persists when we focus on the connection between immigrants from a specific foreign region and offshoring R&D to the same foreign region, which offers additional support for
the role of immigrants in reducing information frictions. Third, only the presence of immigrant
researchers, not other types of immigrants, increases the likelihood of offshore R&D. This result
suggests that the interaction we document is within R&D, rather than between R&D and otheractivities. Finally, we also show that the result is not due to reverse causality by using a shiftshare instrumental variable (IV) for firms’ employment of immigrants, which exploits variations
across Danish regions and industries in the stock of immigrants from different foreign regionsin 2000 and the nation-wide inflow of immigrants between 2001 and 2015. We summarize thesefindings in Fact 1.
Fact 1: Firms with immigrant researchers are more likely to start offshore R&D. This pattern isrobust to a number of firm-level controls and an IV strategy that addresses the reverse causality
concern.
The literature has documented that R&D-active firms tend to be more productive than nonR&D firms and that firms’ participation in R&D is persistent (see, e.g., Griliches, 2007 and thereference thereto). The statistics in Table 2 show that in our data, both the performance premiumand the persistence of R&D apply to the mode of R&D as well. For example, 62.5% of firms inmode N IF and 67.5% of firms in mode N I will stay in the same mode in the following year. Panel
B of the table reports the average of labor productivity—defined as value added per worker—by
R&D mode. Firms doing R&D with foreign inputs tend to be more productive than firms in the
N mode. These patterns lead to the second fact:
Fact 2: Firms doing R&D with foreign inputs are more productive on average than non-R&D
firms and firms doing R&D without foreign inputs. Both firms’ participation in R&D and themode in which they carry out R&D are persistent.
The systematic variation in productivity between firms in different R&D modes suggests
possible self-selection into the adoption of foreign inputs, which motivates a heterogeneous firms
model with fixed costs for using foreign inputs. The persistence in firms’ R&D mode choices, inturn, can either be simply reflecting such self-selection in the presence of persistent productivity
differences among firms, or be due to additional, sunk costs for entry into an R&D mode. Ourmodel features both forces, and we will separate them in the structural estimation.
Having documented patterns consistent with selection into using foreign R&D inputs byproductivity, we now examine whether this use increases the return to R&D. We estimate theimpact of doing R&D with foreign inputs on productivity using the following specification:

ωit = ρωit−1 + γR&D I(R&Dit−1 ) + γoff. I(off. it−1 ) + γimmi. I(immi.it−1 ) + ~βXit + φj(i)t + ζ it . (1)In equation (1), ωit denotes the log labor productivity of firm i in year t. We specify ωit to11

be a function of ωit−1 and firm i’s R&D status at t − 1. This specification follows the knowledge capital model of productivity dating back to Griliches (1979), according to which ωit , theknowledge capital that determines firm performance, is the sum of un-depreciated knowledge
capital from the previous year, ρωit−1 , and the new knowledge capital created through R&D.
We postulate that the amount of knowledge capital created depends not only on whether a firm
conducts R&D, but also on how. Therefore, in addition to the indicator for firms’ R&D status(I(R&Dit−1 )), we include the indicators for the use of offshore R&D services (I(off. it−1 )) andimmigrant researchers (I(immi.it−1 )) in the specification. We should expect γoff. and γimmi. to bepositive, if drawing ideas from foreign inputs increases R&D efficiency. In some specifications,
we will replace I(R&Dit−1 ) with intensive margin measures of R&D expenditures to allow forvariation in R&D intensity. Decisions on R&D likely depend on the characteristics of the industry and other firm-level decisions, both of which can impact firm performance. Denoting firm i’s
industry by j(i ), we will control for these confounding factors using industry-time fixed effects
φj(i)t and time-varying firm characteristics Xit .
Table 3 presents the estimation results for equation (1). Column 1 shows that participation
in R&D is associated with 2.4% higher productivity and that conditional on participation in
R&D, the use of imported R&D services is associated with an additional 3.1% productivity gains.
Column 2 shows a similar finding for the use of immigrant R&D workers. In column 3, whenboth types of foreign R&D inputs are included in the regression at the same time, each of themhas a large, positive, and statistically significant coefficient.
A robust finding from the trade literature is that participation in import and export (of goods)
is strongly correlated with firm productivity (see Bernard et al., 2012 for a review). If the R&D
decision also depends on trade participation (Aw et al., 2011; Bøler et al., 2015), then the correlation between R&D and future productivity could be driven by firms’ participation in trade.
To address this concern, column 4 controls for firms’ importing and exporting status in periodt.12 Consistent with previous findings from the literature, the coefficients on the indicators offirms’ importing and exporting status are both positive and statistically significant. However, thecoefficients of immigrant researchers and offshore R&D remain similar. This result suggests thatthe correlation documented between firm productivity and the use of foreign R&D inputs is not
picking up the effects of trade in physical goods found in the literature.
A plausible explanation for the results reported in columns 1-4 is that the firms using foreign
R&D inputs are significantly out-investing other firms and that a part of their extra R&D investment is attributed to immigration and offshore R&D dummies. To investigate this possibility,
columns 5 through 8 measure R&D using the log of domestic R&D expenditures. The coefficientsof log domestic R&D expenditures are statistically significant but generally not big enough forthe estimated coefficients on the foreign R&D input indicators to be explained by the higher R&D
expenditures of these firms.13 Correspondingly, the coefficients associated with the offshore and
12 Controlling for the lagged importing and exporting status gives essentially the same result.
13 With a point estimate of 0.003 as in column 8, for example, for the 3% additional productivity gains enjoyed byfirms doing offshore R&D to be entirely explained by the extra R&D investment made by these firms, the total log

12Table 3: Sourcing of R&D Inputs and Labor Productivity
Outcome var.
Key control
Labor Productivityi,t−1
I(R&Di,t−1 )Labor Productivityi,tExtensive margin of R&D Status(1)0.657***(0.012)0.024***(0.005)(2)0.659***(0.011)0.025***(0.005)(3)0.658***(0.012)0.020***(0.005)(4)0.653***(0.012)0.014**(0.005)

Log domestic R&D i,t−1

Intensive margin: domestic R&D(5)0.656***(0.012)(6)
0.658***(0.011)(7)0.657***(0.012)(8)0.653***(0.012)0.004***(0.001)0.004***(0.001)0.004***(0.001)0.003***(0.001)

Log total R&D i,t−1
I(off. i,t−1 )0.031***(0.012)I(immi.i,t−1 )0.031***(0.012)0.021***(0.006)
0.043***(0.006)0.016***(0.006)0.023**(0.011)0.026***(0.005)0.029**(0.012)0.025***(0.006)37,859Yes

32,914Yes

32,914Yes

33,064
Yes

Import dummyi,tExport dummyi,tObservations
Industry×year FE

33,064
Yes

Total R&D
(9)
0.653***(0.012)0.023***(0.005)0.022*(0.011)0.023***(0.006)0.025**(0.011)0.019***(0.006)0.042***(0.006)0.015***(0.006)0.003***(0.001)
0.022*(0.012)0.019***(0.006)0.042***(0.006)0.015***(0.006)37,859Yes

32,914Yes

32,914Yes

32,914
Yes

Notes: Labor productivity is defined as log real value-added per worker. Domestic R&D refers to domestic R&D expenditures.
Total R&D refers to the sum of domestic R&D and offshoring R&D expenditures. All specifications include log firm size as well as
industry*year fixed effects. Industries are defined following the NACE Rev.2 intermediate level aggregation (see Appendix Table
A.3). The sample includes private sector firms with at least 10 employees, and the sample period covers 2001-2015. Standard
errors are clustered at the firm-level. ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01.

immigrant R&D indicators are very similar to the ones in columns 1-4. Finally, in the last column,
we directly control for log of firms’ total, instead of domestic, R&D expenditures. The estimates
for the coefficients on the foreign R&D input indicators are virtually the same.
It is still possible that the results reported in Table 3 are due to a simultaneity bias: sincefirms observe their productivity—at least partially—when making input choices, our productivity measure could be biased. The bias in the measurement of ωit−1 shows up in the error term
and can be correlated with firms’ R&D decisions in period t − 1, if these decisions are made withthe knowledge of ωit−1 . In Section 4, we address this concern in a theory-consistent way by using
a control function approach in productivity estimation. Based on these empirical results, we havethe third fact.
Fact 3: Conditioning on current productivity and total R&D expenditures, firms that use foreign
R&D inputs tend to have higher future productivity.
Fact 3 and the very fact that some firms conduct R&D with both domestic inputs and the two
types of foreign inputs suggest that these inputs are not perfect substitutes. These facts motivate
us to model foreign inputs as providing different, potentially better ideas to the R&D process.
Summary and Robustness. Taking stock, we find that foreign R&D inputs in the form of
R&D investment of these firms needs to be 1,000 log points above that of other firms.

13

immigrant researchers or imported R&D services account for a substantial fraction of total R&D
spending made by firms in Denmark. On the one hand, there is evidence of selection into using
foreign R&D inputs by productivity. On the other hand, the use of these foreign R&D inputs
is associated with improved future performance beyond what can be explained by firms’ total
R&D expenditures. Moreover, these two types of foreign R&D inputs are tightly connected: thepropensity to offshore R&D is higher among firms employing immigrant researchers.
We show in Appendix A.3 that these patterns are robust to alternative definitions of immigrants (e.g., based on whether a person moves to Denmark above a certain age or after completing
all education) and other categorizations of R&D modes (e.g., by varying the minimum employment of immigrant researchers for a firm to be classified as hiring immigrant researchers; by
examining 3- and 5-year transitions instead of year-to-year transitions). We also show that theresults are not driven by the Danish affiliates of foreign multinational firms.
Together, these facts underscore the importance of foreign inputs in R&D. They also imply
that policies affecting the adoption of one foreign R&D input would affect the adoption of theother input, which could reinforce the direct impact of such policies on R&D decisions. The main
goal of our structural model in the next section is to disentangle these forces and quantify theirimpact on firm’s performance.

3

Model

In this section, we introduce a dynamic model where heterogeneous firms make productivityenhancing R&D investment by combining inputs from domestic and foreign sources. Statically,
given current productivity and the aggregate demand, firms choose the output quantity to maximize their profit. Dynamically, firms decide how to organize R&D using inputs from different
sources: native researchers, immigrant researchers, and offshore R&D services.
3.1

Production, Demand, and Static Profit

We start by describing firms’ static decisions. The production function for firm i at time t has thefollowing form:
qi,t = exp (ωi,t ) li,t ,(2)where li,t is the production labor of firm i at period t; ωi,t denotes firm i’s current (log) productivity, which depends on the firm’s past productivity and R&D investment, as will be explainedin the next subsection; qi,t is the output. Denoting the wage for each unit of production labor as
Wi,tWi,t , the marginal cost of production is exp(ω
.14
)
i,t

Firms sell their output in a monopolistic competitive output market, characterized by the
14 When taking the model to the data, we will extend the production function to incorporate capital and materials
as additional production inputs.

14following Dixit-Stiglitz demand:qi,t =

pi,t
Pt

η
Qt ,

(3)

where qi,t and pi,t are the quantity and the price of the variety that firm i produces; η < 0 is thedemand elasticity; Qt is the aggregate demand faced by the firm; and Pt is the corresponding
ideal aggregate price index. We interpret Qt and Pt as capturing the conditions of the entire
market faced by all Danish firms, including the condition in other European Union (EU) states
and the rest of the world. In keeping with this interpretation, we make two simplifications. First,
we abstract from firms’ endogenous export decision. We motivate this assumption from the highdegree of integration of Denmark in the world economy.15 In empirical specifications, we willcontrol directly for firm’s exporting status to ensure that it does not confound the main channels.
Second, we assume that Qt and Pt are exogenous to individual firms and do not change inthe counterfactual experiments considered later in this paper. This assumption is motivated by
the fact that the counterfactual shocks we consider lead to only moderate changes in aggregate
productivity, so these shocks alone are unlikely to drive a substantial general equilibrium change
in Qt and Pt .
Firms choose lit and pit to maximize their static profit. Given the monopolistically competitivetmarket structure, the optimal pricing rule implies pi,t = η +1 · expW
, with η +1 being the markup
(ω )

η

η

i,t

t
t
] η +1 Q
over the marginal production cost. The total sales of firm i is then given by [ η +1 expW
η.
(ω )
P

η

i,t

Therefore, conditional on its productivity, firm i earns the following static profit in period t:




η
1
− (η + 1)ωi,t ,
πt (ωi,t ) = − Φt · exp (η + 1) lnηη+1in which Φt ≡

η +1

Wt

η

Pt

Qt

t

(4)

is a shifter common to all firms, capturing the overall profitability due towages, demand, and the market competition.
3.2

The Evolution of Productivity and the Love for Variety of Ideas

Firm i’s productivity evolves according to the following law of motion:
ωi,t = ρωi,t−1 + γ · I(rdi,t−1 > 0) · log (rdi,t−1 ) + ζ i,t ,(5)where ωi,t−1 is the lagged (log) productivity of firm i; rdi,t−1 is firm i’s total effective investment in
R&D in year t − 1, with the coefficient γ being the R&D elasticity of productivity; I(rdi,t−1 > 0)
is an indicator for firm i doing R&D in year t − 1; ζ i,t is an idiosyncratic error term representing
unanticipated innovation in the productivity evolution process, which has a mean of zero and astandard deviation of σζ .
As documented in Section 2, some firms use multiple R&D inputs at the same time, suggesting these inputs are not necessarily perfect substitutes. Moreover, these firms see larger produc15 The openness of Denmark, measured as import plus export over GDP, is well over 100%.

15

tivity gains than firms relying on only domestic inputs. To rationalize these empirical regularities
parsimoniously, we assume that firms can combine three types of R&D inputs—domestic researchers (N), immigrant researchers (I), and offshore R&D services (F)—via a constant elasticity
of substitution function. The effective R&D investment of firm i in year t is:rdi,t =AN

 1θ 

Nrdi,t θ −θ 1



+ A

I

 1θ 

Irdi,t θ −θ 1



+ A

F

 1θ 

Frdi,t θ −θ 1  θ −θ 1

, 1 < θ < ∞.

(6)x̃ for each x̃ ∈ { N, I, F } denotes the R&D input of type x̃ used by firm i. A x̃In this function, rdi,tfor each x̃ ∈ { N, I, F } denotes the efficiency of input x̃. Based on the values of A x̃ , our model
can accommodate a case where foreign inputs are more technically advanced than domestic
researchers, as well as a case of their being inferior, possibly due to frictions in communication.
Under the restriction of 1 < θ < ∞, different R&D inputs are not perfectly substitutable.
This imperfect substitution can be rationalized as different inputs being embedded with ideas
and techniques from different sources, thus bringing in the gains from a diversity of ideas to the
R&D process. We call this mechanism the love for variety of ideas. Similar setups have been widely
employed in the literature to explain firms’ use of foreign intermediate production inputs (e.g.,
Halpern et al., 2015) and to analyze the impacts of immigrants on domestic workers and the local
economy (e.g., Yeaple, 2018; Ottaviano et al., 2018). In our model, this channel is the reason why
firms have an incentive to adopt diverse inputs for R&D activities in the first place. The strengthof this channel depends critically on the value of θ, which we will estimate structurally.
Firms can choose among different combinations of inputs in R&D. In principle, it is possible
for firms to use only foreign inputs but no domestic inputs. In our data, however, this rarely happens. Thus, following the classification in Section 2, we assume that there are four combinationsof R&D inputs for firms to choose from: using only inputs from native researchers (N); using inputs from both native and immigrant researchers (N I); using inputs from native researchers andforeign suppliers of R&D services (NF); using all three types of inputs simultaneously (N IF). As
previously, we call these combinations of R&D activities R&D modes. By denoting the mode for
non-R&D firms as 0, the mode choice of firms is given by x ∈ X ≡ {0, N, N I, NF, N IF }.
The cost for an effective unit of R&D investment for firms choosing R&D mode x, denoted byc x , is given byNN 1−1 θc = ApN  1− θ 1−θ  1−1 θ
NI
N
N
I
c = A
p
+ A pI
c

NF

c

N IF



= A

N



= A



N

 1− θ

p

N



N

p

+A

 1− θ

FpF

1−θ  1−1 θ  1− θ 1−θ  1−1 θ
I
F
+A p
,
+ A pFI

16

where p x̃ denotes the unit price for R&D input x̃ ∈ { N, I, F }. These costs apply to all firms
in the economy and do not change over time, so we suppress the firm and time subscripts for
simplicity. Our setup implies c x < c N , ∀ x ∈ { N I, NF, N IF }. Therefore, conditional on their R&D
expenditures, firms using multiple sources of ideas in R&D would have larger effective R&D
investment. This in turn translates into a larger estimated increase in productivity for these firms
than for the firms spending the same budget only on domestic inputs, which is exactly what Fact
3 in Section 2 states. As previously mentioned, how much larger the increase in productivity isfor firms using foreign R&D inputs will depend on our estimate of θ.
In addition to giving firms a reason to use either offshore R&D or immigration researchers,
equation (6) also introduces the first source of interaction between these two inputs—via thereturn to R&D. For example, with c N IF < c NF , firms in the N IF mode can reap a higher returnfrom the same R&D expenditures than firms in the NF mode. Thus, the presence of immigrants
gives firms a stronger incentive to participate in not only R&D but also offshore R&D.
Despite the benefits from the employment of immigrant researchers and from the adoptionof imported R&D services, not all firms engage in these activities, hinting at significant upfront
costs for these options. Moreover, the persistence of R&D mode decisions observed in the data
(Fact 2 in Section 2) naturally motivates a dynamic model. We now introduce the fixed and sunkcosts of R&D and describe firms’ dynamic decisions.
3.3

Dynamic Decisions

Firms’ dynamic decisions unfold as follows. At the beginning of period t, firms discover therealization of ζ i,t , hence their current productivity ωi,t , given by equation (5). Knowing ωi,t , firm
i chooses output qi,t to maximize the static profit, as described in Section 3.1, and then decides
the current period’s R&D mode and total R&D expenditures.
For the firms having chosen R&D mode x in the previous period, switching to mode x 0 re000x . In this total cost, F̃ x,x is the systematic component
quires an irreversible investment of F̃ x,x + ιi,tthat is common to all firms switching from mode x to mode x 0 . The dependence of this component on firms’ previous R&D status reflects the upfront costs associated with entering a new
0xmode, e.g., the cost of setting up a new R&D team or finding a reliable overseas R&D supplier. ιi,t
0

x is drawn
is the idiosyncratic component of the cost for the new mode choice. We assume that ιi,trandomly and independently (across i, t, and x 0 ) from a mean-zero Type-I extreme value distribution with a scale parameter ν > 0. This idiosyncratic cost can be associated with a number offactors: for example, some firms might be in a better position to recruit immigrant researchers
because they are located in a region where many immigrants live; firms might also encounter atalented researcher or a reliable foreign supplier by sheer luck. Such factors lead firms to makedifferent decisions on R&D modes but are unobserved to the econometrician, so we capture themin the idiosyncratic term.
0x and then deFirms observe the current draw of their idiosyncratic cost for each R&D mode ιi,tcide whether to carry out R&D and how. We denote firm i’s state in period t as si,t = (ωi,t , xi,t−1 ),17where xi,t−1 is firm i’s R&D mode choice in period t − 1. Then, the expected value before thex of a firm with state s , denoted by V ( s ), is given by:realization of ιi,t
t i,t
i,t

Vt (si,t ) = π (ωi,t ) +

Z

max

h

x∈X

x
Vtx (si,t ) − Fexi,t−1 ,x − ιi,t

i

dι,

(7)

where X ≡ {0, N, N I, NF, N IF }δ · Et Vt+1 (si,t+1 | si,t ), for x = 0
and Vtx (si,t ) ≡ max {−rdi,t · c x + δEt Vt+1 (si,t+1 | si,t , x, rdi,t )} , for x ∈ X \ {0}rdi,tIn equation (7), the Vtx (si,t ) term inside the integral is the present discounted value of R&D mode
x for firm i at time t; δ ∈ (0, 1) is the discount rate; rdi,t is the effective investment in R&D
0

x , theaside from the fixed and sunk cost payments. Under the distributional assumption for ιi,t

probability of a firm switching from R&D mode x to R&D mode x 0 is given by:exp

0

mtx,x (si,t ) =

1 ex,x 0
1 x0
ν Vt ( si,t ) − ν F∑ x00 ∈X exp

1 x 001 ex,x 00
ν Vt ( si,t ) − ν F

.

(8)

0
We parameterize the average cost of changing R&D modes, Fex,x , with various interpretable0components. Specifically, we assume that the cost Fex,x consists of a fixed operation cost com0

ponent independent of firms’ previous R&D status, denoted by f x , and a status-dependent0

component that governs the cost associated with switching between modes, denoted by F x,x . The
0
total cost Fex,x is the sum of the two components. Putting this structure in a matrix form, we haveF̃5×5 = 15×1 · f1×5 + F5×5 ,where the subscript of each variable denotes the dimension of the variable. 1 is a 5 by 1 vector ofones; f = ( f 0 , f N , f N I , f NF , f N IF ) is a vector of fixed operation costs; F is a 5 by 5 matrix of sunkcost components. The element in the m-th row and the n-th column of matrix F̃, for example,
corresponds to the sunk cost of switching from the m-th mode in X to the n-th mode in X.
We assume that a decision to do no R&D (x 0 = 0) incurs neither cost, i.e., f 0 = 0 and F x,0 = 0
for every x. We also assume that there is no sunk cost if firms do not switch R&D modes, i.e.,0

F x,x = 0 if x = x 0 . We parameterize the remaining components of F as
0

FN

FN + FI

FN + FFF N + F I + F F − F IF




 0

F=
 0

 0

0

FI

FF

F I + F F − F IF

F I0

0

F F + F I0

F F − F IF

F F0

F I + F F00

FIF I0 + F F0

F F0

F I0




,




0



0

(9)

where each row and each column correspond to each of the five R&D modes in the order of18

{0, N, N I, NF, N IF }, with rows indicating firms’ current mode x and columns indicating theirmode x 0 in the next period.
Components in F have intuitive explanations. First, F N , F I , and F F capture the cost of setting
up new R&D operations to be carried out by domestic workers, immigrant workers, and offshore
sources, respectively. These costs are only to be paid by firms that did not use the R&D inputs ofthe corresponding type in the previous period. Second, F I0 and F F0 represent the cost associatedwith dropping immigrant workers and offshore R&D services from the R&D process, respectively.
Dropping an input from R&D could be costly because the rest of the R&D team may need to bereorganized to accommodate the change.16 Last but not least, the reduced-form facts suggest that
adding offshore R&D into the R&D bundle can be easier for firms with immigrant R&D workers.
Our parameterization of F̃ allows the presence of immigrants to reduce the cost of offshore R&D
through two components: in the sunk cost via F IF > 0 and in the fixed cost via f N IF < f N I .
We will let the data tell whether these inequalities are satisfied and which component is more
important.
A plausible explanation for why we might estimate f N IF < f N I and/or F IF > 0 is that immigrants in the R&D team, knowing the language and affiliate logistics better, can facilitate communication between the headquarters and offshore R&D affiliates. This explanation is consistent
with the empirical results reported in Appendix A.2, which show a strong connection between
the origin country of immigrant researchers and the destination for offshore R&D. Following
the extensive literature that documents the importance of immigrants in facilitating international
business (e.g., Rauch and Trindade, 2002; Burchardi et al., 2019), we label the cost advantage inoffshoring from the presence of immigrants as the information channel. This is the second sourceof interaction between the two foreign R&D inputs.
In summary, the model rationalizes firms’ use of diverse R&D inputs through the notionof the love for variety of ideas. It further accommodates the higher propensity of offshoringamong firms with immigrant researchers via two channels: through the increased return to R&D
when both foreign R&D inputs are used simultaneously, and through the information channel.
We will estimate the model in the next section to uncover the quantitative importance of thesemechanisms for R&D decisions.
3.4

Discussion on Model Assumptions

Before turning to the estimation, we discuss the rationale for four modeling choices. First, atthe center stage of our model are the decisions of firms in Denmark looking to optimally source
inputs for their R&D. This setup fits the measure of offshore R&D in the survey but overlooks
the possibility that some firms in the sample are the Danish affiliates of foreign MNCs. A naturalconcern, then, is that because MNCs already have an international network, having immigrant
16 Since in the data, virtually all R&D active firms hire native researchers, we assume that when firms drop input

from native researchers, they shut down R&D all together. In this case, they do not need to pay the reorganization
cost required to continue R&D, so we assume the cost of dropping the N mode to be zero.

19

researchers in their Danish affiliate might have a smaller impact on the cost of sourcing R&D
inputs from abroad. Thus, to the extent that MNCs indeed do not benefit much from the information channel, our structural estimation will underestimate the importance of this channel forthe firms originating in Denmark. For robustness, we show in Appendix A.3 that the empiricalpatterns are similar when affiliates of foreign MNCs operating in Denmark are excluded fromour sample.
Second, in the model, the benefit from the information channel accrues only to firms withimmigrant R&D workers, but not to firms with other types of immigrant workers. This choice ismotivated by the data: as shown in Appendix A.2, when indicators for both R&D and non-R&D
immigrants are included in the regression specification for the information channel, only theindicator for R&D immigrants has a robust correlation with offshore R&D.
Third, we incorporate an interaction between immigrant researchers and offshore R&D via
higher returns embedded in the CES function, but we do not allow for richer interactions via A x̃ .
For example, one might think that firms are able to increase A F in equation (6) by hiring more
immigrant researchers. An implication of this mechanism is that the shares of R&D expenditures
on inputs I and F should be positively correlated among the firms using both. Since the support
for this implication is relatively weak in our data, we choose not to incorporate this mechanismin the model.17
Finally, we assume that each firm makes binary decisions of whether to hire immigrants andto offshore R&D, rather than a decision of which foreign regions to hire immigrant researchers
from and to offshore R&D to. This assumption greatly simplifies the structural estimation but
may seem too restrictive for the information channel of immigrants. Note, however, that mostfirms in our data source R&D only from one foreign region.18 Even among firms with morethan 250 employees, the average number of offshore R&D destination regions is only 1.6. Ourmodel can be viewed as a special case of a more general model with the following two-step R&D
decision: firms first choose whether to hire immigrant and/or whether to offshore R&D, andthen pick one foreign region to do so.

4Model Estimation

This section explains how we estimate the model. Some parameters can be estimated without
fully solving for firms’ dynamic optimization problem, so we estimate these parameters independently. Other parameters will be estimated jointly via an indirect inference procedure.
17 Specifically, when we regress the immigrants’ share of firms’ total R&D wage bill on the offshore share of R&D
expenditures, we find a positive but statistically insignificant coefficient. This finding also guides us to adopt a generic
CES specification, as opposed to a nested-CES specification, for R&D.
18 Examples of foreign regions in the data are Eastern Europe, North America, China, India, etc.

20

4.1

The Distribution of Idiosyncratic Cost Shocks

A key set of parameters in our model is the matrix F̃ that governs the cost of switching R&D
modes. An intuitive approach to identify F̃ is to use the patterns of transition between R&D
modes in the data. A challenge for this approach, however, is that because F̃ enters firms’ mode
choice only jointly with the reciprocal of ν, as shown in equation (8), transition patterns alone donot separately identify F̃ and ν.
We overcome this challenge by taking advantage of a natural experiment in Denmark, theintroduction of an R&D subsidy policy in 2011, to identify ν. This policy rebates 25% of total
R&D expenses for firms incurring a loss, thereby reducing their effective cost of R&D. This, inturn, could encourage more firms to conduct R&D. We can identify ν by examining how thesubsidy changes the probability of switching R&D modes among the eligible firms.
To see this, consider the choice of the firms entering period t with R&D mode N and productivity ωi,t , i.e., si,t = (ωi,t , N ). Combining equations (7) and (8) gives us the log of the ratio
between the share of these firms quitting R&D and the share staying in mode N:
log(

mtN,0 (si,t )mtN,N (si,t )1∗) = [c N × rdi,t(ωi,t , N ) + f N ]
ν|
{z
}

(10)

R&D expenses

+



δ
∗
(ωi,t , N ) ].
[ Et Vt+1 ωi,t+1 |ωi,t , rdi,t = 0 − Et Vt+1 ωi,t+1 |ωi,t , rdi,t = rdi,tν|{z}Improvement in continuation value from optimally chosen R&D∗ (·) is the optimal effective R&D given firm i’s current productivity
In the above expression, rdi,tand its choice to be in mode N.19 The expression shows that the log odds ratio is the sum of
two components: static R&D expenses, and dynamic gains due to the improvement in expected
future productivity.
With the aforementioned R&D subsidy in place, equation (10) becomes:
N,0

log(

m0 t (si,t )m0 tN,N (si,t )1∗0) =(1 − τ ) × [c N × rdi,t(ωi,t , N ) + f N ]
(11)
ν


δ
∗0
+ [ Et Vt0+1 ωi,t+1 |ωi,t , rdi,t = 0 − Et V 0 t+1 ωi,t+1 |ωi,t , rdi,t = rdi,t(ωi,t , N ) ],
νin which τ is the subsidy as a share of R&D expenses. Equation (11) differs from equation (10)in two aspects. First, the user cost of R&D is now (1 − τ ) fraction of the pre-policy level. Second,in principle the value and policy functions could change in response to the subsidy, so they are0∗ (·), respectively.
denoted by Vt0+1 (·) and rdi,t19 As firms’ choice between modes 0 and N can be inferred from their choice of rd , (i.e., rdi,ti,t = 0 means∗ (ω , N ) means the firm continues with mode N), we suppress
the firm chooses to quit R&D; rdi,t = rdi,ti,t
firms’ mode from their value functions. In the rest of this section, we use Et Vt+1 ωi,t+1 |ωi,t , rdi,t = 0 as∗ (ω , N ) as shorthand forshorthand for Et Vt+1 (ωi,t+1 , 0)|(ωi,t , N ), rdi,t = 0 and Et Vt+1 ωi,t+1 |ωi,t , rdi,t = rdi,ti,t∗
Et Vt+1 (ωi,t+1 , N )|(ωi,t , N ), rdi,t = rdi,t (ωi,t , N ) .

21

Given the uncertain and temporary nature of this policy and the restriction on eligibility for
only loss-making firms, we assume that firms perceive the value function in the post-policy world0

as similar to the one before policy, i.e., Vi,t (·) ≈ Vi,t (·).20 Under this assumption, we can express
firms’ continuation value net of R&D investment as the following:

1
∗0
∗0
Et V 0 t+1 ωi,t+1 |ωi,t , rdi,t = rdi,t(ωi,t , N ) − (1 − τ ) × [c N × rdi,t(ωi,t , N ) + f N ]ν1= max{ Et V 0 t+1 ωi,t+1 |ωi,t , rdi,t − (1 − τ ) × (c N × rdi,t + f N )}
ν
rdi,t

1
≈ max{ Et Vt+1 ωi,t+1 |ωi,t , rdi,t − (1 − τ ) × (c N × rdi,t + f N )}
ν
rdi,t
|
{z
}

(12)

≡ f (rdi,t , τ )∂ f (rdi,t , τ )|rdi,t =arg maxrd { f (rdi,t , 0)}
i,t
∂τ
 1
1
∗
∗
∗
= Et Vt+1 ωi,t+1 |ωi,t , rdi,t = rdi,t(ωi,t , N ) − [c N × rdi,t(ωi,t , N ) + f N ] + τ × [c N × rdi,t(ωi,t , N ) + f N ].
νν≈ max{ f (rdi,t , 0)} + τ ·rdi,t

The two equalities in (12) follow from the definition of rdi,t as the solution to the Bellman equation
0(7). The two approximations stem from our assumption of Vi,t (·) ≈ Vi,t (·) and the Envelope
Theorem, respectively. Condition (12) shows that up to the first order, the net (of R&D expenses)
continuation value of the firm in the presence of R&D subsidy τ is simply the pre-policy net
continuation value plus the subsidy that the firm can now receive. By combining this condition
0

with equations (10) and (11), and the approximation of Vi,t (·) ≈ Vi,t (·), we get:log(

m0tN,0 (si,t )) − log(

mtN,0 (si,t ))mtN,N (si,t ) δδ= Et Vt0+1 ωi,t+1 |ωi,t , rdi,t = 0 − Et Vt+1 ωi,t+1 |ωi,t , rdi,t = 0
ν
ν
 1
δ
∗
∗
+ Et Vt+1 ωi,t+1 |ωi,t , rdi,t = rdi,t(ωi,t , N ) − [c N × rdi,t(ωi,t , N ) + f N ]
ν
ν

δ
1
∗0
∗0
− Et V 0 t+1 ωi,t+1 |ωi,t , rdi,t = rdi,t(ωi,t , N ) + (1 − τ ) × [c N × rdi,t(ωi,t , N ) + f N ]νν1∗(ωi,t , N ) + f N ].
≈ − × τ × [c N × rdi,tν
m0tN,N (si,t )(13)

According to (13), the change in the propensity of a loss-making firm continuing R&D due∗ ( ω , N ) + f N , and theto the R&D subsidy depends on the amount of the subsidies τ c N × rdi,ti,tparameter ν, which governs firms’ responsiveness to the subsidy. In the model, firms’ charac20 From the perspective of firms qualifying for this subsidy in year t, they would qualify again in the next year only

if all of the following conditions hold: i) the subsidy policy is still active; ii) they continue to be in a loss position; iii)
they are actively doing R&D. Given the uncertainty in policy and the potential upside risk of R&D-active firms, it is0
likely that firms do not anticipate all three conditions to hold in the future. We also note that assuming Vi,t (·) ≈ Vi,t (·)
does not mean that firms perceive their continuation values to be the same as before. Rather, the assumption is that,the perceived continuation value, given the mode of R&D chosen by the firm and the realization of productivity in thenext period, is the same as before.

22

Table 4: R&D Decisions of Loss-Making Firms
Loss-making firms in 2011

Loss-making firms in 2012

Panel A: all industries
2011
N
0
2010

N
0

113
27

2012

39
427

2011

N
0

Panel B: manufacturing
2011
N
0
2010

N
0

52
15

N

0

144
37

24
373

2012

17
135

2011

N
0

N

0

67
19

11
116

Notes: The sample consists of loss-making firms in 2011 and 2012 with at least 10 employees for all industries (Panel A) andmanufacturing only (Panel B). N refers to firms reporting positive domestic R&D expenditures while 0 refers to firms reporting zero
domestic R&D expenditures.

teristics are uniquely determined by their current productivity and their participation in R&D in
the previous period. Equation (13) suggests that we can determine ν by checking if, conditionalon their productivity, loss making firms are less likely to quit doing R&D after the policy is introduced and if the decrease in their propensity to quit is higher for firms incurring larger R&D
expenditures.
Table 4 reports the transition of loss-making firms in 2011 (before the policy) and 2012 (after
the policy) between R&D mode N and R&D mode 0. There are in total around 600 loss-making
firms making transitions between these modes in each period. Before the subsidy was enacted,
26% of the firms in mode N stopped doing R&D; this share decreases to 14% in 2012, after thepolicy took effect. As Panel B shows, similar patterns hold among the sample of approximately
220 loss-making manufacturing firms. These patterns are consistent with the goal of the subsidy
policy to encourage R&D participation.
To control for differences in firm productivity, we split the observations in 2011 and 2012
into B bins by their lagged labor productivity. We then examine, within each bin, whether theobservations from 2012 show a higher or lower likelihood of quitting R&D than those from 2011.
In effect, we are using the firms in 2011 with similar productivity as a comparison group forfirms in 2012. Formally, we estimate the following linear probability model:B

I(i quits R&D in t) = β 0 I(t = 2012) + ∑ β b I(ωi,t−1 ∈ Ωb ) + β emp ln(empi,t−1 ) + ei,t ,b =1

where I(i quits R&D in t) is an indicator variable that takes a value of 1 if a firm-year observation
stops doing R&D; β b is a fixed effect for all observations belonging to the b-th productivity binΩb ; β 0 is the key coefficient of interest, capturing the effect of the policy. To rule out a possibility
23

Table 5: R&D Subsidy and R&D Participation
Linear Probability Model

Panel A

Loss-making firms

Placebo: profitable firms

β0(1)-0.124***(0.047)(2)-0.116**(0.046)(3)-0.122***(0.046)(4)-0.132***(0.045)(5)-0.026(0.024)(6)-0.026(0.025)(7)-0.027(0.024)(8)-0.022(0.024)

Observations
Firm sizei,t−1
Productivityi,t−1
Number of bins
Industry FE

299
Yes
5
Yes

299
Yes
10
Yes

299
Yes
15
Yes

299
Yes
Yes
Yes

952
Yes
5
Yes

952
Yes
10
Yes

952
Yes
15
Yes

952
Yes
Yes
Yes

Logistic Model

Panel BAll industries

Manufacturing only

β0(1)-0.165***(0.043)(2)-0.156***(0.043)(3)-0.165***(0.043)(4)-0.166***(0.041)(5)-0.239**(0.102)(6)-0.240**(0.110)(7)-0.330**(0.140)(8)-0.197**(0.085)Observations
Firm sizei,t−1
Productivityi,t−1
Number of bins
Industry FE

253
Yes
5
Yes

253
Yes
10
Yes

253
Yes
15
Yes

253
Yes
Yes
Yes

103
Yes
5
Yes

103
Yes
10
Yes

89
Yes
15
Yes

103
Yes
Yes
Yes

Notes: Panel A reports the results from a linear probability model; Panel B reports the results from a logistic model on loss-making
firms. All specifications control for lagged log firm size, lagged firm productivity (defined as log valued added per worker), andindustry fixed effects. Columns 1-3 and 5-7 report specifications using productivity bin fixed effects with a varying number of bins,
while columns 4 and 8 use a quadratic function of lagged productivity. The sample consists of firms in the entire private sector or
manufacturing in 2011 and 2012 that have at least 10 employees. Robust standard errors are in parentheses ∗ p < 0.10, ∗∗ p < 0.05,∗∗∗ p < 0.01.

of systematic differences in firms’ behavior based on their size and industry, we always control
for industry fixed effects and lagged log firm employment.
Columns 1 through 3 in Panel A of Table 5 report the results from this specification, with thenumber of productivity bins, B, ranging from 5 to 15. Column 4 controls for a flexible functionof productivity instead of the bin dummies. All columns give similar estimates: after the policy
was introduced, the probability that firms quit doing R&D decreased by around 12%. Columns
5 through 8 provide a placebo test by focusing on firms making a profit, which were ineligible
for the subsidy. This placebo test shows that the results in columns 1-4 are not due to a change
in the macroeconomic conditions between 2011 and 2012 that affected all firms simultaneously.
Estimates reported in Panel A do not easily translate into the structural parameter of interest1
ν . We thus estimate a logistic specification with the independent variable being the log of R&D

24

expenditures, as below:I(i quits R&D in t) =B
1, if β0 · I(t = 2012) · log(r&di,t−1 ) + ∑ β b I(ωi,t−1 ∈ Ωb ) + β emp log(empi,t−1 ) + ei,t > 0

b =1




0, otherwise.

(14)
Assuming that ei,t is drawn from the standard logistic distribution, this specification is the
reduced-form counterpart of the structural equation (13), with the only difference being thatlog(r&di,t−1 ), instead of r&di,t−1 , is included in the specification.21 Because of this difference, weestimate an elasticity from equation (14), before converting it to a semi-elasticity.22
Columns 1 through 4 of Panel B report the results from the logistic regression. The estimatedcoefficients are all around −0.16. Since our subsequent productivity estimation and counterfactual simulations will focus on the manufacturing sector, columns 5 through 8 report results for
manufacturing firms. The estimated coefficients for manufacturing firms are qualitatively similar
but larger in magnitudes.
Our preferred specification, reported in column 7 of the table, gives an estimate of −0.330.
To convert this number into the value for the semi-elasticity given in equation (13), − τν , weassume that the elasticity estimate holds for the firm with the median R&D expenditures. With
the median R&D expenditures in the regression sample being 0.44 million USD, we have − τν =−0.3300.44 = −0.75. Plugging in τ = 0.25 gives us ν = 0.33.

4.2

R&D and the Evolution of Productivity

In the second step of the estimation, we estimate the parameters governing the evolution offirm productivity. These parameters include ρ, γ, the standard deviation σζ of the error termin equation (5), and the cost for each effective unit of R&D investment (c x for each R&D modex ∈ { N, N I, NF, N IF }). These cost parameters, in turn, depend on the efficiency A x̃ and the pricep x̃ of each type of R&D input x̃ ∈ { N, I, F }.
Letting ei,t−1 > 0 denote the R&D expenditures that firm i spends at time t − 1 within Denmark, i.e., on native researchers and/or immigrant researchers, the period-t productivity of firm
21 To see this, note that the logistic assumption in equation (14) implies that the pre- and after-policy log odds ratios

are, respectively, log(

mtN,0 (si,t )m0 N,0 (s )) = ∑bB=1 β b I(ωi,t−1 ∈ Ωb ) + β emp log(empi,t−1 ) and log( m0 N,N (si,t ) ) = β 0 log(r&di,t−1 ) +i,t
mtN,N (si,t )∑bB=1 β b I(ωi,t−1 ∈ Ωb ) + β emp log(empi,t−1 ). Taking the difference between the two gives an elasticity-specification ofequation (13).
22 Alternatively, we could have used the level of R&D expenditure as the explanatory variable to directly estimate− τν . We do not adopt this alternative because with the distribution of R&D expenditures highly skewed, specifications
with the level of expenditure as the explanatory variable are heavily influenced by a small number of big firms.
Nevertheless, using a level specification gives qualitatively similar results.

25

i is given by:
ωit =ρωit−1 + γ log(eit−1 ) − γ log(c N )ζ i,t , if xi,t−1 = Nγ(log(c N ) − log(c N I )) + ζ i,t , if xi,t−1 = N I+γθ [log(c N ) − log(c NF )] + ζ i,t , if xi,t−1 = NF





γ[θ (log(c N I ) − log(c N IF )) + (log(c N ) − log(c N I ))] + ζ i,t , if xi,t−1 = N IF

(15)

where xi,t−1 denotes firm i’s R&D mode choice at time t − 1 as previously defined. Each linein the curly bracket of this equation indicates one mode of doing R&D. For example, the firstline in the curly bracket states that for firms in R&D mode N, the effective R&D bundle islog(rdi,t−1 ) = log(eit−1 ) − log(c N ); the second line indicates that compared to the firms in mode
N with the same domestic R&D expenditures, the N I firms will see a larger productivity increase,N

captured in γ · log ccN I > 0, due to the gains from variety of ideas.
The third line inside the curly bracket of equation (15) completes the specification for the
productivity of firms in R&D mode NF. Conditional on the total R&D spending within DenN

mark, these firms would see an additional boost of γθ · log ccNF in productivity. The coefficientN

before log ccNF is γθ instead of γ as in the N I mode. It captures that, first, conditional on R&D

investment in Denmark, firms in mode NF also make additional spending on imported R&D
services; second, given the total spending on R&D, the effective R&D will be larger. Finally, thelast line inside the curly bracket of equation (15) is for the firms using all three types of R&D
inputs. Because c N I > c N IF and c N > c N I , the systematic boost on productivity in the N IF modeis also positive and greater than in the N I mode.
Based on the interpretation of equation (15), we specify the following regression:ωit = ω + ρ̃ωit−1 + γ̃0 log(ei,t−1 ) + γ̃1 I( xi,t−1 = N I ) + γ̃2 I( xi,t−1 = NF ) + γ̃3 I( xi,t−1 = N IF ) + ζ i,t ,(16)
in which ω is a productivity shifter that captures the cost of domestic R&D common to all firms.
ρ̃ and γ̃m for m = 0, 1, 2, 3 are the structural parameters corresponding to the parameters inequation (15).23 We stack γ̃m in a vector denoted by γ̃ = (γ̃0 , γ̃1 , γ̃2 , γ̃3 ).
Comparison between equations (15) and (16) clarifies how γ̃ summarizes the benefit of having
access to additional sources of ideas. These parameters contain all information about θ, and A x̃and p x̃ for x̃ = N, I, F that firms need to know when deciding whether to adopt an additional
input in R&D. Once γ̃ has been estimated, we can plug it back in equation (15) and treat it as thelaw of motion of productivity that firms perceive when making R&D decisions.
There are, however, two challenges in estimating equation (16). First, ωi,t is unobserved tothe econometrician. Second, firm-level R&D expenditures are notoriously difficult to measure,23 Concretely, ρ̃ = ρ; γ̃ = γ; γ̃ = γ · log c N ; γ̃ = γθ · log c N ; γ̃ = γ ( θ · log c N I + log c N ).
0
2
3
1
cN I
c NF
c N IFcN I

26

so eit−1 is likely subject to severe measurement errors. Moreover, only a few firms in the sample
are in the NF mode. These factors limit our ability to estimate all reduced-form parameters inequation (16) precisely, even if ωi,t is known.
To address the first challenge, we apply a two-step control function approach, which recovers
ωi,t jointly with the parameters governing firms’ productivity evolution.24 To meet the second
challenge, instead of taking the estimates for equation (16) as the structural parameters, we
specify an auxiliary regression that is less susceptible to biases from measurement errors andthe small number of firms in the NF mode. We then discipline the structural parameters bymatching the estimates from the auxiliary regression. We now explain each step of the estimation
procedures in detail.
In productivity estimation, we introduce capital, labor, and materials as inputs in production.
The log output quantity of firm i in year t, denoted by q̃i,t , is:q̃i,t = ωi,t + β k k̃ i,t + β l l˜i,t + β m m̃i,t ,(17)

where k̃ i,t , l˜i,t , and m̃i,t denote the log of capital, labor, and materials, respectively. The log of the
optimally chosen price for the output of firm i, p̃i,t , is:p̃i,t =

11q̃i,t + P̃ − Q̃,
η
η

(18)

where P̃ and Q̃ are the log of aggregate price and demand, respectively.
By combining equations (17) and (18), we obtain the following expression for the measured
revenue (the data):ỹi,t ≡ q̃i,t + p̃i,t + ẽi,t

(19)

η+1
1
ωi,t + β̃ k k̃ i,t + β̃ l l˜i,t + β̃ m m̃i,t + P̃ − Q̃ + ẽi,t ,
η
η
η+1
η+1
η+1
where β̃ k ≡β k , β̃ m ≡β m , β̃ k ≡
βm .
η
η
η

=

In this specification, ẽi,t is the log of a multiplicative measurement error in revenue.25 β̃ a , a ∈{m, k, l } is the revenue elasticity of input a that takes into account the demand elasticity of
consumers.
Firms’ productivity evolves according to equation (16). We allow capital and labor to be dynamic inputs that are subject to adjustment costs, which implies that k̃ i,t and l˜i,t do not necessarily
capture all information contained in ωi,t . On the other hand, materials are assumed to be a static
24 Our estimation of ω takes into account that firms’ R&D mode choice both depends on their current productivity
i,tand affects their future productivity. This approach addresses the concern raised by De Loecker (2013) that if productivity is estimated without taking into account firms’ endogenous decisions (such as R&D or export), one might failto detect the impact of these endogenous decisions on productivity.
25 Alternatively, ẽ can be interpreted as an additional productivity shock that realizes after all production decisions,i,tincluding the decision on material use, have been made.

27

input, chosen after firms observe ωi,t and have decided k̃ i,t and l˜i,t , so it can be inverted to recoverproductivity. Following the insight of Levinsohn and Petrin (2003) and Ackerberg et al. (2015),
we use materials as a control for productivity in a two-step estimation procedure detailed below.
Step 1. The first step is to come up with a control function for ωi,t . By noting that m̃i,t is chosen
given k̃ i,t , l˜i,t , and ωi,t , we write the material use as a general function m̃i,t = mt (ωi,t , k̃ i,t , l˜i,t , zi,t ).
We include in zi,t a number of firm-level controls that might affect material use but are absent
from our structural model. The first set of controls are on firms’ participation in international
trade. Participation in importing might affect material use because the access to foreign suppliers can reduce the effective price of intermediate goods. Participation in exporting might also
affect material use because exporters face a larger demand than non-exporters and might choose
to produce more for any given level of capital and labor. Therefore, we include lagged firms’
importing and exporting status in zi,t . Second, since the quality of workers differs across firms(Fox and Smeets, 2011), l˜i,t might be a noisy proxy for the effective labor at a firm. Following
Doraszelski and Jaumandreu (2013), we include firms’ average wage in zi,t . Finally, firms’ capital stock, calculated based on the perpetual inventory method, might not accurately reflect theefficiency-adjusted capital stock. In particular, newer vintages of machines might be more efficient than the old ones. We include the investment rate in zi,t to control for the potentially higher
efficiency of more recent capital installations.
Conditional on capital, labor, and all these other factors, firms’ material use increases monotonically in their productivity. We can thus invert m(·, k̃ i,t , l˜i,t , zi,t ) to express ωi,t as a generalfunction of k̃ i,t , l˜i,t , m̃i,t , and zi,t , i.e., ωi,t = ω̃t (k̃ i,t , l˜i,t , m̃i,t , zi,t ). Plugging this expression into
equation (19) gives:1ỹi,t = β̃ k k̃ i,t + β̃ l l˜i,t + β̃ m m̃i,t + ω̃t (k̃ i,t , l˜i,t , m̃i,t , zi,t ) + P̃ − Q̃ + ẽi,tη≡ ht (k̃ i,t , l˜i,t , m̃i,t , zi,t ) + ẽi,t .
We specify ht (·) as the sum of the following components: a cubic function of capital, investment,
employment, wage, and the interaction between these variables; the indicators for firms’ importing and exporting status; and the yearly and industry dummies. The first step comes down toestimating hi,t (·) using the OLS, which separates hi,t (·) from measurement errors in revenue, ẽi,t .
We denote the estimated value for firm i in period t as h̃i,t .
ηStep 2. With h̃i,t in hand, we express ωi,t = η +1 [h̃i,t − β̃ k k̃ i,t − β̃ l l˜i,t − β̃ m m̃i,t − P̃ + η1 Q̃]. By

28

substituting this expression into equation (16), we obtain:(h̃i,t − β̃ k k̃ i,t − β̃ l l˜i,t − β̃ m m̃i,t ) − ρ̃ · (h̃i,t−1 − β̃ k k̃ i,t−1 − β̃ l l˜i,t−1 − β̃ m m̃i,t−1 )η+1−· [γ̃0 log(ei,t−1 ) + γ̃1 I( xi,t−1 = N I ) + γ̃2 I( xi,t−1 = NF ) + γ̃3 I( xi,t−1 = N IF )]
η
η+1
1
−[
ω + (1 − ρ)( P̃ − Q̃)]
η
η
η+1
=
ζ i,t .
η(20)

The left hand side in the equation is either the data or the parameters to be estimated. The
right hand side is the innovation in firms’ productivity. We estimate equation (20) using thegeneralized method of moments (GMM).
GMM Sample, Identification, and Results. Since the production function specified in (19)is most appropriate for the manufacturing industry, in this GMM estimation and all subsequent
structural estimations, we restrict the sample to manufacturing firms. To form the moment conditions, recall that k̃ i,t , ei,t−1 , and xi,t−1 are determined before the innovation term in productivity
ζ i,t realizes, so they are independent of ζ i,t . Labor use, on the other hand, may react to ζ i,t . Sincel˜i,t−1 and k̃ i,t−1 are chosen before ζ i,t is known, they can serve as instrumental variables for l˜i,t .
η +1

The term [ η ω + (1 − ρ)( P̃ − η1 Q̃)] captures the R&D cost and the aggregate market demand
shifters that are common to all firms. We allow this term to vary across industries by including
industry dummies in the specification and use these dummies as their own instruments. Finally,
under our timing assumption, m̃i,t is chosen after the realization of ζ i,t , so it is endogenous. As
discussed in Ackerberg et al. (2015), we cannot use m̃i,t−1 to instrument for m̃i,t because once
capital, labor, and productivity are controlled for, m̃i,t−1 should in principle not contain additional information about m̃i,t . Instead, we estimate β̃ m by exploiting firms’ first-order condition
for materials (see e.g., Griliches, 1979; Gandhi et al., 2020).
Specifically, we show in Appendix B.2 that the first-order condition for material use implies:
Pm,t · exp(m̃i,t )
exp ỹi,t|{z}· exp(ẽi,t ) =

β̃ m
|{z}

,

(21)

revenue elasticity of materials

measured material revenue sharein which Pm,t is the price for materials. The first term on the left-hand side is the measured
revenue share of materials. Assuming that multiplicative revenue measurement errors exp(ẽi,t )have a mean of 1, we can use the method of moments to estimate β̃ m from equation (21).26 In thebaseline analysis, we assume that β̃ m is common across industries and estimate it by pooling all
firms in the sample. In a robustness exercise reported in the appendix, we allow for industryspecific β̃ m . In both cases, we plug in the estimated value for β̃ m to equation (20) and estimate all
26 Alternatively, we can assume that ẽ

i,t has a zero mean, in which case a log-linearized version of equation (21) canbe estimated via the OLS to obtain β̃ m . It turns out that these two approaches give very similar estimates.

29remaining parameters jointly. To account for the uncertainty in the generated regressors h̃i,t andβ̃ m , we calculate standard errors by bootstrapping the entire estimation procedure.
Columns 1-3 in Table 6 report the GMM estimates for equation (20). In the baseline specification reported in the first column, the estimated coefficient for the intensive margin of R&D
is statistically significant, but fairly small, as we find in Section 2. This result could be due to adownward bias from the measurement errors in R&D expenditures or potential heterogeneous
effects by firm size.27
More important to our purpose, we find statistically significant and economically sizableeffects from the adoption of N I and N IF modes. The estimated coefficient for the NF indicator
is marginally negative but statistically insignificant, which could be the result of there being onlya small number of firms in the NF mode. The lower panel of Table 6 reports the estimates forrevenue elasticities of capital, labor, and materials. All estimates are of reasonable values andstable across specifications.
The second column includes a dummy variable for firms’ importing status both in the control
function h(·) and in the law of motion for productivity. This specification allows importing toplay two roles: directly improving firms’ productivity, and altering firms’ use of intermediatematerials conditional on their productivity. The result from this specification shows that our
main finding is not due to a possible correlation between the use of foreign R&D inputs andimporting. Column 3 further includes exporting status in both the control function and the lawof motion for productivity. The estimated coefficients remain largely the same.
Auxiliary Regression. As discussed earlier, due to possible measurement errors in R&D
expenditures and the small number of observations in the NF mode, we may not be able toestimate all coefficients in equation (20) precisely. Thus, we estimate an auxiliary regression, in
which the intensive margin measure of R&D is replaced with a dummy, and the three diverse
modes of R&D—N I, NF, and N IF—are grouped together. We introduce this auxiliary regression
in two steps for transparency.
In the first step, in the results reported in columns 4 through 6 of Table 6, we include anindicator for conducting R&D in place of log(ei,t−1 ) in the specification. This indicator captures
the impact of log(ei,t−1 ) for the firm with the average log R&D expenditures. We find that theestimated coefficient for the R&D dummy is around 1% and statistically significant, while thecoefficients for the other variables do not change much.
In the second step, reported in columns 7 through 9, we further replace the mode-specificdummies for N I, NF, N IF with a joint indicator, which takes a value of one if any of these modesis switched on. This indicator can be loosely viewed as the frequency-weighted average value ofthe coefficients for I( xi,t−1 = N I ), I( xi,t−1 = NF ), and I( xi,t−1 = N IF ). Our preferred estimate incolumn 9 of Table 6 suggests that on average, doing R&D increases productivity by 1% and that
adopting foreign R&D inputs adds an additional 2.3% productivity gain.
27 Our estimate is in line with the literature. Focusing on a neighbouring country, Norway, Bøler et al. (2015) estimate
heterogenous R&D returns by size. They find a larger coefficient for large firms and a negative coefficient for small
firms, implying an average return that is similar to ours.

30Table 6: R&D and Productivity Evolution
GMM estimation of (20)ωi,t−1log(ei,t−1 )(1)0.465***(0.146)0.002***(0.001)(2)
0.473***(0.130)0.002***(0.001)(3)0.474***(0.123)0.002***(0.001)I( xi,t−1 = N )I( xi,t−1 = N I )I( xi,t−1 = NF )I( xi,t−1 = N IF )0.022***(0.007)-0.006(0.006)0.042***(0.014)0.022***(0.006)-0.006(0.006)
0.043***(0.014)0.022***(0.006)-0.006(0.006)
0.043***(0.014)

GMM estimation of the auxiliary regressions(4)
0.465***(0.129)(5)0.472***(0.110)(6)
0.473***(0.155)(7)0.460***(0.146)(8)
0.465***(0.149)(9)0.465***(0.149)0.010***(0.004)0.024***(0.007)-0.003(0.007)0.048***(0.014)0.009***(0.004)0.023***(0.006)-0.003(0.006)0.049***(0.014)0.009**(0.004)0.023***(0.008)-0.003(0.008)0.049***(0.015)0.010***(0.004)0.010***(0.004)0.010***(0.004)0.023***(0.007)0.023***(0.007)0.023***(0.007)

0.461***(0.014)
0.109***(0.014)0.454***(0.002)yes

0.460***(0.015)0.108***(0.014)0.454***(0.002)
yes
yes

9,320

9,320

0.460***(0.015)0.108***(0.014)0.454***(0.002)
yes
yes
yes
9,320

I( xi,t−1 ∈ { N I, NF, N IF })Revenue elasticities
β̃ l
β̃ k
β̃ m
Industry fixed effects
Lag import dummy
Lag export dummy
Number of observations

0.457***(0.010)0.107***(0.014)0.454***(0.002)yes

0.457***(0.009)0.106***(0.012)0.454***(0.002)
yes
yes

9,320

9,320

0.457***(0.011)0.106***(0.011)0.454***(0.002)
yes
yes
yes
9,320

0.459***(0.009)0.108***(0.012)0.454***(0.002)yes

0.458****(0.009)0.107***(0.010)0.454***(0.002)
yes
yes

9,320

9,320

0.458***(0.015)0.107***(0.014)0.454***(0.002)
yes
yes
yes
9,320

Notes: I( xi,t−1 = N ) is an indicator for doing domestic R&D, identified from the R&D Survey if firms report positive domestic
R&D expenditures. I( xi,t−1 = N I ) is an indicator for having R&D immigrants; I( xi,t−1 = NF ) is an indicator for offshore R&D;
I( xi,t−1 = N IF ) is an indicator for firms having both R&D immigrants and offshore R&D. I( xi,t−1 ∈ { N I, NF, N IF }) is an indicatorfor diversified R&D, i.e. whether the firm either has immigrant R&D, offshore R&D, or both. βm is estimated via equation (21). All
specifications include industry fixed effects, with industries defined at the NACE Rev.2 intermediate level aggregation. The sample
is manufacturing firms with at least 10 employees. Bootstrapped standard errors are clustered by firm and reported in parentheses.
* p < 0.10, ** p < 0.05, *** p < 0.01.

We take three estimates from Column 9 of Table 6: the estimated autocorrelation, and theestimated coefficients of the R&D indicator and the diverse R&D mode indicator. We supplement
these estimates with three additional empirical moments: the average R&D expenditure share on
domestic inputs among N I firms (0.903, denoted by s N
N I ), the average R&D expenditure shareon domestic inputs among N IF firms (0.558, denoted by s N
N IF ), and the standard deviation oflog firm sales (1.27). The R&D expenditure shares contain information on the cost differenceNN
between different R&D modes (e.g., log ccN I and log ccNF ), and are therefore informative about γ̃ .
The standard deviation of log firm sales will pin down σζ .
We arrange these moments in a vector as below
α = (0.465, 0.010, 0.023, 0.903, 0.558, 1.27).
α̂

(22)

α will serve as the target in the indirect inference procedure that pins down the structural paα̂rameters ρ̃, γ̃ , and σζ . We stack the structural parameters to be estimated as λ = (ρ̃, γ̃ , σζ ).
31

Formally, for any given value of λ , we simulate the model and use the simulated data to
α that are from column 9 of Table 6.28 We also calculate
generate the regression coefficients in α̂
N
the standard deviation of log sales as well as firms’ R&D shares s N
N I and s N IF from the simulated
data.29 We can then choose λ so that the moments from the simulated data match their empiricalcounterparts. Since the model moments hinge on the distribution of firms over different R&D
modes, which depends also on the fixed and sunk costs F̃, we combine this indirect inference approach with the estimation of the other remaining parameters of the model, as will be describedin the next subsection.
Robustness. We report three sets of robustness exercises for Table 6 in Appendix B.3. First,
in the baseline analysis, we estimate a revenue function derived from firms’ optimal quantity
choice under a CES demand. As an alternative, we estimate a value added production function,
which does not take a stand on firms’ optimal output choice. Second, in the baseline analysis,
we classify firms as engaging in R&D with domestic researchers if they report incurring R&D
expenditures. While this definition is conventional and consistent with existing estimates of the
return to R&D (e.g., Aw et al., 2011; Doraszelski and Jaumandreu, 2013; Bøler et al., 2015), one
might be concerned about possible inconsistencies between this measure and our definition of
immigration researcher that is based on occupations. We show that the results are robust if we
define participation in domestic R&D based on the occupations of a firm’s employees. Third, inthe baseline analysis, we assume that material shares are common across industries. The results
are similar if we estimate material shares for each industry separately.
4.3

Joint Estimation of the Remaining Parameters

Aside from the parameters governing the law of motion of firm productivity, collected in λ ,the remaining parameters to be internally pinned down include the aggregate demand shifter
e We estimate (λ , Φt , Fe) jointly. For given
Φt and the fixed and sunk costs of R&D modes F.
parameters, we solve firms’ optimization problem and simulate the steady state of the model.
We then search over the parameter space to minimize the distance between the model’s steadystate moments and their empirical counterparts. As in the productivity estimation, this process
focuses on manufacturing firms. We describe the moments that identify each parameter and ourestimation procedures below.
Aggregate Demand Shifter. Φt from equation (4) is the aggregate demand shifter that affects
the scale of all firms. The median sales of the firms in our sample are 144 million DKK, or about
28 Note from equation (20) that the R&D coefficient estimated from the GMM is the product of the true R&D

coefficients governing firms’ evolution of productivity, defined in equation (16), and the elasticity of substitution inη +1
α , we also scale the regression
the product market, η . For consistency, in generating the model counterpart of α̂η +1

coefficients from the simulated data by η .
29 Appendix B.4 shows that for a given guess of γ̃ and without the knowledge of A x̃ or p x̃ , for x̃ ∈ { N, I, F }, we canNverify whether the expenditure shares in the model, s N
N I and s N IF , are equal to their empirical counterparts, whichmeans that we can estimate all parameters relevant for firm’s R&D decisions without having to first estimate A x̃ or p x̃for all x̃ ∈ { N, I, F }.

32

25.6 million USD. Focusing on the steady state of the model, we assume that Φt = Φ is a constantand choose Φ so that the median sales among the model firms would be 25.6 million USD.
e directly determines the probability that a given firm
Fixed and Sunk Costs of R&D Modes. F
e using the observed transition
switches from one R&D mode to another. We can thus pin down F
matrix between R&D modes. Since each row of the transition matrix sums up to 1, it leaves us
e as specified in equation
with 20 independent moments to pin down a total of 10 parameters in F,(9). We weight the transition probabilities by the number of firms in each origin mode.
e) ∈ Λ, where
Estimation Procedures. We collect all parameters to be estimated in (λ , Φ, F
Λ denotes the parameter space. These parameters fall into two categories. The parameters in
the first category, λ and Φ, are just-identified, with the same number of moments as there are
e are over-identified. To maintain a tightparameters. The second category of the parameters, F,
connection between the parameters and the moments identifying them, our estimation solves thefollowing constrained optimization problem:

∑0 n(x) · mx,x (λ , Φ, Fe) − m̂x,xe)∈Λ
(λ ,Φ,F
min

0

0

2

(23)

x,x

e) = α̂α,s.t. α (λ , Φ, F
where the variables with a hat denote empirical moments and the variables without a hat aree) ∈ Λ. In the objectivemodel-implied values under a particular choice of the parameter (λ , Φ, F0e) is the model-implied fraction of firms in mode x that move to mode x 0 in
function, m x,x (λ , Φ, Fe); n( x ) is the fraction of firms in mode x in the steady state.
the next period conditional on (λ , Φ, F20e) − m̂ x,x0 simply adds up the discrepancies in the transition
Therefore, ∑ x,x0 n( x ) · m x,x (λ , Φ, F
patterns between the model and the data, weighted by the steady-state share of firms in eachmode.
α in the constraint, as defined in equation (22), are the first three
The first three elements of α̂α are theestimated coefficients reported in Column 9 of Table 6. The remaining three elements of α̂
N
two R&D expenditure shares (s N
N I and s N IF ) and the standard deviation of the log of firm sales.
e) are the model-generated values for those six moments conditional on the parameterα (λ , Φ, Fe). This constraint ensures that all moments in α̂α are matched exactly.
choice (λ , Φ, F

Estimation Results and Fit of the Model. Panel A of Table 7 reports the parameters that wetake as given in the indirect inference. We pick ν = 0.33 based on the estimates in Table 5. We
set the demand elasticity η to be −6.56. This choice follows the estimate of Aw et al. (2011) and
implies a constant markup of around 18%. Finally, we set the discount rate δ = 0.95.
Panel B of Table 7 summarizes the results from the indirect inference procedure. The estimate
for ρ̃ is 0.463, which is very close to the moment that pins it down (0.465). γ̃0 from the joint
estimation is larger than the estimated coefficient in column 3 of Table 6, which is consistent withan attenuation bias due to errors in the continuous measure of R&D expenditures. Likely because
intensive margin returns pick up a larger fraction of the total returns to R&D, the estimates for33

Table 7: Summary of Structural Parameters
Parameters

Descriptions

A. Estimated Independently/calibratedν
scale parameter for the idiosyncratic cost in R&Dηdemand elasticity
δdiscount rate

Source/Target

Value(s.e.)

Table 5
Aw et al. (2011)
-

0.33
-6.56
0.95

(-)
(-)
(-)

0.463
(0.0095)γ̃0 = 0.0032 (3.7e-4)γ̃1 = 0.0010 (2.4e-5)γ̃2 = 0.0067 (2.5e-3)γ̃3 = 0.0072 (1.5e-3)
0.20(1.1e-3)
Table 8

B. Jointly EstimatedΦρ̃γ̃

aggregate demand
autocorrelation in productivity
return to R&D

median sales: 25.6 million USD
Table 6 Column 9
Table 6 Column 9 + sharesσξeF

sd. of the innovation term in productivity
fixed and sunk costs in R&D

sd(log(sales))=1.27
Table 8Notes: Panel A reports parameters that are estimated externally or calibrated. Panel B reports the outcome from the structural
estimation. The numbers in parentheses in the last column of Panel B are the standard errors, generated through 200 bootstraps ofthe entire estimation procedure, including the GMM estimation and the indirect inference described in equation (23).

γ̃1 and γ̃3 are smaller than their counterparts in the specification in column 3 of Table 6. Finally,
we estimate a positive value for γ̃2 . The contrast between this estimate and the negative estimate
in Table 6 stems from the difference in the source of identification: in this joint estimation, γ̃2 isidentified from the diversified R&D dummies in combination with the R&D expenditure sharesNsN
N I and s N IF , whereas in Table 6, it is primarily identified from a small number of observationsin the NF mode.
We show in Appendix B.4 that our estimate of γ̃ implies θ = 1.33 as the elasticity of substitution between R&D inputs, i.e., different sources of R&D inputs are not easily substitutable. Thisestimate is tightly connected to the large estimated gains from using diverse R&D modes in theauxiliary regression. The low elasticity estimate also means the love for variety of ideas plays animportant role in accounting for the return from R&D.
Panel A of Table 8 reports the empirical transition matrix for manufacturing firms and themodel counterpart. Our model is able to fit the transition patterns reasonably well, with a meandifference between the model and the data in the order of 0.02. The fit of the NF row is worse
than that of other rows, which is likely due to the relatively lower weight on these moments
given the small number of firms in the NF mode. The last row of Panel A reports the mode
distribution of firms. The model fits the data closely despite the mode distribution not being
directly targeted.
Panel B of Table 8 reports the estimates for fixed and sunk cost parameters. The upper partof the panel is the total cost of transition between R&D modes, combining fixed and sunk cost
components. Two observations are noteworthy. First, the diagonal elements are substantiallysmaller than the other values in the same column, suggesting that sunk costs play an importantrole. In terms of quantitative magnitude, we find that the startup cost of doing R&D with mode
N is around 1.17 million USD. Compared with the average R&D expenditures of 1.78 million
USD in the data, this estimate suggests that an important part of R&D expenditures are on the34

Table 8: Transition Matrix and Cost Estimates
Panel A: Transition probability and steady state distribution: model versus data
0
N
NI
NF
Model
0.007
0.035
0.003
0.387
0.025
0.019

N IF

Data
Model Data
Model Data
Model
0
0.890
0.902
0.061
0.069
0.033
0.015
N
0.276
0.260
0.592
0.560
0.082
0.114
NI
0.115
0.116
0.059
0.059
0.684
0.691
NF
0.140
0.119
0.380
0.256
0.033
0.052
N IF
0.049
0.042
0.011
0.021
0.252
0.248
SS dist.
0.582
0.597
0.134
0.130
0.171
0.157
Panel B: The estimated cost matrix and breakdowns
e x,x0
0
N
NI
F

Data
0.005
0.042
0.011
0.407
0.021
0.021

Data
0.011
0.008
0.131
0.040
0.667
0.092

0
N
NI
NF
N IF

0
0
0
0
0

-

1.167
0.019
0.493
0.019
0.493

(0.039)(0.017)(0.062)(0.017)(0.062)

2.073
0.926
0.014
0.926
0.014

(0.080)(0.073)(0.021)(0.073)(0.021)

3.005
1.857
2.331
0.748
1.222

(0.305)(0.301)(0.292)(0.250)(0.242)

3.545
2.398
1.486
1.472
0.560

(0.203)(0.200)(0.168)(0.174)(0.138)

Breakdown

fN
0.019(0.017)f NI
0.014(0.021)f NF
0.748(0.255)f N IF
0.560(0.145)FN
1.147(0.043)FI
0.912(0.067)FF
1.110(0.105)F IF
0.183(0.102)F I0
0.474(0.069)F F0
0.000(1e-7)

NF

Model
0.007
0.031
0.132
0.186
0.664
0.096
N IF

Notes: Panel A of the table reports the transition probability between modes in the steady state of the estimated model and in thedata, averaged among manufacturing firms with more than 10 employees over the sample period. The steady state distribution forthe data are firms’ frequency distribution across modes over the same period. Panel B reports the estimates for the cost parametere x,x0 and the breakdown of the matrix into individual components as described in Section 3. Numbers in parentheses arematrix F
bootstrapped standard errors. Numbers in the lower panel are in million US dollar.

fixed and sunk cost components. Second, we find that F̃ N,NF > F̃ N I,N IF holds. Compared to
the firms that do not have any immigrant R&D workers, firms with immigrant R&D workers
face 20% lower cost in starting offshore R&D. This finding also suggests that the interaction
between offshore R&D and high-skill immigration via the increased benefit of R&D, embedded
in equation (6), is not enough to generate the higher propensity of starting offshore R&D amongfirms with immigrant researchers observed in the data. The information channel is also needed.30
The last row of Panel B are the breakdowns of the composite cost matrix by mode-specificfixed costs and the sunk costs associated with mode switching. Note that the information value of
immigrants is captured in F̃ N,NF − F̃ N I,N IF and can be decomposed into the sunk cost component
F IF and the fixed cost component f NF − f N IF . According to this decomposition, each of the
sunk and fixed cost components accounts for approximately half of the information value of
immigrants.
30 One might be concerned that the key elements in the transition matrix that identify F̃ N,NF > F̃ N I,N IF , e.g., a higher

frequency of the N I → N IF switch than the N I → NF switch, are entirely driven by large and productive firms doing
more of all activities. If so, our estimation could be forcing a size-driven effect on the information channel. We notethat first, as shown in Appendix A.2, the transition pattern is robust after controlling for firm size and productivity.
Second and more importantly, to the extent that size plays a role in firms’ joint use of imported R&D services andimmigrant researchers, our heterogeneous firm model incorporates such channels. In this sense, our estimate of theinformation channel picks up what cannot be explained by firm size alone.

35

5Counterfactuals

We use the estimated model to conduct counterfactual analysis. Our goals are two-fold. First,
we examine the role of the love for variety of ideas and the information channel in shaping firmlevel R&D decisions and aggregate productivity. Second, we quantify the impacts of policies
that affect firms’ access to foreign inputs or the overall R&D costs, including liberalization in
high-skill immigration and offshore R&D, and an R&D subsidy.
5.1

The Role of the Love for Variety of Ideas and the Information Channel

In the model, firms hire immigrant researchers for two main reasons. First, immigrants bringdifferent, potentially better ideas into the R&D process, which increases the return to R&D.
This love for variety of ideas effect comes from imported R&D services as well as immigrant
researchers. However, because offshore R&D involves significant costs, most firms are not able toreap the full benefit of diversified R&D. This observation leads to the second reason why firms
hire immigrant researchers: they reduce the cost of offshore R&D by facilitating communication
between headquarters and offshore R&D sites. In this subsection, we conduct two experiments
to quantify the gains from the love for variety of ideas and the importance of the information
channel in firms’ R&D decisions.
In the first experiment, we shut down the information channel by increasing f N IF to the levelof f NF and reducing F IF to zero. These two changes remove the cost advantage in doing offshore
R&D enjoyed by firms with immigrants, so the main motivation for any firm to hire immigrants
stems from the diversity they bring to R&D. In the second experiment, we shut down the lovefor variety of ideas by setting θ to infinity, making native researchers, immigrant researchers, andimported R&D services perfect substitutes for one another.31 In this case, the only reason firms
ever consider paying the cost and adopting foreign R&D inputs is because they have a favorable
mode specific idiosyncratic draw.
The first panel in Table 9 reports the distribution of firms by R&D mode in the benchmark
and the two counterfactual economies. When the information channel is eliminated, the numberof firms in mode N IF decreases by more than 80%. Interestingly, the fraction of firms in the
N I mode also decreases by about two fifths, even though firms in this mode are not directly
affected by the elimination of the information value. This decrease reveals that many of the firms
choosing the N I mode in the benchmark economy are motivated by opportunities to transit into
the N IF mode in the future. In total, the fraction of firms doing R&D decreases by 13 p.p., from
40% to 27%, underscoring the importance of the information channel for participation in R&D.
When the love for variety of ideas is eliminated, as shown in the third column of panel (a), lessthan 16% of firms conduct R&D, predominately in mode N. The few firms in the modes N I, NF,
x .
and N IF choose them entirely out of idiosyncratic reasons captured in ιi,t
31 We implement this counterfactual by setting γ̃

m = 0 for m = 1, 2, 3 in the productivity law of motion.

36

Table 9: Firms’ R&D Choice and Aggregate Productivity: Benchmark vs. Alternative Models(a) Share of firms (%)(b) Share of R&D expenditure (%)(c) Aggregate (log) productivity

R&D modes Benchmark No info No variety Benchmark No info No variety Benchmark No info No variety
No R&D
59.74
73.38
84.25
0.257
0.263
0.271
N
13.03
14.09
12.87
30.41
50.68
81.83
0.280
0.291
0.318
NI
15.72
9.05
2.76
36.60
32.88
17.46
0.271
0.293
0.310
NF
1.90
2.10
0.07
5.62
9.96
0.42
0.393
0.422
0.317
N IF
9.61
1.39
0.05
27.37
6.47
0.29
0.369
0.410
0.309
All
100
100
100
100
100
100
0.284
0.282
0.280
Notes: Columns marked as ‘No info’ report the results from the alternative model specification where there is no information
channel for immigrant researchers, and columns marked as ‘No variety’ report the results from the alternative specification where
different types of R&D inputs are perfect substitutes. Panels (a) and (b) report the share (%) of firms by R&D mode and the share(%) of R&D expenditure of firms from each mode, respectively. Panel (c) reports the (sales-weighted) average log productivity
among all firms and among firms in each R&D mode.

The shift in firms’ R&D mode choices translates into a qualitatively similar shift in the distribution of R&D expenditures by mode, reported in panel (b) of the table. Quantitatively, thedecrease in the share of R&D spending by firms in modes N I and N IF is smaller than the decrease in the share of firms in these modes. This difference reflects a compositional change offirms within a mode. For example, in the absence of the information channel, the overall costof the N IF mode is higher than in the benchmark model. Therefore, firms choosing the N IF
mode tend to be larger and more productive than before, and they would outspend firms inother modes of R&D.
We now examine the impact of these model mechanisms on aggregate productivity. Reported
in panel (c) is the sales weighted average log productivity among all firms and among firms ineach R&D mode. Shutting down the information channel reduces aggregate productivity by
0.2%, whereas imposing perfect substitution between different R&D inputs reduces aggregate
productivity by 0.4%.32 Intuitively, both experiments make R&D more costly, so firms participate less in, and benefit less from, R&D. Somewhat counter-intuitively, despite the decrease inaggregate productivity, the average productivity of some modes increases. In fact, the average
productivity increases in all modes upon the elimination of the information channel. This result
is entirely driven by the change in the composition of firms between modes: when entering the
N IF mode is more costly, the most productive firms remain, while the less productive firms
switch to other modes. Because the switchers are still more productive than existing firms inother less costly modes, the average productivity in all mode increases.
To assess the importance of foreign inputs for the gains in aggregate productivity from R&D,
we conduct an additional experiment that eliminates the incentive to conduct R&D by assuming
doing R&D has no effect on firms’ future productivity. Aggregate productivity falls to 0.279,
which is only slightly lower than 0.280, the aggregate productivity when the love for variety ofideas is eliminated. The modest difference between these two numbers shows that in a small open
economy like Denmark, the majority of the productivity gain from R&D realizes only because
32 These moderate impacts on aggregate productivity reflect the small estimates for the returns to R&D in Table 6.

As our main points are on the importance of foreign inputs and the interaction between them, we focus on the relative
magnitudes of aggregate productivity gains across experiments.

37

Table 10: Changes in R&D and Productivity– Benchmark versus Counterfactual Policy Changes(a) Share of firms
by mode (%)
R&D modes
No R&D
N
NI
NF
N IF
All

Benchmark
59.74
13.03
15.72
1.90
9.61
100

Immigration
47.43
14.44
23.00
2.25
12.88
100

(b) Share of total
R&D expenditure (%)
Offshoring
34.12
11.51
28.38
3.19
22.81
100

Benchmark
30.41
36.60
5.62
27.37
100

Immigration
25.64
41.22
4.97
28.17
100

Offshoring
16.09
39.98
5.49
38.44
100

(c) Aggregate(log) productivity
Benchmark
0.257
0.280
0.271
0.393
0.369
0.284

Immigration
0.251
0.270
0.270
0.374
0.366
0.286

Offshoring
0.245
0.261
0.256
0.361
0.348
0.288

Notes: Columns marked as ‘Immigration’ report the results from the counterfactual scenario on the immigration policy, and thecolumns markets as ‘Offshoring’ report the results from the counterfactual change on the offshoring policy, as described in the
text. Panels (a) and (b) report the share (%) of firms by R&D mode and the share (%) of R&D expenditure from each mode,
respectively. Panel (c) reports the (sales weighted) average log productivity among all firms and among firms in each R&D mode.

of the access to foreign inputs. When forced to carry out R&D with only domestic inputs, the0.280−0.279
economy can reap only 20% (= 0.284−0.279 × 100) of the full return from R&D.

In summary, the counterfactual results show that access to foreign inputs account for 60% of
firms’ participation in R&D and 80% of the gains in aggregate productivity from R&D. Moreover, firms’ R&D choices depend crucially on the cost of doing R&D in different modes and theextent to which such costs could be mitigated by immigrant researchers. Accounting for thesemechanisms is important for explaining the observed R&D choices and, as we will show in thenext subsections, for policy evaluations.
5.2

High-Skill Immigration and Offshore R&D Policies

Firms’ access to immigrant researchers and offshore R&D services are both heavily influenced
by national policies, which are often a subject of heated debates. We use the model to study theeffects of two policies: liberalization in high-skill immigration and promotion of offshore R&D.
We model these policies as a 50% reduction in the sunk costs of hiring immigrant researchersand of starting offshore R&D, F I and F F , respectively. The reduction in F I can be thought of asa reform that eases the frictions in hiring foreigners; the decrease in F F could capture either an
improvement in the information technology (IT) that facilitates international collaboration or aninvestment treaty that makes it easier for firms to set up an R&D operation in foreign countries.
These 50% changes might seem unrealistically large, but note that the integration of the newmember states into the EU represents one of the most drastic liberalization in immigration inrecent decades, leading to rapid increases in migration in the region (Caliendo et al., 2021), while
the advancement of IT over the past two decades has made communication easier than ever.
Table 10 reports the results from these experiments. The liberalization in high-skill immigration increases the share of firms with immigrant researchers by a total of 10.5 p.p. About athird of this increase occurs in mode N IF. The liberalization in offshore R&D increases the shareof firms in NF or N IF mode by around 14.5 p.p., more than doubling the share in the baselinemodel. The overwhelming majority of the increase, again, occurs in the N IF mode. With offshore R&D becoming less costly, we also see more firms choosing the N I mode, which reflects
the option value of immigrants: firms hire immigrants first, anticipating that in the future, when38

Table 11: Counterfactual Changes with and without the Information Channel(a) Immigration policy
No R&D(b) Offshoring R&D policy

N

NI

NF

N IF

No R&D

N

NI

NF

N IF

I. Changes in the share of firms by mode (p.p.)with the information channel-12.31

1.41

7.28

0.36

3.26

-25.62

-1.52

12.65

1.29

13.20

without the information channel-11.69

1.69

8.80

0.08

1.13

-10.30

1.83

3.35

2.83

2.29

II. Changes in aggregate productivity (overall, %)with the information channel

0.14

0.37

without the information channel

0.10

0.18

Notes: Panel I reports changes (in percentage points) in the share of firms by R&D mode between the benchmark equilibrium
and the new equilibrium under either the immigration policy (panel (a)) or the offshoring policy (panel (b)), with or without the
information channel in play. Panel II reports changes (in %) the overall aggregate productivity between the benchmark equilibrium
and the new equilibrium under either the immigration policy (panel (a)) or the offshoring policy (panel (b)), with or without the
information channel in play.

they either become productive enough to overcome the switching cost or are hit with a favorable
idiosyncratic shock, they can take advantage of the information channel and switch to the N IF
mode more easily.
We examine the impact of these two policies on aggregate productivity. As shown in the lastrow in panel (c) of Table 10, immigration liberalization increases aggregate productivity by 0.2%
and the offshore R&D policy increases aggregate productivity by 0.4%. The average productivity
in individual modes, on the other hand, declines from the baseline levels. Again, the difference
between the responses in aggregate and mode-specific productivity is due to a compositionalchange: the new participants of R&D are less productive than existing participants but moreproductive than firms staying in the no R&D mode, so their switch brings down the average
productivity in all modes.
The results in Section 5.1 demonstrate the importance of the information channel for firms’
R&D decisions. To understand how this channel moderates the two policies, we simulate both
policies in the alternative model without the information channel as defined in Section 5.1 andcompare the impacts of each policy between the benchmark and the alternative model. Table
11 reports the main findings. For both policies, the information channel clearly amplifies thechanges in firms’ mode choices. The difference between the two models is especially pronounced
in the share of firms in the N IF mode, who benefit most directly from the information channel.
The lower panel in the table reports the impact on aggregate productivity of these two policies
in the benchmark and the alternative model. It shows that 29% of the productivity impact of theimmigration policy and 51% of the productivity impact of the offshoring policy are due to theinformation value of immigrant researchers.

39

Table 12: Changes in R&D and Productivity: Benchmark versus R&D Subsidy(a) Share of firms by mode (%)(b) Share of total R&D expenditure (%)(c) Aggregate (log) productivity

R&D modes Benchmark
R&D subsidy
BenchmarkR&D subsidy
BenchmarkR&D subsidy
No R&D
59.74
14.05
–
0.257
0.217
N
13.03
11.12
30.41
11.34
0.280
0.232
NI
15.72
19.04
36.60
19.85
0.271
0.239
NF
1.90
13.34
5.62
16.19
0.393
0.317
N IF
9.61
42.44
27.37
52.61
0.369
0.324
All
100
100
100
100
0.284
0.292
Notes: Columns marked as ‘R&D subsidy’ report the results from the counterfactual scenario on the R&D subsidy policy as
described in the text. Panels (a) and (b) report the share (%) of firms by R&D mode and the share (%) of R&D expenditure fromeach mode, respectively. Panel (c) reports the (sales weighted) average log productivity among all firms and among firms in eachR&D mode.

5.3

R&D Policy in the Age of Globalized R&D

In the last set of exercises, we study the importance of foreign inputs in the evaluation of R&D
policies. Many countries, Denmark included, adopt policies in the form of direct subsidies or
tax rebates to promote R&D investment. Such policies often amount to substantial costs. For
example, the R&D subsidies for loss-incurring firms, which we exploit in Section 4 to estimate
ν, cover 25% of firms’ R&D expenses up to 5.5 million DKK (0.83 million USD) per year. This
number is more than half of the startup R&D cost estimated in Table 8. Our last exercise captures
the essential features of this policy, which does not make a distinction between the type of R&D
expenditures that firms claim, by decreasing fixed and sunk R&D costs for each mode by halffrom their baseline levels.
Table 12 summarizes the effects of this experiment. With the subsidies, substantially more
firms are engaged in R&D, especially via modes NF and N IF, resulting in a shift in R&D expenditures towards these modes. As was the case for the immigration policy and the offshoring
policy in Section 5.2, although aggregate productivity increases by 0.8%, the shift in composition
toward more diversified R&D leads to decreases in the average productivity among firms in eachR&D mode.
Compared to the existing studies that estimate firms’ return to R&D, the main novelty of thispaper is to allow for the use of foreign R&D inputs. Does this feature matter in evaluating theeffect of subsidies on firm’s R&D choices and aggregate productivity? To answer this question,
Table 13 compares the effect of the same R&D subsidy policy between the benchmark model andan alternative model with θ → ∞, in which case firms reap no benefit from the diversity of ideas.
We find that in this alternative model, the R&D subsidy leads to a much smaller increase in firms’
participation in R&D. Moreover, this small increase in participation is concentrated among the N
and N I modes, as opposed to among the N IF mode, where the return to R&D is the highest. The
different responses in R&D mode choices lead to a significantly different prediction on aggregate
productivity: without the love for variety of ideas, the same R&D subsidy policy generates only
0.12% aggregate productivity gains, less than one-sixth the prediction of the benchmark model.
In the age of globalized R&D, foreign R&D inputs are playing an increasingly important roleand have become a major source of returns to R&D. Our experiment suggests that omission of40

Table 13: Counterfactual Changes from an R&D Subsidy
No R&D

N

NI

NF

N IF

I. Changes in the share of firms by mode (pp)BenchmarkWithout the love for variety of ideas channel-45.69-25.48

-1.91
12.78

3.32
10.09

11.45
1.27

32.83
1.34

II. Changes in the aggregate productivity (overall, %)BenchmarkWithout the love for variety of ideas channel

0.81
0.12

Notes: Panel I reports changes (in percentage points) in the share of firms by R&D mode between thebenchmark equilibrium and the new equilibrium under the R&D subsidy policy, with or without the lovefor variety of ideas channel in play. Panel II reports changes (in %) the overall aggregate productivity
between the benchmark equilibrium and the new equilibrium under the R&D subsidy policy, with orwithout the love for variety of ideas channel in play.

these inputs could lead to a substantial bias in the evaluation of R&D policies.33

6Conclusion

While a large literature has examined the sourcing of foreign inputs in production, less is known
about the sourcing of R&D inputs. Using unique data from Denmark, this paper examines
firms’ decision to use two foreign R&D inputs—immigrants researchers and imported R&D services—and the impacts of this decision on firm performance and aggregate productivity.
We find that investment in R&D generates a higher return when firms are able to use eitherof the two foreign inputs, which we interpret as the love for variety of ideas in R&D. We also
document evidence consistent with the information value of immigrants: firms can reduce thebarriers they face in sourcing R&D services from abroad by employing immigrant researchers.
We conceptualize these mechanisms in a model of firm dynamics with endogenous R&D choices.
Through counterfactual experiments, we highlight that access to foreign inputs is essential forfirms’ participation in R&D and that these inputs play a complementary role in overall R&D. We
further show that omitting these inputs or the interaction between them would result in biased
assessments of the effectiveness of innovation policies, and immigration and offshoring policies.
The reliance of firms on foreign R&D inputs has been steadily increasing in many developed
countries. This paper is a step towards a better understanding of firms’ global organizationof R&D. We consider the R&D sourcing decision of Danish firms, for which there is uniqueinformation in our data. Some large global firms carry out R&D in foreign locations to be used
for local production, which neither our measure nor our model captures. Understanding firms’
decision to carry out R&D in different locations, for both local and global uses, and how thesedecisions interact with immigration policies is an important avenue for future research.
33 It is possible that if we estimate a model with only domestic R&D to fit the same return to overall R&D observedin the data, such bias could be smaller. This alternative, however, is subject to the Lucas critique. For example, if
the model is estimated in an open economy with foreign R&D inputs, its predictions for an R&D subsidy in a closed
economy would still be wrong.

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44

Appendix For Online Publication
High-Skill Immigration, Offshore R&D, and Firm Dynamics
Jingting Fan
Pennsylvania State University

Eunhee Lee
University of Maryland, College Park

Valerie Smeets
Aarhus University and CEPR

Appendix A Data and Empirics

2

A.1 Data Source and Variable Construction . . . . . . . . . . . . . . . . . . . . . . . . . .

2

A.2 Regression Evidence on the Information Channel . . . . . . . . . . . . . . . . . . . .

6

A.3 Robustness Exercise for Reduced-Form Facts . . . . . . . . . . . . . . . . . . . . . . . 12
A.4 Descriptive Statistics on the Source of Immigrants . . . . . . . . . . . . . . . . . . . . 18
Appendix B Theory and Structural Estimation

20

B.1 Derivation of Equation (4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
B.2 Estimation of the Share of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
B.3 Robustness Exercise for Production Function Estimation . . . . . . . . . . . . . . . . 21
B.4 More on the Constraint Optimization Problem (23) . . . . . . . . . . . . . . . . . . . 25

1

Appendix A
A.1

Data and Empirics

Data Source and Variable Construction

Summary. Our analysis uses multiple datasets on both workers and firms, linked together
through unique worker and firm identifiers. Table A.1 summarizes where each piece of information is from. The rest of this subsection introduces individual datasets and explains theconstruction of the key variables.
Table A.1: Summary of Data Sources
Information on firms

Information on workers

Dataset
IDA

Variable
worker Id

Dataset
IDA

Variable
employment status, hourly
wage, occupation, city

FIRE

main industry, and balance
sheet and income statement
items

BEF

immigration
statuscountry of origin

FUI (The R&D Survey)

domestic R&D and offshore
R&D status/expenditures, foreign region of R&D affiliates

UDDA

education

The Offshoring Survey

whether a firm has offshore activities in 2011, and in which
foreign regions

UHDI

firm import and export flows

FATI

whether a firm is an affiliate ofa foreign firm

andNote: This table summarizes the sources of information on workers and firms.

IDA. The Integrated Database for Labor Market Research (IDA) is a linked employer-employee
database provided by Statistics Denmark (DST, hereafter) that contains the universe of workers
and firms in Denmark. The IDA database is organized into four datasets containing informationon persons, employment, workplaces and firms, which we link together through common identifiers. The employment data are a snapshot in November for each year, so workers out of thelabor force in November are not included. For workers reporting multiple employment spells in
November, we keep their primary job.
We identify workers in R&D-related tasks based on their reported occupation in IDA, coded
according to the Danish equivalent of the International Standard Classification of Occupations(DISCO codes, hereafter). For each occupation, we inspect its task contents and classify it as
being R&D related or not based on whether the job likely involves testing, creation, or designing,or requires technical knowledge of a STEM subject. This strategy follows Bernard et al. (2020),
who classify occupations into four groups: R&D, management, production and manual work,and services and support activities.
2

Table A.2: R&D occupations in DISCO88 and DISCO08 Classifications
DISCO 88 Classification (3-digit)
Professionals
211 Working on topics in physics, chemistry, astronomy, meteorology, geology and geophysics
212 Working with mathematical and statistical concepts, theories and methods
213 Computer planning and system development
214 Architectural and engineering work, etc.
221 Working on topics within the biological branches of science
222 Work on topics in medicine, dentistry, veterinary science and pharmacy
Technicians and Associate Professionals
311 Technician work in physics, chemistry, mechanics and so on
312 Computer technical work
313 Work with sound, light and images at film and theater performances, etc. and operation of medical equipment
321 Technician work in biology, medicine, agriculture and so on
DISCO 08 Classification (3-digit)
Professionals
211 Work in Physics and Geology
212 Working with mathematical, actuarial and statistical methods and theories
213 Working in life sciences
214 Engineering (except in electrical engineering)
215 Engineering work in electrical technology
216 Working with architecture, infrastructure and design
221 Medical work
222 Nursing and midwifery work
223 Work in natural medicine and alternative medicine
224 Paramedical work
225 Veterinary work
226 Other health work
251 Development and analysis of software and applications
252 Working with databases and networks
Technicians and Associate Professionals
311 Engineering work in the physical sciences and engineering
314 Technician work in life sciences
321 Technician work in the medical and pharmaceutical field
351 Operations technician work and user support work in the field of information and communication technology
352 Technician work in audiovisual media and telecommunications

Our empirical analysis focuses on year 2001 to year 2015. A change in DISCO took place in2008. We classify occupations in DISCO codes both before and after the change (DISCO88 andDISCO08, respectively). We check and make sure that the change in occupation classifications in2008 does not in itself lead to abrupt changes in the share of R&D workers.
Table A.2 reports the occupations classified as R&D-related in DISCO88 and in DISCO08. In
general, the occupations related to R&D activities are a subset of DISCO Groups 2 (Professionals)
and 3 (Technicians and Associate Professionals). Note also that R&D-related occupations under
our classification do not include managers (often associated with DISCO Group 1). This way weare not selecting occupations based on the skill level or the wage level ex ante but selecting thembased on the nature of required tasks.
The dataset includes around 2.4 million individuals aged between 15 and 70, and 140,000
firms per year. Many firms in Denmark are small. Restricting the sample to firms with at least
10 employees leaves us with around 2.1 millions workers and 28,000 firms per year. Focusing on
this sample, we construct workers’ hourly wage and the municipality of their workplace, which3we use to compute the main (or modal) geographic location of each firm in Denmark.
BEF. We supplement IDA with information from the national registers (BEF, provided by
DST, which covers the universe of individuals in Denmark) to identify immigrants. In the baseline analysis, we define immigrants as those who are born outside Denmark. In various robustness exercises reported in Appendix Section A.3, we also consider alternative definitions ofimmigrants, taking advantage of the rich set of demographic information we have in the data.
UDDA. We use the education register (UDDA, provided by DST) to supplement IDA witheducation information. We consider two levels of higher education: at least some college education and at least a master’s degree. In the data, the first group corresponds to the following
codes: ‘short higher education’, ‘medium-term higher education’, ‘bachelor’, ‘master’s and PhD
programs’, while the second group includes only ‘master’s and PhD programs’.
FIRE. We match IDA with the Accounting Statistics (FIRE) over the period 2000 to 2015. FIRE
provides accounting information such as revenues, value-added, investments, materials, wage
bill, and employment. This dataset also provides information about the firm’s main industry,based on the NACE industry classification, concorded to NACE Rev.2.
The information in FIRE originates from the Tax Authorities, which require the accounting
information to be reported by companies with an annual turnover above 0.5 million Danish krone(DKK), and by individually owned companies with an annual turnover above 0.3 million DKK
as part of their individual tax return. Due to this sampling strategy, we exclude firms withan annual turnover of less than 0.3 million DKK. We exclude government activities and public
services firms, not-for-profit firms (based on a firm’s legal status such as not-for-profit funds,
associations, non-profit associations, government owned, church owned, and not specified), or
firms in agriculture or extraction. After matching this FIRE sample with the IDA sample, we end
up with around 95,000 firms per year. Restricting to firms with at least 10 employees leaves us
with around 17,000 firms per year.1
We deflate the wage bill by the consumer price index and deflate revenues, value-added,
capital, investment, and materials by their respective industry-specific deflators, all provided by
DST. Since these industry-specific deflators are at the NACE Rev.2 Intermediate Aggregation level(A*38 Codes, see Table A.3), we define the industry firms accordingly. This leaves us with a totalof 25 industry groups for the entire private sector and 11 industry groups for the manufacturingsector.
We calculate firms’ capital stock by applying the perpetual inventory method to their fixed
r . In the first year
capital investments, assuming a depreciation rate of 8%: Ki,t = 0.92 ∗ Ki,t−1 + Ii,twhen a firm appears in the sample, we use its total assets as the initial capital stock.
FUI (the R&D Survey). We match the IDA×FIRE matched data with FUI, which is an R&D
Survey released by DST since 1991. The survey is the Danish equivalent of the European Community Innovation Survey. It covers all firms that either have over 250 employees, have more
1 To avoid biases from reporting errors in our structural estimation, we exclude observations showing abnormal
accounting statistics. More specifically, we exclude observations with either revenue labor ratio, material labor ratio,or capital labor ratio falling outside of the 1 to 99 percentile of their broad industry groups.

4

Table A.3: NACE Rev.2 Intermediate Level Aggregation - Private Sector Classification
A*38 Code
CA
CB
CC
CD
CE-CF
CG
CH
CI-CJ
CK
CL
CM
D-E
F
G
G
G
H
H
I
JA
JB
JC
K
L
M-N

ISIC Rev. 4/ NACE Rev. 2

Divisions (NACE-2)

Manu. of food products, beverages and tobacco products
Manu. of textiles, apparel, leather and related products
Manu. of wood and paper products, and printing
Manu. of coke, and refined petroleum products
Manu. of chemicals, chemical products and pharmaceuticals
Manu. of rubber and plastics products, and other non-metallic mineral products
Manu. of basic metals and fabricated metal products, except machinery and equipment
Manu. of computer, electronic, optical products, electrical equipment
Manu. of machinery and equipment n.e.c.
Manu. of transport equipment
Other manu., and repair and installation of machinery and equipment
Utilities
Construction
Wholesale and retail trade and repair of motor vehicles and motorcycles
Wholesale trade, except of motor vehicles and motorcycles
Retail trade, except of motor vehicles and motorcycles
Transportation and storage
Postal and courier activities
Accommodation and food service activities
Publishing, audiovisual and broadcasting activities
Telecommunications, IT and other information services
IT and other information services
Financial and insurance activities
Real estate activities
Professional services

10 to 1213 to 15
16 to 18
19
20 to 21
22 to 23
24 to 25
26 to 2728
29 to 30
31 to 33
35 to 39
41 to 4345
46
47
49 to 52
53
55 to 56
58 to 60
61
62 to 63
64 to 66
68
69 to 82

than 1 billion DKK in revenue, spend at least 5 million DKK in R&D activities, or operate in
R&D industries (defined as NACE 2-digit Rev.2 industry 72). In addition, it includes a stratified
sample of all the remaining firms that do not satisfy any of these criteria. The R&D sample is an
unbalanced panel of around 4,000 firms per year.
The survey reports firms’ R&D expenditures in Denmark, which we label as domestic R&D
expenditures, for all years from 2001. We classify firms as doing domestic R&D in year t if theyreport positive domestic R&D expenditures that year. The survey also asks about R&D expenditures bought overseas, either via a foreign subsidiary, foreign consultants, foreign unrelated
firms, or foreign research institutes. This variable is available for the following years: 2001-2003,
2005 and 2007-2014. The survey question is specific in that only R&D expenditures for the exclusive use of the reporting firm in Denmark should be included.2 We classify a firm as doing offshore
R&D in year t if it reports positive R&D expenditures bought overseas for the use of the entity
being surveyed in Denmark that year.
Finally, the survey also asks whether firms have R&D workers present in their foreign affiliates, broken down by broad geographic locations. This information is available from 2009 to 2012
for 4 geographic areas (Europe, United States and Canada, China, Rest of the World) and from2013 to 2016 for 8 geographic areas (EU15, New European Member States, Other European Countries, United States and Canada, China, India, Central or South America, Rest of the World). We
2 The exact wording of the questionnaire is ‘FoU udført i udlandet og anvendt internt i virksomheden,’ whichmeans ‘R&D performed abroad and used internally in the company.’5

group the 2013-2016 geographic information into the 4 geographic areas of 2009-2012 and define
firms as having R&D workers in a foreign region n in year t if they report having R&D personnel
in that region in year t.
Our final IDA×FIRE×FUI sample, restricted to firms with at least 10 workers, contains approximately 47,000 firm-year observations over 2001-2015, which amounts to around 3,000 firms
per year. This is the sample on which we calculate descriptive statistics in Section 2 of the paper.
The Offshoring Survey. For corroborative measures of offshore R&D, we also use a survey onoffshoring conducted in 2012 by DST (in partnership with Eurostat). The survey samples all firms
with 50 or more employees and a representative set of firms with 10-49 employees, resulting ina sample of around 4,500 firms. The survey asks whether a firm conducts R&D activities abroadin 2011, in house or through arms’ length contracts.3 This information is further broken downby 8 broad geographical areas (EU15, New European Member States, Other European Countries,
United States and Canada, China, India, Other Asian Countries, Rest of the World). As the data
can be quite sparse in the last two regions (Other Asian Countries and Rest of the World), whenusing the geographical dimension of the Offshoring Survey, we only consider the first six regions.
Matching the Offshoring Survey with our IDA×FIRE×FUI sample, we end up with around 1,900
firms for 2011.
UHDI. We supplement our data with the information on firms’ participation in international
trade over 2001-2015 (UHDI, provided by DST). UHDI is based on two main sources: Intrastat
and Extrastat. Intrastat is based on reports to DST from around 7,000 companies per year about
their trade in goods with companies in other EU countries. The reporting thresholds under
Intrastat have been set so that the reporting companies’ trade volume amounts to at least 93% of
all Danish EU imports and 97% of all Danish EU exports. Extrastat covers the universe of importand export transactions between Denmark and non-EU countries.
We aggregate the UHDI data, which are at the firm×year×product×country level, to either
the firm×year or the firm×year×country level. From this, we identify whether firms are exporting or importing goods in a given year, and to/from which foreign regions.
FATI. In a robustness exercise in Section A.3, we show that the information channel exists
among firms that are not an affiliate of a foreign multinational. To this end, we supplement themain data with FATI (provided by DST), which identifies foreign multinational firms in Denmark.
A.2

Regression Evidence on the Information Channel

Table 2 in the text shows that a higher fraction of firms with immigrants than firms without
immigrants start doing offshore R&D in the next period, a pattern consistent with immigrants
researchers reducing the frictions firms face in sourcing R&D services from abroad. One concern
with this interpretation is that this pattern could be confounded by other firm characteristics,
3 Note that the offshore R&D measure from this survey differs from the one from the R&D Survey.

While theOffshoring Survey reports offshore R&D performed by suppliers and affiliates, it does not specify whether it is to be
exclusively used by the firm in Denmark, so that it could also include R&D conducted for the sole use of the firm’s
affiliates.

6

such as their industry or size. In this section, we provide regression evidence to address this andadditional concerns.
Specifically, in Section A.2.1, we estimate firm-level regressions to directly control for industry
and firm characteristics that might be correlated with R&D offshoring decisions. In Sections A.2.2
and A.2.3, we exploit variation at the firm-foreign region level, which increases the credibility of
the information channel. We will also use a shift-share design that exploits the increase in the
supply of immigrant researchers from different foreign regions in Denmark to further address
the reverse causality concern—i.e., firms may hire immigrants because establishing a foreignsource of imported R&D services decreases the cost of hiring immigrants.
A.2.1

Firm-Level Evidence

Our firm-level specification of the information channel is as below:
I(off. R&Dit ) = β I(immiit−1 ) + ν̃d(i) j(i)t + ~α̃ ~Xit + ẽit .

(A.1)

In this specification, the outcome variable is an indicator for whether firm i in industry j(i )located in a Danish location d(i ) reports in the R&D Survey that it does offshore R&D in periodt. We split Denmark into 5 geographic regions and call each geographic region as a ‘city’ toavoid confusion when we explore variations across foreign regions later. The key explanatory
variable is I(immiitn −1 ), an indicator for whether firm i has an immigrant employee in R&D
related occupations in period t − 1. ν̃d(i) j(i)t are city-industry-year fixed effects, which ensures that
our estimate of β does not pick up a higher propensity of hiring immigrants or offshoring R&D
among firms in specific cities or industries. ~Xit is a vector of time-varying firm characteristics,
including firm size, labor productivity, and lagged importing and exporting status.
Table A.4 reports the estimation results. The first column controls for the fixed effects only. In
the second and third columns, we further control for log employment and labor productivity of
the firm, which rules out the possibility that the correlation is simply due to large and productive
firms being more likely to engage in both activities. The coefficient of interest, β, is positive andstatistically significant in all of the first three columns.
The literature has documented a strong impact of the presence of immigrants on regional
and industry-level imports and exports (e.g. Ottaviano et al., 2018). To show that our estimate is
not picking up the relationship documented in these studies, columns 4 and 5 control for firmlevel import and export status, which barely changes the point estimate of β. Column 5 is ourpreferred specification. It suggests that, compared to similar firms in the same city and industry,firms with immigrant researchers have a 4 percentage point higher likelihood of conducting
offshore R&D.
The role of immigrants working outside R&D. On the basis of the specification in column
5, we include an indicator for whether a firm employs immigrants outside R&D-related occupations. We find a small negative coefficient for this indicator, so the presence of non-research

7

immigrants is not positively correlated with offshore R&D.4 More importantly, the coefficient for
the immigrant researcher indicator does not change, which lends support to the focus of ourmodel on the information value of immigrant researchers.
Table A.4: The Information Channel: Firm-Level Regressions
OLS (2001-2014)
I(R&D immii,t−1 )

(1)

(2)

(3)

(4)

(5)

(6)

0.081***(0.007)0.041***(0.006)

0.038***(0.006)

0.038***(0.006)

0.038***(0.006)

0.038***(0.006)-0.011**(0.004)30,93030,930yes

30,589yes
yes

30,589
yes
yes
yes

yes

yes

yes

yes

30,589
yes
yes
yes
yes
yes

30,589
yes
yes
yes
yes
yes

I(Non-R&D immii,t−1 )Observations
Firm sizei,tProductivityi,tImport statusi,t−1
Export statusi,t−1
City×industry×year FE

Notes: The sample is private sector firms with at least 10 employees over 2001-2014. The outcome variable is an indicator taking
a value 1 if firm i offshores R&D to any destination in year t, and 0 otherwise. Offshoring is defined based on the R&D Survey.
Firm size is log employment and productivity is log value added per worker. Cities are defined as the five main geographic regions
within Denmark. Industries are defined at the NACE Rev.2 two-digit level. Standard errors (in parentheses) are clustered by firm. *p < 0.10, ** p < 0.05, *** p < 0.01.

A.2.2

Firm-Destination-Level Evidence and Results from a Shift-Share Design

Table A.4 shows that conditional on other characteristics, firms with immigrant researchers are
more likely to engage in offshore R&D. A mechanism that could be driving this correlation is that,by hiring immigrants, firms gain tacit knowledge about the home countries of these immigrants,
thereby reducing the frictions they face in sourcing R&D services from these countries. Thismechanism is in line with the reduced-form research on the network effect of immigrants on
international business (Rauch and Trindade, 2002). To the extent that this channel is indeed thedriving force, we should expect the effect to be specific to the origin country of immigrants. For
example, immigrant researchers from China might use their knowledge of the language and local
business to help the firm source R&D services from China, but their knowledge would be lessuseful for firms looking to source R&D services from Latin America.
In this subsection, we use firm-destination-level variation to test whether having immigrant
researchers from a foreign region n is correlated with offshoring R&D to the same foreign regionn. An added benefit of using a firm-destination-level specification is that we will be able toexploit the variation in the supply of immigrant researchers from different foreign regions toestablish a causal effect of the presence of immigrant researchers.
4 While the coefficient for non-research immigrants is statistically significant in this particular specification, inother specifications (OLS or IV, firm-level or firm-destination level; see Table A.5), both the sign and the statisticalsignificance of the coefficient differ. Thus, there is no robust evidence for the correlation between the presence of
non-research immigrants and offshore R&D in either direction.

8

OLS specification. Our firm-destination-level specification is as follows:
Xitn + ẽitn .
I(off. R&Ditn ) = β I(immiitn −1 ) + φ̃it + ν̃dn(i)t + η̃ jn(i)t + ~α̃ ~(A.2)

Compared to Equation (A.1), the main difference in this specification is that the outcome variable
and the main explanatory variable are specific to each foreign region n.
We use the R&D Survey to construct I(off. R&Ditn ). Between 2009 and 2015, the R&D Survey
asks in which foreign regions a firm has affiliate R&D employment, which gives us an extensive
margin measure of offshore R&D by firm i in foreign region n.5 Between 2009 and 2012, the survey groups foreign countries into 4 regions: EU, USA and Canada, China, and the RoW. Between
2013 and 2015, the survey groups foreign countries into 8 regions: EU15, EU New Member States(former Eastern European countries), Other European countries, USA and Canada, Central andSouth America, China, India, and RoW. For brevity, in what follows, we group the latter 8 regions
into the 4 regions in 2009-2012, which ensures that our sample has consistently defined foreign
regions for 2009-2015.6
The key explanatory variable is I(immiitn −1 ), an indicator for whether firm i has immigrants
from region n in R&D related occupations, constructed from the IDA database. φ̃it are firm-year
fixed effects, which will absorb time-varying firm characteristics that might drive the correlation
between I(off. R&Ditn ) and I(immiitn −1 ). Some firms might be located in a Danish region (city)with a strong connection to a foreign region or operate in an industry in which foreign region n is
a common offshore destination. These factors could influence both I(off. R&Ditn ) and I(immiitn −1 ).
Our inclusion of industry-destination-time and city-destination-time fixed effects, denoted byν̃dn(i)t and η̃ jn(i)t , addresses this concern. In fact, we will include the more demanding ν̃dn(i)t ×
η̃ jn(i)t fixed effects as a control. Finally, X̃itn are control variables which capture other potential
connections between firm i and region n.
Columns 1 to 3 of Table A.5 report the OLS estimation results. We find that firms with immigrant researchers from foreign region n are more likely to engage in offshore R&D with region n.
This effect is present when city-industry-destination-year fixed effects are controlled for. It is also
not due to the correlation between either of the two decisions and firms’ importing/exporting
relationship with region n. The point estimate suggests that firms hiring immigrant researchers
from a foreign region n will have a 1% increase in the probability of conducting offshore R&D inlocation n. This coefficient is smaller than the coefficient from the firm-level regressions (which
was around 4%), which could be due to the battery of fixed effects magnifying the attenuationbias.
A shift-share design. A remaining concern is that firms might choose to hire immigrant andconduct offshore R&D due to firm-destination-specific factors unobserved to the econometrician.
5 This measure contains geographic variation, but does not capture offshore R&D conducted through arms’ lengthtransactions. In Section A.2.3 of this appendix, we use a measure from the Offshoring Survey, which includes bothin-house and arms’ length offshore R&D by geographic region.
6 As an alternative, we also focus on 2013-2015 and use the 8-region grouping, which enables us to separate India
and different parts of the EU from bigger groups. The result is similar and available upon request.

9

Table A.5: The Information Channel: Firm-Destination-Level Regressions
OLS (2009-2015)
n
I(R&D immii,t
−1 )

(1)

(2)

(3)

(4)

(5)

(6)

0.011***(0.004)0.011***(0.004)0.124***(0.039)0.125***(0.039)89,32089,320
yes
yes
yes
yes

0.010***(0.004)0.005***(0.002)89,320
yes
yes
yes
yes

79,624

yes

79,624yes
yes
yes

0.123***(0.038)-0.002(0.002)
79,624
yes
yes
yes

yes
yes
yes

yes
yes
yes

yes
yes
yes

6.052***(1.235)24.00

6.024***(1.225)24.18

6.309***(1.295)23.72

nI(Non-R&D immii,t−1 )Observationsn
Import statusi,t−1nExport statusi,t−1
Firm×year FE
City×industry×destination×year FE
City×destination×year FE
Industry×destination×year FE
Exclude 2000 firms
First stagensnj(i),d(i),2000 · ( Lnt − L2000)

IV (2009-2015)

yes
yes

Robust first-stage F

Notes: This table reports the results from the estimation of Equation (A.2). In this table a firm is classified as offshoring if it reports
having R&D workers at its foreign affiliates in destination n (this information is available for 2009-2015). Destinations comprise of 4groups: European Union, United States and Canada, China and the rest of the world. The indicators for immigrant R&D workers
and immigrant non-R&D workers reflect immigrants from destination n. Cities and industries are defined as in Table A.4. Columns
1 to 3 report the OLS specifications, while columns 4 to 6 report the IV specifications. For the IV specifications, we exclude firms
reporting having immigrant R&D workers in 2000. The sample consists of private-sector firms over 2009-2015, with at least 10
employees. Standard errors are reported in parentheses and clustered by firm*year in 1-3 and by industry*city*destination in 4-6. *p < 0.10, ** p < 0.05, *** p < 0.01.

It is also possible that our finding is driven by reverse causality—by sourcing R&D services
from a foreign region, firms can more easily tap into the local talent pool and bring immigrant
researchers to work in Denmark.7
To address this concern, we employ an alternative approach, which is based on a shift-share
instrumental variable that exploits the variation in firms’ exposure to immigrant researchers
in their Danish location and industry. Specifically, we use the following as an instrument forI(immiitn −1 ):nsnj(i),d(i),2000 · ( Lnt−1 − L2000).

where j(i ) and d(i ) denote the industry and the (Danish) city of firm i, respectively; snj(i),d(i),2000 is
the share of immigrant researchers from a foreign region n in year 2000 working in city d(i ) andn) is the increase in the total number of immigrant researchers fromindustry j(i ); ( Lnt−1 − L2000

country n between 2000 and year t − 1.
The relevance of this instrument comes from the fact that immigrants tend to be attracted to
7 Our OLS specification partly addresses this concern by using the lagged immigrant researcher indicator as the

explanatory variable. We also note that the reverse causality concern in itself does not invalidate our model—it also
implies that the two activities are complements and that policies affecting one will have an indirect effect on the other,which is exactly what our model seeks to capture.

10

locations and industries with a high density of existing immigrants from the same origin. The
exclusion restriction that we impose for identification is that, conditioning on firm fixed effects
and a number of industry, city, and foreign region controls, the initial distribution of immigrant
researchers affects offshoring decisions through firms’ employment of immigrant researchers.
Since the instrument is constructed using the 2000 distribution of high-skill immigrants, thisassumption would be violated if firms employing immigrant researchers in 2000 show up in
our regression panel, leading to a mechanical first stage. To rule out this concern, in the IV
specifications, we exclude firms that hire immigrant researchers in 2000.8
Columns 4 to 6 of Table A.5 report the IV estimation results. Our design has a reasonably
strong first stage, with the expected sign and the K-P F statistics of above 20. The point estimateof the coefficient of interest is positive and statistically significant. Interestingly, the coefficient isan order of magnitude larger than the OLS estimate. A part of this difference might be due tomeasurement errors being addressed by the instrumental variable approach. Perhaps more importantly, this difference could also arise from heterogeneous effects. Recall that the instrument
exploits variation in the supply of immigrants from a particular origin in the local labor market.
Firms in a local labor market with more immigrants from a particular origin might reap more
returns from the information channel, if the hired immigrant is able to provide valuable information exactly from their connection to the home country through the local immigrant community.
This finding also echoes the results from the literature that uses regional and industry-level data
and argue for the external values of immigrants.
The difference in magnitude notwithstanding, the OLS and the IV results provide the evidence of complementarity—based on entirely orthogonal variations—showing that the presenceof immigrant researchers in a firm encourages offshore R&D. On the other hand, the presence ofother non-R&D immigrants does not have a robust correlation with offshore R&D.
A.2.3

Corroborative Evidence from the Offshoring Survey

As discussed earlier, the foreign-region-specific measure of offshore R&D from the R&D Survey
is for in-house employment only, but firms can also source R&D services from independent
foreign suppliers. One concern is that if in-house employment crowds out outside suppliers,
then the results in Table A.5 might capture simply this substitution effect and does not imply
that firms use imported R&D services more frequently.9 To address this concern, we use analternative measure of offshore R&D from the Offshoring Survey, which captures in-house as
well as outsourced offshore R&D. Because this survey is only available for the year 2011, we use
a cross-sectional specification.
Table A.6 reports the estimation results. Columns 1 and 2 are at the firm-level as in Equation
8 For robustness, we use 1995 as the base year for constructing the instrument while excluding firms hiring immi-

grant researchers in 1995. This specification gives us similar results. Because firms’ industry classification prior to2000 is different from that between 2000 and 2015, we choose to focus on the instrument using 2000 as the base year
for consistency with the rest of the paper.
9 This concern does not apply to the results in Table A.4.

11

Table A.6: The Information Channel: Corroborative Evidence from the Offshoring Survey
OLS (2011)
Firm-Level
I(R&D immii,t−1 )(1)0.048***(0.015)

4,042
Yes
Yes

(2)
0.048***(0.015)-0.005(0.011)
4,042
Yes
Yes

Yes
Yes
yes

Yes
Yes
yes

I(Non-R&D immii,t−1 )Observations
Firm sizei,tProductivityi,tFirm FE
Importi,t−1
Exporti,t−1
City×industry FE
City×industry×destination FE

Firm-Destination-Level(3)
0.013*(0.007)

24,336(4)0.012*(0.007)0.008**(0.003)24,336

Yes
Yes
Yes

Yes
Yes
Yes

yes

yes

Notes: In this table a firm is classified as offshoring if it reports in the Offshoring Survey to have R&D activities abroad in 2011.
The sample consists of private-sector firms with at least 10 employees. Specifications are at the firm level (columns 1 and 2) andthe firm-foreign region-level (columns 3 and 4). Foreign regions in columns 3 and 4 comprise of 6 groups: EU15, New European
Member States (former Eastern European countries), other European countries, United States and Canada, China, and India. Control
variables are defined as in Table A.4 and Table A.5. Standard errors (in parentheses) are clustered by firm. * p < 0.10, ** p < 0.05,*** p < 0.01.

(A.1); and columns 3 and 4 are at the firm-foreign region-level, with 6 foreign regions: EU15,
New European Member States (former Eastern European countries), other European countries,
United States and Canada, China, and India. The results show that this alternative measure ofoffshore R&D leads to quantitatively similar estimates for both firm- and firm-foreign region-levelspecifications, even though it is from a different source and covers only one year. Moreover, we
continue to find that the coefficient of non-R&D immigrants has different signs, with or without
statistical significance, across specifications, suggesting that the information value for offshore
R&D is primarily through immigrants working in R&D-related occupations.
A.3

Robustness Exercise for Reduced-Form Facts

In this section, we report additional robustness exercises for the reduced-form facts. Together,
they address three broad categories of concerns: on the definition of immigrants, on possible
measurement errors associated with the categorization of firms’ R&D modes, and on the role offoreign multinational firms in driving our findings.
A.3.1

Alternative Definitions of Immigrants

The first broad concern is on the definition of immigrants. In the baseline analysis, we define
immigrants as those born outside Denmark. Our model highlights two roles of immigrants: thatthey possess specific knowledge about their home country—thus bringing information value
to the firm—and that their different backgrounds and expertises add extra value to the R&D
process. Not all researchers born outside Denmark can play these two roles. For example,12

an immigrant brought into Denmark as an infant might not be able to speak the language ofher home country; educated in Denmark, she might not provide the diversity of ideas to the
R&D process. Related to this concern, immigrant researchers from other Scandinavian countries
might be relatively more similar to Danish researchers. Our reduced-form facts might simply
capture the close economic ties between Scandinavian countries, rather than the broader rolethat immigrants possibly play in their local economy.
We note that to the extent that such concerns are empirically relevant, by including all
immigrants—rather than only the ones that are likely to play the two roles a priori—our empirical analysis would underestimate the role of immigrants. In this subsection, we provide direct
evidence that excluding the immigrants who might not be very different from native workers
does not weaken our reduced-form results. Specifically, we consider the following alternative
definitions of immigrants: those who enter Denmark at age 18 or above; those who enter Denmark at age 22 or above; those who enter Denmark after receiving their highest level of education.
We also exclude immigrants from Sweden and Norway.
Table A.7 reports the evidence for the information channel under these narrower definitionsof immigrant researchers. For brevity, we focus on the firm-level OLS specifications. Column 1
replicates our preferred specification, reported in column 5 of Table A.4. The remaining columnsof the table report the results using the various alternative definitions of immigrant researchers.
If any, we find that the information channel is stronger when we focus on immigrant researchers
likely to be more different from Danish researchers by using these alternative definitions.
Table A.8 reports the robustness exercises for Table 3 in the paper on the sourcing of R&D inputs and firm performance. The first two columns reproduce our preferred specification, columns
4 and 8 of Table 3, respectively. The remaining columns estimate the same specifications withalternative definitions of immigrant researchers. Across specifications, we find that estimates forthe immigrant researcher indicator with alternative definitions are similar to or slightly larger
than the ones in the baseline specification.
Table A.7: The Information Channel: Alternative Definitions of Immigrants

I(R&D immii,t−1 )Observations
Firm sizei,tProductivityi,tImport statusi,t−1
Export statusi,t−1
City×industry×year FE

baseline> 18 yr> 22 yrcompleted education

non-Scandinavians

(1)

(2)

(3)

(4)

(5)

0.038***(0.005)32,858
yes
yes
yes
yes
yes

0.044***(0.006)32,858
yes
yes
yes
yes
yes

0.048***(0.006)32,858
yes
yes
yes
yes
yes

0.058***(0.007)32,858
yes
yes
yes
yes
yes

0.041***(0.006)
32858
yes
yes
yes
yes
yes

Notes: This table reports the robustness for the information channel based on different definitions of immigrants. Specifications
follow column 5 of Table A.4. Column 1 replicates the baseline result; columns 2 and 3 focus on immigrants arriving in Denmark
after age 18 and 22, respectively; column 4 focuses on immigrants arriving in Denmark after having completed all education; column
5 exclude immigrants from Norway and Sweden. Standard errors (in parentheses) are clustered by firm. * p < 0.10, ** p < 0.05, ***p < 0.01.

13

Table A.8: Sourcing of R&D Inputs and Labor Productivity: Alternative Definitions of Immigrants
baseline(1)
I(R&Di,t−1 )0.014**(0.005)

Log domestic R&D i,t−1
I(off.i,t−1 )I(immi.i,t−1 )Observations
Industry×year FE
Other firm-level controls(2)0.031***(0.012)0.021***(0.006)32,914Yes
Yes>18 yr(3)>22 yr(4)(5)

0.014**(0.005)0.003***(0.001)0.025**(0.011)0.019***(0.006)32,914
Yes
Yes

0.031***(0.012)0.021***(0.006)32,914
Yes
Yes

(6)

0.014**(0.005)0.003***(0.001)0.024**(0.011)0.019***(0.006)32,914
Yes
Yes

0.031***(0.012)0.022***(0.006)32,914
Yes
Yes

completed education

non-Scandinavians

(7)

(9)

(8)

0.014***(0.005)0.003***(0.001)0.024**(0.011)0.020***(0.006)32,914
Yes
Yes

0.030**(0.012)0.023***(0.006)32,914
Yes
Yes

(10)

0.014**(0.005)0.003***(0.001)0.024**(0.011)
0.021***(0.006)32,914
Yes
Yes

0.031***(0.012)0.023***(0.006)32,914
Yes
Yes

0.003***(0.001)0.024**(0.011)
0.021***(0.006)32,914
Yes
Yes

Notes: This table reports the robustness for the relationship between firms’ labor productivity and sourcing of R&D inputs. The firsttwo columns reproduce columns 4 and 8 of Table 3. The remaining columns estimate the exact same specifications as the first twocolumns, but using different definitions for immigrant researchers. See the notes of Table A.7 for these alternative definitions. All
specifications control for firms size, lagged productivity, and import and export status. Standard errors (in parentheses) are clusteredby firm. * p < 0.10, ** p < 0.05, *** p < 0.01.

14

A.3.2

Measurement Errors in Firms’ R&D Modes

In the baseline specifications, we classify a firm as employing immigrant researchers if at least
one immigrant researcher is on its payroll. One might be concerned that this classification is
too liberal—perhaps, more than one employee is needed for a firm to reap the full benefit from
immigrant researchers. If so, our classification introduces measurement errors in firms’ R&D
modes. Such measurement errors could have implications for both reduced-form and structural
analyses. For the reduced-form facts, they tend to bias the coefficient of interest towards zero;for the structural estimation, in the presence of measurement errors, the year-to-year transition
matrix we use to recover the fixed and sunk costs of R&D might differ from the actual transition
patterns, which could lead to biases on the strength of the inferred information channel.
We address the concern on reduced-form and structural estimation separately. Tables A.9 andA.10 report the evidence on the information channel and on the relationship between international sourcing of R&D and firm performance, with different cutoffs of the number of immigrant
researchers to classify firms as hiring immigrants for R&D. The results are consistent across specifications. In particular, in line with the biases due to measurement errors, when we increase thethreshold for a firm to be considered as having immigrant researchers, the estimated effect for
the information channel increases.
Table A.9: The Information Channel: Alternative Mode Classifications

I(R&D immii,t−1 )baseline# of immi ≥ 2# of immi ≥ 5

(1)

(2)

(3)

0.038***(0.005)I(R&D immii,t−1 ≥ 2)

0.079***(0.006)I(R&D immii,t−1 ≥ 5)
Observations
Firm sizei,tProductivityi,tImport statusi,t−1
Export statusi,t−1
City×industry×year FE

32,858
yes
yes
yes
yes
yes

32,858
yes
yes
yes
yes
yes

0.133***(0.006)32,858
yes
yes
yes
yes
yes

Notes: This table reports robustness results for different thresholds when classifying firms as employing immigrant researchers.
Specifications follow column 5 of Table A.4. Column 1 replicates the baseline result; columns 2 and 3 define a firm as employing
immigrant researchers if at least two and five immigrant researchers, respectively, are on the payroll. Standard errors (in parentheses)
are clustered by firm. * p < 0.10, ** p < 0.05, *** p < 0.01.

To demonstrate that the baseline classification does not introduce significant biases into thestructural estimation, we report two additional sets of results. First, in Table A.11 we report thefirms’ transition patterns between different R&D modes under three different classifications ofhiring immigrant researchers. Since the structural estimation focuses on manufacturing firms, we
do so for manufacturing firms only. The left panel of Table A.11 replicates the transition matrix
in Table 8 of the text. The middle and right panels correspond to the cases where at least two
15

Table A.10: Sourcing of R&D Inputs and Labor Productivity: Alternative Mode Classifications
baseline(1)
I(R&D_i, t − 1)

0.014**(0.005)

Log domestic R&D i,t−1
I(off.i,t−1 )I(immi.i,t−1 )(2)0.031***(0.012)0.021***(0.006)# of immi. ≥ 2# of immi. ≥ 5

(3)

(5)

(4)

0.012**(0.005)0.003***(0.001)0.025**(0.011)0.019***(0.006)

I(immi.i,t−1 ≥ 2)

0.015***(0.005)0.028**(0.012)0.002***(0.001)
0.022*(0.011)

0.041***(0.007)0.039***(0.007)I(immi.i,t−1 ) ≥ 5
Observations
Industry×year FE
Other firm-level controls

32,914
Yes
Yes

32,914
Yes
Yes

32,914
Yes
Yes

(6)

32,914
Yes
Yes

0.029**(0.012)0.003***(0.001)
0.022*(0.012)0.036***(0.010)32,914
Yes
Yes

0.032***(0.010)32,914
Yes
Yes

Notes: The first two columns reproduce columns 4 and 8 of Table 3. The remaining columns estimate the exact same specifications as
the first two columns, but require a firm to have at least two and five immigrant researchers respectively to be considered as having
immigrant researchers. Standard errors (in parentheses) are clustered by firm. * p < 0.10, ** p < 0.05, *** p < 0.01.

and five immigrant researchers respectively need to be on the payroll for a firm to be consideredas hiring immigrant researchers. Not surprisingly, fewer firms move to either N I or N IF mode
under these classifications. Nevertheless, the key patterns that identify the importance of sunkcosts, and the presence and the direction of the information channel, are consistent across thethree panels. First, the diagonal elements tend to be larger than off-diagonal ones, indicating
substantial sunk costs. Second and third, highlighted in bold: the frequency of the N I to N IF
transition is much higher than the frequency of the N to NF transition, but the frequency of the
NF to N IF transition is not much higher than the frequency of the N to N I transition. These
patterns are consistent with the information value of immigrant researchers for offshore R&D,
but not the other way around. Thus, even though different classifications of firms’ R&D modes
generate different transition matrices, these transition matrices will lead to qualitatively similar
estimates for the fixed and sunk costs.
A distinct, though related, concern is that by focusing on the year-to-year mode changes,
we might introduce excess mobility in the transition matrix. In particular, if a firm lost its only
immigrant researcher in November but was not able to fill the position until a month later, we
would count this firm as transitioning out of the N I mode in the current year, only to transition
back in the next year. To address this concern, we report in Table A.12 both three- and fiveyear transition matrices. The qualitative patterns that identify the information channel and its
direction are robust.

16

Table A.11: Transition between R&D Modes: Alternative Classifications# of Immi. ≥ 2

Baseline definition# of Immi. ≥ 5

t+1

t+1

t+1

t

0

N

NI

NF

N IF

t

0

N

NI

NF

N IF

t

0
N
NI
NF
N IF

0.89
0.28
0.11
0.14
0.05

0.06
0.59
0.06
0.38
0.01

0.03
0.08
0.68
0.03
0.25

0.01
0.04
0.01
0.41
0.02

0.01
0.01
0.13
0.04
0.67

0
N
NI
NF
N IF

0.89
0.24
0.09
0.13
0.04

0.08
0.64
0.08
0.36
0.02

0.02
0.06
0.65
0.05
0.21

0.01
0.05
0.02
0.40
0.03

0.01
0.01
0.16
0.06
0.70

0
N
NI
NF
N IF

0

N

NI

NF

N IF

0.89
0.21
>0.05
>0.08
0.03

0.09
0.69
0.10
0.37
0.02

0.01
0.02
0.61
<0.03
0.16

0.01
0.08
<0.02
0.49
0.02

0.00
0.00
0.22
0.04
0.76

Notes: The left panel reproduces the transition matrix used to discipline the model (Table 8 of the text). The middle and right panels require firms to employ at least 2 and5 immigrant researchers, respectively, to be in the N I or N IF modes. In some cells in the right panel, only the range is reported because tabulating the status of firms forgroups below a certain size is prohibited per the confidentiality requirement of Statistics Denmark.

Table A.12: Transition between R&D Modes: Longer Durations
17

Baseline (1 year transition)
t+1

3 year transition

5 year transition
t+3

t+5

t

0

N

NI

NF

N IF

t

0

N

NI

NF

N IF

t

0

N

NI

NF

N IF

0
N
NI
NF
N IF

0.89
0.28
0.11
0.14
0.05

0.06
0.59
0.06
0.38
0.01

0.03
0.08
0.68
0.03
0.25

0.01
0.04
0.01
0.41
0.02

0.01
0.01
0.13
0.04
0.67

0
N
NI
NF
N IF

0.81
0.37
0.18
0.26
0.08

0.09
0.42
0.07
0.32
0.02

0.08
0.16
0.54
0.15
0.31

0.01
0.04
0.01
0.16
0.03

0.01
0.02
0.19
0.11
0.56

0
N
NI
NF
N IF

0.72
0.35
0.18
0.24
0.07

0.12
0.33
0.11
0.35
0.05

0.12
0.22
0.50
0.20
0.31

0.01
0.06
0.01
0.12
0.02

0.03
0.04
0.20
0.10
0.55

Notes: The left panel reproduces the year-to-year transition matrix used to discipline the model (Table 8 of the text). The middle and right panels are 3- and 5- year transition
matrices, respectively.

A.3.3The Role of Foreign Multinationals

Finally, we discuss the possibility that the evidence on the information channel is entirely driven
by Danish affiliates of foreign multinational firms. Suppose, for example, that the Danish subsidiary of General Electric hires American engineers while using R&D services produced at the
U.S. headquarters at the same time. This might not be necessarily due to these American engineers bringing knowledge about the U.S. headquarters that could help the affiliate use theimported R&D services. Instead, the use of American engineers and American R&D services
could be independent decisions within the conglomerate.
To address this concern, we show that excluding the affiliates of multinational firms fromthe sample does not affect our findings. Table A.13 reports the results from firm- and firmdestination level regressions focusing on domestic firms only. The first two columns of the table
replicate columns 5 and 6 of Table A.4. Columns 3 and 4 replicate columns 2 and 3 of Table A.5.
The sample shrinks by around 25%, but the estimates are essentially the same.
Table A.13: The Information Channel: Excluding Affiliates of Foreign Multinationals

I(immii,t−1 )Firm-Level (2001-2014)

Firm-Destination (2009-2015)(1)
0.036***(0.007)(3)0.014**(0.006)I(Non-R&D immii,t−1 )Observations
Firm sizei,tProductivityi,tImporti,t−1
Exporti,t−1
City×industry× year FE
Firm-year FEnImport statusi,t−1nExport statusi,t−1
City×industry×destination× year FE

23,371
Yes
Yes
Yes
Yes
Yes

(2)
0.036***(0.007)-0.009**(0.004)23,371
Yes
Yes
Yes
Yes
Yes

67,636
Yes
Yes
Yes
Yes

(4)
0.013**(0.006)0.006***(0.002)
67,636
Yes
Yes
Yes
yes

Notes: This table provides evidence for the information channel, excluding affiliates of foreign multinationals from the sample.
Columns 1 and 2 follow the specifications in columns 5 and 6 of Table A.4; columns 3 and 4 follow the specifications in columns 2
and 3 of Table A.5. Standard errors (in parentheses) are clustered by firm. * p < 0.10, ** p < 0.05, *** p < 0.01.

A.4

Descriptive Statistics on the Source of Immigrants

Table A.14 reports the shares of the top 10 source countries for immigrants working in R&D or
non-R&D for the year 2011. Immigrant researchers are mostly from other advanced countries(Germany, the UK, etc.) and countries with an abundant supply of engineer talents, such as Iran,
Poland, China, and India. On the other hand, a higher share of immigrants in non-R&D related
fields are from South Asia. Germany and Poland are among the top senders of both types ofimmigrants, likely because of their large size, their geographic proximity to Denmark, and their
EU membership.

18

Table A.14: The Origin Countries of Immigrants

Immigrants in R&D

Immigrant not in R&D

Country

ShareCountry

Share

GermanyUK
Iran
PolandSwedenChina
BosniaIndia
NorwayUSA
All others

8.55%
6.92%
5.18%
4.90%
4.24%
4.04%
3.81%
3.78%
3.66%
3.55%
51.37%

PolandTurkeyGermany
BosniaSri Lanka
Thailand
Vietnam
Iraq
Philippines
Romania
All others

11.35%
8.27%
5.58%
5.18%
3.31%
3.28%
3.13%
3.00%
2.98%
2.91%
51.00%

Note: All statistics are based on the same sample underlying Table 1. The left panel reports the top 10 sending countries of immigrant
researchers; the right panel reports the top 10 sending countries of immigrant non-researchers.

19Appendix B
B.1

Theory and Structural Estimation

Derivation of Equation (4)Under the monopolistic competition setting,profit margin

sales

z

}|
{
Wt
η
η +1 Q t
π (ωi,t ) =·[]ηη + 1 exp(ωi,t )
Pt




η +1
η
1 Wt Qt=− ·· exp (η + 1) ln− (η + 1)ωi,t ,
η
η
η+1
Pt




η
1
≡ − · Φt · exp (η + 1) ln− (η + 1)ωi,t ,
η
η+1
z}|{
1
−
η

where Φt ≡
B.2

η +1

Wt

η

Pt

Qt

is an aggregate demand shifter that is common to all firms.

Estimation of the Share of Materials

Under our assumption on the timing of firms’ actions, firms choose materials to maximize theirprofit, given k̃ i,t , l˜i,t , and ωi,t . The profit of firm i as a function of its material use is:
exp ỹi,t (m̃i,t |ωi,t , k̃ i,t , l˜i,t ) − Pm,t · exp(m̃i,t ),in which Pm,t · exp(m̃i,t ) is the cost of material with Pm,t being the material price, and ỹi,t (m̃i,t |ωi,t , k̃ i,t , l˜i,t )is the firm’s actual revenue:ỹi,t (m̃i,t |ωi,t , k̃ i,t , l˜i,t ) =1
η+1
ωi,t + β̃ k k̃ i,t + β̃ l l˜i,t + β̃ m m̃i,t + P̃t − Q̃t .
ηηTaking the first order condition of profit with respect to m̃i,t gives us:
exp ỹi,t (m̃i,t |ωi,t , k̃ i,t , l˜i,t ) · β̃ m = Pm,t · exp(m̃i,t ).

(B.1)

We measure the revenue of firm i with a (log-additive) error ẽi,t , i.e., the actual log revenue offirm i is the measured log revenue minus ẽi,t :ỹi,t (m̃i,t |ωi,t , k̃ i,t , l˜i,t ) = ỹi,t − ẽi,t .

20

From equation (B.1) we thus have:Pm,t · exp(m̃i,t )= β̃ m exp(−ẽi,t )exp ỹi,t⇐⇒ log((B.2)

Pm,t · exp(m̃i,t )) = log( β̃ m ) − ẽi,t .
exp(ỹi,t )In this specification, the left hand side is the measured log revenue share of materials. The
right hand side is the log revenue elasticity with respect to materials (scaled by a function of thedemand elasticity) and a measurement error. Since material use is independent of measurement
error, we can use the method of moments to estimate β̃ m by computing the sample average ofP·exp(m̃ )log( m,texp(ỹ )i,t ).
i,tIn the baseline estimation (Table 6 ), we pool all firms to estimate the average material share.
For robustness, we also estimate equation (B.2) by industry to obtain industry-specific material
shares, which we then plug into the GMM estimation of equation (20). The main findings fromthis exercise, reported in Section B.3 of this appendix, are essentially the same as the baseline
results.
B.3

Robustness Exercise for Production Function Estimation

In this section, we conduct three sets of robustness exercises on the GMM estimation of the
production function. In the first exercise, we consider an alternative definition of firms’ R&D
status; in the second and third sets, we treat materials in the production function in two different
ways: by estimating a value-added production function, implicitly assuming materials enter total
revenue additively, and by extending the baseline specification to incorporate industry-specificmaterial shares. The key findings—the positive impact of R&D on productivity and the value ofusing diverse R&D inputs—remain robust to these alternative choices.
B.3.1

Alternative Definition of R&D Modes

Recall that in estimating the law of motion of productivity, we include the indicators for whether
a firm conducts R&D and in which mode. We use the employment of immigrant researchers andthe sourcing of R&D from abroad, reported in the R&D Survey, to define the modes with I and
F options, respectively. In defining the modes with N, i.e., R&D with native researchers, there
are two options. In the baseline, we define mode N based on whether a firm reports positivedomestic R&D expenditures. This treatment has the advantage of being consistent with how
R&D has been measured in existing studies, but can lead to some discrepancies. For example,
some firms might report incurring R&D expenditures, but do not have employees in R&D-related
occupations; and vice versa. Such discrepancies arise because the expenses firms can include as‘R&D expenditures’ according to the accounting principles do not always align with the occupational contents of their employees. An alternative option is to define modes with N based on the21

employment of Danish workers in R&D-related occupations. We show that our main finding isrobust to this alternative.
In this exercise, a firm is considered to be in the N mode only if it employs native researchers;
correspondingly, a firm is considered to be in N I, NF, or N IF modes, if in addition to I and/orF, it also employs native researchers. Table B.1 reports the results, which follow the specificationsin Table 6. The coefficients on R&D and different modes of R&D are similar to those in Table 6.
Table B.1: R&D and Productivity Evolution: Alternative Classification of R&D Modes
GMM estimation of (20)(1)
0.460***(0.149)0.002***(0.001)

ωi,t−1log(ei,t−1 )(2)0.468***(0.114)0.002***(0.001)(3)
0.469***(0.113)0.002***(0.001)I( xi,t−1 = N )I( xi,t−1 = N I )0.023***(0.007)-0.003(0.007)0.043***(0.015)I( xi,t−1 = NF )I( xi,t−1 = N IF )I( xi,t−1 ∈ N I

S

NF

S

0.023***(0.006)-0.004(0.007)0.044***(0.013)0.023***(0.006)-0.004(0.007)0.044***(0.013)

GMM estimation of the auxiliary regressions(4)
0.468***(0.114)(5)
0.474***(0.112)(6)
0.474***(0.119)(7)0.466***(0.140)(8)0.470***(0.110)(9)0.470***(0.117)0.013**(0.007)0.038***(0.011)0.016**(0.009)0.067***(0.018)0.012**(0.006)
0.036***(0.010)0.014*(0.009)0.066***(0.017)0.012**(0.006)
0.036***(0.011)0.014*(0.009)0.066***(0.018)0.011*(0.007)0.010**(0.006)0.010**(0.006)

0.036***(0.012)0.035***(0.010)
yes

yes
9,238

yes
9,238

0.035***(0.010)
yes
yes
yes
9,238

N IF )

Import dummyi,t−1
Export dummyi,t−1
Industry FE
Number of observations

yes
yes
9,237

yes
9,237

yes
yes
yes
9,237

yes
yes
9,238

yes
9,238

yes
yes
yes
9,238

Notes: This table replicates Table 6 in the text under different classifications of R&D indicators. In particular, a firm is considered
to be in mode N if it employs native researchers; a firm is considered to be in N I, NF, or N IF modes, if in addition to I and/or F,
it also employs native researchers. Bootstrapped standard errors are clustered by firm and reported in parentheses. * p < 0.10, **p < 0.05, *** p < 0.01.

B.3.2

Estimation of the Value Added Production Function

In the baseline specifications, we estimate the law of motion parameters by specifying a production function for total revenue. This specification has the advantage of being compatible with themonopolistic competition environment. An alternative approach is to focus on value added as in
the seminal work by Olley and Pakes (1996), Levinsohn and Petrin (2003), and Ackerberg et al.
(2015), which implicitly treat materials as additive in the total revenue function.
Formally, we assume that firms’ log value added is:ỹi,t = ωi,t + β̃ k k̃ i,t + β̃ l l˜i,t + ẽi,t ,in which ẽi,t is a measurement error; l˜i,t and k̃ i,t are log labor and capital; ωi,t is total factor
productivity for the value added equivalent of equation (16). As in Olley and Pakes (1996),
firms make their investment decision in period t − 1, after the realization of ζ i,t−1 but before the22realization of ẽi,t .
We write the investment policy function as ii,t = it (ωi,t , k̃ i,t , l˜i,t , zi,t ), where zi,t is the set of controls that might affect the investment decision of a firm, such as the firm’s import/export status
and average wage. Given our assumption on the evolution of productivity, strict monotonicity
of investment in ωi,t holds, so we can invert the investment function for a proxy for productivity,i.e.,
ωi,t = i−1 (ii,t , k̃ i,t , l˜i,t , zi,t ).
We adopt the two-step procedure as in Olley and Pakes (1996). In the first step, we include a
flexible function of ii,t , k̃ i,t , l˜i,t and zi,t to purge out the measurement errors in the value added.
In the second stage, we estimate β̃ k , β̃ l , along with the other parameters in the productivity lawof motion using GMM, as in the baseline analysis. We bootstrap (by firm) the entire procedure
for statistical inference.
Table B.2 reports the results. Focusing on value added, this approach estimates a higher
persistence in productivity than in the baseline specifications. The key coefficients of interest—
those associated with R&D status—are similar to Table 6.
Table B.2: R&D and Productivity Evolution: Value-Added Production Function
GMM estimation(1)
0.739***(0.100)0.002***(0.001)

ωi,t−1log(ei,t−1 )(2)0.745***(0.100)0.002***(0.001)

GMM estimation of the auxiliary regressions(3)
0.749***(0.097)0.002***(0.001)I( xi,t−1 = N )I( xi,t−1 = N I )0.017**(0.009)-0.021***(0.008)0.023**(0.013)I( xi,t−1 = NF )I( xi,t−1 = N IF )I( xi,t−1 ∈ N I

S

NF

S

0.017**(0.009)-0.021***(0.009)0.023*(0.014)0.017**(0.009)-0.021***(0.009)0.023*(0.014)(4)0.733***(0.100)(5)0.738***(0.094)(6)0.742***(0.097)(7)0.721***(0.097)(8)0.725***(0.096)(9)0.729***(0.094)0.011***(0.004)0.016**(0.009)-0.018**(0.008)0.029**(0.015)0.010***(0.004)0.016**(0.009)-0.018**(0.008)0.029**(0.016)0.010***(0.004)0.016**(0.009)-0.018**(0.008)0.029**(0.016)0.010***(0.004)0.009**(0.004)0.009**(0.004)0.016**(0.008)0.015**(0.008)
yes

yes
9260

yes
9260

0.015**(0.008)
yes
yes
yes
9260

N IF )

Import dummyi,t−1
Export dummyi,t−1
Industry FE
Number of observations

yes
yes
9260

yes
9260

yes
yes
yes
9260

yes
yes
9260

yes
9260

yes
yes
yes
9260

Notes: This table follows the same sample and specifications as in Table 6. Different from in Table 6, in which we estimate a revenue
production function, in this table we estimate a value-added production function. Bootstrapped standard errors are clustered byfirm and reported in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.

B.3.3

Industry-specific Material Shares

By focusing on the value added production function, the robustness exercise reported in Table
B.2 allows individual firms to differ in their material use. In this subsection, we conduct an23alternative robustness exercise, in which we estimate a revenue production function, allowing
for material shares to differ by industry.
To this end, we first estimate equation (B.2) by industry, obtaining industry-specific material
shares. We plug in these shares into equation (20), which we then estimate via GMM using thesame set of instruments as in the baseline analysis. Table B.3 reports the results. The estimatesare essentially the same as when a common material share is applied to all firms.
Table B.3: R&D and Productivity Evolution: Industry Specific Material Shares
GMM estimation of (20)(1)
0.452***(0.165)0.002***(0.001)

ωi,t−1log(ei,t−1 )(2)0.468***(0.174)0.002***(0.001)(3)
0.468***(0.170)0.002***(0.001)I( xi,t−1 = N )I( xi,t−1 = N I )0.026***(0.009)-0.005(0.007)0.041***(0.016)I( xi,t−1 = NF )I( xi,t−1 = N IF )I( xi,t−1 ∈ N I

S

NF

S

0.025***(0.009)-0.006(0.007)0.042***(0.017)0.025***(0.009)-0.006(0.007)0.042***(0.017)

GMM estimation of the auxiliary regressions(4)
0.452***(0.169)(5)0.468***(0.165)(6)
0.468***(0.162)(7)0.445***(0.190)(8)0.459***(0.168)(9)0.458***(0.181)0.010***(0.004)0.027***(0.010)-0.003(0.007)0.046***(0.017)0.009***(0.004)0.026***(0.009)-0.003(0.007)0.047***(0.018)0.0109***(0.004)0.026***(0.009)-0.003(0.008)0.047***(0.017)0.010****(0.004)0.009***(0.004)0.009***(0.004)0.025***(0.010)0.025***(0.009)
yes

yes
9,320

yes
9,320

0.025***(0.009)
yes
yes
yes
9,320

N IF )

Import dummyi,t−1
Export dummyi,t−1
Industry FE
Number of observations

yes
yes
9,320

yes
9,320

yes
yes
yes
9,320

yes
yes
9,320

yes
9,320

yes
yes
yes
9,320

Notes: This table replicates Table 6 in the text allowing industry-specific material shares. Bootstrapped standard errors are clusteredby firm and reported in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01.

24

B.4

More on the Constraint Optimization Problem (23)e) in the parameter space deIn the constraint optimization problem (23), we search for (λ , Φ, F
noted by Λ to solve the following problem:

∑0 n(x) · mx,x (λ , Φ, Fe) − m̂x,xe)∈Λ
(λ ,Φ,F
min

0

0

2

x,x

e) = α̂α,s.t. α (λ , Φ, F
where the variables with a hat denote empirical moments and those without a hat are modele) ∈ Λ.10
implied values under a particular choice of the parameter (λ , Φ, F
Note that among the constraints is the share of R&D spending by N I and N IF firms on nativeNx̃
R&D inputs, ŝ N
N I and ŝ N IF , which depend on the R&D production function parameters, A andp x̃ for x̃ ∈ { N, I, F }. Because these parameters are not included in λ, a natural question is howN
we are able to verify that the chosen parameter can indeed match ŝ N
N I and ŝ N IF . Below we showthat the values of γ̃i , i = 0, 1, 2, 3 are sufficient statistics for us to verify that the model impliedN
R&D spending shares, i.e., s N
N I and s N IF , match their data counterparts.

Concretely, from equations (15) and (16) of the text, we haveγ̃0 = γ, (1)γ̃1 = γ(log(c N ) − log(c N I )), (2)γ̃2 = γθ [log(c N ) − log(c NF )], (3)





γ̃3 = γ[θ (log(c N I ) − log(c N IF )) + (log(c N ) − log(c N I ))],

(B.3)

(4)

In the structural estimation, for any given value of γ̃i , i = 0, 1, 2, 3 , we know the left hand sideof the above equations. We will then be able to use these equations to check whether the modelNN
N
implied s N
N I and s N IF equal their empirical counterparts, ŝ N I and ŝ N IF .

First, note that from line 1 and 2 of equation (B.3), we haveγ = γ̃0 ,cN
γ̃1.
log( N I ) =cγ̃0Plug these two equations into line 4 of equation (B.3) and re-arrange to obtaincN
1
log( N IF ) =[γ̃3 − γ̃1 (1 − θ )].
cθ γ̃0
10 Note that λ = ( ρ̃, γ̃ , γ̃ , γ̃ , γ̃ , σ ).
0 1 2 3 ξ

25

N
For the intensive margin shares to match s N
N I and s N IF , we must havecN
log( N I ) · (1 − θ ) = log(ŝ NNI)ccNlog( N IF ) · (1 − θ ) = log(ŝ N
N IF ),
cin which the right hand side is the data and the left hand side can be backed out from γ̃.
Combing the above equations, we have:γ̃1(1 − θ ) = log(ŝ N
NI)
γ̃0
1−θ
[γ̃3 − γ̃1 (1 − θ )] = log(ŝ N
N IF ).
γ̃0 θ

(B.4)

Thus, to verify whether a given guess of λ can match both R&D spending shares, we can use thefirst line of equation (B.4) to back out θ. We can then plug this θ into the second line of (B.4) andverify whether the equation holds. If the equality holds, then it means that γ̃i , i = 0, 1, 2, 3 cansatisfy both constraints. This result allows us to choose the parameters that can minimize thedeviation of the model from the data on the transition patterns within the set of parameters thatNx̃x̃matches both ŝ N
N I and ŝ N IF , without estimating A and p for x̃ ∈ { N, I, F }.

Backing out θ. Once the estimation routine is complete, we can use the first line in equation(B.4) to find the implied value for θ. Plugging the values for γ̃0 , γ̃1 , and ŝ N
N I gives us θ = 1.33.

26