# Productivity Implications of R&D, Innovation, and Capital Accumulation for
Incumbents and Entrants: Perspectives from a Catching-up Economy††thanks: This
work was supported by the European Union Horizon 2020 Research and Innovation
Action under Grant Number 822781 and Estonian Research Council under Grant
number PRG791. We owe thanks to Statistics Estonia for their indispensable
help in supplying the data. The authors also acknowledge support for the
compilation of the datasets used in the paper from the Estonian Research
Infrastructures Roadmap project ‘Infotechnological Mobility Observatory
(IMO).’ We thank the participants of the $5^{\text{th}}$ RIE Conference and
the $12^{\text{th}}$ Conference on Model-based Evidence on Innovation and
Development (MEIDE) Maastricht, 12/2021, and the participants of the Baltic
Economic Association Conference, Tartu, 06/2021. Thanks are due to Linas
Tarasonis and Priit Vahter for providing valuable comments. The usual
disclaimers apply.

Jaan Masso, Amaresh K Tiwari Jaan Masso: University of Tartu,
<EMAIL_ADDRESS>K Tiwari: University of Tartu<EMAIL_ADDRESS>&
<EMAIL_ADDRESS>
We study the productivity implications of R&D, capital accumulation, and
innovation output for entrants and incumbents in Estonia. First, in contrast
to developed economies, a small percentage of firm engage in formal R&D, but a
much larger percentage innovate. Second, while we find no difference in the
R&D elasticity of productivity for the entrants and incumbents, the impact of
innovation output — many of which are a result of ‘doing, using and
interacting’ (DUI) mode of innovation — is found to be higher for the
entrants. Entrants who innovate are 21% to 30% more productive than entrants
who do not; the corresponding figures for the incumbents are 10% to 13%.
Third, despite the adverse sectoral composition typical of catching-up
economies, Estonian incumbents, who are the primary carriers of ‘scientific
and technologically-based innovative’ (STI) activities, are comparable to
their counterparts in developed economies in translating STI activities into
productivity gains. Fourth, while embodied technological change through
capital accumulation is found to be more effective in generating productivity
growth than R&D, the effectiveness is higher for firms engaging in R&D.
Finally, our results suggest that certain policy recommendations for spurring
productivity growth in technologically advanced economies may not be
applicable for catching-up economies.

Keywords: Productivity, Entrants, Incumbents, R&D, Technological Innovations,
STI & DUI

JEL Classifications: O31, O32

##  1 Introduction

The decline in productivity growth and job reallocation coupled with rising
intra- and inter-industry dispersion in productivity during the last two
decades in the major advanced economies have, as pointed out by Akcigit and
Ates (2021), has coincided with decline in firm entry rate and young firms’
share in economic activity. Since creative destruction — the process by which
newly innovated technologies replace older technologies — plays a central role
in many theories of growth, and since it is mainly attributed to innovation
activities of fast growing, young innovative firms, the decline in
productivity growth and economic activities of the young firms have prompted
many recent studies on the innovative behaviour of the entrants and
incumbents.

While there are many such studies for the developed economies — a partial list
includes Czarnitzki and Delanote (2012), Coad et al. (2016), Acemoglu et al.
(2018), Garcia-Macia et al. (2019), Lubczyk and Peters (2020), and Akcigit and
Ates (2021) — studies on innovative behaviour of entrants and incumbents in
catching-up economies in Central and Eastern Europe (CEE) are lacking.
Studying the innovative behaviour of these groups of firms in catching-up
economies, which are at some distance from the technological frontier, is
important not only because their National Innovation System (NIS) — the web of
linkages that direct flow of technology and information among actors such as
firms, universities and government research institutes — is distinct from
those of the developed economies (Radosevic 1998; Castellacci and Natera 2013;
Cirillo et al. 2019),111Notwithstanding the various theorizations of the NIS
and the continuing work to develop a more robust concept of NIS (Cirillo et
al. 2019), in various studies, such as Castellacci and Natera (2013) and
Cirillo et al. (2019), catching-up economies of the Central and East Europe
are categorized separately from the Western European countries and the US. but
also because policy prescriptions, as we show, for spurring growth in
developed economies may not be applicable to the catching-up economies. Also,
assessing the productivity implications of the firms’ innovative behaviour can
inform how the two groups of firms contribute to the aggregate productivity
growth.

An outcome of Estonia’s — a representative CEE catching-up economy —
distinctive NIS vis-à-vis developed economies is that, in our sample, about
30% of the firm-years have positive R&D expenses, but 74% of the firm-years
have innovated to introduce at least one new product in the market or a new
process. This suggests that in Estonia more firms innovate through the ‘doing,
using and interacting’ (DUI) mode of innovation rather than ‘scientific and
technologically-based innovation’ (STI) (see Jensen et al. 2007). Moreover, as
argued in Peters et al. (2017), while investments in R&D increase the
probability of realising product or process innovations, R&D investment is
neither necessary nor sufficient for firm innovation. Focusing on R&D alone
will, therefore, give a partial picture of the productivity implications of
innovative activities (see also Radosevic and Yoruk 2018, on the inadequacy of
existing measures, that are overly R&D oriented, for gauging technological
change in middle-income economies). We, therefore, in contrast to some of the
papers mentioned above, develop an empirical strategy to simultaneously
estimate (1) the productivity elasticity of own R&D for the entrants and the
incumbents, and (2) the impact of technological — product and process —
innovations on productivity. Also, we pay particular attention to
complementarity between product and process innovation for the two group of
producers.

Various explanations — not limited to those proffered by innovation studies —
for the phenomenon of declining productivity growth and job reallocation have
been proposed. Czarnitzki and Delanote (2012) and Coad et al. (2016) point
that EU start-ups face higher entry and growth barriers, including financial
constraints, than their US counterparts. Akcigit and Ates (2021) argue that
decline in knowledge diffusion is likely to increase market concentration,
which implies that a new entrant is much more likely to compete against a
dominant market. This, they argue, will discourage new firm creation and is
likely to result in decreased economic activity among young firms. Acemoglu et
al. (2018) claim that industrial policies that subsidize (often large)
incumbent firms, may also reduce economic growth by slowing down reallocation
and even discouraging innovation by both continuing firms and new entrants.

Acemoglu et al. (2018), who have a clear policy formulation for enhancing
growth, build on models of endogenous technological change, models of firm-
level innovation (Klette and Kortum 2004) and incorporate major elements from
the reallocation literature222This literature emphasizes selection mechanisms,
which characterise industries as collections of firms that are heterogeneous
in their productivity, and link firm productivity levels to their performance
and survival in the industry (Jovanovic 1982; Hopenhayn 1992; Asplund and
Nocke 2006). This heterogeneity induces a selection effect, by which
reallocation of market shares to more efficient producers, either through
market share shifts among incumbents or through entry and exit, drive
aggregate productivity movements. Low productivity plants are less likely to
survive and thrive than their more efficient counterparts, creating selection-
driven aggregate (industry) productivity increases. Decker et al. (2014)
document that, given initial size, more productive firms grow faster than the
less productive ones; however, the contributions entrants make to growth are
considerably heterogeneous. to construct a model of firm innovation and growth
that enables an examination of the forces that jointly drive innovation,
productivity growth, and reallocation. In their model, incumbents and entrants
invest in R&D in order to improve over (one of) its many products. However,
firms are heterogeneous (high and low types) in their efficiency with which
they innovate. Firms that enter the market are disproportionately of high-
quality type but may become low-quality firms with a certain transition
probability over time. This heterogeneity introduces a selection effect, with
concomitant reallocation occurring with the movement of R&D resources (skilled
workers) from less efficient innovators (struggling incumbents) towards more
efficient innovators (new firms). To promote growth and welfare they,
therefore, propose taxes on the continued operation of incumbents combined
with a small incumbent R&D subsidy.

Aghion and Jaravel (2015) critiquing Acemoglu et al. (2018) point that their
model, in which R&D investments interact with general equilibrium effects,
does not incorporate the notion of absorptive capacity and that it would be
fruitful for future research to do so. Aghion and Jaravel (2015), referring to
Cohen and Levinthal (1989), state that R&D not only creates new knowledge but
also facilitates learning and building absorptive capacity. This is
particularly relevant for catching-up economies such as the Central and
Eastern European (CEE) countries, which lag behind the technological frontier,
and where investing in absorptive capacity through R&D and better education
can improve the ability to innovate and/or imitate leading edge technologies
(Aghion et al. 2011; Radosevic and Yoruk 2018). Griffith et al. (2004) show
empirically that (a) R&D affects both the rate of innovation and technology
transfers, and therefore failing to take into account R&D-based absorptive
capacity results in large underestimates of the social rate of return to R&D,
and (b) countries and industries lagging behind the productivity frontier
catch-up particularly fast if they invest heavily in R&D. These also imply
that many of the policy recommendations in Acemoglu et al. (2018) for the US
and the technologically advanced economies may not be applicable for catching-
up economies.

Parisi et al. (2006) show that fixed capital spending by Italian medium-low
and low-tech firms increases the likelihood of introducing a process
innovation. This, as Parisi et al. (2006) argue, suggests that physical
capital stock embodies technological progress. In catching-up economies (e.g.
Estonia) — (a) which tend to grow more due to the imitation activities of the
firms, and (b) where a higher share of firms are in medium-tech and low-tech
sectors — one could, therefore, expect capital stock accumulation to have
significant productivity implications.

Lubczyk and Peters (2020)(LP hereafter) state that little scholarly research
has assessed the dynamics studied in Acemoglu et al. (2018) with firm level
empirical applications. Czarnitzki and Delanote (2012) using Flemish data show
that young innovative companies grow faster than the other, already fast-
growing firms. Coad et al. (2016) using Spanish data show that young firms —
in terms of sales, productivity and employment growth — benefit more from R&D,
but R&D investment by young firms is riskier than R&D investment by more
mature firms. LP using a novel German data set find that entrants experience
significantly larger gains from investments in R&D than incumbents and that
returns to R&D for entrants are considerably more heterogeneous than that for
incumbents. Besides, LP’s is a comprehensive study of regional spillover
effects for the two groups of firms.

To assess the relevance of the above discussed theories for a catching-up
economy as Estonia, the main objectives we formulate are:

  1. (I)

Given that reallocation, particularly due to entry and exit, accounts for a
substantial proportion of productivity growth and since this reallocation,
both of production and R&D inputs, is to a significant extent due to
productivity impacts of innovation undertaken by heterogeneous incumbents and
entrants, we study the productivity implications of (a) R&D, (b) knowledge
spillover, and (c) technological innovations for incumbents and entrants.

  2. (II)

Since catching-up economies have been known to grow by engaging in
imitation/learning activities (Aghion et al. 2011; Radosevic and Yoruk 2018),
embodied technological change through capital accumulation is likely to have a
significant productivity impact. We, therefore, compare the productivity
impact of capital accumulation with the productivity impact of R&D for both
groups of producers.

  3. (III)

Our third objective is to compare the productivity growth impacts of R&D and
capital stock for Estonia, a catching-up country, to those in LP’s, who have
undertaken a similar analysis for Germany, a more technologically advanced
country, and understand the sources of the difference in the impacts. LP’s, to
our knowledge, is the most recent work that has comprehensively looked at
productivity impact of R&D and regional spillovers for the two groups of
producers in a developed economy. While the comparison puts our results in
perspective, we believe it will also inform better innovation and growth
enhancing policies for Estonia and catching-up economies.

Before proceeding further, we document some of our findings. To begin with,
though all firms gain from investing in R&D, we do not find any difference in
the average productivity elasticity with respect to R&D for the incumbents and
the entrants. Our results therefore do not match the findings in Coad et al.
(2016), Acemoglu et al. (2018) and LP, where the impact of R&D on productivity
is much higher for entrants as compared to the incumbents’. However, we do
find that impact of technological innovation — many of which are a result of
DUI mode of innovation — on productivity is much higher for the entrants as
compared to the incumbents. We explored the sources of the productivity gain
for both the groups of producers, and found that the gain is largely due to
complementarity between product and process innovation; innovating entrants,
however, realize a much higher complementarity than incumbents.

Now, while Estonian entrants were found to be less able than their
counterparts in Germany in translating R&D into productivity gains, we found
an average Estonian incumbent to be on par with an average German incumbent.
This is despite the adverse sectoral composition of the Estonian economy,
where, as is typical of catching-up CEE economies, compared to an average
European Union member state, there are fewer firms and fewer people employed
in sectors where the returns to R&D are highest. Moreover, because the bulk of
STI based innovative activities in Estonia is carried out by the incumbents,
we find Estonian incumbents to be playing an important role as carriers of STI
based innovative activities.

We find a robust evidence that embodied technological change through capital
accumulation is more effective in generating productivity growth than R&D
expenditure. However, since R&D or STI based innovative activities itself help
build absorptive capacity, we also find that productivity elasticity with
respect to capital is higher for firms that report engaging in formal R&D.
Finally, in results related to spillover effects, we find it is mostly the
incumbents who benefit from intra- and inter-industry knowledge that is
generated by other firms — primarily by the incumbents — situated in close
proximity. However, the spillover effects are higher for firms that do not
reportedly engage in formal R&D, suggesting that these firms, too, work on
building absorptive capacity.

The remainder of this paper is structured as follows. Section 2 reviews
related literature and in section 3 we describe the data used for our study.
In section 4, we explain the empirical strategy employed in the paper. In
Section 5, we present and discuss the empirical results, while section 6 draws
concluding remarks. Certain details of the econometric methodology have be
relegated to the appendix.

##  2 Literature Review

In subsection 2.1 we discuss some literature on the relationship between firm
age, innovation and productivity, while in subsection 2.2 we review some
relevant studies on innovation, reallocation, and productivity growth for the
CEE countries.

###  2.1 Innovation among Entrants and Incumbents

Among the large strand of literature on how different firms contribute to
productivity and productivity growth, many studies have examined how dynamics
between entrants and incumbents impact aggregate productivity development,
highlighting both differential and interrelated effects. In this section, we
review some of the literature on the innovative behaviour of the two groups of
firms.

Entrants and incumbents have been described as two distinct groups of firms
(Berchicci and Tucci 2009; Lubczyk and Peters 2020). Entrants wanting in
experience, still need to learn about the economic environment in which they
operate. Incumbents, on the other hand, have accumulated considerable
experience in their competitive environment and command well established
capabilities. Entrants, however, are seen as being more expeditious than
incumbents due to lack of structural inertia to reorganisation, faster
decision-making processes, streamlined operations, and targeted innovation.
These result in a timely response to changing industry environments, and also
make them more efficient innovators compared to incumbents.

However, entrants are often financially constrained, and investing a large
part of the limited resource endowment in R&D activities, which are inherently
uncertain, can pose a significant business risk. Lack of experience and
limited expertise may create further complications for the innovation process,
especially when unforeseen circumstances arise. On the other hand, however,
entry is envisaged as the way in which firms explore the value of new ideas in
an uncertain context, and that entry, the likelihood of survival, and
subsequent conditional growth are determined by barriers to survival
(Audretsch 1995; Huergo and Jaumandreu 2004). In this framework, entry is
innovative and occurs at a higher rate at the start of an industry when
uncertainty is high (Klepper 1996); the likelihood of survival is lower the
higher the risk; and the growth from successful innovation is higher the
higher the barriers to survival. Successful innovation, therefore, is likely
to result in substantial relative productivity growth for newly established
enterprises. Given that most young firms are small, successful innovation can
often disproportionately spur growth and contribute to substantial increases
in employment, revenue and future profitability (Haltiwanger et al. 2013).
Therefore, one would expect the impact of R&D spending on productivity to be
volatile for the new entrants.

Incumbents, having survived through time and participated longer in the
market, and have many factors working in their favour as far as innovative
activity is concerned. First, even though incumbents often lack the
organisational agility of smaller and younger competitors, they may compensate
for this with resources — such as financial and marketing capabilities — and
innovation capacity built over time (Berchicci and Tucci 2009). Moreover, an
incumbent can build on its existing infrastructure even as existing business
experience and infrastructure may enable the incumbent to pursue more
ambitious R&D projects. Also, the experience of having conducted successful
innovation in the past increases the likelihood of future innovation (Peters
2009; Raymond et al. 2010) and may help such organisations to achieve higher
levels of efficiency in carrying out their R&D activities (Lööf and Johansson
2014).

The nature of innovations, too, is often different for the two groups of
producers. Since incumbents would like to safeguard their profits from the
established products and production technologies in place, their innovative
activity is therefore more often of an incremental nature, whereas young
firms, in order to create higher quality products and overtake product lines
previously operated by incumbents, are more inclined to exploit new ideas and
engage in radical innovation (Acemoglu and Cao 2015). Besides, radical
innovation often entails costly organisational restructuring, which may deter
incumbents from undertaking radical innovation (Berchicci and Tucci 2009).

###  2.2 Relevant Studies on Innovation and Reallocation in CEE Countries

While there are many studies on innovation, reallocation, and productivity
growth for the US and Western European countries, there are only a few as far
as Central and East European (CEE) countries are concerned. Studies on
productivity growth due to selection and reallocation for the CEE countries
are by Masso et al. (2004) and Bartelsman et al. (2013). Masso et al. (2004)
find that newly formed firms had a higher survival rate than incumbents, and
that the reallocation of production factors, especially due to the exit of low
productivity units, contributed to the productivity growth. Bartelsman et al.
(2013) find that, although the covariance between firm-size and productivity,
a measure of resource misallocation, is low in Eastern Europe, it has been
increasing substantially over the last couple of decades.

Masso and Vahter (2008) point out that to sustain initial growth rates during
the transition period in CEE countries, which was based on initial capital
accumulation and imitation of technologies applied elsewhere, these countries
will need to rely increasingly on their own innovation. Due to their attempts
to establish knowledge-based economies and to increase business R&D, there is
growing interest in studying the relationship between innovation, productivity
and growth in the CEE countries. Among the few studies that have studied the
productivity impact of R&D in a CEE country is one by Liik et al. (2014), who
estimate elasticities using industry level data to conclude that in comparison
to OECD economies, R&D investments play a relatively limited role in
determining the productivity and efficiency levels of Estonian industries.
Lacasa et al. (2017), studying the technological capabilities of CEE economies
based on patent data, find that the CEE economies reduced their technological
activities drastically after 1990, and that the recovery of CEE economies with
respect to technological capabilities is unfolding very slowly. They find that
CEE countries innovate in less dynamic technological sectors and contribute
only to a limited number of fields with growing technological opportunities.

Recent studies, such as Bruno et al. (2019), find that while R&D intensity has
been effective in closing the distance to the productivity frontier, R&D
embedded in purchased equipment and machinery have played an important role in
reducing the distance. Filippetti and Peyrache (2015), studying the role of
the technology gap in explaining labour productivity differences in 211
European regions over the years 1995—2007, find that labour productivity
growth in CEE (or lagging behind) regions, productivity growth is mainly
driven by capital accumulation.

##  3 Data and Variables: Definitions and Description

For our study, we use eight waves of the Estonian Community Innovation Survey
(CIS), CIS2004 to CIS2018, which is a biennial survey about innovation
activities in Estonian enterprises. For a detailed description of the CIS data
and the usage of the data for scholarly analysis of various issue related to
innovation, see Mairesse and Mohnen (2010). Firm balance sheet information
containing profit and loss statements was obtained from the Estonian Business
Registry, which is a census data. Wherever possible, the missing information
in the Business Registry data was obtained from EKOMAR, a survey data.

One of the key variables from the CIS surveys used for our analysis is the R&D
expenditure of firms. However, as non-innovative firms — firms that have not
innovated any product or process, or have no unfinished innovative activities
— in the CIS data are not required to report their R&D expenses, we do not
observe R&D expenditure for the non-innovative firms. The CIS questionnaire,
however, allows us to distinguish between ‘potentially’ innovative firms and
firms that do not intend to engage in R&D among the non-innovative firms (see
Savignac 2008). This distinction is made on the basis of firm responses to the
question on factors that might have thwarted their R&D and innovative
activities. We classify non-innovative firms who face such factors as
potentially innovative, whereas non-innovating firms that do not face any of
these factors are classified as firms that do not intend to engage in R&D
activities. For these non-innovators that do not wish to engage in R&D
activities, it can be safely assumed that they have no R&D expenses.

Since we do not observe R&D expenditure of potentially innovative firms, we
drop such firms from our analysis. However, non-innovative firms that do not
wish to engage in R&D activities are retained. This, as discussed in the next
section, allows for us to estimate the spillover effects of external knowledge
stock as well as the impact of product and process innovation on productivity
for all firms: firms that have and that do not have R&D expenses. After
further removing firms with missing data, our sample comprised of 7,586 firm-
year observations from 3,068 firms. The minimum number of observations per
firm is 1, the maximum, 8, and the average number is about 2.5 years.

Since one of our aims is to compare our findings to those in LP, we, as in LP,
define entrants as firms that are new to the market and have been active for
eight or less years, while incumbents are those that have been active for more
than eight years. Our set of entrants excludes firms resulting from mergers,
break-ups, split-off or restructuring of a set of enterprises. Those resulting
from change of activity, too, are excluded. There is no theoretical basis for
the above definition of an entrant; in the literature, an entrant’s maximum
age has ranged from three to ten years. Of the 7,586 firm-year observations,
6,086 are incumbents and 1,500 are entrants. Estonian firms are relatively
young, where the average age of incumbents is 17 years, while that of entrants
is 5.5 years.

Also, we define a firm, $j$, in year, $t$, to be an innovator, $I_{jt}=1$, if
the firm had introduced new products, $\mathcal{P}^{D}_{jt}=1$ or processes,
$\mathcal{P}^{C}_{jt}=1$, to the market. Value-added productivity is our
dependent variable and performance outcome measure. It is the ratio of value-
added, the difference between sales revenues and the value of intermediate
inputs, to the number of employees.

In order to convert the book value of the gross capital stock into its
replacement value, we use the perpetual inventory method described in Salinger
and Summers (1983). According to this method, the replacement value of the
capital stock is equal to the book value of fixed assets for the first year
the firm appears in the data. For the subsequent years, first, the useful life
of capital goods, $L_{jt}$, at time $t$ is calculated as:

$\displaystyle L_{jt}=\frac{GK_{j,t-1}+I_{jt}}{DEPR_{jt}},$

where $GK_{j,t-1}$ is the reported value of gross property, plant, and
equipment at time $t-1$, $I_{jt}$ is the investment in the same for the period
$t$, and $DEPR_{jt}$ is the reported depreciation. Then $L_{jt}$ is averaged
over time to obtain $L$, which is then used in the following formula to obtain
the replacement value of the capital stock of a firm in industry $k$:

$\displaystyle
K_{jt}=\biggr{(}K_{j,t-1}\dfrac{p^{k}_{t}}{p^{k}_{t-1}}+I_{jt}\biggr{)}(1-2/L_{jt}),$

where $p^{k}_{t}$ is the deflator for industry, $k$. The second term
represents the amount of capital stock that depreciates each year and is based
on the assumption that economic depreciation is a double declining balance.
For new firms and for existing firms that appear again after a gap in later
time periods in the data, the book value of the capital stock in the first
year is taken as the replacement value. However, for firms that after a gap
reappear in later years, this method will not yield as good an estimate of the
replacement value as for the firms for whom a long, continuous time-series is
available.

In Table 1, we can see that the incumbents on average have significantly
higher labour productivity, larger capital stocks, higher investment and more
employees. As far as innovative behaviour of the firms is concerned, as can be
seen in Table 1, a majority of the firms (about 74%) in the estimation sample
are innovative even as the percentage of firms that have positive R&D is only
about 30%. Secondly, incumbents have a higher propensity to invest in R&D and
are also likely to invest more in R&D than the entrants. However, it is the
entrants who are more innovative as far as technological — product and process
— innovations are concerned. Also, for the incumbents, log of R&D intensity
increased substantially from an average of 1.76 in the pre Financial Crisis
years to an average 6.93 in the post Crisis years; the corresponding figures
for the entrants are, 2.03 and 6.95.

In Table 2, we can see that high-tech and medium-high-tech manufacturing,
which are most R&D intensive and most innovative, constitute about 13% of the
firms in the sample. Majority of the firms (70%) are in the low-tech and
medium-low-tech manufacturing and less knowledge intensive services; these
sectors, though less R&D intensive, are still quite innovative.

In our analysis we include a dummy for north Estonia, which takes value 1 if
the company is located in Harju county. Harju county is the biggest of all
Estonian counties in terms of population and economic activity, and includes
the national capital city, Tallinn. The rational for including this dummy is
that firms located in Harju county, which qualifies as the economic hub of
Estonia, are likely to be better networked with implications for productivity
due to agglomeration. We find that a significantly higher proportion of
entrants are based in northern Estonia (see Table 1).

The external knowledge capital, $E_{jt}$, is intended to capture knowledge
spillovers among firms. In our empirical analysis, we differentiate between
different types of spillovers: intra-industry and inter-industry R&D
spillovers to measure to what extent entrants and incumbents differ in their
capacity to benefit from R&D knowledge that is available to the firm within
and outside its own industry.

The measure of the intra-industry knowledge capital of firm $i$ in industry
$k$ (based on two digit NACE Rev. 2 codes) in period $t$ is the weighted sum
of R&D expenditures per employee of other firms in industry $k$:

$\displaystyle\text{ Intra-Industry R\&D }=\sum_{j\neq
i}w_{ij}\frac{R^{k}_{jt}}{L^{k}_{jt}},$ (3.1)

where $R_{jt}$ is the R&D expenditure of firm $j$, $L_{jt}$ is the number of
employees employed by the firm, and the weight, $w_{ij}$, is the inverse of
the geographical distance between the capital of the county in which firm $i$
is located and capital of the county in which firm $j$ belonging to the same
industry, $k$, is located; if firm $j$ happens to be in the same county then
$w_{ij}$ is taken as 1. The measure of the inter-industry knowledge of firm
$i$ in industry $k$ (NACE two digit) in period $t$ is the weighted sum of R&D
expenditures per employee of firms in other industries:

$\displaystyle\text{ Inter-Industry R\&D }=\sum_{l\neq
k}\sum_{j}w_{ij}\frac{R^{l}_{jt}}{L^{l}_{jt}},$ (3.2)

where, again, the weight $w_{ij}$ is the inverse of the geographical distance
between the capital of the county in which firm $i$ is located and the capital
of the county in which firm $j$ belonging to a different industry, $l$, is
located.

In Table 1 we can see that incumbents on average are based in or based close
to regions/counties with higher average external knowledge; the differences
hold for both within and across industry comparisons. Here, we would like to
note that even at this broader definition of industry (NACE 2-digit), about 2%
of the firm-year observations had zero intra-industry knowledge flows. This is
because a relatively smaller number of firms, about 30%, in the estimation
sample invested in R&D.

[Table 1 about here]

[Table 2 about here]

##  4 Empirical Strategy

For firm $j=1,\ldots,J$ and time $t=1,\ldots,T$, we observe revenue
($Y_{jt}$), labour ($L_{jt}$), capital ($K_{jt}$), material inputs ($M_{jt}$),
R&D expenses ($R_{jt}$), which can also be zero, and ($E_{jt}$), which is some
measure of external knowledge capital.

Now, while a measure of R&D capital stock would be preferred as an innovation
input, we are unable to estimate the knowledge capital from the past R&D
expenditures using the perpetual inventory method. This is because CIS surveys
are conducted once every two years and, secondly, we do not have a balanced
panel data. Instead, following Crépon et al. (1998) and more recently Raymond
et al. (2015) and Baumann and Kritikos (2016), we proxy knowledge capital
using current R&D expenditure, $R_{jt}$. This proxy is based on the implicit
assumption that firm R&D investments are strongly correlated (and roughly
proportional) to their R&D capital stock measure, and that R&D engagement and
intensity persists over time.333With a big overlap of firms between the
different waves in the Estonian CIS, we find some evidence of this
persistence.

Let $\omega_{jt}$ be the firm $j$ and time $t$ specific total factor
productivity (TFP), which is observed by the firms but not by the
econometricians. For notational convenience, we drop the subscript, $jt$, as
of now. For estimation, we employ the “control function” methodology developed
by Ackerberg et al. (2015) (ACF), who consider a value-added production
function. The value-added production function, as ACF explain, can be derive
from the gross output production function that is Leontief in material inputs,
$M$. So, when R&D expenditure is positive, i.e. $R>0$, output is given by

$\displaystyle Y$
$\displaystyle=\min\\{BL^{\beta_{l}}K^{\beta_{k}}R^{\beta_{r}}E^{\beta_{e}}e^{\omega},\beta_{m}M\\}.$

The above implies that the value-added productivity, $\dfrac{Y-M}{L}$, when
$R>0$ can be written as

$\displaystyle\dfrac{Y-M}{L}=(1-\frac{1}{\beta_{m}})BL^{\beta_{l}+\beta_{k}+\beta_{r}-1}\biggr{(}\dfrac{K}{L}\biggr{)}^{\beta_{k}}\biggr{(}\dfrac{R}{L}\biggr{)}^{\beta_{r}}E^{\beta_{e}}e^{\omega}.$
(4.1)

As discussed in the section on data, not all firms, innovating or otherwise,
have positive R&D expenditure. We nonetheless keep such firms in our analysis
for two reasons. First, this allows us to estimate the spillover effects of
external knowledge capital for firms that do not engage in R&D. Second, as
discussed below, we are able to use the information on product and/or process
innovation, even for firms that do not have positive R&D expenses, to
endogenise the evolution of $\omega$ and assess the implications of innovation
on productivity, $\omega$. The Leontief production function when R&D
expenditure, $R$, is equal to zero and when material input is proportional to
output is given by

$\displaystyle Y$
$\displaystyle=\min\\{B_{0}L^{\beta^{0}_{l}}K^{\beta^{0}_{k}}E^{\beta^{0}_{e}}e^{\omega},\beta^{0}_{m}M\\},$

which implies that the value-added productivity when $R=0$ is given by

$\displaystyle\dfrac{Y-M}{L}=(1-\frac{1}{\beta^{0}_{m}})B_{0}L^{\beta^{0}_{l}+\beta^{0}_{k}-1}\biggr{(}\dfrac{K}{L}\biggr{)}^{\beta^{0}_{k}}E^{\beta^{0}_{e}}e^{\omega}.$
(4.2)

Taking logarithm of the value-added production functions when $R>0$ and when
$R=0$ and combining the two we get

$\displaystyle y=$
$\displaystyle(1-D^{0})(\beta+\beta^{+}_{l}l+\beta_{k}k+\beta_{r}r+\beta_{e}e)+D^{0}(\beta^{0}+\beta^{0+}_{l}l+\beta^{0}_{k}k+\beta^{0}_{e}e)+\omega+\epsilon,$
(4.3)

where $y$ is the natural logarithm of the value-added productivity and $D^{0}$
is a dummy variable that takes the value 1 when R&D expenditure is zero. The
term $\beta^{+}_{l}=\beta_{l}+\beta_{k}+\beta_{r}-1$ and
$\beta^{+0}_{l}=\beta^{0}_{l}+\beta^{0}_{k}-1$. The lower-case symbols, $l$,
$k$, $r$, and $e$, on the RHS represent natural logs of $L$, $\dfrac{K}{L}$,
$\dfrac{R}{L}$, and $E$ respectively. The constants $\beta$ and $\beta^{0}$
are $\ln(B)$ and $\ln(B_{0})$ respectively. The term $\epsilon$ is the
measurement error in value-added productivity.444See Ackerberg et al. (2015)
for a discussion on the interpretation of $\epsilon_{jt}$. Since the
specification in (4.3) log-linear, the coefficients of the input variables can
be interpreted as elasticities. As is evident from the equation, we allow the
productivity elasticities with respect to the input variables to be different
for firms that engage in R&D and firms that do not.

Since the unobserved productivity shocks, $\omega$, are known to the firm when
it makes its input choices, we are confronted with the problem of endogeneity.
To resolve the issue of endogeneity, as stated earlier, we employ the ‘control
function’ method by ACF. The method requires that the outcome variable be
value added, and depending on the timing of investment and input decisions, it
involves the use of economic theory to derive a ‘proxy’ for the anticipated
productivity shock, $\omega$. The proxy is obtained by assuming that $\omega$
can be inverted out from certain firm inputs if the firm has adjusted these
inputs optimally in response to the $\omega$ it observed.

Now, in ACF the evolution of productivity, $\omega_{jt}$, has been assumed to
be exogenous; that is, productivity shocks evolve according to the first order
Markov Process:
$p(\omega_{j,t+1}|\mathcal{I}_{jt})=p(\omega_{j,t+1}|\omega_{jt})$, where
$\mathcal{I}_{jt}$ firm’s information set at $t$, which includes current and
past productivity shocks $\\{\omega_{j\tau}\\}^{t}_{\tau=0}$ but does not
include future productivity shocks $\\{\omega_{j\tau}\\}^{\infty}_{\tau=t+1}$.
The distribution, $p(\omega_{j,t+1}|\omega_{jt})$, which is stochastically
increasing in $\omega_{jt}$, is known to the firm.555If only to mention, the
transitory shocks, $\epsilon_{jt}$, in (4.3) satisfy
$\mathrm{E}[\epsilon_{jt}|\mathcal{I}_{jt}]=0$.

Griliches (1979), however, points out that while R&D affects output, R&D is
determined both by past output and the expectations of future output. And thus
past R&D efforts and innovation output affect the evolution of productivity,
$\omega_{jt}$, and the expectation of $\omega_{jt+1}$ affects the endogenous
choice of $R_{jt}$. Doraszelski and Jaumandreu (2013)(DJ) endogenize
productivity evolution by including a measure of R&D investment:
$p(\omega_{j,t+1}|\omega_{jt},R_{j,t})$. According to this formulation, a firm
by making investments in R&D alters the probability of receiving a innovation,
which in turn alters the distribution of productivity that it faces in future
periods.

Peters et al. (2017), endogenize productivity evolution by making
$\omega_{jt}$ depend on innovation output instead of past innovation input.
More specifically, productivity, $\omega_{jt}$, is modelled to evolve
according to the following controlled Markov process:
$p(\omega_{jt}|\omega_{j,t-1},\mathcal{P}^{D}_{j,t},\mathcal{P}^{C}_{j,t})$,
where $\mathcal{P}^{D}_{j,t}$ is an indicator variable that takes the value 1
if firm $j$ innovated at least one product and 0 otherwise, and
$\mathcal{P}^{C}_{j,t}$ is an indicator variable that takes the value 1 if
firm $j$ innovated new processes in period $t$ and zero otherwise. Here the
assumption about the innovation process is that both $\mathcal{P}^{D}_{j,t}$
and $\mathcal{P}^{C}_{j,t}$ are a result of R&D efforts in the past. By
including the innovation process in the model, rather than linking R&D
directly to productivity as in DJ, Peters et al. (2017) aim to gain additional
insight into whether R&D improves productivity through the demand side or the
cost side of the firm’s operations. This is because product innovations
increase revenue by expanding the firm’s demand, whereas process innovations
increase revenue by improving the efficiency of scarce factors and thereby
reducing firm’s cost of production (see also Hall 2011).

The Markovian assumption implies that

$\displaystyle\omega_{jt}$
$\displaystyle=\mathrm{E}(\omega_{jt}|\omega_{j,t-1},\mathcal{P}^{D}_{j,t},\mathcal{P}^{C}_{j,t})+\xi_{jt}=g(\omega_{j,t-1},\mathcal{P}^{D}_{j,t},\mathcal{P}^{C}_{j,t})+\xi_{jt}.$
(4.4)

In the above, productivity $\omega_{jt}$ in period $t$ has been decomposed
into expected productivity,
$g(\omega_{j,t-1},\mathcal{P}^{D}_{j,t},\mathcal{P}^{C}_{j,t})$, and a random
shock, $\xi_{jt}$. While the conditional expectation function $g(.)$ depends
on the already attained productivity $\omega_{j,t-1}$ and
$(\mathcal{P}^{D}_{j,t},\mathcal{P}^{C}_{j,t})$, $\xi_{jt}$ does not. The
residual, $\xi_{jt}$, by construction is mean independent of $\omega_{j,t-1}$
and $(\mathcal{P}^{D}_{j,t},\mathcal{P}^{C}_{j,t})$. As discussed in DJ, the
productivity innovation, $\xi_{jt}$, represents the uncertainties that are
naturally linked to productivity and the uncertainties inherent in the
innovation process such as degree of applicability and success in
implementation.

The formulation of productivity evolution in (4.4) (a) captures the lag
dependence of productivity, $\omega_{jt}$, and (b) by allowing innovations to
affect the expected productivity, $g(.)$, and hence labour productivity, it
captures the fact that R&D expenditures alone are not sufficient to generate
productivity improvements. This formulation, therefore, allows us to estimate
the productivity impact of technological innovations. The conditional
expectation function $g(.)$ for the specification in (4.3) is estimated non-
parametrically along with the parameters of the production using the two step
control function procedure proposed in ACF.666We use the STATA’s ‘prodest’
command, which has been developed by Rovigatti and Mollisi (2018), to
implement the control function method in ACF. The endogenous() option allows
users to specify one or more variables that endogenously affect the dynamics
of productivity, $\omega_{jt}$.

Since we are interested in estimating the impact of technological innovations
on productivity for incumbents and entrants, we estimate the difference,

$\displaystyle\Delta=\mathrm{E}[g_{1\vee
1}(\omega_{j,t-1},.)]-\mathrm{E}[g_{0\wedge 0}(\omega_{j,t-1},.)]$ (4.5)

for the entrants and the incumbents, where

$\displaystyle g_{1\vee 1}(.)\equiv
g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}_{jt}^{C})\text{ such that
}\mathcal{P}^{D}_{jt}=1\textit{ and/or }\mathcal{P}^{C}_{jt}=1\text{ and }$
$\displaystyle g_{0\wedge 0}(.)\equiv
g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}_{jt}^{C})\text{ such that
}\mathcal{P}^{D}_{jt}=0\textit{ and }\mathcal{P}^{C}_{jt}=0,$ (4.6)

and the expectations are taken over $\omega_{j,t-1}$. The difference,
$\Delta$, in (4.5) is the average treatment effect (ATE) of innovation on
productivity; details on the identification of ATE can be found in Appendix A.

To understand how (i) product innovation only, (ii) process innovation only,
and (iii) product and process innovations contribute to the ATE, $\Delta$, of
technological innovation we estimate the following:

$\displaystyle\Delta_{10}=\mathrm{E}[g_{1\wedge 0}(.)]-\mathrm{E}[g_{0\wedge
0}(.)],$ $\displaystyle\Delta_{01}=\mathrm{E}[g_{0\wedge
1}(.)]-\mathrm{E}[g_{0\wedge 0}(.)],\text{ and }$
$\displaystyle\Delta_{11}=\mathrm{E}[g_{1\wedge 1}(.)]-\mathrm{E}[g_{0\wedge
0}(.)],$ (4.7)

where

$\displaystyle g_{1\wedge 0}(.)\equiv
g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}_{jt}^{C})\text{ such that
}\mathcal{P}^{D}_{jt}=1\textit{ and }\mathcal{P}^{C}_{jt}=0,$ $\displaystyle
g_{0\wedge 1}(.)\equiv
g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}_{jt}^{C})\text{ such that
}\mathcal{P}^{D}_{jt}=0\textit{ and }\mathcal{P}^{C}_{jt}=1,\text{ and }$
$\displaystyle g_{1\wedge 1}(.)\equiv
g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}_{jt}^{C})\text{ such that
}\mathcal{P}^{D}_{jt}=1\textit{ and }\mathcal{P}^{C}_{jt}=1.$ (4.8)

Given the definitions of $g_{1\wedge 0}(.)$, $g_{1\wedge 0}(.)$, and
$g_{1\wedge 0}(.)$ in (4) and $g_{0\wedge 0}(.)$ in (4.6), it is clear that
$\Delta_{10}$ in (4.7), for the matched sample of product innovators only and
non-innovators, is the ATE of product innovation only; $\Delta_{01}$, the ATE
of process innovation only; and $\Delta_{11}$, the ATE of product and process
innovation.777Ideally, $\Delta$ in (4.5) is the weighted sum,
$\Delta=w_{10}\Delta_{10}+w_{01}\Delta_{01}+w_{11}\Delta_{11}$. The weights,
$w_{10}$, $w_{01}$, and $w_{11}$, respectively are $\dfrac{N_{10}}{N}$,
$\dfrac{N_{01}}{N}$, and $\dfrac{N_{11}}{N}$, where $N_{10}$ is the number of
firms that innovated only products, $N_{01}$ is the number of firms that
innovated only processes, $N_{11}$ is the number of firms that innovated both
products and processes, and $N=N_{10}+N_{01}+N_{11}$. However, if, for
example, we use different matching criteria for computing $\Delta_{11}$ and
$\Delta$ so that the sample of firms used for computing $\Delta_{11}$ is not
contained in the sample of firms used to compute $\Delta$, then the equality
may not hold. As shown in Appendix A, if

$\displaystyle\Delta_{11}\geq\Delta_{10}+\Delta_{01},$ (4.9)

that is, if the impact of product and process innovation exceeds the sum of
the impacts of only product innovation and only process process innovation,
then the product and process innovation can be said to be complementary. We
refer to Milgrom and Roberts (1990) for a general treatment of
complementarities between organizational decisions, and to Athey and
Schmutzler (1995) for complementarities between product and process
innovation.

##  5 Results

First, in subsection 5.1, we discuss the results obtained from the estimation
of the production functions in equations (4.3), focusing on the average
impacts of internal R&D investments and capital accumulation on productivity
for the entrants and incumbents. In this subsection, we also compare our
estimates of the impact of internal R&D and capital accumulation on
productivity with those estimated by Lubczyk and Peters (2020)(LP) for
Germany. In subsection 5.2 we study the differential spillover effects from
knowledge that is produced outside the firms’ boundaries. Finally, in
subsection 5.3, we discuss the estimates of the impact of technological
innovation on productivity for the two group of producers.

###  5.1 Average Returns to Own R&D and Capital Accumulation for Entrants and
Incumbents

Using the empirical framework outlined in section 4, we first study how the
productivity effects of (1) innovation effort as proxied by R&D expenditure
and (2) capital accumulation differ between entrants and incumbent firms. In
Table 3, we display the results of estimating equation (4.3).

In Table 4 we compare the estimated elasticities of productivity with respect
to own R&D and capital stock with those estimated in LP for Germany. An
important difference when compared to Germany is that in Estonia, a large
percentage of innovating firms do not engage in formal R&D. Estimating only
the productivity elasticity with respect to R&D would, therefore, give a
partial picture of productivity implication of innovation. We, therefore, in
addition to estimating productivity elasticity with respect to R&D, as
discussed earlier, in subsection 5.3 estimate the impact of technological
innovations on productivity along. This required us to keep all firms in the
estimation sample, and since the productivity elasticities with respect to
other inputs such as labour and capital could well differ for firms with
positive R&D (firms that engage in STI based innovative activities) and zero
R&D, we estimated separate productivity elasticities for firms with positive
R&D and firms with zero R&D.

We find that the average productivity elasticity of R&D expenditures is
significantly positive for both entrants and incumbents. However, entrants’
elasticity of productivity with respect to R&D does not differ from that of
incumbents’ systemically across specifications and methods. This is contrary
to the findings in Acemoglu et al. (2018) and LP, where entrants are
disproportionally abler than incumbents in translating their R&D endeavours
into productivity gains.

Now, in our sample there are fewer firms in sectors that are R&D and knowledge
intensive, and where returns to R&D is high. In our sample, about 30% of the
firm-years have positive R&D, which is mostly concentrated in high-tech and
medium-high-tech manufacturing (see Table 2). However, in terms of value-
added, we find that the average (averaged over the years) share of high-tech
manufacturing within manufacturing is less than 7%, and average share of
medium-high-tech manufacturing is about 22%. Though the shares have generally
increased over the year, they are lower than the corresponding EU27 2006
shares of 12.5% and 32% respectively (see European Commission 2011, chapter 5,
p. 121). Therefore, it could be due what is known as the compositional effect
(see Castellani et al. 2019) that our result is not consistent with the
theoretical argument that young firms that do not have a well established
product portfolio on the market benefit more from investing in R&D.

To examine whether, compared to the technologically advanced countries, the
lower average elasticity with respect to R&D for Estonian entrants is due to
the compositional effect, in Table 5 we estimated separate elasticities for
(a) firms in the high-tech and medium-high-tech manufacturing and (b) firms in
the remaining sectors. We find that entrants in high-tech and medium-high-tech
manufacturing are not particularly abler than entrants in other sectors in
translating R&D into productivity gains. Having ruled out compositional effect
as a likely cause for the lower average elasticity with respect to R&D, we
take it as given that compared to their counterparts in technologically
advanced economies, Estonian entrants’ are inefficient in STI mode of
innovative activities. Further exploration of the causes behind the
comparatively lower elasticity with respect to R&D is outside the scope of the
paper.

Incumbents in high-tech and medium-high-tech manufacturing, as we can see in
Table 5, do earn a significantly higher reward for investing a unit more of
R&D than incumbents in other sectors. In other words, had the sectoral
composition of the Estonian economy been similar to the technologically
advanced countries or to the EU average, the average elasticity with respect
to R&D for Estonian incumbents would have been higher.

So, (a) despite the limitation posed by the sectoral composition, as can be
seen in Tables 3 and 4, Estonian incumbents are no less abler than Estonia
entrants and on par with German incumbents in translating R&D efforts into
productivity gains. Now, unlike in LP’s paper for Germany, where more than
half of the firms are entrants, and all of whom engage in formal R&D, in our
sample, about 20% of the firms are entrants,888Since CIS considers only those
firms which have more than ten employees and since smaller firms are likely to
be younger, our sample might be biased against the entrants. However, even if
we were to consider all the young firms, it is unlikely that the number of
entrants would have increased substantially. Also, it would be unlikely that
among the entrants left out, a higher percentage of them would be engaging in
formal R&D. of which only 30% are engaged in formal R&D. In other words, (b)
the bulk of STI based innovation in Estonia is carried out by Estonian
incumbents. Given (a) and (b), we can, therefore, conclude that in Estonia,
incumbents play an important role as carriers of STI mode of innovation. STI
mode of innovation, which involves highly skilled scientific personnel,
exploits possibilities at the frontier of knowledge and, through innovations,
pushes the frontier, too. Besides, also through it’s interconnections with the
DUI mode, the STI mode enhances the ability of economies to import and adapt
new technologies and innovations developed elsewhere (Jensen et al. 2007).

[Table 3 about here]

[Table 4 about here]

[Table 5 about here]

The coefficient of $D_{0}$ is positive and significant for the baseline
specification. This result, however, is reversed once we allow for spillover
effects by augmenting the baseline specification with measures of external
knowledge. Since, as discussed in the next subsection, the spillover effects
are particularly significant for the firms that do not engage in R&D, it is
likely that $D^{0}$, which is a dummy for zero R&D investment, is capturing
the spillover effects in the baseline specification. This then suggests that
firms that do not engage in R&D are less productive.

We also find that both incumbents and entrants experience larger productivity
gains from additional capital accumulation than R&D expenditure, suggesting
that in Estonia ‘embodied technological change’ through capital accumulation,
most of which is imported, has been more effective in generating productivity
growth (Castellani et al. 2019). Importantly, the average elasticity with
respect to capital for R&D performing firms was found to be higher than for
those firms that did not engage in R&D. For incumbents, the estimated
elasticity with respect to capital for R&D performing firms was found 1 to 3
percentage points higher than for those firms that did not engage in R&D. As
the test of equality of elasticity of productivity with respect to capital for
firms with and without R&D has been rejected (see Table 3), these differences,
though small, are significant. The fact that R&D performing firms gain more
from capital accumulation than non-R&D firms suggests that R&D helps firms
build absorptive capacity, which enables more efficient transfer of technology
embodied in capital good (Griffith et al. 2004; Aghion and Jaravel 2015).

Comparing elasticity of productivity with respect to capital for the two
countries in Table 4, we find that, the elasticity is higher for the Estonian
incumbents as compared to the German ones. Now, Ortega-Argilés et al. (2014,
2015) find that in traditional low-tech industries, which focus on process
innovation, productivity gains turn out to be more related to capital
accumulation rather than to R&D expenditures. Supporting this argument,
Castellani et al. (2019) point out that complex and radical product innovation
generally relies on formal R&D, while process innovation is much more related
to embodied technological change achieved by investment in new machinery and
equipment (see also Parisi et al. 2006). In Estonia, (i) 47% of the firm-year
observations from low-tech and medium-low-tech manufacturing and 23% are from
less knowledge intensive services, and (ii) process innovation being more
prevalent than product innovation (Table 1). This could potentially explain
why productivity gains from capital accumulation is (a) higher than that from
R&D, and (b) higher for the Estonian incumbents as compared to the German
ones.

We find that the coefficient estimates of log(Employees) is negative for all
firms. Now, in the value-added production function in (4.3), the coefficient
of log(Employees) for R&D performing firms is
$\beta^{+}_{l}=\beta_{l}+\beta_{k}+\beta_{r}-1$ and
$\beta^{0+}_{l}=\beta^{0}_{l}+\beta^{0}_{k}-1$ for non-R&D firms. The negative
estimates of $\beta^{+}_{l}$ and $\beta^{0+}_{l}$, then suggest that the
cumulative share of some of the inputs is less than 1. In other words, it
suggests that the returns to scale is decreasing. As far as age is concerned,
the estimates suggest that, within the two groups of firms, age does not play
a significant role as determinant of productivity. As a positive coefficient
of age is associated with learning effects which causes improvements in
productivity with time (Lubczyk and Peters 2020),999A negative coefficient of
firm age, at least for incumbents, indicates that these learning effects
associated with firm age become much smaller and phase out in later stages of
firm life. the ACF estimates suggest that there are no learning effects.
Finally, we also find a robust evidence that firms located in northern
Estonia, which is the economic hub of the nation, are more productive; this
suggests that firms in northern Estonia benefit from a positive agglomeration
effect.

###  5.2 Spillover Effects

Knowledge spillover effects, as we know, are highly relevant for both firms
and policy makers, as they point to situations where the benefits of
accumulating knowledge in one firm result in performance and productivity
gains in a larger agglomeration or group of firms, further resulting in a sub-
optimal low level of R&D from a social point of view. Therefore, an important
question related to the productivity effects of R&D activities is the degree
to which a firm’s own R&D efforts impact other firms’ performances. Research
on knowledge spillovers at the micro-level finds that the different mechanisms
through which spillovers occur are indeed localised to a large extent (see
Audretsch 1998; Storper and Venables 2004; Ponds et al. 2010). Besides the
importance of local labour markets and spin-off dynamics, studies have
emphasized the role of networking between individuals and between
organizations as a mechanism for knowledge spillovers that takes place at the
regional level. For each firm, then, we define external knowledge capital as
the accumulation of knowledge that is generated by other firms that are
geographically close to the focal firm.

Since knowledge spillovers can take place both within and between industries,
we further differentiate the group of other firms into those firms that are
within and those that are outside of the focal firm’s own industry, and
accordingly construct measures of inter- and intra-industry knowledge capital
(see section 4 for the definition of the two). These measures of external
knowledge capital are then added to the production functions in equations
(4.3). To test if there is differential impact of knowledge spillover for R&D
performing firms and non-R&D firms, we interact the measures with two binary
variables: $D^{0}$ and $1-D^{0}$.

Now, in our data, we find that the average R&D expenditure of firms is higher
in counties/regions where there is a higher concentration (number of
firms/geographical area of the county) of firms. Moreover, we find that there
is a positive correlation between R&D expenses and the average R&D expenses of
other firms situated in the same region. It, therefore, seems that location is
not a random but a deliberate choice made by the firms. In other words, the
measures of external knowledge capital, through the endogenous choice of
location, and firm’s total factor productivity, $\omega_{jt}$, are correlated.
The endogeneity of measures of external knowledge capital is accounted for by
treating measures of external knowledge capital and the dummy for north
Estonia as state variables when using control function methods.

Table 3, columns 2a and 2b, illustrates the estimated results when measures of
external knowledge capital are added to the productivity functions. The
estimates suggest that it is mainly the incumbents who benefit from external
knowledge produced outside the firms’ boundaries. However, among the
incumbents, the R&D performing incumbents seem to gain from only within
industry external knowledge, whereas the incumbents who do not engage in R&D
activities gain from external knowledge both within and without their own
industry.101010Instead of the measure based on geographical distance, future
research should consider estimating productivity response to measures of
inter-industry external knowledge, which are based on ‘technological distance’
as in Bloom et al. (2013) (see also Hall et al. 2010, on measuering
spillovers). The estimates also suggest it is mainly the incumbents who
benefit from knowledge capital produced outside their own firm. In other
words, these results indicate that mature firms are on average better at
incorporating diverse knowledge that stems from sources both within and
outside their industry. The results also show that for the incumbents, the
social returns to external knowledge capital are comparable to, if not higher
than, the private returns to R&D.

We find that non-R&D firms among the incumbents benefit more from external
knowledge than innovating firms. Given that there exists complementarity
between absorptive capacity and external knowledge and that at sufficiently
low levels of absorptive capacity further increases in external knowledge may
not increase marginal private incentives to build absorptive capacity to
benefit from it (see Aghion and Jaravel 2015), the results indicate that
incumbents that do not engage in R&D activities, nonetheless do invest in
building absorptivity capacity to benefit from external knowledge even though
they do not invest in STI based innovation. Second, since by definition
non-R&D firms do not invest in ‘frontier innovation,’ the results suggest that
such incumbents are most likely benefiting from ‘technological adaptation or
imitation,’ which is aided by geographical proximity to R&D intensive firms
operating in the same industry.

###  5.3 Productivity Implication of Technological Innovation for Entrants and
Incumbents

As mentioned earlier, about 30% of the firm-years have positive R&D expenses,
but about 75% of the firm-years in the sample have innovated to introduce at
least one new product in the market or a new process. Also, about 7% of the
firms that invested in R&D did not innovate a new product or process. These
suggest that more firms innovate through the DUI mode of innovation rather
than STI and that having positive R&D expenses is neither a necessary nor a
sufficient condition for innovation.

Now, it has been found that firms in the low- and medium-tech sectors are
usually engaged in the DUI mode of innovation while drawing on advanced
science and technology results available through the common knowledge bases
(Robertson et al. 2009; Trott and Simms 2017). Given that the majority of
firms in our sample are in the low-tech and low-medium-tech manufacturing and
less knowledge intensive services (see Table 2), and many of whom innovate
without formally engaging in R&D, we, by estimating the average treatment
effect (ATE) of technological innovation, $\Delta$, given in equation (4.5),
assess how technological innovations affect total factor productivity (TFP)
and labour productivity consequently. As discussed in Appendix A, we first
estimate the residual,
$\omega_{jt}+\epsilon_{jt}=g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}^{C}_{jt})+\xi_{jt}+\epsilon_{jt}$,
in equation (4.3) as a measure of TFP, and then use a matching method to
estimate $\Delta$. In Table 7 we report the estimated ATEs.

[Table 6 about here]

[Table 7 about here]

To assess if there is complementarity between product and process innovation
and to understand how (a) only product innovation (b) only process innovation
and (c) both product and process innovation contribute to $\Delta$, we also
estimate the ATE of only product innovation ($\Delta_{10}$), the ATE of only
process innovation ($\Delta_{01}$), and the ATE of product and process
innovation ($\Delta_{11}$) (see equation (4.7)). The control variables on the
basis of which we match innovators with the non-innovators for estimating the
ATEs in (4.5) and (4.7) are stated in the following. For estimating $\Delta$
in (4.5), we match ‘exactly’ on year dummies (2006 to 2018) and 2-digit
industry dummies, and match to ‘nearest neighbourhood’ on the lags of the
following variables: (1) residual, $\omega_{jt}+\epsilon_{jt}$, as a proxy for
TFP, (2) estimate of $\omega_{jt}$ (see footnote 11 in Appendix A), (3)
product innovation, (4) process innovation (5) technological innovation (6)
log of R&D intensity (7) dummy for positive R&D, (8) labour productivity, (9)
log of number of employees, (10) log of capital stock, (11) log of material
cost, (12) log of intra-industry external knowledge, (13) log of inter-
industry external knowledge, and (14) age. However, because there were much
fewer firms who only innovated products, only innovated processes, or both, we
could not match exactly on industry dummies while estimating $\Delta_{10}$,
$\Delta_{01}$, and $\Delta_{11}$. We, therefore, matched exactly on year and
to nearest neighbourhood on the rest of the variables while estimating
$\Delta_{10}$, $\Delta_{01}$, and $\Delta_{11}$.

As we can see in Table 7, for productivity estimates from both the
specifications, the ATE, $\Delta$, of technological innovation on productivity
is larger for the entrants as compared to the incumbents’. We find that the
ATE ranges from 0.19 to 0.27 for the entrants, and same for the incumbents
ranges from 0.1 to 0.13. These ATEs, however, are in logarithmic scale; at the
mean, these difference in linear scale implies that an entrant who innovates
is about 21% to 30% more productive than an entrant who does not. For the
incumbents, it implies that, on average, the incumbent firm that innovates is
about 10% to 13% more productive than the one which does not.

Given that a higher percentage of entrants (78%) compared to incumbents (72%)
reported innovation, our results suggests that not only are entrants more
innovative, but that entrants are abler than incumbents in translating their
innovations into productivity gains. To understand how the two group of
producers benefit from technological innovations, we look at a more
disaggregated picture by estimating the ATE of only product innovation
($\Delta_{10}$), the ATE of only process innovation ($\Delta_{01}$), and the
ATE of product and process innovation ($\Delta_{11}$). In Table 7, we can see
that $\Delta_{10}$ is significantly positive for incumbents, implying that
incumbents who innovated new products only realized productivity gains. And
with $\Delta_{01}$ significantly positive for entrants, it implies that
entrants who implemented innovative processes only realized productivity
gains. However, those firms that have innovated both product and process
realized the highest gain. The productivity of entrants who innovated both
product and process is about 35% higher than an average entrant’s, and such
incumbents’ productivity is about 13% higher than the average incumbent’s.

Since for the incumbents, the ATE of process innovation only did not turn out
significant, we can assume that for the incumbents $\Delta_{01}=0$; similarly
we can assume that $\Delta_{10}$ is 0 for the entrants. We, therefore, find
that for both the group of producers: $\Delta_{11}>\Delta_{10}+\Delta_{01}$.
In other words, we find the existence of complementarity between product and
process innovations. Now, as can be seen in Table 6, a higher percentage of
innovating entrants (50%) and incumbents (40%) innovate both products and
processes. That is, both the groups of producers, especially the entrants,
prefer to invest in both the activities at the same time to maximize their
productivity.

Complementarity between product and process innovations arises when the
returns to implementing a product innovation are highest when the firm also
implements a process innovation. This occurs because product innovations,
which shift out the demand curve, induces the firm to produce a higher
quantity. However, the returns from lowering the unit cost through process
innovations are highest precisely when quantity produced is highest, and thus
firms tend to implement product and process innovations together.

Athey and Schmutzler (1995) emphasize that flexibility in product designs and
processes, which lowers the adjustment costs of implementing product and
process innovations, enhances the complementarity between product and process
innovations. Since (a) entrants are found to have gained from implementing
process innovations and (b) complementarity between product and process
innovations is higher for the entrants, these results indicate that entrants
do leverage their flexible and non-hierarchical structures — due to which they
lack the structural inertia for reorganisation and which allow for faster
decision-making processes — for implementing the complementary process
innovations, and consequently realize a higher complementarity.

Before proceeding further, we would like to point out that since a smaller
percentage of firms — incumbents (31%) and entrants (29%) — reported engaging
in formal R&D, this result suggests that a lot of the productivity gains is
being made through DUI mode of innovation. This assertion is also supported by
our data: ‘DUI Exclusive mode of cooperation’ or cooperation with other
enterprises for innovative activities excluding R&D was higher (53%) for
innovating firms that reported zero R&D, whereas ‘STI Exclusive mode of
cooperation’ was higher (73%) for firms with positive R&D. While our data
indicates that many innovations are likely a result of DUI mode of innovation,
we are unable to identify which innovations are a result of DUI mode of
innovation and which are STI based. We are thus unable to estimate the
efficacy of STI based innovations vis-à-vis DUI based innovations, or for that
matter the efficacy of the combination of two, for the two group of producers.
We leave the exercise of assessing the efficacy of STI and DUI based
innovations for future research.

Finally, we compare the estimated TFP for the entrants and incumbents. As can
be seen in Table 7, on average, the TFP of the entrants is higher than that of
the incumbents. This is in contrast to labour productivity, which on average
is found to be higher among the incumbents than the entrants (see Table 1).
Since labour productivity could change due to (a) changes in technology, which
improves the efficiency with which the factors operate, or (b) due to changes
in factor accumulation, it, therefore, seems that a higher labour productivity
of the incumbents is because of a higher capital-labour ratio than due to more
efficient technology. TFP, on the other hand, measures firm ability or
efficiency, such as managerial talent, quality of inputs, innovation, etc.,
that are not accounted for by the observed inputs (Syverson 2011). That
surviving young firms have above average productivity and that they grow
faster than their mature counterparts, has been documented elsewhere (Foster
et al. 2008; Haltiwanger et al. 2013).

Also, in Table 7 we can see that entrants’ TFP have higher standard deviation
as compared to the TFP for the incumbents. As discussed in Haltiwanger et al.
(2013), young firms exhibit an ‘up or out’ dynamic — they either grow fast on
average or they exit. These ‘up or out’ dynamics imply that exiting young
firms have very low productivity while surviving young firms — where survival,
more often than not, is because of successful innovation — have above average
productivity. Related to the ‘up or out’ dynamics, Foster et al. (2018)
explain that entry is associated ‘experimentation,’ which is critical for
innovation and which results high degree of within-industry productivity
dispersion. Following this experimentation phase is the ‘shakeout’ period, in
which entrepreneurs that successfully innovate and/or adopt grow while
unsuccessful entrepreneurs contract and exit yielding productivity growth.
Foster et al. (2018) discuss a variety of mechanisms which can help understand
how ‘experimentation’ can generate heterogeneity in the factors that cause
dispersion.

##  6 Concluding Remarks

A large proportion of productivity growth, a key driver of economic growth, is
due to reallocation emanating from the entry and exit of firms. Since this
reallocation is induced by the selection effect due to the heterogeneous
productivity impacts of R&D investment and innovation undertaken by incumbents
and entrants, in this paper we study the productivity implications of (a) own
R&D, (b) external knowledge, and (c) and technological innovations for
incumbents and entrants. The third exercise is motivated by the fact that, in
our sample, while only 30% of firm-year report investment in R&D, 74% report
technological — product and process — innovation. Studying the implications of
R&D alone would have provided a partial picture of the innovation activities
of firms in Estonia and other CEE catching-up economies. We, therefore,
develop an empirical strategy to simultaneously estimate (1) the productivity
elasticities of R&D and external knowledge and (2) the impact of technological
innovations on productivity. Also, in studying the productivity implication of
technological innovation, we pay particular attention to complementarity
between product and process innovation for the two groups of producers.
Besides, since physical capital stock embodies technical change and
innovation, we also study the productivity impact of capital accumulation.

Several interesting conclusions emerge from our analysis. To start with, while
both entrants and incumbents gain significantly from investing in R&D, we do
not find any difference in the average productivity elasticity with respect to
own R&D for the two group of producers. This is contrary to the findings in
Acemoglu et al. (2018) and Lubczyk and Peters (2020) for the technologically
advanced economies, where entrants have been found to be disproportionately
abler in translating their R&D into productivity gains. Instead, we find that
the impact of innovation output — many of which are a result of DUI based
innovation — are similar to the results in the aforementioned papers: entrants
who innovate are 21% to 30% more productive than entrants who do not; for the
incumbents, the corresponding figures are 10% to 13%. Furthermore, as we
explored the sources of the productivity gain, we found that the gain is
largely due to complementarities between product and process innovation, with
entrants benefiting more from the complementarities than incumbents.

Estonian incumbents, on the other hand, are no less abler than German
incumbents in translating R&D or STI based innovative activities into
productivity gains. This is despite the adverse sectoral composition of the
Estonian economy, which has a low share of sectors that are R&D intensive and
where returns to R&D are highest. Moreover, because the bulk of STI based
innovative activities in Estonia is carried out by the incumbents, they are
the primary carriers of STI based innovative activities.

We find that productivity elasticity with respect to capital is higher than
with respect to R&D, suggesting that in catching-up economies such as in
Estonia, embodied technological change through capital accumulation has been
an important means, and likely more effective than R&D, for generating
productivity growth. However, since productivity elasticity with respect to
capital is higher for firms that report engaging in formal R&D, it suggests
that STI based innovative activities do help build absorptive capacity.

Finally, in results related to spillover effects, we find it is mostly the
incumbents who benefit from intra- and inter-industry knowledge that is
generated by other firms — primarily by the incumbents — situated in close
proximity. However, the spillover effects are higher for firms that do not
reportedly engage in formal R&D, suggesting that these firms, too, work on
building absorptive capacity.

There are certain limitations in our paper, which are primarily due to lack of
data. First, as Community Innovation Surveys (CIS) consider firms with at
least 10 employees, the entrants included in these data may not be
representative of the population of newly born firms, which are unlikely to
exceed this threshold in the first years of their existence. Relying on CIS
data could therefore limit the number of newly established firms. Second, we
consider only regional spillover effects; future studies could consider
measures of external knowledge that are based on technological distance
between firms and/or forward and backward linkages between industries.

Our results have important policy implications. The finding that technological
innovations benefit entrants disproportionately more than the incumbents
points to the significant impact innovative entry can have on economic
dynamics. These results yet again emphasize policies — in particular those
that facilitate DUI mode of innovation — for promoting innovative
entrepreneurship. However, our results also strongly suggest than in Estonia —
a catching-up economy — incumbents are the primary carriers of STI based
innovative activities, which are instrumental in building absorptive capacity
and help move economies closer to the technological frontiers.

Our results then suggest that the policies advocated in Acemoglu et al. (2018)
for technologically advanced economies may not be applicable for a catching-up
economy like Estonia. Acemoglu et al. (2018) advocate that a large tax on the
continued operation of incumbents combined with a modest R&D subsidy to
incumbent would be both growth and welfare increasing. However, this policy
only leverages the selection effect. As pointed out by Aghion and Jaravel
(2015, p. 539), the recommendations suggested by Acemoglu et al. (2018) do not
take into consideration the notion of absorptive capacity which could have
“novel implications, as it creates another trade-off between incumbents (with
a large stock of R&D and a high absorptive capacity) and new firms.” Policy
makers must, therefore, duly consider the important role incumbents, as
primary carriers of STI based innovative activities, play in catching-up
economies. As argued in Aghion and Jaravel (2015), because the social returns
to absorptive capacity are not fully internalised by the private market,
private market forces may fail to ensure the catching-up process; policies and
institution that foster large incumbents during the catching-up periods have
historical antecedents (see Aghion et al. 2011).

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## Appendices

##  Appendix A Identification of Average Treatment Effect of Innovation and
Testing for Complementarity Between Product and Innovation

Substituting the specification for $\omega_{jt}$ given in equation (4.4) in
the log-linear production function in equation (4.3), we obtain

$\displaystyle y_{jt}=$
$\displaystyle(1-D_{jt}^{0})(\beta+\beta^{+}_{l}l_{jt}+\beta_{k}k_{jt}+\beta_{r}r_{jt}+\beta_{e}e_{jt})+D_{jt}^{0}(\beta^{0}+\beta^{0+}_{l}l_{jt}+\beta^{0}_{k}k_{jt}+\beta^{0}_{e}e_{jt})$
$\displaystyle+g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}^{C}_{jt})+\xi_{jt}+\epsilon_{jt}.$
(A.1)

The coefficients, $\beta$’s, and the function,
$g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}^{C}_{jt})$, as discussed in
section 4, is estimated using the control function methodology by Ackerberg et
al. (2015) (ACF). For notational convenience from here on, we drop the firm
subscript, $j$.

In this appendix, we discuss how we (i) estimate the average treatment effect
(ATE) of the various kinds of innovation ($\Delta$ in Eq. (4.5) and
$\Delta_{10}$, $\Delta_{01}$, $\Delta_{11}$ in (4.7) ) and (ii) assess for
complementarity between product and process innovation.

Now, as discussed in the main text, the function,
$g(\omega_{t-1},\mathcal{P}^{D}_{t},\mathcal{P}_{t}^{C})$, in equation (A.1)
is estimated non-parametrically by approximating it by a polynomial function
of the arguments of $g(\omega_{t-1},\mathcal{P}^{D}_{t},\mathcal{P}_{t}^{C})$.
So, if, for example, $\omega_{t-1}$ is calculated as in footnote 11, one could
employ the estimated coefficients of the polynomial to obtain estimates of
$g_{1\vee 1}(\omega_{t-1},.)$ and $g_{0\wedge 0}(\omega_{t-1},.)$, where the
two are defined in equation (4.6), for every $\omega_{t-1}$, and then by
averaging over $\omega_{t-1}$ one can obtain, for example, $\Delta$, the
average treatment effect of technological innovation:

$\displaystyle\Delta=\mathrm{E}[g_{1\vee
1}(\omega_{t-1},.)]-\mathrm{E}[g_{0\wedge 0}(\omega_{t-1},.)].$ (A.2)

For inference, we could either (a) first obtain bootstrapped standard errors
of the coefficients of the polynomial function, and then use the delta method
to obtain the standard error of $\Delta$, or (b) directly bootstrap $\Delta$.
Both procedures are, however, computationally intensive. Rather than following
these laborious procedures of computing the ATEs and their standard errors,
we, as discussed below, develop a simple procedure to estimate the ATEs.

In the following we show that we can still obtain $\Delta$ in (A.2) without
using the estimates of the function, $g(\omega_{t-1},.)$. The alternative
procedure entails first estimating the residuals

$\displaystyle r_{t}$ $\displaystyle\equiv
y_{t}-\big{(}(1-D_{t}^{0})(\beta+\beta^{+}_{l}l_{t}+\beta_{k}k_{t}+\beta_{r}r_{t}+\beta_{e}e_{t})+D_{t}^{0}(\beta^{0}+\beta^{0+}_{l}l_{t}+\beta^{0}_{k}k_{t}+\beta^{0}_{e}e_{t})\big{)}$
$\displaystyle=g(\omega_{t-1},\mathcal{P}^{D}_{t},\mathcal{P}_{t}^{C})+\xi_{t}+\epsilon_{t}$

in equation (A.1) and then using the matching methods for estimating the ATE,
$\Delta$. The alternative procedure works because these residuals, which are a
proxy for the total factor productivity (TFP), contain information on
$g(\omega_{t-1},.)$. The residuals for firm-years that innovated are
$r_{t}(I_{t}=1)=g_{1\vee 1}(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}$, and for
those that did not are $r_{t}(I_{t}=0)=g_{0\wedge
0}(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}$.

Having obtained the residuals, $g(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}$, to
estimate the impact of technological innovations on productivity, we can
obtain the difference

$\displaystyle\mathrm{E}[g_{1\vee
1}(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}]-\mathrm{E}[g_{0\wedge
0}(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}],$ (A.3)

where the expectation is taken over $(\omega_{t-1},\xi_{t},\epsilon_{t})$.

Note that we only know $r_{t}(I_{t}=1)$ for firm-years that have innovated and
$r_{t}(I_{t}=0)$ for firms that did not innovate. Our problem is, therefore,
same as the missing data problem in treatment effect literature:
$r_{t}(I_{t}=0)$ is unobserved for firm-years that innovated, and
$r_{t}(I_{t}=1)$ is unobserved for firm-years that did not innovate. The
comparison, therefore, between $\mathrm{E}[g_{1\vee
1}(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}]$ and $\mathrm{E}[g_{0\wedge
0}(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}]$ for assessing the effect of
innovation can only be possible if $\omega_{t-1}$ for firms that have
innovated (treatment group) are same as $\omega_{t-1}$ for firms that did not
(control group).

To select firms in control group with $\omega_{t-1}$ similar to the firms in
the treatment group, we resort to the matching method in Abadie and Imbens
(2006). The method rigorously selects control units with $X_{t-1}$ similar to
the treated units. The control variables (or ‘observable confounders’),
$X_{t-1}$, on the basis of which we match firms in treatment group to the
firms in the control group are variables that likely affect both the treatment
(innovation) and the outcome (TFP). In $X_{t-1}$ we include (i)
$\omega_{t-1}$,111111In ACF, firm’s intermediate input demand is given by
$m_{t}=f_{t}(l_{t},k_{t},r_{t},e_{t},x_{t},\omega_{t})$, where $x_{t}$ is the
set of additional state variables, and the function,
$m_{t}=f_{t}(.,\omega_{t})$, is strictly monotonic in the unobserved TFP,
$\omega_{t}$. Given the monotonicity assumption, a proxy for $\omega_{t}$ is
obtain by inverting the intermediate input demand function:
$\omega_{t}=f^{-1}_{t}(l_{t},k_{t},r_{t},e_{t},x_{t},m_{t})$. STATA’s prodest
command gives an estimate of $\omega_{t}$ as
$\displaystyle\hat{\phi}(D^{0}_{t},l_{t},k_{t},r_{t},e_{t},x_{t},m_{t})$
$\displaystyle-[(1-D_{t}^{0})(\hat{\beta}+\hat{\beta}^{+}_{l}l_{t}+\hat{\beta}_{k}k_{t}+\hat{\beta}_{r}r_{t}+\hat{\beta}_{e}e_{t})+D_{t}^{0}(\hat{\beta}^{0}+\hat{\beta}^{0+}_{l}l_{jt}+\hat{\beta}^{0}_{k}k_{t}+\hat{\beta}^{0}_{e}e_{t})],$
where $\phi(.)$, which is estimated in the first stage, is given by
$\displaystyle\phi(D^{0}_{t},l_{t},k_{t},r_{t},e_{t},x_{t},m_{t})=$
$\displaystyle[(1-D_{t}^{0})(\beta+\beta^{+}_{l}l_{t}+\beta_{k}k_{t}+\beta_{r}r_{t}+\beta_{e}e_{t})+D_{t}^{0}(\beta^{0}+\beta^{0+}_{l}l_{t}+\beta^{0}_{k}k_{t}+\hat{\beta}^{0}_{e}e_{t})]$
$\displaystyle+f^{-1}_{t}(l_{t},k_{t},r_{t},e_{t},x_{t},m_{t}).$ Note that
given $\omega_{t}=f^{-1}_{t}(l_{t},k_{t},r_{t},e_{t},x_{t},m_{t})$, the next
period productivity is
$\omega_{t+1}=g(\omega_{t},\mathcal{P}^{D}_{t},\mathcal{P}^{C}_{t})+\xi_{t}$,
and it is $g(\omega_{t},\mathcal{P}^{D}_{t},\mathcal{P}^{C}_{t})$ that is our
quantity of interest, not
$\omega_{t}=f^{-1}_{t}(l_{t},k_{t},r_{t},e_{t},x_{t},m_{t})$. (ii) all the
state variables and control variables from period $t-1$, and (iii)
$\mathcal{P}^{D}_{t-1}$ and $\mathcal{P}^{C}_{t-1}$. The control variables,
$X_{t-1}$, are mean independent of the error terms, $\xi_{t}+\epsilon_{t}$
(see also discussion following Eq. (4.4)).

The identification assumption is that conditional on $X_{t-1}$, the treatment
is independent of the ‘potential’ outcome, $r_{t}(I_{t})$. In the other words,
for the matched sample, the treatment (here innovation) can then be considered
to be randomly assigned between the treatment and the control group. Under
this assumption, for the matched sample, we, therefore, have

$\displaystyle\Delta(X_{t-1})$
$\displaystyle=\mathrm{E}(r_{t}(I_{t}=1)-r_{t}(I_{t}=0)|X_{t-1})$
$\displaystyle=\mathrm{E}[g(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}|I_{t}=1,X_{t-1}]-\mathrm{E}[g(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}|I_{t}=0,X_{t-1}]$
$\displaystyle=\mathrm{E}[g_{1\vee
1}(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}|X_{t-1}]-\mathrm{E}[g_{0\wedge
0}(\omega_{t-1},.)+\xi_{t}+\epsilon_{t}|X_{t-1}]$
$\displaystyle=\mathrm{E}[g_{1\vee
1}(\omega_{t-1},.)|X_{t-1}]-\mathrm{E}[g_{0\wedge
0}(\omega_{t-1},.)|X_{t-1}],$ (A.4)

where the last equality follows also because $\xi_{t}+\epsilon_{t}$ is mean
independent of $X_{t-1}$.

Under the overlap assumption, $\mathrm{Pr}(I_{t}=1|X_{t-1})<1$, (see Abadie
and Imbens 2006) the difference on the right-hand side of (A.4) is identified
for almost all $X_{t-1}$ in the support of $X_{t-1}$. Therefore, the average
effect of the treatment can be recovered by averaging $\mathrm{E}[g_{1\vee
1}(\omega_{t-1},.)|X_{t-1}]-\mathrm{E}[g_{0\wedge 0}(\omega_{t-1},.)|X_{t-1}]$
over the distribution of $X_{t-1}$. That is,

$\displaystyle\mathrm{E}[\Delta(X_{t-1})]=\mathrm{E}[g_{1\vee
1}(\omega_{t-1},.)]-\mathrm{E}[g_{0\wedge 0}(\omega_{t-1},.)]=\Delta,$ (A.5)

which is what we wanted to estimate in (A.2).

We now come to assessing of complementarity between product,
$\mathcal{P}^{D}_{t}=1$, and process, $\mathcal{P}^{C}_{t}=1$ innovation. The
study of complementarities between activities can be traced back to the theory
of supermodularity (Milgrom and Roberts 1990). According to this theory, the
necessary condition for product and process innovation to be complementary is
that the expectation,
$\mathrm{E}[g(\omega_{t-1},\mathcal{P}^{D}_{t},\mathcal{P}^{C}_{t})]$, be
supermodular in $\mathcal{P}^{D}_{t}$ and $\mathcal{P}^{C}_{t}$:

$\displaystyle\mathrm{E}[g_{1\wedge 1}(.)]-\mathrm{E}[g_{0\wedge
1}(.)]\geq\mathrm{E}[g_{1\wedge 0}(.)]-\mathrm{E}[g_{0\wedge 0}(.)],$ (A.6)

where

$\displaystyle g_{1\wedge 0}(.)\equiv
g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}_{jt}^{C})\text{ such that
}\mathcal{P}^{D}_{jt}=1\textit{ and }\mathcal{P}^{C}_{jt}=0,$ $\displaystyle
g_{0\wedge 1}(.)\equiv
g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}_{jt}^{C})\text{ such that
}\mathcal{P}^{D}_{jt}=0\textit{ and }\mathcal{P}^{C}_{jt}=1,$ $\displaystyle
g_{1\wedge 1}(.)\equiv
g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}_{jt}^{C})\text{ such that
}\mathcal{P}^{D}_{jt}=1\textit{ and }\mathcal{P}^{C}_{jt}=1\text{ and }$
$\displaystyle g_{0\wedge 0}(.)\equiv
g(\omega_{j,t-1},\mathcal{P}^{D}_{jt},\mathcal{P}_{jt}^{C})\text{ such that
}\mathcal{P}^{D}_{jt}=0\textit{ and }\mathcal{P}^{C}_{jt}=0.$

The inequality in (A.6) can be interpreted as follows: on average,
implementing a product innovation when the firm also implements a process
innovation has a higher incremental effect on productivity than implementing a
product innovation in isolation.

We can write the inequality in (A.6) as

$\displaystyle\mathrm{E}[g_{1\wedge 1}(.)]-\mathrm{E}[g_{0\wedge 0}(.)]$
$\displaystyle\geq$ $\displaystyle(\mathrm{E}[g_{0\wedge
1}(.)]-\mathrm{E}[g_{0\wedge 0}(.)])$ $\displaystyle+$
$\displaystyle(\mathrm{E}[g_{1\wedge 0}(.)]-\mathrm{E}[g_{0\wedge 0}(.)])$
$\displaystyle\Longleftrightarrow$ $\displaystyle\quad\qquad\Delta_{11}$
$\displaystyle\geq$ $\displaystyle\quad\qquad\Delta_{01}$ $\displaystyle+$
$\displaystyle\quad\qquad\Delta_{10},$ (A.7)

where $\Delta_{10}$ is the ATE of only product innovation, $\Delta_{01}$ is
the ATE of only process innovation, and $\Delta_{11}$, the ATE of both product
and process innovation. That is, if the productivity impact of product and
process innovation exceeds the sum of the impacts of only product innovation
and only process innovation, then the product and process innovation can be
said to be complementary. The ATEs, $\Delta_{10}$, $\Delta_{01}$, and
$\Delta_{11}$, can be estimated using the matching method as in (A.5).

Table 1: Test of Equality of Means between Entrants and Incumbents

| Entrants | Incumbents | Difference | $\mathrm{Pr}(|T|>|t|)$
---|---|---|---|---
log(Value-Added Productivity ) | 10.2 | 10.33 | -0.13 | 0.00
log(Gross Output Productivity) | 11.16 | 11.27 | -0.11 | 0.00
log(No. of Employees) | 3.5 | 3.75 | -0.25 | 0.00
log(Capital) | 12.4 | 13.36 | -0.96 | 0.00
log(Material Cost) | 13.57 | 14.01 | -0.44 | 0.00
log(Investment in Fixed Assets) | 11.17 | 11.53 | -0.36 | 0.00
log(R&D Expenditure) | 7.17 | 7.78 | -0.61 | 0.000
Dummy for Positive R&D Expenditure | 0.29 | 0.31 | -0.02 | 0.16
Dummy for Innovator | 0.78 | 0.72 | 0.06 | 0.00
Dummy for Product Innovation | 0.56 | 0.45 | 0.11 | 0.00
Dummy for Process Innovation | 0.61 | 0.56 | 0.04 | 0.00
Dummy for North | 0.59 | 0.54 | 0.05 | 0.00
log(Intra-Industry R&D) | 4.27 | 4.56 | -0.28 | 0.02
log(Inter-Industry R&D) | 9.39 | 10.07 | -0.68 | 0.00
Note: (a) The two sample t-test assumed unequal variances. (b) The data used
for the tests is the estimation sample.

Table 2: Sectoral Distribution of Estonian Firms in the Estimation Sample

Percentage Positive R&D Technological
$\log\Big{(}\dfrac{\text{R\&D}}{\text{Employees}}\Big{)}$ of Firms Innovation
Entrants High-Tech Manufacturing 2.3 37.5 97 3.41 Medium High-Tech
Manufacturing 10.14 35.5 86 2.54 Medium Low-Tech Manufacturing 22.01 22.9 75
1.57 Low-Tech Manufacturing 28.42 27.1 81 1.84 Knowledge Intensive Services
19.93 43 82 3.47 Less Knowledge Intensive Services 17.19 19.2 69 1.15 Total
100 28.9 78 2.1 Incumbents High-Tech Manufacturing 2.26 54.1 83 4.7 Medium
High-Tech Manufacturing 11.02 46 82 3.78 Medium Low-Tech Manufacturing 15.13
27.1 71 2 Low-Tech Manufacturing 31.62 28.2 77 1.94 Knowledge Intensive
Services 15.59 41 72 3.52 Less Knowledge Intensive Services 24.39 21.5 64 1.68
Total 100 30.7 72 2.4 No. of Entrants: 1500, No. of Incumbents: 6086. Note:
(a) All figures excepts for log(R&D/Employees) are in percentages. (b)
Technological classification borrowed from Eurostat is based on NACE Revision
2 2-digit level.

Table 3: Productivity Effects of R&D and Capital Accumulation for Entrants and
Incumbents

Specification: Baseline Specification: Baseline + External Knowledge Incumbent
Entrant Incumbent Entrant (1a) (1b) (2a) (2b) log(Employees)$\times(1-D^{0})$
-0.16 ∗∗∗ -0.035 -0.234 ∗∗∗ -0.188 ∗∗∗ (0.001) (0.011) (0.001) (0.013)
log(Employees)$\times D^{0}$ -0.147 ∗∗∗ -0.109 ∗∗∗ -0.141 ∗∗∗ -0.101 ∗∗∗
(0.001) (0.03) (0.001) (0.007) log(Capital/Employees) $\times(1-D^{0})$ 0.304
∗∗∗ 0.194 ∗∗∗ 0.300 ∗∗∗ 0.186 ∗∗∗ (0.002) (0.023) (0.001) (0.009)
log(Capital/Employees) $\times D^{0}$ 0.293 ∗∗∗ 0.198 ∗∗∗ 0.289 ∗∗∗ 0.174 ∗∗∗
(0.002) (0.016) (0.002) (0.007) log(R&D/Employees) 0.046 ∗∗∗ 0.064 ∗∗∗ 0.081
∗∗∗ 0.079 ∗∗∗ (0.005) (0.02) (0.002) (0.009) $D^{0}$: Dummy Zero R&D 0.047 ∗∗∗
0.067 ∗∗∗ -0.308 ∗∗∗ -0.276 ∗∗∗ (0.001) (0.009) (0.001) (0.013) log(Intra-
industry R&D)$\times(1-D^{0})$ 0.022 ∗∗∗ 0.019 ∗∗∗ (0.003) (0.001) log(Intra-
industry R&D)$\times D^{0}$ 0.025 ∗∗∗ 0.01 (0.002) (0.001) log(Inter-industry
R&D)$\times(1-D^{0})$ -0.009 -0.04 (0.007) (0.009) log(Inter-industry R&D)
$\times D^{0}$ 0.035 ∗∗∗ 0.015 ∗∗ (0.001) (0.001) Age 0.000 0.017 0.003 -0.005
(0.001) (0.019) (0.002) (0.008) North Estonia 0.326 ∗∗∗ 0.268 ∗∗∗ 0.192 ∗∗∗
0.314 ∗∗∗ (0.002) (0.009) (0.000) (0.009) Test of Equality of Elasticity of
Productivity with respect to Capital for firms with and without R&D. Test
Statistic: $C$ 6.92 ∗∗∗ 0.06 6.03 ∗∗ 0.78 $\mathrm{Pr}(\chi^{2}(1)>C)$ 0.008
0.799 0.014 0.376 No. of Observations 6086 1500 5877 1464 No. of Firms 2443
1072 2394 1052 Note: Dependent Variable: log(Value-Added/Employees). Every
specification includes Time and Industry Dummies. Significance levels : $\ast$
: 10% $\ast\ast$ : 5% $\ast\ast\ast$ : 1%

Table 4: Comparison of Elasticity of Productivity with respect to Own R&D and
Capital with those obtained for Germany

| Specification: Baseline | Specification: Baseline + External Knowledge
---|---|---
| Method: ACF | Method: OP | Method: ACF | Method: OP
| Incumbent | Entrant | Incumbent | Entrant | Incumbent | Entrant | Incumbent | Entrant
| (1a) | (1b) | (1c) | (1d) | (2a) | (2b) | (2c) | (2d)
Estonia
log(Capital/Employees) $\times(1-D^{0})$ | 0.304 | ∗∗∗ | 0.194 | ∗∗∗ | 0.179 | ∗∗∗ | 0.164 | ∗∗∗ | 0.300 | ∗∗∗ | 0.186 | ∗∗∗ | 0.193 | ∗∗∗ | 0.128 | ∗∗∗
| (0.002) |  | (0.023) |  | (0.017) |  | (0.057) |  | (0.001) |  | (0.009) |  | (0.002) |  | (0.033) |
log(Capital/Employees) $\times D^{0}$ | 0.293 | ∗∗∗ | 0.198 | ∗∗∗ | 0.148 | ∗∗∗ | 0.116 | ∗∗ | 0.289 | ∗∗∗ | 0.174 | ∗∗∗ | 0.176 | ∗∗∗ | 0.074 | ∗∗∗
| (0.002) |  | (0.016) |  | (0.017) |  | (0.051) |  | (0.002) |  | (0.007) |  | (0.002) |  | (0.027) |
log(R&D/Employees) | 0.046 | ∗∗∗ | 0.064 | ∗∗∗ | 0.026 | ∗∗ | 0.032 | ∗∗ | 0.081 | ∗∗∗ | 0.079 | ∗∗∗ | 0.062 | ∗∗∗ | 0.037 | ∗∗
| (0.005) |  | (0.02) |  | (0.012) |  | (0.015) |  | (0.002) |  | (0.009) |  | (0.002) |  | (0.009) |
Germany
log(Capital/Employees) | 0.127 | ∗∗∗ | 0.281 | ∗∗∗ | 0.076 | ∗∗∗ | 0.147 | ∗∗∗ | 0.133 | ∗∗∗ | 0.255 | ∗∗∗ | 0.021 |  | 0.148 | ∗∗∗
| (0.000) |  | (0.001) |  | (0.026) |  | (0.029) |  | (0.002) |  | (0.003) |  | (0.026) |  | (0.007) |
log(R&D/Employees) | 0.057 | ∗∗∗ | 0.125 | ∗∗∗ | 0.024 | ∗∗∗ | 0.029 | ∗∗∗ | 0.050 | ∗∗∗ | 0.120 | ∗∗∗ | 0.022 | ∗∗∗ | 0.026 | ∗∗∗
| (0.002) |  | (0.002) |  | (0.004) |  | (0.010) |  | (0.002) |  | (0.003) |  | (0.002) |  | (0.009) |
Note: Lubczyk and Peters (2020) estimated the elasticities using two different
control function methods: one, the method by ACF, and the other by Olley and
Pakes (1996) (OP). For the purpose of comparison, we also estimate using both
the methods. The dependent variable is log(Value-Added/Employees) when
employing ACF and log(Revenue/Employees) when employing OP. Also, though not
reported here, log(Material/Employees) interacted with $D^{0}$ and $1-D^{0}$
are additional explanatory variables when using the OP method, where $D^{0}$
is a dummy variable that takes value 1 if the firm reports zero R&D expense.
Every specification includes Time and Industry Dummies.
Significance levels : $\ast$ : 10% $\ast\ast$ : 5% $\ast\ast\ast$ : 1% |  |  |  |  |  |  |  |  |  |  |  |  |  |

Table 5: Productivity Elasticity with respect to R&D for (a) firms in High-Tech and Medium-High-Tech Manufacturing and (b) firms in the Remaining Sectors  | Specification: Baseline |  Specification: Baseline + External Knowledge
---|---|---
| Incumbent | Entrant | Incumbent | Entrant
log(R&D/Employees) $\times D_{HM}$ | 0.061 | ∗∗∗ | 0.045 | ∗∗ | 0.094 | ∗∗∗ | 0.074 | ∗∗∗
| (0.002) |  | (0.021) |  | (0.006) |  | (0.005) |
log(R&D/Employees) $\times(1-D_{HM})$ | 0.037 | ∗∗∗ | 0.080 | ∗∗∗ | 0.085 | ∗∗∗ | 0.091 | ∗∗∗
| (0.001) |  | (0.022) |  | (0.001) |  | (0.005) |
Test of Equality of Elasticity of Productivity with respect to R&D for (a)
firms in High-Tech and Medium-High-Tech Manufacturing and (b) firms in the
Remaining Sectors
Test Statistic: $C$ | 10.04 | ∗∗∗ | 1.51 |  | 68.4 | ∗∗∗ | 4.50 | ∗∗
$\mathrm{Pr}(\chi^{2}(1)>C)$ | (0.00) |  | (0.22) |  | (0.00) |  | (0.03) |
Note: $D_{HM}$ is binary variable that takes value 1 if the firm is in the
high-tech manufacturing or medium-high-tech manufacturing and 0 otherwise. For
lack of space, we only display the productivity elasticities with respect to
R&D for (a) firms in the high-tech and medium-high-tech manufacturing and (b)
firms in the remaining sectors.
Significance levels : $\ast$ : 10% $\ast\ast$ : 5% $\ast\ast\ast$ : 1% |  |  |  |  |  |
Table 6: Description of innovative activity: Product
($\mathcal{P}^{D}_{jt}=1$) and Process ($\mathcal{P}^{C}_{jt}=1$) Innovation

Incumbents
---
| $\mathcal{P}^{C}_{jt}=1$ | $\mathcal{P}^{C}_{jt}=0$ | Total
$\mathcal{P}^{D}_{jt}=1$ | 1695 | 1650 | 3345
| (27.85) | (27.11) | (54.96)
$\mathcal{P}^{D}_{jt}=0$ | 956 | 1785 | 2741
| (15.71) | (29.33) | (45.04)
Total | 2651 | 3435 | 6086
| (43.56) | (56.44) | (100)

Entrants
---
| $\mathcal{P}^{C}_{jt}=1$ | $\mathcal{P}^{C}_{jt}=0$ | Total
$\mathcal{P}^{D}_{jt}=1$ | 329 | 333 | 662
| (21.93) | (22.2) | (44.13)
$\mathcal{P}^{D}_{jt}=0$ | 260 | 578 | 838
| (17.33) | (38.53) | (55.87)
Total | 589 | 911 | 1500
| (39.27) | (60.73) | (100)

Note: Cell percentage in parentheses.

Table 7: Average Treatment Effect of Technological Innovation on Estimated Total Factor Productivity for Entrants and Incumbents | Specification: Baseline | Specification: Baseline +
---|---|---
|  | External Knowledge
| Incumbent | Entrant | Incumbent | Entrant
ATE of Product and/or Process | 0.129 | ∗∗ | 0.267 | ∗∗∗ | 0.102 | ∗ | 0.191 | ∗∗∗
Innovation, $I_{jt}$, on Productivity: $\Delta$ | (0.051) |  | (0.072) |  | (0.054) |  | (0.079) |
No. of matches for computing the ATE | 1001 | 378 | 1000 | 346
ATE of only Product | 0.097 | ∗ | 0.193 |  | 0.116 | ∗∗ | 0.135 |
Innovation on Productivity: $\Delta_{10}$ | (0.057) |  | (0.123) |  | (0.058) |  | (0.196) |
No. of matches for computing the ATE | 934 | 123 | 910 | 114
ATE of only Process | 0.048 |  | 0.227 | ∗∗ | 0.066 |  | 0.223 | ∗∗
Innovation on Productivity: $\Delta_{01}$ | (0.046) |  | (0.089) |  | (0.047) |  | (0.107) |
No. of matches for computing the ATE | 1286 | 172 | 1250 | 158
ATE of Product and Process | 0.134 | ∗∗∗ | 0.305 | ∗∗∗ | 0.122 | ∗∗∗ | 0.300 | ∗∗∗
Innovation on Productivity: $\Delta_{11}$ | (0.043) |  | (0.093) |  | (0.045) |  | (0.104) |
No. of matches for computing the ATE | 1414 | 198 | 1381 | 183
Mean of Productivity | 7.496 | 8.235 | 7.879 | 8.894
Standard Deviation of Productivity | 0.742 | 0.832 | 0.735 | 0.815
Note: While estimating estimating $\Delta$, we matched ‘exactly’ on year
dummies (2006 to 2018) and 2-digit industry dummies, and matched to ‘nearest
neighbourhood’ on the lags of the variables mentioned in the text. However,
because there were much fewer firms who only innovated products, only
innovated processes, or both, we could not match ‘exactly’ on industry dummies
while estimating $\Delta_{10}$, $\Delta_{01}$, and $\Delta_{11}$. As a result
of two different matching criteria, we find that for the incumbents, the
number of matches are higher when estimating $\Delta_{10}$, $\Delta_{01}$, and
$\Delta_{11}$ even as the number of incumbents who only innovated products, or
only innovated processes, or both were, by definition, smaller than the number
of incumbents who innovated either products, or processes, or both.
Significance levels : $\ast$ : 10% $\ast\ast$ : 5% $\ast\ast\ast$ : 1% |  |  |  |  |  |