ISSN 1403-2473 (Print)  
ISSN 1403-2465 (Online) 
 
 
 
 
 
 
 
 
 
Working Paper in Economics No. 793 
 
 
 
The Dynamic Impact of Exporting on Firm 
R&D Investment  
 
Florin G. Maican, Matilda Orth, Mark J. Roberts & Van Anh 
Vuong 
 
Department of Economics, October 2020 
 
 
The Dynamic Impact of Exporting on Firm R&D Investment∗
Florin G. Maican
University of Gothenburg, IFN, and CEPR
Matilda Orth
Research Institute of Industrial Economics (IFN), Stockholm
Mark J. Roberts
The Pennsylvania State University and NBER
Van Anh Vuong
Maastricht University
October 2020
Abstract
This article estimates a dynamic structural model of firm R&D investment in twelve
Swedish manufacturing industries and uses it to measure rates of return to R&D and to
simulate the impact of trade restrictions on the investment incentives. R&D spending is
found to have a larger impact on firm productivity in the export market than in the domestic
market. Export market profits are a substantial source of the expected return to R&D.
Counterfactual simulations show that trade restrictions lower both the expected return to
R&D and R&D investment level, thus reducing an important source of the dynamic gains
from trade. A 20 percent tariff on Swedish exports reduces the expected benefits of R&D
by an average of 32.2 percent and lowers the amount of R&D spending by 13.9 percent in
the high-tech industries. The corresponding reductions in the low-tech industries are 30.4
and 8.9 percent, respectively. R&D adjustments in response to export tariffs mainly occur
on the intensive, rather than the extensive, margin.
Keywords: R&D, innovation, trade, export, productivity
JEL Classification: L6, O3, L13, F13
∗We are grateful for helpful comments and discussions to Pere Arque-Castells, Jan DeLocker, Alessandro
Gavazza, Bronwyn Hall, Jordi Jaumandreu, Panle Jia Barwick, Jacques Mairesse, Marc Melitz, Andreas Moxnes,
Stephen Redding, Carlos Santos, Fabiano Schivardi, Philipp Schmidt-Dengler, Otto Toivanen, Jo Van Biese-
broeck, and Frank Verboven. Florin Maican and Matilda Orth gratefully acknowledge financial support from
Formas, the Swedish Competition Authority, and the Jan Wallander and Tom Hedelius Foundation.
1
1 Introduction
The theoretical literature on growth and trade, as developed by Grossman and Helpman (1993,
1995), is built on a framework of endogenous innovation where a firm’s incentives to undertake
costly innovation expenditures are impacted by their exposure to international markets. For
exporting firms, the expected return on investments in innovation can be larger than for pure
domestic firms. This can be due to the larger market size, an ability to learn from knowledge
spillovers in the foreign country, or because of competitive pressure from exporting firms based
in other countries. Regardless of the source, this higher expected return should motivate
exporting firms to invest more in innovation activities such as R&D which help them realize
higher productivity and profit gains relative to their non-exporting counterparts.
While it has been well-established that exporting firms are more likely to innovate than
others, the underlying causal mechanism linking export market conditions, such as the size of
the export market or the cost of exporting, and firm innovation is less well studied. Yet, when
assessing the dynamic impacts of trade policy, it is important to understand how opening to
trade, or, as more applicable in the present policy environment, imposition of tariffs, impacts
firm investment in innovation.
Two empirical approaches have been used to quantify the impact of trade exposure on
innovation. The first uses exogenous export market shocks to identify an impact of exporting
on firm innovation. The second approach estimates a dynamic structural model of the firm’s
export and R&D investment decisions. The advantage of the structural model is that, by
quantifying the pathways linking R&D investment and long-run profits, it can measure the
expected return to R&D for both exporting and non-exporting firms. This framework provides
a natural measure of the return to R&D: the change in long-run firm value resulting from R&D
investment. Also, by estimating the dynamic decision rule for R&D, the model can analyze
counterfactuals including the response of firm R&D investment to changes in export market
profits or to R&D subsidies.
In this article we use Swedish firm-level data to estimate a dynamic, structural model
of a firm’s R&D investment while allowing the investment to interact with the firm’s export
participation. We generalize the discrete choice models of Aw, Roberts, and Xu (2011) and
Peters, Roberts, and Vuong (2018) by treating R&D investment as a continuous decision and
analyze both the intensive and extensive margin of the investment process. In our framework,
the firm’s optimal choice of R&D is based on comparing the expected long-run payoff with
the incurred cost of innovation. For an exporting firm, the payoff to R&D investment comes
from its impact on the path of future productivity, sales, and profits separately in the domestic
and export markets. In addition to these sales and profit impacts, R&D-induced productivity
improvements can raise the likelihood a non-exporting firm enters the foreign market. In our
model, the return to R&D can differ in the export and domestic market, not just because
one market is larger than the other, but because the R&D investment differentially impacts
productivity in the two markets. We estimate the innovation cost function which consists of
both variable and fixed cost components. The variable cost depends on the firm’s actual R&D
expenditure and allows for adjustment costs or diminishing returns to R&D spending. The
fixed cost can vary with the firm’s R&D history to reflect differences in the cost of starting or
maintaining an R&D program.
2
Both trade policy and innovation policy can alter the amount of innovation in a country
by altering the incentives of firms to invest in R&D. The structural model we estimate allows
us to quantify the effects of policy changes on R&D investment and long-run firm value. We
simulate how firm R&D investments, including the proportion of firms investing and the level
of expenditure, respond to several counterfactual policy environments including tariff changes
and R&D subsidies. Changes in tariffs affect the size and profitability of the export market,
and impact the firm’s R&D decisions on the intensive and extensive margins. The magnitude
of these effects depends on the firm’s productivity and size. By simulating the effect of export
market tariffs, we measure one source of dynamic losses from trade restrictions. R&D subsidies
are often used to promote innovation and these can be granted proportionately to the firm’s
actual R&D spending or as lump-sum payments directed at R&D startups. Changes in subsidies
alter the firm’s cost of innovation and can have direct effects on both investment margins.
With a relatively small domestic market, Swedish firms rely heavily on sales in foreign
markets. In manufacturing, export sales account for more than 47 percent of the sector’s
total sales. Many Swedish firms produce high-tech products and are significant investors in
R&D. Overall R&D spending equals 3.7 percent of GDP. This combination of reliance on high-
tech products and export markets makes the linkage between exporting and R&D investment
particularly important for the future success of these firms. Our data also show clear patterns in
the relationship between exporting and R&D investment within industry. Both the probability
a firm invests in R&D (extensive margin) and the R&D-sales ratio (intensive margin) rise with
the firm’s export share. These patterns are consistent with an increase in the incentive to invest
in R&D as export participation increases.
The empirical results show that a firm’s R&D investment raises its future productivity in
both the domestic and export market with a larger impact in the export market. Productivities
in both markets are highly persistent, implying that R&D expenditures will have a long-lasting
impact on firm profitability. The expected long-run payoff to R&D, measured as the increase
in firm value per krona spent on R&D, is substantially higher for exporting firms than non-
exporters in each industry and higher in the high-tech industries when compared with the
low-tech industries. For the median firm in each high-tech industry, this payoff varies from
0.526 to 3.867 for the non-exporting firms but 10.174 to 56.595 for the exporting firms. The
return to R&D can also be measured as the proportional increase in firm value resulting from
the total R&D investment. For the median firm in the high-tech industries, this increase varies
from a low of 3.4 percent in the metals industry to 82.7 percent in chemicals, with virtually
all of the impact coming from exporting firms. In the low-tech industries the returns are much
lower. The impact at the median firm varies from 0.6 percent to 1.3 percent, with a larger
impact for exporting firms.
Counterfactual simulations show that a 20 percent tariff on Swedish exports reduces the
expected net benefits of R&D by an average of 32.2 percent in high-tech industries and 30.4
percent in low-tech industries. Consequently, it reduces the amount of R&D spending by
13.9 percent and 8.9 percent in the high-tech and low-tech industries, respectively. Most of
the adjustment occurs on the intensive margin with firms continuing to invest in R&D, but
reducing their R&D spending in response to the reduction in export market profits that results
from the tariff. Additionally, we simulate the joint effect of the output tariff and a retaliatory 20
percent tariff on inputs. The decline in the expected net benefits of R&D is at least three times
3
larger than from the output tariff alone. The addition of the input tariff has a particularly large
negative impact on the firms with low foreign-market productivity. These are firms that are
heavily committed to the domestic market. The impact of direct innovation policy is analyzed in
a counterfactual that simulates a 20 percent R&D subsidy. This reduces the cost of innovation
and raises both the expected net benefits to R&D, by 3.8 percent, and the amount of R&D
spending, by 11.2 percent, for the high-tech industries. The corresponding numbers in the low-
tech industries are 4.2 and 6.0 percent. Overall, the counterfactual simulations show that not
only innovation policy but also trade policy can have significant effects on the R&D investment
by Swedish manufacturing firms.
The findings are important for policy discussions because they show that restrictions on
free trade will undermine efforts to use innovation policies to increase R&D and innovation
activity. For countries such as Sweden, that are both export-oriented and innovative, trade and
innovation policies cannot be implemented or analyzed in isolation from each other.
The next section briefly reviews the literature that focuses on the causal linkage between
exporting and innovation. The third section summarizes some empirical patterns between
exporting and R&D investment in the Swedish manufacturing industries. The fourth and fifth
sections develop the theoretical and empirical model of firm’s R&D investment and export
participation. Sections six and seven discuss the empirical results and counterfactual exercises.
2 The Impact of Trade on Investment in Innovation
A large theoretical literature, much of it based on the framework developed by Melitz (2003),
has shown how firms that differ in their productivity will face different payoffs to selling in
export markets, importing material inputs, or making foreign direct investments of production
facilities. This leads to the self-selection of more productive firms into these activities. Shu
and Steinwender (2018) review a large number of empirical studies that document productiv-
ity differences between exporting and domestic firms as well as firms that source their inputs
domestically or import them. These studies generally support the theoretical predictions that
more productive firms are more likely to be engaged in international trade. While these het-
erogenous productivity models do not incorporate endogenous firm-level productivity dynamics,
they have been used to explain dynamic changes in the composition of trading firms in response
to trade liberalizations, and cost or demand shocks in foreign markets.1
A second line of research focuses on the source of these firm-level productivity differences.
The theoretical literature on growth and trade is built on models of endogenous investment in
innovation activities where the incentives to invest are affected by whether the firm is engaged in
trade. Theoretical models in this literature include Grossman and Helpman (1993, 1995), Con-
stantini and Melitz (2008), Atkeson and Burstein (2010), Van Long, Raff, and Sta¨hler (2011),
Burstein and Melitz (2013) and Akcigit, Ates, and Impullitti (2018). These models emphasize
the role of firm investment in innovation activities such as R&D, patenting, new product in-
troduction, process innovations, quality improvements, or adoption of new technologies as the
source of firm dynamics. The interesting issue is to what extent participation in international
1Syverson (2011, Section 4.2.2) reviews the literature linking changes in trade competition to within-firm
changes in productivity and changes in the composition of firms in an industry because of selection effects.
4
markets, through either exporting output or importing inputs, leads firms to increase their in-
novation efforts and thus generates dynamic gains that are not fully captured by static models
of trade. Of particular relevance to this article, Burstein and Melitz (2013) analyze models in
which firms make decisions about entry/exit, exporting, and investment in innovation. One
implication is that trade liberalizations lead to differential response of innovation investments
between exporting and non-exporting firms which then amplifies the productivity differences
between the two groups.
Many empirical studies have shown that exporting firms are more likely to invest in inno-
vation, but the direction of causation is generally not clear.2 The questions we address in this
article are related to the small empirical literature that focuses on the causal impact of changes
in export market conditions on the firm’s investment in innovation. The first group of studies in
this literature uses exogenous export market shocks, often from a trade liberalization episode,
to identify a causal effect of exporting on firm innovation.3 Bustos (2010) documents a positive
effect of a tariff reduction facing Argentine firms on their expenditure on technology upgrading.
Lileeva and Trefler (2010) find that Canadian firms that were induced to expand exporting
in response to U.S tariff reductions, also increased product innovation and had higher rates
of technology adoption. Coelli, Moxnes, and Ultveit-Moe (2015) use data from 60 countries
and find a positive effect of the trade liberalization in the 1990s on firm patenting. Aghion,
Bergeaud, Lequien, and Melitz (2018) find that high-productivity French firms increase their
patenting activity in response to positive export market shocks while low productivity firms
decrease their patenting. They explain this with a combination of an expansion of the export
market, which differentially benefits high-productivity firms, and an increase in competition in
the destination markets, which disadvantages low-productivity firms.
Alternatively, dynamic structural models of the firm’s export and R&D decisions have
been used to measure the impact of exporting on the return to R&D investment. Aw, Roberts,
and Xu (2011) model R&D investment as a discrete decision that increases firm productivity
and study the extensive margin of firm R&D investment. The authors analyze firm data for
Taiwanese electronics producers and find that, conditional on current productivity, exporting
firms have larger productivity gains than non-exporters and that an expansion of the export
market substantially increases the probability of investing in R&D. This mechanism contributes
to the productivity gap between exporting and domestic firms.4 Peters, Roberts, and Vuong
2The empirical literature showing that exporting is positively correlated with measures of innovation includes
Bernard and Jensen (1997), Aw, Roberts, and Winston (2007), Van Beveren and Vandenbussche (2010), Al-
tomonte, Aquilante, Bekes, and Ottaviano (2013), Becker and Egger (2013), and Damijan, Kostevc, and Rojec
(2017).
3A related literature has studied how exogenous import market shocks, often from China’s expansion into
new markets after it joined the WTO, affected innovation. Bloom, Draca, and Van Reenen(2016) find a positive
effect on firm patents, IT spending, and R&D spending for 12 European countries. In contrast, Autor, Dorn,
Hanson, Pisano, and Shu (2017) find a negative effect on patenting and R&D expenditure for U.S. firms. Using
U.S. data, Xu and Gong (2017) find a negative effect on R&D spending for low-productivity firms but a positive
impact for high-productivity firms.
4Using a similar framework with Spanish firm data, Ma´n˜ez, Rochina-Barrachina, and Sanchis-Llopis (2015)
find that two activity variables, exporting and R&D, increase both productivity and the probability of undertak-
ing the complementary activity in future periods. An exception to the finding of a positive relationship between
trade exposure and technology upgrading is the study by Santos (2017). He finds that reductions in trade costs
increase competition among domestic firms and reduce their incentives to adopt new technologies.
5
(2018) also treat R&D as a discrete decision but allow a more flexible relationship between
R&D and the impact on export and domestic productivity. They estimate the investment
model using data on German high-tech manufacturing firms and find that an increase in firm
R&D raises the probability that the firm realizes new product or process innovations and these
innovations raise future productivity. Both effects are larger for export market productivity, so
that exporting firms will have substantially higher expected returns to R&D and thus a higher
probability of investing. Simulating contractions in the foreign markets due to tariffs, they find
that a 20 percent output tariff on German exports reduces the long-run payoff to R&D by 24.2
to 46.9 percent for the median firm across five high-tech manufacturing industries. This leads to
a reduction in the probability of investing in R&D by between 5.0 and 16.0 percentage points.
In both cases the payoff to R&D investment is significantly impacted by the profitability of the
export market.
Two other empirical studies also utilize a structural framework to quantify the effect of
trade exposure on the firm’s incentive to innovate. Lim, Trefler, and Yu (2018) use a calibrated
structural model to focus on the roles of export market expansion and competition on the
patterns of patenting, R&D spending, and new product sales for Chinese manufacturing firms.
They find that market expansion positively impacts innovation measures and competition neg-
atively impacts them, but firms can escape the competition effects if they are able to innovate
into less-competitive niche markets. Using a general equilibrium model calibrated to U.S. data,
Akcigit, Ates, and Impullitti (2018) find that import tariffs provide small welfare gains in the
short run, but reduce the incentives to innovate which results in large welfare losses in the long
run. They also find that R&D subsidies are effective in promoting R&D investment for new
and incumbent firms.
The empirical model developed in sections 4 and 5 will be used to analyze differences in the
rate of return to R&D between exporting and non-exporting firms and measure how each will
respond, on both the intensive and extensive margin of R&D investment, to changes in export
market profitability and R&D subsidies.
3 R&D Investment and Exporting by Swedish Manufacturing
Firms
In the Swedish manufacturing sector, high-tech products account for a substantial fraction of
output, and many industries are both export and R&D intensive. Firm export and innovation
strategies are closely linked and firm-level decisions in these two dimensions must be analyzed in
concert. This is particularly true when using counterfactual simulations to analyze the impact
of innovation and trade policies. This section describes some patterns of R&D investment and
exporting among Swedish manufacturing firms that will be important in the specification of the
structural model.
The data set we construct contains firm-level observations for the years 2003-2010 on do-
mestic and export sales, input use, and R&D investment for a sample of Swedish manufacturing
firms. We aggregate the firms into twelve industries, and categorize six of them as high-tech and
six as low-tech industries based on the R&D-sales ratios in the industry. A detailed description
of the data set construction is given in the Appendix.
6
Table 1 summarizes R&D intensity, measured as industry R&D expenditure relative to
total industry sales, and export intensity, industry exports as a share of total industry sales.
There is a marked difference in R&D investment between the high-tech and low-tech groups.
In the high-tech industries R&D expenditure equals 6.5 percent of sales, on average across the
years, while in the low-tech industries it equals 0.9 percent of sales. Both industry groups are
dependent on export market sales. In the high-tech industries, exports account for 53.0 percent
of total industry sales and in the low-tech industries they account for 47.6 percent of sales. The
structural model developed in the next section allows for a different impact of R&D in the two
industry groups and between export and domestic market sales.
Table 2 looks within the industry groups and summarizes the variation in R&D investment
across firms with variation in their export intensity. The top half of the table summarizes the
relationship for firms in the high-tech industry group and the bottom half summarizes it for the
low-tech group. Firm observations are divided into four export categories. The first group are
the non-exporting observations. In the remaining three, exporting firms are assigned into three
groups based on their export intensity: below the 25th percentile of the intensity distribution,
between the 25th and 50th, and above the 50th percentile. For observations in each of these
four groups, the columns of the table summarize the distribution of R&D investment. The first
column is the fraction of firms that invest in R&D, the remaining three columns give the 10th,
50th, and 90th percentile of the distribution of R&D intensity.
The table shows that there is substantial variation within each group in both the extensive
and intensive margin of R&D investment and both margins are correlated with export intensity.
Focusing on the high-tech industries, the first column shows that the fraction of firms investing
in R&D, the extensive margin, rises with the export intensity of the firm. Among the non-
exporters, the probability of investing in R&D is 0.175 and this rises monotonically to 0.776 for
firms that are in the upper half of the export intensity distribution. Among the firms that invest
in R&D, the intensity of investment varies substantially across observations. Among the non-
exporters, 10 percent of the observations have R&D expenditure that is less than two-tenths
of one percent of sales (0.0017). The median firm has an expenditure equal to 1.54 percent of
sales and the firm at the 90th percentile has R&D expenditure equal to 13.80 percent of annual
sales. The R&D investment can be undertaken by the firm to impact future profits from its
domestic market sales but also in order to increase expected future profits from export sales
and possibly induce entry into exporting. Among the firms that export, the R&D intensity
varies substantially, from 0.0021 at the 10th percentile to 0.1442 at the 90th percentile. The
table also documents a clear positive relationship between R&D intensity and export intensity
among exporting firms.
For the low-tech industries, there are two primary differences in these patterns. The rela-
tionship between exporting and R&D investment is weaker and, consistent with the evidence
seen in Table 1, there is less overall investment in R&D. The first column shows that the prob-
ability of investing in R&D rises from 0.162 among the non-exporters to 0.464 for firms with
an export intensity above the median. Only about 46 percent of the high-intensity exporters
invest in R&D compared with 77 percent in the high-tech industries. The R&D intensity levels
are much smaller than in the high-tech industries. At the median, the R&D intensity varies
from 0.0066 to 0.0099 across the export groups. At the 90th percentile the R&D intensity varies
from 0.0414 to 0.0686 across export categories but does not increase monotonically with the
7
export intensity at either the 50th or 90th percentiles.
These simple summary statistics indicate a positive correlation between exporting and
R&D investment on both the extensive and intensive margin but the strength of the correlation
differs between the low-tech and high-tech industry groups. There are also a substantial group
of firms that invest in R&D but do not export and still others that export at a high rate but
do not invest in R&D. The dynamic model of R&D investment developed in the next sections
contains two sources of firm-level heterogeneity, an export market productivity and a domestic
market productivity, that can each be impacted by the firm’s R&D expenditure. These two
productivity shocks will help to explain the observed relationship between exporting and R&D
investment on both the extensive and intensive margin. The large difference in R&D investment
rates between the two industry groups also suggests substantial differences in the benefits or
costs of R&D and the model will be estimated separately for the two industry groups as a
result.
4 A Model of the Firm’s Investment in R&D
In this section we develop a dynamic model of the firm’s R&D investment. We begin by deriving
the firm’s revenue functions in the domestic and export market and its static profit function.
In each period t, firm j observes its capital stock, productivity in domestic and export market
sales, and past R&D investments. The firm maximizes its period t profits by choosing its
optimal output prices, production quantity, and whether or not it sells to foreign markets. The
firm then chooses its R&D investment which acts to improve the expected future values of its
productivities and profits at home and abroad. We develop the firm’s dynamic decision rule for
R&D incorporating both the intensive and extensive margin of investment.
4.1 Domestic Revenue, Export Revenue, and Short-Run Profits
In period t, firm j produces output at constant, short-run marginal cost
ln cjt = β0 + βk ln kjt + βw lnwt − ψjt,
where kjt is the firm capital stock, wt contain the prices of variable inputs, which are assumed
to be equal across all firms, and ψjt is the firm’s production efficiency, which is known by the
firm but not observed by the researcher.
The demand curve for firm j’s product in the domestic market is given by
qdjt = Φ˜
d
t (p
d
jt)
ηd exp(φdjt), (1)
where Φ˜dt denotes the industry aggregate demand for this product, p
d
jt is the price for firm j’s
product in the domestic market, ηd is the constant elasticity of demand (ηd < 0), and φdjt is
a firm-specific domestic demand shock. The latter represents differences in consumer demand
across firms and is known to the firm but not the researcher.
Each firm also faces a CES demand for its output in the export market
qfjt = Φ˜
f
t (p
f
jt)
ηf exp(φfjt) (2)
8
where Φ˜ft is the aggregate component of demand in the aggregate export market, p
f
jt is the
price firm j charges in the export market, and ηf is the constant elasticity of demand. φ
f
jt
is a firm-specific export demand shifter that captures differences in the total demand for the
firm j’s output in the export market due to consumers’ taste for firm j’s product or the firm’s
export scope. Because firms can export to a different number of destinations, firms with a large
number of export destination will tend to have larger values for φfjt. This demand representation
abstracts from differences in demand across destinations, but allows us to represent the firm’s
total export demand as a function of a firm-specific demand component φfjt. Similar to ψjt and
φdjt, φ
f
jt is known to the firm but is not observed by the researcher.
In the domestic market, the firm chooses its output price to maximize its domestic profit.
The firm’s revenue in the domestic market at the optimal price is:
lnRdjt = β
d
0 + Φ
d
t + (ηd + 1)(βk ln kjt − ωjt) + ε
d
jt (3)
where βd0 = (ηd + 1)
[
ln ηd1+ηd + β0
]
captures all constant terms, and Φdt =ln Φ˜
d
t + (1 + ηd)βwln
wt incorporates all time-varying demand and cost factors that are common across firms. The
term ωjt = ψjt − ( 1ηd+1)φ
d
jt captures all variation in domestic revenue for firm j arising from
unobserved cost and demand factors. We refer to ωjt as the firm’s domestic productivity and
differences across firms can arise from differences in production efficiency, product quality, or
markups. Domestic productivity will be a key state variable in the firm’s dynamic choice of
R&D. The error term εdjt captures transitory shocks to domestic revenue that are unknown to
the firm when it maximizes profits.
Not all firms participate in the export market. When deciding to export firms observe an
export cost czjt that contains, for instance, transaction costs related to the export activities, sunk
costs, and adjustment costs when firms alter their set of export destinations.5 Given knowledge
of ψjt, φ
f
jt, and c
z
jt, firm j maximizes its foreign market profits by choosing its optimal foreign
market prices and whether or not to export. If the firm chooses to export, its export revenue
at the optimal output price is:
lnRfjt = β
f
0 + Φ
f
t + (ηf + 1)(βk ln kjt − µjt) + ε
f
jt (4)
where βf0 = (ηf + 1)
[
ln ηf1+ηf + β0
]
and Φft =ln Φ˜
f
t + (1 + ηf )βwln wt. All the firm-specific
unobserved cost and demand factors are captured in µjt = ψjt − ( 1ηf+1)φ
f
jt which we will
label the firm’s unobserved foreign revenue productivity. The error term εfjt captures transitory
shocks to export revenue that are unknown to the firm when it maximizes profits.
If firm j competes in monopolistically competitive markets and has the cost and demand
structure specified, their short-run profits in the domestic and export markets are fractions of
their sales in the respective market. Specifically, the gross profits in domestic (pid) and export
5We do not distinguish fixed costs of exporting from sunk entry costs because very few firms in our data
switch their export status. Das, Roberts, and Tybout (2007) discuss how switches in export status are used
to identify fixed and sunk costs. Export choice is endogenous in this model but it is not treated as a dynamic
decision.
9
(pif ) markets are:
pidjt = −
1
ηd
Rdjt(Φ
d
t , kjt, ωjt)
pifjt = −
1
ηf
Rfjt(Φ
f
t , kjt, µjt).
(5)
Because exporting firms also have to incur export costs, a firm will choose to export if the
net profit from exporting is greater than zero. Before the export cost is realized the probability
of exporting for firm j is given by
P fjt = Pr(ejt = 1) = Pr(pi
f
jt > c
z
jt), (6)
where ejt takes the value 1 if firm j exports to any destination and zero otherwise. The expected
short-run total profit of the firm is
pi(kjt, ωjt, µjt) = pi
d(Φdt , kjt, ωjt) + P
f
jt[pi
f (Φft , kjt, µjt)− E(c
z
jt|pi
f
jt > c
z
jt)], (7)
where E(czjt|pi
f
jt > c
z
jt) is the expected firm export cost conditional on the firm exporting. The
short-run expected profits of the firm are determined by its capital stock, market level factors
in both the domestic and export market, the cost of exporting, and the firm-specific revenue
productivities ωjt and µjt.
4.2 The Role of R&D
The two key factors that capture unobserved firm heterogeneity in the domestic and export
market are ωjt and µjt. We let these two factors evolve persistently and stochastically over time
but also allow for them to be affected by the firm’s R&D expenditure. We specify the firm’s
domestic revenue productivity process as
ωjt = gω(ωjt−1, rdjt−1) + ξjt, (8)
where ωjt−1 is the firm’s previous productivity level, allowing for productivity to persist over
time. The firm’s last period’s R&D expenditure is denoted by rdjt−1, allowing for R&D in-
vestment to affect the path of future productivity. Through the persistence in the productivity
process, the impact of R&D investment will be carried over time and allow for the gain from
R&D to be long-lived. The stochastic component of the process is ξjt, which is assumed to
be iid across firms and time with E[ξjt] = 0 and V ar[ξjt] = σ2ξ . The productivity shocks ξjt
are realized in t and are not correlated with ωjt−1 or rdjt−1. This allows for firms with the
same previous period productivity and R&D expenditure to differ in their current productivity
through luck or other sources of randomness in the innovation process.
Similarly, we model the firm’s export market productivity to depend on its previous level,
its R&D effort, and a stochastic component
µjt = gµ(µjt−1, rdjt−1) + νjt (9)
where the shocks νjt are iid with E[νjt] = 0 and V ar[νjt] = σ2ν . There is both persistence and
randomness in the export market productivity, captured by the presence of lagged µjt−1 and
νjt. The process of foreign market productivity evolution is allowed to differ from the process
10
for domestic market productivity as discussed in the trade and endogenous growth literature.
Grossman and Helpman (1993, 1995) point out that firms operating in international markets
may have access to a broader set of opportunities for innovation, be exposed to new products
or production processes by their foreign competitors, or be better able to exploit innovations
that they develop as a result of their R&D investment. This will be captured in our framework
by different processes for productivity evolution in each market. These processes specify the
impact of R&D on firm productivity, a crucial component of the return to R&D investment
and thus the firm’s incentives to invest.6
Our framework allows for two underlying sources of persistent heterogeneity and each of
them can be affected in a different way by the firm’s choice of R&D expenditure. If R&D
investment has a larger impact on µ than on ω, it can induce new firms to enter the export
market but also lead to differences in the profitability path between exporting firms and those
that focus solely on the domestic market.
4.3 Dynamic R&D Investments
In this section we model the firm’s dynamic decision to invest in R&D. In this framework, the
firm uses R&D investment to buy improvements in expected future productivity. How much
it costs the firm to achieve the desired level of improvement depends on the returns to scale
in the innovation process, adjustment costs, and any startup costs that the firm must occur
when it begins to invest in R&D. The cost of a productivity improvement is specified with an
innovation cost function that is the sum of a variable cost and a fixed cost:
CI(rdjt, υjt, I(rdjt−1)) = V C(rdjt, υjt) + FC(I(rdjt−1)). (10)
The variable cost of innovation V C(·) is a function of the firm’s current spending on R&D, rdjt,
and a firm-time specific shock υjt. The shock captures, for example, differences in the firm’s
cost efficiency in producing productivity improvements, differences in the portfolio of investment
projects, or differences in subsidies or tax treatment of the firm’s R&D spending. The shock is
observed by the firm at the time it chooses rdjt but is not observed by the econometrician. This
specification recognizes that the variable cost is endogenous because of the endogenous choice
of R&D expenditure. Since the dynamic choice of R&D depends on the firm’s productivities ω
and µ, which evolve with some persistence over time, this will introduce a source of persistence
in the firm’s variable cost of innovation.7 The fixed cost FC(·) captures any differences in the
6Several studies have generalized the original model of exogenous productivity evolution by Olley and Pakes
(1996) to incorporate endogenous firm choices. Doraszelski and Jaumandreu (2013) allow a firm’s productiv-
ity index to evolve endogenously with investments in R&D. Peters, Roberts, Vuong, and Fryges (2017) model
revenue productivity as evolving endogenously with realizations of product and process innovations by the firm.
Aw, Roberts, and Xu (2011) extend the stochastic productivity framework to interrelated export and domestic
markets where productivity evolution is affected by the firm’s discrete investment in R&D and discrete partic-
ipation in the export market. The latter allows for learning-by-exporting that is potentially important in their
developing country context. Foreign revenue productivity evolves exogenously and is not affected by the firm’s
R&D investment. Peters, Roberts and Vuong (2018) allow R&D to differentially affect productivity in the export
and domestic market where productivity evolution depends on indicators of product and process innovation.
7The models by Aw, Roberts, and Xu (2011) and Peters, Roberts, and Vuong (2018) treat the total cost of
innovation as a stochastic shock which does not allow for persistence in a firm’s innovation cost over time.
11
cost of innovation that are not related to the amount of R&D spending and can include its
past experience and expertise in innovation. Denoting I(rdjt−1) as a discrete indicator of prior
period expenditure, fixed costs will differ between firms that are paying a start-up cost to begin
R&D investment I(rdjt−1) = 0 or a maintenance cost for ongoing operations I(rdjt−1) = 1.
FC is treated as a draw from a known distribution that differs depending on I(rdjt−1).
In this environment, the firm chooses the optimal R&D expenditure to maximize the dis-
counted sum of future profits. The firm’s value function, before the R&D fixed cost and variable
cost shock is realized, is given by:
V (kjt, ωjt, µjt, I(rdjt−1)) = pi(kjt, ωjt, µjt) +
∫
max{V 0(kjt+1, ωjt+1, µjt+1), (11)
max
rd>0
[
V 1(kjt+1, ωjt+1, µjt+1)− CI(rdjt, υjt, I(rdjt−1))
]
}dυdFC
where V 0(·) and V 1(·) are the discounted expected future value of the firm if they choose to
not invest in R&D or invest in R&D, respectively. They are defined as
V 0(kjt+1, ωjt+1, µjt+1) = β
∫
ξ
∫
ν
V (k, gω(ω, ξ), gµ(µ, ν)|rdjt = 0)dξdν (12)
and
V 1(kjt+1, ωjt+1, µjt+1) = β
∫
ξ
∫
ν
V (k, gω(ω, rd, ξ), gµ(µ, rd, ν))dξdν (13)
where β is the discount rate. The firm that does not invest in R&D has its subsequent period
value of ω and µ determined solely by the persistence in the Markov process and the random
shocks ξ and ν. The firm that invests in R&D at the optimal, positive level, has its future value
additionally affected by the shifts in the ω and µ processes that result from R&D investment.
The optimal choice of R&D rd∗jt is a function of the state variables and satisfies the first-order
condition:
∂V (kjt, ωjt, µjt, I(rdjt−1))
∂rdjt
= 0 (14)
5 Estimation
5.1 The Evolution of Domestic and Foreign Market Productivity
The first goal of the empirical model is to estimate the parameters of the revenue functions,
equations (3) and (4), the parameters of the productivity processes, equations (8) and (9), and
to construct estimates of firm domestic and foreign-market productivity ωjt and µjt. To do
this we rely on the insights from the stochastic productivity literature as originally developed
by Olley and Pakes (1996), and extended to the case of two unobserved firm-level shocks in
Ackerberg, Benkard, Berry, and Pakes (2007).8
8Jaumandreu and Yin (2018) estimate a production model with both unobserved demand and cost shocks.
They use data on the revenue of Chinese firms in the domestic and export market to recover the two shocks.
12
Though not explicitly modelled in our framework, we assume a firm makes capital investment
decision in each period based on its current capital stock, and levels of domestic and foreign
revenue productivity
ijt = it(kjt, ωjt, µjt). (15)
When the firm decides about its export activities that maximize total period profit, it
implicitly chooses the number of destination markets it exports to. The log of the number of
destination markets ndjt then depends on the state variables
ndjt = ndt(kjt,ωjt, µjt). (16)
The variable ndjt provides information about the destination networks of the exporters. It does
not only measure pure demand shocks in foreign markets, it also provides information about
exporter efficiency in expanding its network of countries.9 Under certain regularity conditions
(monotonicity and supermodularity, Pakes (1994)), the two policy functions can be inverted to
express the unobserved productivities as functions of the observable capital stock, investment,
and number of export destinations:10
ωjt = i
−1
t (kjt,ijt, ndjt) (17)
µjt = nd
−1
t (kjt,ijt, ndjt)
Substituting these expressions into the domestic and export revenue functions, equations (3)
and (4), allows us to write sales in each market as a function of observable variables. Replacing
ωjt in the domestic revenue function with a general function of kjt, ijt and ndjt gives:
lnRdjt = γI + γt + ht(kjt,ijt, ndjt) + u
d
jt (18)
where the function ht(kjt,ijt, ndjt) = (ηd + 1)(βk ln kjt − ωjt(kjt,ijt, ndjt)), γI is an industry
intercept, γt captures common, time-varying factors in ln Φdt , and u
d
jt is a transitory error.
Similarly, replacing µjt in the export revenue function gives:
lnRfjt = ρI + ρt + bt(kjt,ijt, ndjt) + u
f
jt (19)
where the function bt(kjt,ijt, ndjt) = (ηf + 1)(βk ln kjt − µjt(kjt,ijt, ndjt)), ρI is an industry
intercept, ρt captures common, time-varying factors in ln Φ
f
t , and u
f
jt is a transitory error.
9Recent empirical studies have shown that several dimensions of firm heterogeneity are important in explaining
patterns of export participation, the number of markets a firm serves, the specific destinations a firm enters, and
the distribution of exporting firm sales. Eaton, Kortum, and Kramarz (2011), Das, Roberts and Tybout (2007),
and Arkolakis (2010) find that differences in efficiency and entry costs are two important dimensions of firm
heterogeneity that are related to export patterns. Roberts, Xu, Fan, and Zhang (2018) find that productivity,
demand, and entry cost differences are important in explaining pricing, output, and entry decisions across
destination markets for Chinese exporters.
10See also Maican and Orth (2020) for a detailed discussion of the properties of policy functions in complex
dynamic programming problems with endogenous states.
13
We approximate ht(kjt,ijt, ndjt) and bt(kjt,ijt, ndjt) by polynomial functions in their argu-
ments and estimate equations (18) and (19) using ordinary least squares.11 We can then express
the lagged unobserved domestic and foreign productivities as functions of these fitted values hˆ
and bˆ and the unknown parameters ηd, ηf , and βk:
ωjt−1 = −
1
(ηd + 1)
hˆjt−1 + βk ln kjt−1 (20)
µjt−1 = −
1
(ηf + 1)
bˆjt−1 + βk ln kjt−1
To estimate the processes for productivity evolution, we specify the functions gω(·) and gµ(·)
as:
ωjt = α1ωjt−1 + α2ω
2
jt−1 + α3rdjt−1 + α4rd
2
jt−1 + α5ωjt−1rdjt−1 + ξjt (21)
µjt = δ1µjt−1 + δ2µ
2
jt−1 + δ3rdjt−1 + δ4rd
2
jt−1 + δ5µjt−1rdjt−1 + νjt. (22)
Substituting equations (20), (21), and (22) into the revenue functions, equations (3) and (4)
gives domestic and foreign market revenue in terms of observables and the structural parameters
βk, ηd, ηf , α1...α5, δ1, ...δ5:
lnRdjt = −(ηd + 1)
[
α1ωjt−1 + α2ω
2
jt−1 + α3rdjt−1 + α4rd
2
jt−1 + α5ωjt−1rdjt−1
]
) (23)
+(ηd + 1)βkkjt + γI + γt − (ηd + 1)ξjt + u
d
jt
lnRfjt = −(ηf + 1)
[
δ1µjt−1 + δ2µ
2
jt−1 + δ3rdjt−1 + δ4rd
2
jt−1 + δ5µjt−1rdjt−1
]
) (24)
+(ηf + 1)βkkjt + ρI + ρt − (ηf + 1)νjt + u
f
jt
The error terms are −(ηd + 1)ξjt + udjt and −(ηf + 1)νjt + u
f
jt which consist of the period t
transitory shocks to productivity evolution and the revenue functions. The moment conditions
specify that these errors are uncorrelated with Zjt =(hˆjt−1, hˆ2jt−1, bˆjt−1, bˆ
2
jt−1, kjt, kjt−1, rdjt−1,
rd2jt−1, (rdjt−1· hˆjt−1), (rdjt−1· bˆjt−1), Dt, DI) where the latter two arguments are year and
industry dummies. To identify the demand elasticities ηd and ηf , we rely on the static demand
11Relying solely on export revenues of exporting firms to uncover the foreign revenue productivity µjt, induces
a selection effect that affects the identification of βk. Similar to Olley and Pakes (1996), we control for the
selection bias by including the export probability into the Markov process of the foreign productivity:
µjt = gµ(µjt−1, rdjt−1, Pˆ
f
jt) + νjt.
The probability of exporting is estimated as P fjt = λ(ijt−1, kjt−1, ndjt−1), where the nonparametric function
λ(·) is approximated by a second-order polynomial. This estimate of the probability of exporting does not
take full advantage of the structure of the export decision outlined in section 4.2, but rather is a reduced-form
approximation that controls for the endogenous choice of exporting when estimating the process for the foreign
revenue productivity µjt. The results show that the terms that include P
f
jt are not statistically significant in the
foreign revenue productivity process, which implies that our estimates are not affected by export selection bias.
14
and short-run marginal cost assumptions. At profit maximizing prices and quantity, marginal
cost is equal to marginal revenue in each market, such that
tvcjt = q
d
jtcjt + q
f
jtcjt = R
d
jt(1 +
1
ηd
) +Rfjt(1 +
1
ηf
) + ujt, (25)
where the error term ujt is the measurement error in total variable cost. We add two additional
moment conditions specifying that ujt is uncorrelated with Rdjt and R
f
jt. This gives a total of
40 moment conditions. Minimizing the sum of the weighted moment conditions, using Z ′Z as
the weighting matrix, provides estimates of the structural parameters of the profit function and
productivity processes.12
5.2 R&D and Export Cost Functions
The second goal of the empirical model is to estimate the dynamic parameters for the innovation
and export cost. The variable cost of innovation is specified as:
V C(rdjt, υjt) = θ1rdjt + θ2rd
2
jt + rdjtυjt. (26)
The parameter θ2 > 0 reflects the adjustment cost or increasing marginal cost of innovation.
The deviations υjt are stochastic and we assume υ ∼ N(0, σ2υ). The structural error term υjt
allows for differences in the variable and marginal costs of innovation across firms and will
account for heterogeneity in the level of R&D expenditure across firms. The parameter συ
reflects the dispersion in the marginal cost of innovation across firms.13 The shocks are rescaled
as υ = συυ∗ where υ∗ ∼ N(0, 1) and the variable cost function becomes
V C(rdjt, υ
∗
jt) = θ1rdjt + θ2rd
2
jt + συrdjtυ
∗
jt. (27)
The fixed cost of innovation is modeled as a firm-time specific shock. It is specified as a
draw from an exponential distribution where the mean of the distribution depends on the firm’s
prior period R&D experience I(rdjt−1):
FC(I(rdjt−1)) ∼ exp(γ
mI(rdjt−1 > 0) + γ
s(1− I(rdjt−1 > 0))) (28)
The parameter γm is interpreted as the mean fixed cost for firms that are maintaining an
ongoing R&D investment and γs is the mean fixed cost for firms that are just starting to invest
in R&D. The variable cost of R&D investment affects the firm’s investment decision on the
intensive margin, while the fixed cost does so on the extensive margin.
We also specify the distribution of exporting cost faced by the firms when making their
export decision. The export cost is assumed to be a firm-time specific draw from an exponential
12The measure bˆjt is estimated from the export revenue equation. Thus, the equation (20) only gives us µjt
for exporting firms. To impute the revenue productivity µjt for non-exporting observations, we invert the capital
investment equation (15) and regress the obtained µjt for exporters on their (kjt, ijt, ωjt). Because the investment
policy function is given for all firms, the foreign revenue productivity for non-exporters is then constructed as
the fitted value of µjt using the non-exporters’ information on (kjt, ijt, ωjt).
13Barwick, Kalouptsidi, and Bin Zahur (2019) and Ackerberg, Benkard, Berry, and Pakes (2007) develop
dynamic models with shocks that affect the continuous part of the firm’s choice variable.
15
distribution with mean parameter γf : czjt ∼ exp(γ
f ). Therefore, according to the equation (6),
the probability of exporting is
P fjt = 1− exp(−pi
f
jt/γ
f ) (29)
and the mean export cost, conditional on exporting is E(czjt|pi
f
jt > c
z
jt) = γ − pi
f
jt[(1− P
f
jt)/P
f
jt].
The expressions for P fjt and E(c
z
jt|pi
f
jt > c
z
jt) can be substituted into the firm’s short-run profit
function, equation (7) to complete the specification of the model parameters.
5.3 The Firm Value Function and R&D Policy Function
The sources of firm-level heterogeneity in long-run profits and R&D investment at the extensive
and intensive margin are the state variables kjt, ωjt, µjt, I(rdjt−1). To estimate the dynamic
parameters for innovation and export costs, we approximate the value function for each firm at
a given value of the dynamic parameters using basis functions. We approximate the two value
functions, equations (12) and (13) as:
V 1(k, gω(ω, rd, ξ), gµ(µ, rd, ν)) ≈ Φ(k, gω(ω, rd, ξ), gµ(µ, rd, ν))c1
V 0(k, gω(ω, ξ), gµ(µ, ν)) ≈ Φ(k, gω(ω, ξ), gµ(µ, ν))c0
where c0 is a vector of approximation parameters for firms that do not do R&D, c1 is a
vector of approximation parameters for firms that do R&D, and the basis functions Φ(k, gω, gµ)
are Chebyshev polynomials. The left hand side of the value function equation (11) can be
approximated as either V 0 or V 1 depending on the firm’s past R&D:
V (kjt, ωjt, µjt, I(rdjt−1)) = (1− I(rdjt−1))Φ(kjt, ωjt, µjt)c0 + I(rdjt−1)Φ(kjt, ωjt, µjt)c1 (30)
The full set of parameters estimated in the dynamic stage is Γ = (θ1, θ2, συ, γf , γm, γs, c0, c1).
For given values of the parameters Γ, we solve the first-order condition, equation (14) to find
the optimal R&D level at each state and draw of the cost shock υ. Using the optimal R&D
investment, we find the value function approximation parameters c0 and c1 by solving the Bell-
man equation (11) at a set of approximation nodes. Since the fixed costs of innovation and
exporting are assumed to follow exponential distributions, we obtain analytical expressions for
their integrals as functions of the parameters γm, γs, and γf . We use numerical quadrature to
integrate over the variable cost shocks υ and productivity shocks ξ and ν in the domestic and
foreign markets, respectively.
The structural parameters Γ are estimated using the method of indirect inference (Gourier-
oux, Monfort, and Renault (1993), Gourieroux and Monfort (1996), and Li(2010)). For firms
that invest in R&D, the estimator matches the percentiles of the observed log R&D distribution
Qx, where x = (0.05, 0.10, 0.15, 0.20, · · · , 0.95), with percentiles of average R&D generated by
the model. It also matches the mean probability of investing in R&D (conditional on past
R&D) and the mean probability of exporting. Thus, the coefficients of the R&D variable cost
function, θ1, θ2, συ, are estimated from the percentiles of the distribution of log R&D expendi-
ture for firms that invest in R&D. The fixed costs γm and γs are identified by matching the
mean of the discrete R&D decision conditional on the previous R&D decision, and the export
cost γf is identified by matching the mean of the discrete export decision. In each case, denote
16
the vector of moments generated by the model as Q˜(Γ), and Q as the corresponding vector of
data moments. The criterion function minimizes the distance between the moments Q˜(Γ) and
Q
J(Γ) = [Q− Q˜(Γ)]′A[Q− Q˜(Γ)], (31)
where A is the weighting matrix A = V ar[Q]−1.
6 Empirical Results
In this section we summarize the parameter estimates for the productivity processes, profit
function, and costs function for innovation. We then use the estimates to summarize the
distribution of expected benefits from R&D investment and show how this differs between
exporting and non-exporting firms.
6.1 Productivity Evolution and the Profit Function
Table 3 reports the estimates of the structural parameters for the profit functions and pro-
ductivity processes. The qualitative patterns in the coefficients are similar across the four
industry-market pairs. The coefficient on lagged productivity is positive and large. This means
firm productivity is highly persistent, therefore productivity gains resulting from R&D will be
long lived. The coefficient on the squared value of lagged productivity is negative, indicating
that the degree of persistence will be smaller for high-productivity firms. The positive coeffi-
cient on R&D and the negative coefficient on R&D squared indicate that R&D has a positive
but diminishing effect on productivity in the four industry-market pairs. The interaction term
between R&D and lagged productivity is positive, showing that the return to R&D is increasing
in the firm’s own productivity. The magnitude of the R&D coefficients do differ across industry
and market groups. The first-order coefficient on R&D is larger in the high-tech industries
relative to the low-tech industries and in the export markets relative to the domestic markets,
implying a larger impact of R&D on productivity and profits in the export market relative to
the domestic market.
The elasticities of productivity with respect to R&D expenditure and lagged productivity
depend on the current R&D expenditure and productivity and therefore vary across firms. Table
4 summarizes the distribution of these elasticity estimates across the firm-year observations.
The top two lines report elasticities with respect to R&D. In the high-tech industries, the
elasticity of domestic market productivity with respect to R&D, ∂ωit∂ln(rdit−1) , varies from 0.004
at the 10th percentile to 0.0130 at the 90th. The median value is 0.0082. The elasticity of
foreign market productivity is larger, with a value of 0.0104 at the median and 0.0165 at the
90th percentile. Both elasticities are smaller in the low-tech industries but the foreign market
elasticity remains larger than the domestic market elasticity.
The elasticity of market x revenue (x = d, f) with respect to R&D is a measure of the short-
run return to R&D, and is calculated by multiplying the productivity elasticity by −(1 + ηx).
For the high-tech industries, the median values are 0.0180 and 0.0206, in the domestic and
foreign markets, respectively. In the low-tech industries the medians are 0.0040 and 0.0084.
The larger values for the foreign market revenue imply that an increase in R&D spending will
17
have a larger impact on total firm profits through their foreign market sales than their domestic
market sales. This means that firms with a larger share of sales in the foreign market will have
a higher return to R&D investment. Within each market, there is substantial heterogeneity in
the R&D elasticity across firms - the 90th percentile is about three times larger than the 10th
percentile in high-tech which implies different returns to R&D across firms.14
The last two rows of the table report the persistence in each market’s productivity. These
elasticities are uniformly high, between 0.88 and 0.98 across all firms in both markets. This
implies that the productivity gains from R&D expenditure depreciate slowly, so that current
investments have a long-lasting impact on future firm profits and thus firm value. The similarity
in elasticities within each market implies that differences in productivity depreciation rates are
not a major source of across-firm differences in the return to R&D. The across-firm differences
are more heavily affected by the elasticities of R&D.
6.2 The Firm’s R&D Investment Decision
The results reported in Table 4 indicate that both domestic and export productivities ω and µ
improve over time if the firm invests in R&D. This provides the firm with positive incentives
to invest in R&D. In our model, the firm’s optimal choice of R&D and exporting are both
functions of the productivities ωjt, µjt, and capital stock kjt. Before estimating the firm’s
dynamic demand for R&D, we assess the importance of these state variables in explaining the
firm’s R&D investment and export market participation by estimating the reduced-form policy
functions for the three choice variables: the discrete R&D decision, the log expenditure on
R&D, and the discrete export decision. We specify each of the policy functions as a quadratic
function of the three state variables. The results for the high-tech industry are reported in the
second, third, and fourth columns of Table 5. Columns labeled ”Discrete” report estimates of
logit regressions using a discrete indicator of exporting or R&D. Columns labeled ”Log Expend”
report OLS estimates with log R&D expenditure as the dependent variable.
Overall, the policy function estimates for the high-tech industries demonstrate that ωjt, µjt,
and kjt are all important determinants of the firm’s export and R&D decisions. In the case of the
R&D reduced forms, some of the individual coefficients are not statistically significant, while
most of the individual coefficients are significant for the export decision. More importantly,
we test the null hypotheses that the coefficients related to each of the three state variables are
jointly equal to zero. The test statistics for these hypotheses are presented in the last three rows
of the table and show that the null hypothesis that one of the state variables is not important
is rejected in every case.
The estimates of the parameters characterizing the cost of innovation and exporting are
14These estimates are in line with the results of related studies. In their review of the literature, Hall, Mairesse,
and Mohnen (2010) report that revenue elasticity estimates vary across studies from 0.01 to 0.25 and are centered
around 0.08. Doraszelski and Jaumandreu (2013, Table 7) report estimates of the elasticity of output, not
revenue, for ten Spanish manufacturing industries. The average value over all firms is 0.015, and the average
at the industry level varies from -0.006 to 0.046 across the ten industries, with half of the industries falling
between 0.013 and 0.022. Peters, Roberts, Vuong, and Fryges (2017, Table 11) report estimates based on the
extensive margin of R&D investment, comparing the revenue of firms that invest in R&D and firms that do not,
for German manufacturing industries. The average value of the revenue elasticity is 0.122 for a group of five
high-tech industries and 0.061 for seven low-tech industries.
18
reported in Table 6. The parameter estimates satisfy three conditions on the firm’s choices:
(i) the firm chooses the R&D expenditure that satisfies the first-order condition implicit in
the second line of equation (11), (ii) the net payoff to this expenditure is greater than the
payoff to not investing in R&D, and (iii) the firm chooses to export if the current period profits
from exporting are greater than a fixed cost. The parameters to be estimated are θ1, θ2, and
συ in the variable cost function of R&D, γm and γs, which are the unconditional means of
the fixed maintenance and fixed startup cost distributions of R&D, and γf the unconditional
mean of the fixed cost distribution for exporting. The parameter θ2 is positive in all industries,
indicating rising marginal cost of innovation as the firm increases its R&D expenditure. In the
electrical machinery industry θ2 is virtually zero, implying constant marginal cost of innovation.
The parameter συ measures the dispersion in the marginal cost of innovation, holding the
level of R&D expenditure fixed. The estimates are between 0.1345 and 0.5622 in the high-
tech industries and between 0 and 0.2024 in the low-tech industries. These estimates indicate
substantial dispersion in the marginal cost of innovation across firms and time, which also
implies substantial dispersion in the expected benefits of R&D investment across firms and
time.
The R&D maintenance cost parameter γm is always smaller than the startup cost γs. This
implies that firms with positive R&D investment in the previous year face lower fixed costs if
they continue their investment than firms without previous R&D spending. Because their fixed
cost is drawn from an exponential distribution with lower mean, they also face less uncertainty
in their total R&D cost. The fixed cost of exporting is a measure of the level of export profits
needed to induce the firm to export. In the high-tech industries the export cost parameter γf
implies that average export costs are less than 2.5 million SEK in five out of six industries.15
This reflects the fact that the export participation rates in our sample are high, with only a
few firms not exporting. In contrast, the fixed cost parameters in the low-tech industries are
higher, ranging between 1.6 and 13.6 million SEK, indicating that fewer Swedish firms in these
industries will find it profitable to export.
Table 7 summarizes the distribution of the expected marginal cost of innovation (EMC)
across observations where the expectation is taken over the random shock υ. In the high-
tech industries it shows substantial heterogeneity arising from differences in the level of R&D
expenditure. Both the level of EMC and its dispersion within-industry differs across industries.
The level is particularly large in the metal and vehicle industries indicating that all firms in those
industries face high costs of innovation. In low-tech industries, the marginal cost of innovation
is high in the upper percentiles of the distribution, indicating that for a substantial number
of firms the long-run payoff to R&D will have to be high in order to make R&D investment
profitable for them.
After estimating the structural parameters of the model, we assess the ability of our model
to explain the R&D and exporting patterns in the data. Table 8 summarizes the fit of the model
with respect to the discrete R&D and export decisions for high-tech and low-tech industries.
In the case of the discrete R&D decision, we distinguish between firms that are paying a
maintenance cost to continue investing, columns two and three, versus paying a startup cost to
begin investing, columns four and five. Overall, the mean frequencies of the maintenance cost
15In 2010, 1 USD=7.2 SEK and 1 EUR=9.54 SEK
19
of R&D and the start up cost of R&D are matched well for all industries. The mean frequencies
of the export cost are also matched almost perfectly. Table 9 reports the fit of the model with
respect to the level of R&D expenditure for observations with positive R&D investment. In
each industry the ability of the model to replicate the distribution of R&D expenditures across
firms and over time is very good.
6.3 The Long-Run Return to R&D Investment
Measuring the private rate of return to R&D has been a goal of productivity researchers for
many years. The most commonly used measure of the gross rate of return is constructed from
production function estimates of the marginal product of knowledge capital, measured as a
depreciated sum of past R&D expenditures, on output. In their comprehensive review of the
literature, Hall, Mairesse, and Mohnen (2010) summarize a wide range of estimates that are
generally in the 20 to 30 percent range, but can be as high as 75 percent. The model we
develop here provides an alternative measure based on the increase in firm value resulting from
R&D spending. As part of our estimation, we solve for the value functions and construct the
expected payoff to R&D at each state. We define the long-run expected benefit of R&D as the
difference between the value function when investing at the optimal level of R&D minus the
value function when not investing in R&D: EB = V 1−V 0. It is normalized in two ways. First,
as EB/R&D, which summarizes the total payoff to the R&D investment per krona spent, and,
second, as EB/V 0, which summarizes the proportional gain in long-run firm value from the
optimal R&D investment.
Table 10 summarizes the 25th, 50th, and 75th percentiles of the distribution of EB/R&D
across firm observations for both the non-exporting and exporting firms. Three patterns stand
out. First, the distribution of expected benefits for exporters stochastically dominates the
distribution for non-exporters in every industry. For example, in the chemical industry, the
25th and 75th percentiles among the non-exporters are 1.006 and 1.712, while the values for
the exporters are 4.477 and 110.797. The median values among the non-exporters vary from
0.526 to 5.372 across industries. For two industries, electrical machinery and instruments, the
values are less than one, implying that the total benefits to R&D investment would not exceed
the expenditure. Second, there is also substantially more heterogeneity among the exporting
firms. The fourth and last columns report the interquartile range relative to the median.
The dispersion among exporting firms is, in general, larger than for non-exporting firms. The
difference in dispersion is largest for the metals, vehicles, plastics, and miscellaneous industries.
This reflects the role played by the heterogeneity in export market productivity µ among the
exporters.
Third, among the non-exporters, the benefits of R&D are larger in several of the low-
tech industries than in the high-tech industries. For example, in the paper, ceramics, and
miscellaneous industries, the benefits at the 75th percentile of the distribution are larger than
the corresponding percentiles in all the high-tech industries. This finding does not extend to the
exporting firms. Among exporting firms the benefits at the 25th percentile are not substantially
different between the high- and low-tech industries, but at the median and 75th percentile the
benefits from the optimal R&D expenditure in the high-tech sectors are substantially higher in
most industries. Overall, the table demonstrates that there are large differences in the benefits
20
of R&D across firms within the same industry. The upper tails of the payoff distribution
are particularly large for exporting firms in the high-tech industries, emphasizing the positive
relationship between exporting and incentives to invest in innovation.
The median value of the proportional gain in firm value resulting from R&D investment,
EB/V 0, is reported in Table 11 for each industry. This clearly illustrates the differences in the
gain from R&D between the high-tech and low-tech industries and between firms with different
export status. For the non-exporting firms, the median gain is less than 2.2 percent in all
but one high-tech industry and less than 0.7 percent in all low-tech industries. Non-electrical
machinery is the one outlier in this pattern. For the exporting firms, the proportional gains are
much higher in the high-tech industries, exceeding 38.6 percent in four of the six industries. In
contrast, they never exceed 1.4 percent in the low-tech industries. R&D investment clearly has
the largest impact on long-run firm value among the exporting firms in the high-tech industries,
particularly chemicals, nonelectrical and electrical machinery and instruments.
The patterns reported in Tables 10 and 11 indicate that across-firm variation in the long-
run payoff to R&D is substantial and arises from differences in domestic and foreign market
productivity and firm size. This firm-level heterogeneity in long-run benefits is an important
factor contributing to the differences in R&D investment across industries and between export-
ing and non-exporting firms that were seen in Table 2. In the next section we simulate how
R&D investment on both the extensive and intensive margin responds to changes in the export
market conditions and innovation costs.
7 Counterfactual Analysis of Tariffs and R&D Subsidies
While Sweden has long advocated free trade policies, policy makers have recently noted that,
because of increasing threats to free trade, the role of innovation is particularly important to
maintaining the international competitiveness of Swedish exports and have focused efforts on
improving Sweden’s position in world markets (Swedish government, 2012, 2019). However, the
Organization for Economic Co-operation has emphasized the lack of accurate evaluations of the
role of R&D investment across sectors that can help guide policy choices (OECD, 2013).
The structural model of R&D investment developed in this article provides the necessary
framework to analyze the impact of trade and innovation policies that impact the benefits
or costs of R&D investment. Export tariffs on Swedish manufactured products will impact
the profitability of export market sales, which, as shown in the previous section, contributes
substantially to the return on R&D. Import tariffs that raise the cost of imported materials
will also reduce the profitability of Swedish producers in both domestic and export markets and
affect the payoffs to R&D investment. Subsidies to firms that invest in R&D, either through
direct payments or through beneficial tax treatment of R&D expenditures, impact the cost of
innovation and can affect the amount of R&D investment undertaken. In this section we use
the estimated model to simulate the effect of tariffs and R&D subsidies on the intensive and
extensive margin of R&D investment.16
16In the counterfactual analysis we change one or more of the structural parameters and resolve the model
for the optimal R&D spending in the new environment. Changes in the optimal R&D yield changes in future
productivities and short- and long-run profits.
21
7.1 Output and Input Tariffs
Most of the empirical literature summarized in section 2 has focused on the impact of trade lib-
eralizations on the incentives of firms to invest in innovation-related activities and generally find
that openness encourages innovation investments. In this section we simulate how restrictions
in international markets due to output and input tariffs affect both the probability of investing
in R&D (the extensive margin) and the amount of R&D spending (the intensive margin) by
Swedish manufacturing firms. Countries like Sweden, that are technologically advanced but
have small domestic markets, rely heavily on export markets for their sales and the return to
R&D can be substantially affected by access to those markets.17
Table 12a reports the results from a simulation of a permanent 20 percent tariff on Swedish
exports. In the model this is equivalent to reducing the intercept of the export market revenue
function. This results in a change in the optimal amount of R&D spending and thus affects
both the total benefits and total costs of the investment. To summarize the total impact
on the firm we define the expected net benefits of R&D as the expected benefits net of the
total cost of innovation: ENB = V 1 − V 0 − CI(rd). The table reports five dimensions in
which the tariff affects the endogenous variables for firm choices and outcomes. The first
two columns report the percentage change in the continuous variables, ENB and the optimal
R&D expenditure, respectively. The last three columns report the impacts on the extensive
margins: the probability of a firm continuing to invest in R&D, beginning to invest in R&D, and
exporting. The values reported are the median values across firms in each industry.18 For the
six high-tech industries, the net benefit of investing in R&D falls by between 27.06 and 42.05
percent. This leads to a reduction in expenditure on R&D of between 10.47 and 18.02 percent
for the median firm across industries. The largest impacts are in the instruments industry and
the smallest in the vehicle industry. There is also a large impact on the intensive margin of
R&D investment in five of the six low-tech industries. With the exception of the food industry,
the net benefit of R&D investment falls between 25.45 and 40.76 percent, resulting in a decline
in R&D expenditure in these industries of between 7.25 and 12.03 percent. Reductions in the
profitability of the export market lead to significant downward adjustments in the amount of
R&D spending.
On the extensive margin the changes are much smaller. For the high-tech industries, there
is no impact on the probability that a firm that is investing in R&D will stop completely and
there is a small reduction, between 0.6 and 2.1 percentage points, in the probability that a firm
will begin investing in R&D. There is also a reduction in the probability of exporting in two
industries, metals and instruments, which contributes to the reduction in the expected payoff
to R&D. The impact on the extensive margins in the low-tech industries are larger than in
the high-tech industries, with three of the industries showing a reduction in the number of
firms that continue R&D of a least one percentage point, and four of the industries showing at
least a one percentage point reduction in the probability of starting to invest in R&D. Export
17In practice, export and import tariffs are set by the European Union and Sweden is not free to vary tariffs
independently. These counterfactuals are designed to show how restrictions in the export or import markets
affect long-run firm value and the return to R&D.
18We also construct the total reduction in R&D spending over all sample firms and this number is very similar
to the reduction for the median firm that is reported in Tables 12a-14a. For clarity we will focus on the impact
on the median firm, but this is a good estimate of the impact on total R&D investment in the industry.
22
participation is reduced by between 2.39 and 13.42 percent in five of the six industries. Overall,
the reduction in export market profitability due to the output tariff discourages some firms from
undertaking R&D but the larger impact occurs on the intensive margin where the reduction
in the amount of R&D spending by the investing firms is substantial. The export market is a
significant source of the firms’ overall return to R&D and restrictions on exporting lead to less
investment in R&D, thus reducing a source of the dynamic gains from exporting.
While Table 12a reports impacts for the median firm in the sample, Table 12b summarizes
impacts across the distribution of firms. In this case, firms are distinguished by their level of
domestic and foreign market productivity ω and µ. Each firm is assigned to a cell based on the
industry quartile in which its productivities lie. Moving across each row, the foreign market
productivity µ increases, and moving down each column domestic productivity ω increases.
The table reports the percentage change in expected net payoff to R&D, ENB, at the median
within each cell.
Focusing on the high-tech industries, the tariff has a larger negative impact on firms with
larger foreign productivities. The reduction in net benefits is between -31.12 and -60.62 percent
for the most productive foreign-market firms. This is consistent with the fact that firms with
high foreign productivity will tend to have larger foreign sales and thus be more heavily impacted
by the export market tariff. However, there is a more heterogeneous pattern when both µ and
ω vary. The loss in benefits is increasing with ω when µ is low, but decreasing with ω when
µ is high. The former pattern implies that high productivity domestic firms that export little
are affected as options to expand exports are reduced, while the latter pattern implies that the
firms with high foreign productivity are less impacted by the tariff if they are simultaneously
good in the domestic market.
The counterfactual reported in Table 13a maintains the 20 percent output tariff on Swedish
exports and adds a 20 percent tariff on imported materials.19 This represents the case where a
retaliatory tariff is imposed to protect domestic suppliers of intermediate materials. This input
tariff raises the cost of the Swedish manufacturers and impacts sales in both the domestic and
export markets. The results in Table 13a show the same qualitative pattern as the export
tariff alone, but the magnitudes of the effects are magnified. Across all the high- and low-tech
industries, the expected net benefit of investing in R&D falls by between 37.89 and 56.89 percent
with the largest impacts in the low-tech industries. This reduction generates reductions in the
amount of R&D spending by between 15.99 and 24.80 percent, with the largest reductions
in spending in the high-tech industries. The dual tariffs also have a larger impact on the
probability of maintaining R&D investment in the low-tech industries. The probability of
maintaining R&D falls by 2.64 to 7.7 percent in five of the industries (and by 25.22 percent
in the remaining industry). The probability of starting R&D investment falls by a magnitude
that is approximately twice as large as what was observed with just the output tariff, with
reductions between 1.38 and 4.55 percent in all but one industry. Finally, the reduction in
the probability of exporting is approximately equal to what was observed with just the output
tariff.
Focusing on the distribution of the reduction in benefits across firms with different produc-
19In the data we do not observe the fraction of materials that are imported by each firm. We impute the
fraction of imported materials using the average value in the industry. These account for approximately half of
input expenditures in Swedish industries.
23
tivities in Table 13b, the reduction in the expected benefits, relative to the output tariff alone,
is much larger. The decline in net benefits is particularly large for the firms with lower levels of
foreign productivity µ. For the firms in the lowest quartile of µ, the median percentage decline
in ENB varies from 25.39 to 48.96 percent across industries. This decline is at least three times
larger than was observed with the output tariff alone. Penalizing all firms with the additional
tariff impacts the firms least exposed to the foreign market most heavily.
7.2 Subsidies to R&D expenditure
Firm R&D investments can be below the socially desired level. Reasons for this include R&D
investments being costly to firms that are financially constrained; the outcome of the R&D
process being subject to high level of uncertainty; and firms not internalizing the full benefits
of innovations resulting from their R&D undertakings. To encourage R&D investment, gov-
ernments often promote policies designed to lower the R&D cost incurred by firms, such as
applying tax credits or accelerated depreciation. Relying on our model estimates, we assess
the effectiveness of policies that subsidize innovation costs in terms of their impact on firm’s
investment and export activities.20 In particular, we simulate the firm’s R&D investment and
export decisions for a 20 percent reduction in the variable cost of innovation.
To simulate the effect of a 20 percent subsidy of the firm’s R&D expenditure, we set
θ1 = 0.80θˆ1 in the variable cost function equation (27) which reduces the marginal cost of
investment but does not affect the slope of the marginal cost curve by leaving the adjustment
cost component θ2 unaffected. We simulate the effect of this cost change on the same five
firm-level outcomes as the tariff counterfactuals. Table 14a summarizes the median of these
measures for firms in the high-tech and low-tech industries, respectively.
With a 20 percent subsidy, lower marginal cost leads to a higher optimal R&D investment
level. Across industries, the percentage change in R&D investment is heterogeneous. The R&D
level increases between 1.84 (chemical) and 28.57 percentage points (electrical machinery). A
substantial increase in R&D spending, such as the rise observed in electrical machinery, reflects
a marginal benefit curve ∂V 1/∂rd that is fairly flat, so that cost reductions generate significant
increases in the intensive margin of R&D investment.
The second column reports the growth in the total net benefits ENB to the firm from
the expansion in its R&D. The results show that the 20 percent subsidy increases firm’s total
benefits from R&D between 0.79 (chemical) and 5.91 percent (vehicle) in high-tech industries.
For example, the median firm in the chemical industry has an R&D net benefit that amounts to
82.7 percent of firm value (see Table 11); an increase of 0.79 percent in R&D benefit is therefore
non-negligible. The growth in firm’s net benefit is a multiple of the innovation cost saving firms
receive from the subsidy because the growth reflects the impact of additional R&D investment
on two sources: the increase in marginal benefits from improved future (ω, µ) paths and the
reduction in future marginal costs due to the subsidy.
20The empirical literature on the effects of R&D subsidies on investment and innovation is vast. Hall and Van
Reenen (2000) provide a survey. Recent works by Gonza´lez, Jaumandreu, and Pazo´ (2005) and Arque´-Castells
and Mohnen (2015) using Spanish firm data, and Takalo, Tanayama, and Toivanen (2013, 2017) using Finnish
data, estimate structural models of firm R&D investment and use them to conduct counterfactuals on the level
of subsidies.
24
The change in the marginal cost has little impact on increasing R&D participation rates for
both firms continuing and starting R&D. At the median, the change in R&D at the extensive
margin for continuing firms amounts to zero while it is below 1 percent for firms starting new
R&D investments. One reason for the small impact of the subsidy is that a large proportion of
firms in these industries already invest in R&D and have a high probability of continuing even
without the subsidy. Another reason is the subsidies do not generate sufficient additional R&D
spending and hence sufficient additional benefit to cover the maintenance and startup costs that
would occur in case of investment. The same pattern can be observed for the export market
participation. The median change in export participation is zero for most of the industries.
While an expansion in R&D investment has a positive impact on firm productivity (ω, µ),
increases its export sales, and enhances its chance of exporting, this gain does not sufficiently
offset the fixed cost for exporting to make exporting profitable for the firm.
A similar pattern characterizes the low-tech industries. The reduction in firm’s R&D vari-
able cost generates positive gains in R&D investment levels and R&D net benefits. The gains
are smaller and have smaller variation than those of the high-tech industries. Except for the
food industry, the percentage change in R&D spending across industries is below 5.48 percent
and below 2.86 percent in the R&D net benefit. The cost reduction also shows little impact
on the extensive margin in the low-tech industries. The change in R&D participation and the
export participation rate is positive but close to zero.
Focusing on the percentage change of R&D benefit by their productivity levels ω and µ
reported in Table 14b, firms in the high-tech industries enjoy a higher percentage gain in R&D
benefit than those in the low-tech industries. The percentage gain ranges between 25.16 percent
in the lowest (ω, µ) quartile and 1.08 percent in the highest productivity quartile in high-tech.
In low-tech those numbers range between 6.45 and 0.33 percent. As productivity levels (ω, µ)
increase the percentage gain decreases monotonically in high-tech, whereas no clear pattern
emerges in the low-tech industries.
In an alternative policy experiment, we simulate firms’ responses to a 20 percent reduction
in the startup cost for R&D investment, and find that this cost reduction causes between 1
and 3 percent more firms to start investing in R&D. At the same time there is virtually zero
change in the industry level of R&D investment. This indicates that a startup cost subsidy
creates incentives for firms to invest in R&D, which would not have done so without the cost
reduction; however, these firms invest only a small amount.
Overall, the counterfactual simulations show that subsidies reducing the variable cost of
R&D investment have significant impacts on R&D expenditure by firms that are already invest-
ing. However, it has little impact on inducing new R&D participation in Swedish manufacturing
industries.
8 Conclusion
This article develops an empirical model of the firm’s dynamic decision to invest in R&D,
where the decision is both whether or not to invest and how much to spend on R&D. The
firm’s investment choice impacts the path of future productivity in both domestic and export
market sales. The model provides a measure of the expected long-run gain from investing in
25
R&D that depends on the firm’s export and domestic market productivities. It also estimates
the cost function for innovation, which includes the actual expenditure on R&D, adjustment
costs, fixed costs of maintaining an R&D program, and startup costs for firms beginning to
invest.
The empirical results show that R&D expenditures operate through both domestic and
export productivity channels and increase expected future firm value substantially. Investment
in R&D is found to have a larger impact on revenue and profits in export markets than in the
domestic market. At the median across firms in a group of high-tech industries, the elasticity
of revenue with respect to R&D expenditure is 0.018 for domestic sales and 0.0206 for foreign
market sales. This difference will contribute to a higher return on R&D for firms that are
substantial exporters and act as a source of dynamic productivity gains for exporters relative
to non-exporting firms.
The model provides a direct measure of the return to R&D as the increase in long-run firm
value resulting from the R&D investment. This return is much larger in a group of six high-tech
industries than in a group of six low-tech industries, and a large premium for exporting firms
is also found. The median of the expected gain in firm value from investing in R&D is less
than 0.7 percent and 1.4 percent for non-exporters and exporters, respectively, in the low-tech
industries. The expected gain is generally less than 2.2 percent for non-exporting firms in the
high-tech industries but is substantially larger for the exporting firms. Across the six high-tech
industries the median gain varies from 5.1 to 84.7 percent, with four of the industries having
values above 38 percent.
The estimated decision rules for R&D investment and export market participation allow us
to study counterfactual environments where profitability in both markets is impacted by export
and import tariffs and the cost of innovation is reduced by R&D subsidies. The results show
that a 20 percent export tariff on Swedish high-tech exports reduces the expected net payoff
to R&D by between 27.06 to 42.05 percent across the six high-tech industries. This decline
in benefit of R&D generates a reduction in R&D spending on the intensive margin of between
10.47 and 18.02 percent in the high-tech industries. A similar decline is seen in five of the six
low-tech industries. These results indicate that the ability to export to a larger world market
has a substantial effect on the return to R&D and the level of R&D spending in the Swedish
manufacturing industries. More modest effects of the export tariff on the extensive margin of
R&D investment are observed in the counterfactual results. The output tariff has virtually
no impact on the decision of firms to stop investing in R&D and reduces the probability of a
firm to begin invest in R&D by one to two percentage points. Another set of counterfactuals
finds that a 20 percent subsidy to R&D spending increases R&D expenditure by 1.84 to 28.57
percent across the high-tech industries with three of the industries having an increase of more
than 10 percent.
This study has explored the differences in long-run benefits of R&D investment between
exporting and non-exporting firms and how this impacts their decisions to undertake R&D
investment, how much to spend on R&D, and whether or not to export. The underlying
mechanism is that R&D spending can have a different impact on the productivity of a firm
in each market. The export market is shown to be an important source of profits for Swedish
manufacturing firms and high productivity in export market sales substantially increases the
payoff to R&D investment. Policies that reduce export market profitability or reduce innovation
26
costs do impact the amount of R&D spending that firms undertake on the intensive margin
but have relatively small effects on the extensive margin decisions to begin investing in R&D
or begin exporting.
Our results are relevant to recent policy concerns about promoting innovation in an envi-
ronment with increasing restrictions to free trade. In particular, we find that the imposition
of tariffs that reduce export market profitability will significantly reduce the amount of R&D
spending that firms will undertake, and will offset innovation policies designed to stimulate
R&D investment. The linkages between the firm’s trade exposure and innovation decisions are
important for policy makers to recognize when attempting to stimulate investment in innova-
tion.
27
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31
Table 1: R&D and Export Intensity (Share of Value of Shipments)
High-Tech Industries Low-Tech Industries
Year R&D Intensity Export Intensity R&D Intensity Export Intensity
2003 0.078 0.540 0.006 0.600
2004 0.073 0.531 0.010 0.430
2005 0.064 0.532 0.009 0.532
2006 0.058 0.516 0.009 0.435
2007 0.068 0.554 0.017 0.585
2008 0.054 0.521 0.006 0.384
2009 0.070 0.529 0.011 0.480
2010 0.056 0.517 0.007 0.365
Average 0.065 0.530 0.009 0.476
32
Table 2: R&D Investment by Export Category
Pr(R&D>0) Percentiles for R&D Intensity
P(10) P(50) P(90)
High-Tech Industries
No Exports 0.175 0.0017 0.0154 0.1380
Export Intensity ≤P(25) 0.393 0.0021 0.0167 0.1442
P(25)<Export Intensity≤P(50) 0.582 0.0028 0.0190 0.1107
Export Intensity>P(50) 0.776 0.0040 0.0330 0.1429
Low-Tech Industries
No Exports 0.162 0.0009 0.0086 0.0901
Export Intensity≤P(25) 0.259 0.0010 0.0081 0.0686
P(25)<Export Intensity≤P(50) 0.292 0.0010 0.0066 0.0414
Export Intensity>P(50) 0.464 0.0014 0.0099 0.0470
33
Table 3: Revenue Functions and Productivity Evolution (standard errors)
Parameter (variable) High-Tech Industries Low-Tech Industries
Domestic Market Revenue
α1(ωt−1) 0.9944 (0.0296) 1.0376 (0.0060)
α2(ω2t−1) -0.0309 (0.0006) -0.0322 (0.0030)
α3(ln(rdt−1)) 0.0173 (0.0024) 0.0050 (0.0006)
α4(ln(rdt−1))2 -0.0011 (2.4·10−5) -0.0005 (2.4·10−5)
α5(ln(rdt−1)ωt−1) 0.0058 (7.0·10−5) 0.0027 (0.0001)
βk -0.1081 (0.0004) -0.079 (0.0008)
ηd -3.1965 (2.0·10−6) -3.235 (3.0·10−6)
Export Market Revenue
δ1(µt−1) 0.9968 (0.0207) 0.9791 (0.0005)
δ2(µ2t−1) -0.0221 (0.0001) -0.0006 (6.1·10
−5)
δ3(ln(rdt−1)) 0.0229 (0.0029) 0.0098 (6.1·10−5)
δ4(ln(rdt−1))2 -0.0016 (2.6·10−5) -0.0003 (4.3·10−5)
δ5(ln(rdt−1)µt−1) 0.0062 (6.3·10−5) 0.0004 (0.0002)
βk -0.1061 (0.0004) -0.249 (0.0060)
ηf -2.9697 (7.0·10−6) -2.574 (1.0·10−6)
sample size 3374 1834
All models include industry and year dummies
34
Table 4: Elasticities of Productivity
High-Tech Industries Low-Tech Industries
10th Median 90th 10th Median 90th
Impact of R&D
Domestic Market Productivity: ∂ωit∂ln(rdit−1) 0.0040 0.0082 0.0130 0.0002 0.0018 0.0028
Export Market Productivity: ∂µit∂ln(rdit−1) 0.0052 0.0104 0.0165 0.0042 0.0053 0.0067
Impact of Lagged Productivity
Domestic Market Productivity: ∂ωit∂ωit−1 0.883 0.919 0.957 0.906 0.937 0.961
Export Market Productivity: ∂µit∂µit−1 0.883 0.922 0.959 0.975 0.978 0.980
35
Table 5: Reduced Form Policy Functions for R&D and Exporting
High-Tech Industries Low-Tech Industries
R&D R&D Export R&D R&D Export
Discrete Log Expend Discrete Discrete Log Expend Discrete
Intercept -1.259 4.903** 127.359** 0.490 1.521 -5.485
(1.325) (0.645) (15.700) (2.103) (1.553) (3.919)
ωt -0.995 -0.119 -46.888** -3.958 1.785 0.356
(1.546) (0.681) (8.727) (3.054) (1.932) (7.778)
ω2t 0.090 0.093 4.893** -0.172 -0.533 17.281**
(0.508) (0.218) (1.654) (1.262) (0.664) (5.176)
kt 0.656 .687** 37.268** 0.539 0.0004 3.309*
(0.351) (0.196) (4.109) (0.563) (0.346) (1.576)
k2t -0.004 0.025 2.477** -0.051 -0.0008 1.013**
(0.036) (0.024) (0.294) (0.049) (0.024) (0.224)
µt -0.958 -0.210 -116.97** 0.605 0.837 3.914
(0.527) (0.309) (12.983) (0.670) (0.467) (2.590)
µ2t 0.580** 0.348** 26.216** -0.033 0.073 6.642**
(0.104) (0.067) (2.850) (0.116) (0.086) (0.815)
µt × ωt 0.413 0.152 21.332** 0.796 0.169 -22.509**
(0.320) (0.171) (3.109) (0.527) (0.329) (3.666)
kt × ωt 0.205 0.011 -6.581** 0.438 0.227 -7.705**
(0.227) (0.111) (1.113) (0.477) (0.232) (2.072)
kt × µt -0.445 -0.216** -16.304** -0.197 -0.107 3.383**
(0.100) (0.072) (1.738) (0.114) (0.081) (0.691)
Goodness of fita 0.285 0.625 0.825 0.225 0.540 0.716
Sample Size 3374 2260 3374 1834 888 1834
Test Statistics (P-value)b
H0: coefficients on ω =0 16.91 (0.00) 3.53 (0.01) 82.21 (0.00) 13.57 (0.01) 2.27 (0.06) 109.97 (0.00)
H0: coefficients on µ =0 155.92 (0.00) 83.07 (0.00) 492.78 (0.00) 62.89 (0.00) 17.83 (0.00) 220.86 (0.00)
H0: coefficients on k =0 41.53 (0.00) 14.51 (0.00) 471.54 (0.00) 31.80 (0.00) 1.76 (0.10) 108.68 (0.00)
All models contain industry and year dummies.
a Likelihood ratio [1 − LL(β)/LL(0)] for logit models, R2 for OLS models.
b Likelihood ratio test for logit models, F-test for OLS models. All tests have 4 restrictions.
36
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37
Table 7: Expected Marginal Cost of Innovation
Percentiles of the Distribution of EMC(ω, µ, k)
10th 25th 50th 75th 90th
High-Tech Industries
Chemicals 0.538 0.553 0.618 0.741 0.985
Metals 1.165 1.180 1.258 1.362 1.653
Non elect machinery 0.839 0.850 0.908 0.998 1.086
Electrical machinery 0.458 0.459 0.466 0.476 0.494
Instruments 0.313 0.328 0.366 0.449 0.503
Vehicles 1.170 1.182 1.222 1.316 1.402
Low-Tech Industries
Food 0.839 0.860 0.953 1.022 1.121
Textiles 0.494 0.561 0.737 1.090 1.580
Paper 0.421 0.722 1.176 2.136 3.249
Plastics 0.356 0.508 0.778 1.107 1.487
Ceramics 0.440 0.678 0.953 2.088 2.316
Miscellaneous 0.511 0.644 1.046 1.397 1.583
38
Table 8: Model Fit - Actual and Predicted Probabilities (mean)
Maintain R&D Start R&D Export
Actual Predicted Actual Predicted Actual Predicted
High-Tech Industries
Chemicals 0.903 0.904 0.340 0.341 0.984 0.987
Metals 0.806 0.803 0.152 0.152 0.802 0.804
Non elect machinery 0.887 0.889 0.296 0.294 0.936 0.938
Electrical machinery 0.863 0.863 0.212 0.213 0.918 0.918
Instruments 0.880 0.880 0.333 0.333 0.870 0.870
Vehicles 0.804 0.804 0.264 0.264 0.935 0.937
Low-Tech Industries
Food 0.517 0.517 0.104 0.104 0.420 0.420
Textiles 0.537 0.537 0.125 0.125 0.903 0.903
Paper 0.523 0.524 0.125 0.126 0.774 0.775
Plastics 0.636 0.635 0.246 0.246 0.960 0.959
Ceramics 0.589 0.589 0.157 0.157 0.813 0.813
Miscellaneous 0.639 0.639 0.219 0.219 0.898 0.897
39
Table 9: Model Fit - Distribution of log R&D Expenditures (thousands of SEK)
10th Percentile Median 90th Percentile
Actual Predicted Actual Predicted Actual Predicted
High-Tech Industries
Chemicals 6.907 6.478 9.321 9.815 11.229 10.265
Metals 5.991 5.490 8.292 8.597 10.571 10.553
Non elect machinery 6.684 6.312 9.210 9.549 11.708 11.466
Electrical machinery 6.397 6.393 8.987 8.796 10.714 11.356
Instruments 6.404 6.518 8.780 8.654 9.851 9.986
Vehicles 6.331 5.951 8.578 8.804 11.127 11.030
Low-Tech Industries
Food 4.605 4.928 6.955 7.028 8.239 8.158
Textiles 5.298 5.348 6.397 6.620 7.400 7.416
Paper 5.298 5.794 6.895 6.705 7.601 7.615
Plastics 5.298 5.724 7.313 7.263 8.307 7.979
Ceramics 5.962 6.100 6.908 6.790 7.972 7.753
Miscellaneous 5.298 5.683 7.090 7.058 7.824 7.797
40
Table 10: Percentiles of Distribution of R&D Benefits (V 1 − V 0)/R&D
Non-exporters Exporters
P25 P50 P75 IQR/P50 P25 P50 P75 IQR/P50
High-Tech Industries
Chemicals 1.006 1.085 1.712 0.651 4.477 56.595 110.797 1.879
Metals 2.431 3.867 5.726 0.852 3.551 10.174 161.685 15.54
Non elect machinery 1.219 1.894 3.534 1.222 5.483 45.127 103.844 2.180
Electrical machinery 0.213 0.526 0.967 1.433 2.063 21.294 47.711 2.144
Instruments 0.429 0.573 0.802 0.631 3.501 25.145 57.251 2.138
Vehicles 1.237 1.707 3.167 1.131 3.345 11.718 90.606 7.447
Low-Tech Industries
Food 1.798 2.924 4.173 0.812 6.536 9.985 19.095 1.258
Textiles 1.925 2.124 4.046 0.999 2.687 4.628 8.711 1.302
Paper 2.987 5.372 10.469 1.393 5.585 11.126 22.394 1.511
Plastics 1.167 2.180 2.451 0.589 4.310 8.795 79.705 8.572
Ceramics 1.811 2.912 6.385 1.571 7.555 16.498 31.469 1.450
Miscellaneous 2.003 3.347 6.490 1.341 4.581 9.939 54.469 5.019
41
Table 11: Proportional Increase in Firm Value (V 1 − V 0)/V 0 (median)
All Firms Non-exporters Exporters
High-tech Industries
Chemicals 0.827 0.015 0.847
Metals 0.034 0.022 0.051
Non elect machinery 0.543 0.119 0.667
Electrical machinery 0.229 0.004 0.386
Instruments 0.401 0.010 0.547
Vehicles 0.069 0.008 0.089
Low-tech Industries
Food 0.006 0.003 0.013
Textiles 0.009 0.004 0.009
Paper 0.009 0.007 0.010
Plastics 0.013 0.004 0.013
Ceramics 0.013 0.003 0.014
Miscellaneous 0.012 0.003 0.013
42
Table 12a: Change in Variables in Response to 20% Export Tariff (Median)
Percentage Change Change in Probability
ENB R&D Maintain R&D Start R&D Export
High-Tech Industries
Chemicals -0.3018 -0.1303 0.0000 -0.0210 -0.0000
Metals -0.3512 -0.1402 0.0000 -0.0154 -0.0843
Non elect machinery -0.3025 -0.1383 0.0000 -0.0119 -0.0002
Electrical machinery -0.2857 -0.1429 0.0000 -0.0062 -0.0003
Instruments -0.4205 -0.1802 0.0000 -0.0107 -0.0339
Vehicles -0.2706 -0.1047 0.0000 -0.0135 -0.0003
Average - High-Tech -0.3221 -0.1394 0.0000 -0.0131 -0.0198
Low-Tech Industries
Food -0.0550 -0.0178 -0.0113 -0.0004 -0.0770
Textiles -0.3994 -0.1203 -0.0317 -0.0116 -0.0717
Paper -0.3725 -0.1013 -0.0192 -0.0078 -0.1342
Plastics -0.4076 -0.1185 -0.0079 -0.0266 -0.0042
Ceramics -0.2545 -0.0725 -0.0041 -0.0214 -0.0343
Miscellaneous -0.3327 -0.1040 -0.0074 -0.0153 -0.0239
Average - Low-Tech -0.03036 -0.0891 -0.0136 -0.0139 -0.0576
Table12b: Percentage Change in ENB from 20% Export Tariff (Median)
P0 ≤ µ ≤ P25 P25 < µ ≤ P50 P50 < µ ≤ P75 P75 < µ ≤ P100
HighTtech Industries
P0 ≤ ω ≤ P25 -0.0334 -0.4421 -0.5942 -0.6062
P25 < ω ≤ P50 -0.0853 -0.3790 -0.4329 -0.4143
P50 < ω ≤ P75 -0.1346 -0.3023 -0.3448 -0.3515
P75 < ω ≤ P100 -0.1329 -0.2286 -0.2596 -0.3112
Low-Tech Industries
P0 ≤ ω ≤ P25 -0.0816 -0.3376 -0.4158 -0.4975
P25 < ω ≤ P50 -0.1436 -0.2762 -0.4322 -0.5178
P50 < ω ≤ P75 -0.1882 -0.2875 -0.3788 -0.4986
P75 < ω ≤ P100 -0.2014 -0.3030 -0.3379 -0.4120
43
Table 13a: Change in Variables in Response to 20% Export and Import Tariffs (Median)
Percentage Change Change in Probability
ENB R&D Maintain R&D Start R&D Export
High-Tech Industries
Chemicals -0.3789 -0.1818 0.0000 -0.0367 0.0000
Metals -0.5287 -0.2349 0.0000 -0.0268 -0.0849
Non elect machinery -0.3843 -0.2016 0.0000 -0.0225 -0.0002
Electrical machinery -0.4705 -0.2480 0.0000 -0.0185 -0.0003
Instruments -0.5295 -0.2379 0.0000 -0.0251 -0.0342
Vehicles -0.4743 -0.1919 0.0000 -0.0275 -0.0003
Average - High-Tech -0.4610 -0.2160 0.0000 -0.02618 -0.0200
Low-Tech Industries
Food -0.4368 -0.1785 -0.0770 -0.0043 -0.0773
Textiles -0.5689 -0.1964 -0.0622 -0.0192 -0.0719
Paper -0.5580 -0.1756 -0.0446 -0.0138 -0.1344
Plastics -0.5652 -0.1892 -0.0264 -0.0378 -0.0042
Ceramics -0.4981 -0.1599 -0.0331 -0.0455 -0.0344
Miscellaneous -0.5452 -0.2098 -0.0252 -0.0308 -0.0224
Average - Low-Tech -0.5287 -0.1849 -0.0447 -0.0252 -0.0574
Table13b: Percentage Change in ENB from 20% Export and Import Tariffs (Median)
P0 ≤ µ ≤ P25 P25 < µ ≤ P50 P50 < µ ≤ P75 P75 < µ ≤ P100
High-Tech Industries
P0 ≤ ω ≤ P25 -0.2539 -0.6032 -0.6826 -0.6803
P25 < ω ≤ P50 -0.3731 -0.5434 -0.5702 -0.4702
P50 < ω ≤ P75 -0.4402 -0.5201 -0.4395 -0.4101
P75 < ω ≤ P100 -0.4686 -0.4730 -0.3771 -0.3772
Low-Tech Industries
P0 ≤ ω ≤ P25 -0.4566 -0.5465 -0.5893 -0.6224
P25 < ω ≤ P50 -0.4498 -0.5138 -0.5861 -0.6239
P50 < ω ≤ P75 -0.4478 -0.5172 -0.5555 -0.6287
P75 < ω ≤ P100 -0.4896 -0.5257 -0.5323 -0.5775
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Table 14a: Change in Variables in Response to 20% Variable R&D Cost Reduction (Median)
Percentage Change Change in Probability
ENB R&D Maintain R&D Start R&D Export
High-Tech Industries
Chemicals 0.0079 0.0184 0.0000 0.0015 0.0000
Metals 0.0539 0.1777 0.0000 0.0020 0.0003
Non elect machinery 0.0443 0.0527 0.0000 0.0060 0.0000
Electrical machinery 0.0457 0.2857 0.0000 0.0017 0.0000
Instruments 0.0211 0.0312 0.0000 0.0022 0.0001
Vehicles 0.0591 0.1074 0.0000 0.0046 0.0000
Average - High-Tech 0.0387 0.1122 0.0000 0.0030 0.0001
Low-Tech Industries
Food 0.0686 0.2338 0.0021 0.0007 0.0004
Textiles 0.0186 0.0318 0.0017 0.0005 0.0001
Paper 0.0019 0.0038 0.0001 0.0001 0.0000
Plastics 0.0123 0.0228 0.0004 0.0006 0.0000
Ceramics 0.0080 0.0142 0.0006 0.0003 0.0000
Miscellaneous 0.0286 0.0548 0.0009 0.0010 0.0000
Average - Low-Tech 0.1380 0.0602 0.0010 0.0005 0.0001
Table 14b: Percentage Change in ENB from 20% Variable R&D Cost Reduction (Median)
P0 ≤ µ ≤ P25 P25 < µ ≤ P50 P50 < µ ≤ P75 P75 < µ ≤ P100
High-Tech Industries
P0 ≤ ω ≤ P25 0.2516 0.1264 0.0551 0.0392
P25 < ω ≤ P50 0.1816 0.0652 0.0382 0.0148
P50 < ω ≤ P75 0.0909 0.0489 0.0244 0.0146
P75 < ω ≤ P100 0.0459 0.0293 0.0193 0.0108
Low-Tech Industries
P0 ≤ ω ≤ P25 0.0645 0.0230 0.0067 0.0141
P25 < ω ≤ P50 0.0174 0.0208 0.0090 0.0167
P50 < ω ≤ P75 0.0033 0.0048 0.0159 0.0063
P75 < ω ≤ P100 0.0178 0.0056 0.0070 0.0034
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9 Appendix: Construction of the Swedish Firm Data
Estimation of this dynamic model of R&D investment requires firm-level panel data that in-
cludes input and output variables that can be used to measure productivity, R&D expenditures,
the volume of the firm’s exports, and domestic sales. We combine data from four censuses or
surveys that are administered by Statistics Sweden. All the sources use a common firm id which
allows very accurate matching of the firm observations across the four data sources.
The first data source is the Financial Statistics (FS), a census of all Swedish manufactur-
ing firms belonging to the Swedish Standard Industrial Classification (SNI) codes 15 to 37.21
FS is register data collected for tax reporting. Over 99 percent of the firms are single-plant
establishments. It contains annual information on capital, investment, materials, value-added,
labor, wages, and revenues that are sufficient to measure firm productivity.
The second and third data sources are the R&D survey (SCB-RD) and the Community
Innovation Survey (CIS), which together provide information on R&D spending. Each SCB-
RD survey is sent to a representative sample of 600-1000 manufacturing firms including all firms
with more than 200 employees. The SCB-RD is administered in the odd years (1999, 2001,
2003, 2005, 2007, 2009), but also collects R&D information for the even years (2000, 2002, 2004,
2006, 2008, 2010). The CIS survey collects information on own R&D expenditure, outsourced
R&D expenditure, and product and process innovations. It is administered in the even years
(2004, 2006, 2008, 2010), and the design follows the common standard across countries in the
EU.22 The survey covers approximately 2000 manufacturing firms, including all firms with more
than 250 employees. In order to be included in SCB-RD or CIS surveys the minimum number
of full-time adjusted employees per firm is 3-5. Since large manufacturing firms account for
a disproportionate share of economic activity, the CIS and SCB-RD surveys include the firms
that are responsible for the majority of total R&D, exports, and sales in Sweden. For smaller
firms, the SCB-RD and CIS samples are not identical, but combining data from both surveys
gives us broader coverage of the population of small manufacturing firms.
The final data source, Industrins Varuproduktion (IVP), contains firm-level information on
imports and exports. In particular, it contains annual foreign sales for each firm to each of
almost 250 export destinations. The median number of export destinations across the firms is
21, the 90th percentile is 65 and the maximum is 188.
After merging the data sources, we aggregate the firms into two industry groups based on
the average intensity of R&D in the industry in the OECD countries. Industries assigned to the
high-tech group all have R&D-sales ratios that exceed 0.05 while those in the low-tech group all
have R&D-sales ratios less than 0.02. The high-tech industry group includes: chemicals (SNI
23,24), basic and fabricated metals (SNI 27,28), non-electrical machinery (SNI 29), electrical
machinery (SNI 30-32), instruments (SNI 33) and motor vehicles (SNI 34-35). The low-tech
industry group includes: food and beverages(SNI 15,16), textiles (SNI 17-19), wood and paper
(SNI 20-22), plastics (SNI 25), ceramics (SNI 26) and miscellaneous (SNI 36-37).
21These numbers refer to SNI codes for 2002. The SNI standard builds on the Statistical Classification of
Economic Activities in the European Community (NACE). The SNI standard is maintained by Statistics Sweden
(http://www.scb.se).
22Swedish firms are obliged to answer. In 2010 the response rate was over 85 percent, which is substantially
higher than many other European countries.
46