Employment effect of innovation.
Date: 2019-04-11
Institutions: Joint Research Centre
Subjects: econometrics, employment policy, investment, job creation, multinational enterprise, research and development, technological change

Employment Effect of Innovation 

d’Artis Kancs 

Boriss Siliverstovs 

2019 

JRC Working Papers in Economics and Finance, 2019/2 

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Name: d'Artis Kancs 
Address: European Commission, DG Joint Research Centre, Via E. Fermi 2749, 21027 Ispra, Italy. 
Email: d'artis.kancs@ec.europa.eu 
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JRC114588 

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ISBN 978-92-76-00041-9 

ISSN 2467-2203 

doi:10.2760/52757 

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Employment Effect of Innovation(cid:73)

d’Artis Kancsa,b,∗, Boriss Siliverstovsc,d

aEuropean Commission, Joint Research Centre, I-21027 Ispra, Italy 
b LICOS, University of Leuven, B-3000 Leuven, Belgium
cBank of Latvia, LV-1050 Riga, Latvia
dKOF Swiss Economic Institute, ETH Zurich, CH-8092 Zurich, Switzerland

Abstract

We provide a novel evidence about the innovation-employment nexus by decomposing
it by R&D intensity in a continuous setup and relaxing the linearity assumption. Using a
large international ﬁrm-level panel data set for OECD countries and employing a ﬂexible
semi-parametric method – the generalised propensity score – allows us to recover the full
functional relationship between the R&D-driven innovation and ﬁrm employment as well
as address important econometric issues, which is not possible in the standard estimation
approach used in the previous literature. Our results conﬁrm that the relationship
between innovation and employment entails important non-linearities responsible for
signiﬁcant differences in employment response to innovation at different R&D intensity
levels.

Keywords: R&D investment, employment, propensity score, ﬁrm-level data.
JEL code: C14, C21, F23, J20, J23, O30, O32, O33.

(cid:73)

The authors acknowledge helpful comments from Francesco Bogliacino and Daria Ciriaci, Mihails
Hazans, Enkelejda Havari, the editor of the journal, two anonymous referees, participants of the conferences
on Counterfactual Methods for Policy Impact Evaluation in Rome and Milan, the Scottish Economic Society
Annual Conference in Perth and the 57th Meeting of the Italian Economic Association in Milan as well
as participants of the research seminars at the European Commission, Bank of Latvia, KU Leuven and
Stockholm School of Economics in Riga. We are grateful to Alexander Tübke for granting access to the EU
Industrial R&D Investment Scoreboard data. The authors are solely responsible for the content of the paper.
The views expressed are purely those of the authors and may not under any circumstances be regarded
as stating an ofﬁcial position of the European Commission or the Bank of Latvia. Computations were
performed in R (R Development Core Team, 2008).

∗Corresponding author, Competence Centre on Modelling, European Commission.
Email address: d’artis.kancs@ec.europa.eu (d’Artis Kancs)

1. Introduction

In setting the Europe 2020 Strategy, the European Union (EU) has deﬁned ﬁve am-
bitious objectives – on employment, innovation, education, social inclusion and cli-
mate/energy – to be reached by 2020 (European Commission, 2013). Concerning the ﬁrst
two targets, the Strategy aims at: (i) increasing employment by raising the employment
rate of population to at least 75%; and (ii) promoting innovation by increasing research
and innovation expenditures to at least 3% of the GDP.

In the context of these two Europe 2020 Strategy’s objectives, an important policy
question arises whether innovation and employment processes can be complementary
and hence their EU targets can be achieved at the same time? Further, policy makers are
interested to know: (i) are there R&D intensity levels when innovation and employment
are positively related to each other and when innovation may have an adverse impact on
the ﬁrm employment? (ii) what type of innovators create most jobs and hence provide the
highest potential for policy synergies? Answering these questions is the main objective of
the present study, as they may help to design policies, which can efﬁciently contribute to
achieving both the innovation and employment targets of the Europe 2020 Strategy at the
same time.

At a ﬁrst glance, a simultaneous boosting of both employment and innovation may
seem an easy and most natural task to achieve as any type of investments (including
R&D) increases the labour demand, at least in the short-run. However, the theoretical
literature suggests that the relationship between innovation and employment seems to
be far more complicated than one can naively assume initially (Smolny, 1998). Also
the econometric results reported in the literature on employment effects of innovation
are rather contradictory both with respect to their sign and magnitude, suggesting
that increasing the innovation intensity can have not only complementary but also
substitutionary effects on employment (Young, 1993; Piva and Vivarelli, 2005; Antonucci
and Pianta, 2002; Van Reenen, 1997).

In order to accommodate a wide range of possibilities in the innovation-employment
relationship ranging from highly negative to strongly positive, in the present study
we propose an alternative methodological approach that has not been employed in the
innovation-employment literature before. In particular, we relax the linearity assumption
in the functional relationship between innovation and employment and hope that it will
contribute towards sorting out the likely reasons for observing such a large range of
estimated employment elasticities with respect to the ﬁrm innovation activity. There
are several reasons why the innovation-employment relationship may be non-linear.
Conceptually, the non-linearities in the functional relationship between innovation and
employment may arise, for example, due to the coexistence of many mutually inter-

1

dependent transmission mechanisms and general equilibrium feedback loops, as the
employment effect of innovation depends, among others, on the nature of innovation
(product or process innovation); the purpose of innovation (to save labour or capital,
neutral, or biased towards skills) and other factors (Pianta, 2004). Empirically, the employ-
ment effect of innovation depends on the ﬁrm’s sector of activity; formal and informal
institutions; the time frame of analysis; speciﬁcs of the existing production technology;
dimensions of innovation (radical or incremental); consumer preferences; the ﬁerceness
of competition in intermediate input and labour markets; the structure of workforce
skills, etc. which all contribute to differentiated employment effects at different innova-
tion intensities (Bogliacino and Vivarelli, 2012; Bogliacino et al., 2012; Lachenmaier and
Rottmann, 2007).

If the functional relationship between innovation and employment would indeed be
non-linear – a fact conﬁrmed in our econometric analysis – then an accurate estimation
of the functional relationship would depend crucially on the ability to account for these
non-linearities in the innovation-employment nexus, which is highly challenging. Due
to complexities related to a suitable counterfactual at the ﬁrm level and methodological
challenges in the estimation approach, however, there are no studies available in the
literature yet, that would attempt to account for non-linearities in the R&D and ﬁrm
employment relationship in a continuous non-linear setting. The present study attempts
to ﬁll this research gap and estimate the full functional relationship between the ﬁrm’s
innovation and employment in a continuous setup.

To achieve this objective, we rely on a ﬂexible semi-parametric method – the gener-
alised propensity score (GPS) estimator – suggested by Hirano and Imbens (2004). Two
main features of the GPS methodology make it particularly attractive for our purpose: (i)
estimation can be based on a ﬂexible semi-parametric regression allowing for a non-linear
dependence between the variables of interest without imposing any a priori restrictions;
and (ii) the elimination of the selection bias arising from a non-random assignment of
treatment (R&D expenditure) intensity across ﬁrms by conditioning on the observed
ﬁrm characteristics. In applying the GPS methodology, we attempt to identify the R&D
intensity levels under which innovation can be complementary to employment and under
which it may have an adverse impact on employment. To the best of our knowledge,
the application of a ﬂexible semi-parametric counterfactual methods to the employment-
innovation nexus is the ﬁrst of this sort in literature and hence constitutes our main
contribution to literature.

We base our micro-econometric analysis on a large international ﬁrm-level panel data
set for OECD countries and our proxy for technology is a measurable and continuous
variable, while most of previous studies have relied on either indirect proxies of the
technological change or dummy variables (such as the occurrence of product and process

2

innovation). In particular, we employ the EU Industrial R&D Investment Scoreboard
data set, which comprises data on the R&D investment, as well as other ﬁnancial and
economic variables for the top 2500 innovators worldwide. In addition to ﬁrm-level R&D
expenditures, we make use also of other economic and ﬁnancial variables, which allow us
to control for important ﬁrm-speciﬁc characteristics. Moreover, the Scoreboard data also
allow to identify the industrial sector (of the parent subsidiary) as well as the geographical
region of the R&D investment (according to the location of the ﬁrm’s headquarter), which
allows us to control for ﬁxed sector-speciﬁc and location-speciﬁc effects.

Our results enhance previous ﬁndings by facilitating to connect dots of existing point
estimates in literature. Our ﬁndings conﬁrm that the relationship between innovation and
employment entails important non-linearities. There are notable difference in reaction
of employment to the innovation activity of the ﬁrm, depending on the actual level of
the R&D intensity. It is also worthwhile mentioning that our results also remind that the
innovation impact on employment can be negative too – ﬁndings that have been reported
also in previous studies (Pianta, 2004). For example, in our sample this is the case for
companies operating in high-tech sectors, characterising by a comparatively high levels of
the innovation activity. These results imply that a further increase in R&D expenditures by
in high-tech sectors can have a non-negligible labour-saving effect. Furthermore, we ﬁnd
that the labour-saving effect of innovation could also be detected for companies operating
in low- and medium-low-tech sectors, though this effect is much less pronounced than
for highly innovative ﬁrms.

The rest of the paper is organised as follows. Next section contains a review of the
relevant literature. In Section 3 we describe the econometric methodology. The data is
described in Section 4. The empirical results are presented in Section 5. The ﬁnal section
contains conclusions and sets an outline for future research agenda.

2. Previous literature

The question of whether the technological change creates or destroys jobs has been

posed since the beginning of the classical economics of Karl Marx (1867):

"Suppose that the making of the new machinery affords employment to a greater
number of mechanics, can that be called compensation to the carpet makers, thrown
on the streets?" (Marx (1867): 479).

Ciriaci et al. (2013), Bogliacino et al. (2012), Bogliacino and Vivarelli (2012) and
Bogliacino (2014) were among ﬁrst attempts to decompose the employment effect of
innovation according to R&D intensity levels. Using a balanced panel comprising of
3300 Spanish ﬁrms observed of the period 2002-2009, Ciriaci et al. (2013) investigated the

3

employment effect of innovation both for innovative and non-innovative ﬁrms. Ciriaci
et al. (2013) found that those ﬁrms, which engage more intensively in innovation activities,
create more jobs than less innovative ﬁrms. In particular, this effect is more pronounced
for small and young innovative ﬁrms. At the same time they pointed out that for this
group of ﬁrms, a successful launch of new products in the market as a result of boosting
the innovation activity can lead to a higher growth in sales rather than in employment,
which is consistent with the labour-saving effects of technological advances, discussed
above.

Bogliacino et al. (2012) studied the employment effect of R&D expenditure using the
sample of 677 EU ﬁrms observed during the period 1990-2008. Employment elasticities
were estimated using a dynamic panel model allowing for lagged employment by means
of the Least Squares Dummy Variable Corrected (LSDVC) estimator (Bun and Kiviet,
2003; Bruno, 2005). The results were obtained for the sample of all ﬁrms as well as for
sub-samples comprising service-sector ﬁrms, all manufacturing ﬁrms and sub-samples
comprising manufacturing ﬁrms further subdivided into high-tech and non-high-tech
ﬁrms. The estimated short-run elasticities were 0.023% for the whole sample, 0.056% for
service-sector ﬁrms, and 0.049% for high-tech manufacturing ﬁrms. Interestingly, also the
corresponding elasticity estimate for non-high-tech manufacturing ﬁrms was also positive
(0.021%), though not statistically signiﬁcant. Using the estimated coefﬁcient on the lagged
employment variable Bogliacino et al. (2012, Table 1) derived long-run employment
elasticities. The long-run elasticity of employment calculated for the whole sample were
0.075%, 0.097% for service-sector ﬁrms and approximately of equal magnitude of 0.11%
both for all manufacturing ﬁrms and high-tech manufacturing ﬁrms.

Bogliacino and Vivarelli (2012) conducted study on the employment effect of innova-
tion activity using a sample of 2295 ﬁrms from 15 European countries available over the
period 1996—2005. All main results of this study were reported for a number of dynamic
panel data estimators such as random-effects, ﬁxed-effects as well as two versions of the
Generalised Method of Moments [GMM-DIF, Arellano and Bond (1991)] and [GMM-SYS,
Blundell and Bond (1998)], where the last estimator could be identiﬁed as the most reliable
one (Bogliacino and Vivarelli, 2012, Section IV). These estimators were applied for the
whole sample of ﬁrms. The short-run elasticity reported by the GMM-SYS estimator was
0.025%, which was very similar to that reported in Bogliacino et al. (2012). However, the
long-run elasticity was about 0.31%, which was about four times larger than that reported
in Bogliacino et al. (2012) for the whole sample (0.075%). In order to ensure robustness
of estimation results, a distinction was made between ﬁrms with different levels of the
technological sophistication, by allowing for differential employment effects of high-tech,
medium-tech and low-tech ﬁrms. Employment elasticities were obtained by means of the
LSDVC rather than the GMM estimator; as the former estimator outperformed the latter

4

one under given estimation conditions. The main result of Bogliacino and Vivarelli (2012)
was that the job creation effect of the R&D expenditure only was evident for the high-tech
sector; both for medium- and low-tech sectors the estimated short-run elasticities were not
signiﬁcantly different from zero. For the high-tech sector, short- and long-run elasticities
were 0.017% and 0.17%, respectively.

3. Econometric strategy

In light of the diversity in the channels of adjustment and the reverse causality of
interdependencies between innovation and employment, the existing evidence discussed
in Section 2 suggests that very likely the functional relationship between these two
processes is more nuanced than point estimates from previous studies are able to tell us.
This implies that an accurate estimation of the functional relationship depends crucially on
the ability to account for potential non-linearities in the innovation-employment nexus. In
order to allow for a differentiated impact of innovation on employment while accounting
for differences among ﬁrms at different R&D intensity levels, an appropriate estimation
approach is required which does not average across all innovators and employers, but
instead allows for a differentiated employment effect at various R&D intensity levels.

To estimate the full functional relationship between innovation and employment,
we rely on the generalised propensity score (GPS) approach introduced in Hirano and
Imbens (2004).1 The GPS approach is a further elaboration on the popular binary
treatment propensity score estimator of Rosenbaum and Rubin (1983) widely used for
impact evaluations of various programs.2 In the context of the present study, the relevant
features of the GPS methodology are as follows. First, it allows for continuous rather than
binary treatment levels. Second, it allows to estimate the treatment effect also without
a ‘zero’ control group. Third, the GPS procedure eliminates the selection bias arising
due to a non-random assignment (choice) of treatment (R&D) intensity across ﬁrms by
conditioning on observed ﬁrm characteristics. Finally, it captures potential non-linearities
in the functional relationship between the R&D investment and ﬁrm employment, as it
relies on a ﬂexible semi-parametric speciﬁcation.3 As result, the estimated dose-response
functions allow to retrieve the entire interval of average and marginal treatment effects
over all possible treatment levels (R&D intensity).

1This approach was already applied to the following pairs of variables: R&D intensity and productivity
in Kancs and Siliverstovs (2016), migration and trade in Egger et al. (2012), and growth effects of the
regional policy in the European Union in Becker et al. (2012), inter alia.

2For an accessible presentation of the logic underlying the propensity-score matching, see Heinrich et al.

(2010).

3According to Bia et al. (2011), the estimated dose-response function is robust to the choice of a

semi-parametric approach, but it is sensitive to a parametric speciﬁcation.

5

The counterfactual framework of the dose-response analysis naturally involves a
dose or treatment variable – R&D intensity and a response variable – employment, both
observed for ﬁrm i. The difference between usual analysis, typically based on the OLS
regression of the response variable on the treatment variable, is that one introduces an
additional auxiliary variable, called the generalised propensity score, when modelling the
dose-response relationship between the variables of interest. The generalised propensity
score is derived from a vector of observed covariates for ﬁrm i, Xi, and its primary purpose
is to remove estimation and inference biases related to non-random dose assignment in
the data sample, as discussed above.

Application of the GPS methodology in order to estimate the dose-response analysis
typically involves the following three steps (Hirano and Imbens, 2004). In the ﬁrst step
the GPS variable is constructed using the OLS regression of the treatment variable, ri, or,
as most often in literature, its logarithmic transformation, ln ri, on a vector of continuous
and categorical covariates, Xi, characterising each ﬁrm i in the data set:

ln ri = X(cid:48)

i γ + εi,

εi ∼ N(0, σ2).

(1)

Observe that a usual assumption that is made is that the distribution of the error terms
is normal with variance σ2. If this assumption is supported by the data then the GPS
variable is deﬁned as the normal probability density function estimated for the regression
residuals:

(cid:98)si =

√

1
2π(cid:98)σ2

(cid:20)

exp

−

(cid:21)

2

1
2(cid:98)σ2 (cid:98)εi

.

(2)

Hirano and Imbens (2004, Section 7.4) mention that other more ﬂexible distributions can
be used in case if the normality assumption is not supported by the data, for example, this
could be mixture of several normal distributions or a normal heteroscedastic distribution,
which variance is a function of covariates. Alternatively, the departures from normality
can be accommodated by non-parametric approach that relies on the kernel probability
density estimation. In the empirical part of the paper, we resort to the latter option,
since we ﬁnd that the normality assumption is violated in our sample. To the best of our
knowledge, this is the ﬁrst attempt to rely on non-parametric methods for estimation of the
generalised propensity score in the literature and it serves as an additional methodological
contribution to the relevant literature.

The propensity score in Equation (2) fulﬁls its purpose of measuring the degree of
similarity across heterogeneous ﬁrms when the so-called balancing property is satisﬁed,
i.e. for those ﬁrms with assigned equal propensity scores (conditional on ﬁrm-speciﬁc
covariates) the associated treatment level is independent from ﬁrm characteristics. In
this step, we follow the test procedures of Hirano and Imbens (2004) in order to verify

6

whether the balancing property is not violated in our data sample.

In the second step, the expected value of response variable, ln ωi, is modelled as a
ﬂexible semi-parametric function of the treatment variable and the estimated generalised
propensity score, ln ri and si, respectively:

E[ln ωi| ln ri, si] = Incpt + α11 ∗ ln ri + α12 ∗ [ln ri]2 + α13 ∗ [ln ri]3

(3)

+ α21 ∗ si + α22 ∗ [si]2 + α23 ∗ [si]3
+ α3 ∗ (ln ri ∗ si),

where the latter variable is substituted with its estimates, (cid:98)si, from the ﬁrst step. The
ﬂexibility of the functional form can be controlled for by varying the power of variables
ln ri and si and their cross-products.

The average expected response of the response variable, ω, for a given treatment dose,

ρ, is estimated in the third step:

E[ln (cid:98)ω(ln ρ)] =

1
N

N
∑
i=1

(cid:104) (cid:91)Incpt + (cid:98)α11 ∗ ln ρ + (cid:98)α12 ∗ [ln ρ]2 + (cid:98)α13 ∗ [ln ρ]3

(4)

+ (cid:98)α31 ∗ (cid:98)s(ln ρ, Xi) + (cid:98)α32 ∗ [(cid:98)s(ln ρ, Xi)]2 + (cid:98)α33 ∗ [(cid:98)s(ln ρ, Xi)]3
+(cid:98)α3 ∗ (ln ρ ∗ (cid:98)s(ln ρ, Xi))] ,

where the coefﬁcient estimates from Equation (3) are used. The whole dose-response
function is obtained by computing Equation (4) for each treatment level by using a grid
of values in the corresponding range of the treatment variable.

In the ﬁnal step, we derive the treatment effect function as a ﬁrst derivative of
E[ln (cid:98)ω(ln ρ)] with respect to argument ln ρ. By deﬁnition the treatment effect function
computed in this way measures estimated employment elasticity with respect to R&D,
allowing us to directly compare our results with those reported in the existing literature.
Following Hirano and Imbens (2004), conﬁdence intervals around the estimated dose-
response and treatment effect functions are obtained by means of a bootstrap procedure.

4. Data sources, sample and variable construction

4.1. Data sources

The principal data source is the EU Industrial R&D Investment Scoreboard maintained
by the European Commission. The R&D Scoreboard is an annual data set that comprises
ﬁrm-level data on the R&D investment, as well as other ﬁnancial and economic variables
(e.g. net sales, operating proﬁts, employees) for the top 2500 R&D performers worldwide.
In addition to economic and ﬁnancial variables, the R&D Scoreboard also identiﬁes the

7

main industrial sector (of the parent company) as well as the geographical region of R&D
investment (according to the location of company’s head-quarter).

An important limitation of the R&D Scoreboard data concerns the issue of non-random
sample selection, putting under question the general validity of our results. Given the
underlying sampling and selection rules of the R&D Scoreboard data set – ranking and
selecting companies according to the total amount of their R&D expenditures – the
R&D Scoreboard is not a random sample. Hence the R&D Scoreboard data set may be
criticised that it has a sample bias affecting the results, as it only represents top R&D
investors. However, given our interest in the employment effect of innovation, this issue
is of lower order of magnitude, because we are covering almost the entire population of
the world-wide R&D investment (Moncada-Paterno-Castello et al., 2010). As described
below, out of the 2500 ﬁrms listed in the R&D Scoreboard data only for 1659 companies
there were complete data records, prompting us to analyse the available data.4 Still, these
1659 Scoreboard’s companies selected for the present study represent around 80% of
the world-wide business R&D expenditure. While small R&D investors and non-R&D-
performers are excluded from our sample, the aim of the present study is to focus on the
impact of the R&D-driven innovation on employment, but not to examine determinants
of the labour demand in the entire economy. Finally, the particular estimation approach
that we adopt in the present study allows us to estimate counterfactual treatment effects
also without a zero control group.

4.2. Sample construction

In the present study, we use R&D Scoreboard data for the last four available years:
2014-2017. Our choice of this sample is motivated by the fact that it is a reasonably long
period apart from the Great Financial Crisis (GFC) that undoubtedly had pronounced
effects on the ﬁrms’ investment activity. Including observations from years during the
GFC and shortly after its outbreak had a distortive impact on the long-run relationship
between innovation and employment prevailing in the business-as-usual environment
that we aim to capture in our study.

Since the Scoreboard involves individual ﬁrm-level data covering many countries,
industries and technological levels of sophistication, it is rather unsurprising that due to
all this incumbent data heterogeneity the annual data for top 2500 Scoreboard companies
forms an unbalanced panel. There are ﬁrms that were not present among the top 2500
R&D performers either in the beginning or in the end of the sample period or even at
the both ends of the sample period and hence have missing observations. There are also
ﬁrms that were present in the top 2500 Scoreboard sample at the beginning and at the end

4Companies which do not disclose ﬁgures for R&D investment or which disclose only ﬁgures which are

not material enough were also omitted from our analysis.

8

but have missing data points for some years within our sample period. All this implies a
loss of observations, if our identiﬁcation strategy aimed at exploiting both inter-temporal
and cross-sectional dimensions of a balanced panel. Another option would be to focus
solely on the cross-sectional dimension for a particular year, but this again involves loss
of information as well as a certain arbitrariness in the choice of the particular year. Hence,
in order to retain as many observations as possible, we construct our sample from ﬁrms
for which there are at least two consecutive years of observations for all variables of our
interest. For these ﬁrms, we compute averages of their characteristics using the available
observations. This helps us smoothing year-on-year ﬂuctuations in our data and avoid a
potential source of outlier bias.

Finally, we did a sanity check for the resulting sub-sample of ﬁrms and ﬁltered out
ﬁrms that have extreme values of the R&D intensity which, as discussed in Section 4.3, is
deﬁned as the ratio of the R&D investment to net sales. In particular, we removed ﬁrms
for which the estimated R&D intensity exceeds unity. For this sub-group of ﬁrms the
median R&D intensity is 6, whereas the maximum is 1210. It turns out that all these ﬁrms
are characterised by a rather small actual employment (the median employment is 113
persons) and a negative operating proﬁt. The former fact indicates that the share and
hence the impact of these ﬁrms on the total employment is rather small. Moreover, the
latter fact indicates that such business model / innovation pattern is not sustainable in
the long run. Therefore, in order to make our sample more homogeneous we treat these
ﬁrms as outliers that need to be removed from the empirical analysis. As a result of data
cleaning, we are left with 1659 observations that form the basis for our empirical analysis.

4.3. Data set

The dependent (response) variable is a ﬁrm-speciﬁc employment measured by the
number of employees (EMPL). For each ﬁrm in our sample we use the average number
of employees for the available years. These companies included in our sample data
employed around 44.1 mln. workers with largest shares of about 10.6 and 14.5 mln.
workers pertain to companies registered in the US and the EU. The R&D investment
totalled 2,028 milliard Euro with about 42% and 28% of the total sum is attributable to
the companies from the US and the EU, with the Japan and China accounting for about
17% and 6%, respectively.5

The remaining ﬁrm characteristics (Net sales (NSALES), Operating proﬁt (OP), Capital
expenditure (CAPEX)) contained in the Scoreboard were complemented with Market

5Note, however, that data reported by the Scoreboard companies do not inform about the actual
geographic distribution of the number of employees. A detailed geographic analysis should take into
account the location of subsidiaries of the parent Scoreboard companies as well as the location of other
production activities involved in the value-chains.

9

capitalisation (MCAP) sourced from both the Financial Times London Share Service and
Reuters. In order to create a relative measure of R&D expenditure that takes into account
ﬁrm commercial size, we create the treatment variable (R&D intensity) as the ratio of the
nominal R&D expenditure to Net sales.

There are several categorical dummy variables indicating level of technological sophis-
tication (low-tech, medium-low tech, medium-high tech and high-tech) that are further
sub-divided into industrial sectors according to the ICB classiﬁcation as well as dum-
my variables indicating countries. Further details on the deﬁnitions of the explanatory
variables is provided in the online appendix.

Table 1: Median values for variables by tech sector

Tech
sector

Obs.

EMPL
(number)

R&D
(â ´C ˇnmln.)

high
medium-high
medium-low
low

649
718
105
187

4200
10898
14073
20960

79.8
63.8
76.1
74.0

R&D
sectoral
share1

0.532
0.363
0.042
0.063

R&D
intensity

OP
(â ´C ˇnmln.)

NSALES
(â ´C ˇnmln.)

CAPEX
(â ´C ˇnmln.)

MCAP
(â ´C ˇnmln.)

0.115
0.034
0.016
0.011

87.6
184.2
348.3
567.4

907
2368
4636
9589

40.2
95.6
206.6
435.2

2622
2724
5562
5929

1 Indicates share of each tech sector in total volume of R&D expenditure.

The set of covariates used in our analysis is selected based on previous studies (e.g.
see Hall et al., 2008), subject to their availability in our data set. In order to provide an
impression on the magnitude of the main ﬁrm characteristics and their relationship to the
variables of our main interest we report median values of these characteristics evaluated
at each level of technological sophistication, see Table 1.

The ﬁrst observation is that the number of ﬁrms belonging either to high- or medium-
high tech sectors (1367) is much larger than the number of ﬁrms belonging either to low-
or low-tech sectors (292). Such an over-representation of the high-tech ﬁrms in the sample
naturally reﬂects the original intention of collecting and maintaining the database on the
world top R&D performers. In terms of employment, a median ﬁrm-speciﬁc employment
is inversely proportional to the level of technological sophistication: in the high-tech
sector the median employment is 4200 whereas in the low-tech sector it comprises 20960
employees. In nominal terms, the median level of R&D expenditure is about the same
across the different tech sectors with a typical value about 60-80 mln. Euro. However, the
sector-speciﬁc share of R&D expenditure is not equally distributed as indicated in the
column "R&D sectoral share". The lion’s share of the total R&D expenditure (about 90%)
is accounted for the ﬁrms in high- or medium-high tech sectors.

As far as the treatment variable (R&D intensity) concerns, the median level is highest
for the ﬁrms in the high-tech sector and it continuously decreases with the level of the
10

technological sophistication. A median ﬁrm in the high-tech sector spends about 11.5%
of its net sales volume on R&D, whereas the corresponding share for a median ﬁrm in
the low-tech sector is about 1%.

It is also interesting to observe that the median values of the ﬁnancial variables like
operating proﬁt, net sales, capital expenditure, and market capitalisation are highest for
the low-tech ﬁrms and the lowest for the high-tech ﬁrms.

5. Results

This section is sub-divided into two parts. In the ﬁrst part, we report estimation results
from a naive OLS regression of employment on the R&D intensity. Despite the associated
econometric issues, this naive model can serve as a useful benchmark against which we
can compare the results of more sophisticated methodology based on the generalised
propensity score approach applied to the estimation of the functional relationship between
the variables of interest, reported in the second part of this section.

Figure 1: OLS regression: all ﬁrms

5.1. OLS estimation

The scatterplot of employment against R&D intensity is shown in Figure 1 along
with the ﬁtted regression line. The OLS coefﬁcient estimates are shown in the ﬁgure as
well. The OLS estimate of the employment elasticity with respect to the R&D intensity
is reported -0.739 indicating that a 1% increase in the R&D intensity is associated with
0.74% decrease in the number of employees. With the estimated standard error of the

11

ln wi=6.79-0.739(cid:215)ln ri,  R2 = 0.3271001000100001000000.0010.0100.1001.000R&D intensity, log−scaleEmployment, log−scaleslope coefﬁcient 0.026 this elasticity estimate is statistically signiﬁcantly different from
zero and the regression is characterised by a rather goodness of ﬁt with the associated
R2 = 0.327.

5.2. GPS estimation

As explained in Section 3 above, the application of the GPS methodology in order
to estimate the dose-response function involves three steps. The results of the ﬁrst step
GPS estimation procedure (see Equation (1)) are reported in Table 2. They suggest that
the variation in the R&D intensity is best captured by variables such as the total capital
expenditure and its square, market capitalisation and its square, as well as operating
proﬁts. Also the included industry- and region-speciﬁc dummy variables contribute
substantially to the explanatory power of the ﬁrst step of the GPS regression.6 Indeed, the
goodness-of-ﬁt of this regression is quite high, yielding a R2 of 68.2%, which is necessary
in order to create a mighty propensity score able to remove biases when estimating the
dose-response function between the variables of interest.

Table 2: Dose regression

Dependent variable: ln R&D intensity

ln CAPEX
[ln CAPEX]2
ln MCAP
[ln MCAP]2
ln OP+
(cid:2)ln OP+(cid:3)2
ln OP−
(cid:2)ln OP−(cid:3)2
Constant

Observations
R2

−0.326∗∗∗ (0.052)
0.185∗∗∗ (0.057)
−0.292∗∗ (0.120)
0.315∗∗∗ (0.078)
(0.064)
(0.072)
(0.084)
(0.013)
(0.600)

−0.106∗
−0.100
0.030
0.006
−1.070∗
1,659
0.961

Notes: The sign-preserving log transformation of
the Operating proﬁt variable was carried out as
for positive values ln OP+ = if OP >
follows:
0 : ln OP and zero otherwise; for negative values
ln OP− = if OP < 0 : − ln( -OP) and zero other-
wise.

The assumption of normally distributed OLS residuals in Equation (1) is veriﬁed by
means of the Shapiro-Wilk normality test, yielding the p-value of 1.746 × 10−15. Hence

6These are not shown in the regression output table in order to save the space.

12

our data do not support the normality assumption. Therefore it is instructive to take a
closer look at the histogram of the regression residuals, shown in Figure 2. The ﬁtted
normal probability density function is shown as the dashed line. As seen, the residuals are
characterised by too large excess kurtosis and appear to be left-skewed to be compatible
with the normal distribution. Hence, instead of relying on the unfulﬁlled normality
assumption, we estimate the GPS by means of non-parametric approach using a kernel
density estimation (KDE) of the probability density function, since we have a rather large
data set of 1659 observations.

The estimated non-parametric GPS is shown as the solid line in the ﬁgure. Due to
its inherent ﬂexibility, the kernel-estimated GPS matches the empirical distribution of
residuals much better than the one based on the normal distribution. The GPS range is
quite large [ 0.00289,0.734 ], signifying substantial differences in the estimated propensity
of the treatment level assignment across ﬁrms in our sample.

Figure 2: Equation (1): Residuals histogram; parametric (Normal) and non-parametric kernel density
estimation (KDE)

According to the estimation procedure outlined in Hirano and Imbens (2004), the
next step is veriﬁcation of the so-called balancing property of the GPS, preceded by
imposing the common- support restriction on the data in question. The latter procedure
aims to construct a more homogenised sample by ﬁltering out aberrant observations for
which propensity-score based matching turns out problematic. The former procedure
aims at testing whether conditional on observed values of the GPS variable there are
no systematic differences in ﬁrms’ characteristics irrespective of the assigned treatment

13

0.00.20.40.60.8−202KDENormalintensity. As discussed in the online Appendix, the imposition of the common-support
restriction reduced the number of ﬁrms available for the further analysis from 1659 to
1296. At the same time, the balancing property of the constructed GPS in Equation (1) is
supported by the data, see the Appendix for further details.

Next, we proceed to the estimation of the dose-response relationship between the
ﬁrm innovation and employment variables. The estimation results for the second-step
regression corresponding to Equation (3) are reported in Table 3. Second step regression
results clearly show that the employment response to the ﬁrm innovation (proxied by
R&D expenditures) is highly non-linear, as all included polynomial terms of the latter
variable report highly signiﬁcant coefﬁcients. It is also worthwhile noticing that the GPS
variable enters as a statistically signiﬁcant covariate both in levels and via the interaction
term with the (log) of our treatment variable, conﬁrming its relevance in eliminating the
sample selection bias.7 The resulting R2 is 22.6%, which is of a comparable magnitude
reported in other studies (Egger et al., 2012).

Table 3: Conditional regression

Dependent variable: ln EMPL

ln R&D intensity
[ln R&D intensity]2
[ln R&D intensity]3
GPS
GPS ∗ ln R&D intensity
Constant

Observations
R2

−3.150∗∗∗ (0.616)
−0.869∗∗∗ (0.210)
−0.083∗∗∗ (0.022)
−3.040∗∗∗ (0.629)
−0.885∗∗∗ (0.205)
5.510∗∗∗ (0.570)
1,296
0.226

In order to facilitate the interpretation of the estimation results, we have plotted
the estimated dose-response and marginal treatment effect functions in the upper and
middle panels of Figure 3, respectively. The bands around the estimated functions are
95% bootstrap conﬁdence intervals. Observe that in order to facilitate the description
of the results in the lower panel of the ﬁgure we have plotted the cumulative share of
employment in the ﬁrms in our sample as a function of the R&D intensity. The curve in
the lower panel reveals that 90% of employment in our data sample is accounted by ﬁrms
with the R&D intensity in the interval between 0.6% and 15%. There are 1088 out of 1296
ﬁrms, or about 84%, of the total sample in this interval. There are 21 and 187 ﬁrms in

7Higher order power transformations of the GPS variable turned out to be insigniﬁcant and therefore

were omitted them from the model speciﬁcation for the sake of parsimony.

14

the left and right 5% tails of the cumulative employment distribution sorted by the R&D
intensity.

The shape of the estimated dose-response function is generally downward sloping,
which is broadly consistent with the naive OLS estimation results reported in Section 5.1.
However, recall that according to the OLS results the estimated employment elasticity is
uniformly negative at all R&D intensity levels. In contrast, the estimated dose-response
function using the GPS suggests that the magnitude of the response of employment to
changes in the R&D intensity varies with the level of the ﬁrms’ innovation intensity. This
non-linearity in the employment response is well illustrated by the marginal treatment
effect function, which can be interpreted as employment elasticity with respect to R&D
intensity, that is shown in the middle panel of Figure 3.

The estimated elasticity of interest has a hump shaped form. Hence it is convenient to
summarise our ﬁndings by distinguishing between different treatment intensity levels
taking into the consideration such hallmarks as the top and bottom 5% cumulative
employment thresholds. For relatively low treatment intensity levels (below 0.6%) the
employment elasticity increases in the absolute value from -0.5% up to about -1.5% as the
treatment intensity falls. However, given a rather small number of observations in this
part of the distribution these estimate values have to be taken with caution.

For the ﬁrms within the central 90% interval of the treatment intensity one can make
the following two observations. First, for the ﬁrms with R&D intensity in the interval
between 0.6% and 3% the estimated elasticity is not signiﬁcantly different from zero, as the
bootstrapped 95% conﬁdence interval includes zero line. This suggests a labour-neutral
effect of innovation for the ﬁrms with medium-low and medium levels of innovation
intensity. Second, for the ﬁrms with the medium-high levels of the R&D intensity
pertaining to the interval between 3% and 15% the estimated elasticity is negative and
signiﬁcantly different from zero. For these ﬁrms it is estimated around -0.5% with the
associated 95% conﬁdence interval about (-0.3%, -0.7%), suggesting labour-saving effect
of innovation. Notwithstanding that this value is substantially lower than that reported
by the OLS estimation (-0.74%) earlier in the text.

Turning to the ﬁrms with the highest R&D intensity (> 15%), this labour-saving effect
In this interval, the estimated employment
turns out to be even more pronounced.
elasticity gradually increases (in the absolute magnitude) from -0.5% to -2.0%, suggesting
that the innovation leaders tend to react more and more disproportionately stronger to
changes in the R&D intensity in reducing their labour force than innovation followers
and moderate innovators.

All in all, our estimation results when compared to those from the naive OLS regression
suggest that the employment effect of innovation varies with the level of technological
sophistication and warrant against application of estimation techniques that does not

15

Figure 3: Dose-response, treatment effect functions and cumulative employment share

accommodate such level dependence. For the ﬁrms with rather low to medium ratios of
R&D expenditure to net sales this effect tends to be overestimated by the OLS regression
whereas understated for the ﬁrms on the other side of the spectrum characterised by high
values of R&D intensity.

It is instructive to compare our results with traditional point estimates available in
the previous literature, despite the fact that studies summarised in Section 2 focus on
the employment elasticity with respect to a nominal measure of the R&D expenditure,
whereas we focus on the employment elasticity with respect to a relative measure of the

16

7891011120.0030.0100.0300.1000.300R&D intensity r, log scaleE(ln(w))Dose−response function−2.0−1.5−1.0−0.50.00.0030.0100.0300.1000.300R&D intensity r, log scaledE(ln(w))/dlnrTreatment effect function5%95%0.000.250.500.751.000.0030.0100.0300.1000.300R&D intensity r, log scaleCumulative employment shareR&D expenditure. Our results, emphasising the complexity of the non-linear relationship
between employment and innovation, are complementing those of Bogliacino (2014), who
equally ﬁnds that R&D investment expenditures have a non-linear effect on the ﬁrm
employment, depending on the R&D intensity. However, compared to the most of the
published literature, our results reveal no support for a job-creating aspect of innovation at
least when the world top R&D performers are scrutinised. For this particular sub-sample
of ﬁrms we ﬁnd that the effect of innovation is at best labour-neutral at the relatively
low values of the R&D intensity. For higher innovation intensity levels, the labour-saving
effect of innovation becomes increasingly pronounced, as knowledge intensive ﬁrms
are looking for high-skilled labour force which is typically in much shorter supply and
correspondingly more expensive than their low-skilled fellows.

6. Conclusions, policy recommendations and limitations

The objective of the study is to expose the entire innovation-employment relationship
for different R&D intensity levels in a continuous framework. We use a large international
ﬁrm-level panel data set for OECD countries and employing a ﬂexible semi-parametric
method – the generalised propensity score – allows us to estimate the full functional
relationship between the R&D-driven innovation and ﬁrm employment as well as address
important econometric issues, which is not possible in the standard estimation approach
used in the previous literature. This is our main contribution to the academic literature
and policy debate; to the best of our knowledge no comparable studies analysing the
employment effect of innovation in a continuous setting are available in the literature.

In order to answer these questions, we have based our empirical micro-econometric
analysis on a large international ﬁrm-level panel dataset for OECD countries, and our
proxy for technology has been a measurable and continuous variable, while the majority
of previous studies have relied on either indirect proxies of the technological change or
dummy variables (such as the occurrence of the product and process innovation). In
particular, we have employed the EU Industrial R&D Investment Scoreboard data set
for 2500 R&D performers worldwide. In addition to ﬁrm-level innovation expenditures,
we have used also of economic and ﬁnancial variables, which allowed us to control for
important ﬁrm-speciﬁc effects; along with sectoral and regional dummies.

Our results suggest that a care should be taken when analysing employment-innovation
nexus. Depending on the level of R&D intensity, we ﬁnd that the innovation impact on
employment can be negative too – ﬁndings that have been reported also in previous
studies. This labour-saving aspect of innovation is more pronounced for ﬁrms with
medium-high levels of R&D intensity and it tends to increase with the levels of R&D
intensity. In terms of policy recommendation, our results imply that these companies

17

should not be immediately targeted by policies aiming to achieve both innovation and
employment targets of the Europe 2020 Strategy in the same time.

Turning to limitations of our study, an important caveat of our empirical analysis
concerns the nature of the Scoreboard sample. First, while other data sets, such as the
OECD BERD data, can be considered as fully representative of OECD economies, in the
EU Industrial R&D Investment Scoreboard data used in the present study only R&D
"champions" are considered. This is a clear limitation of our data, the results of which
cannot be straightforwardly extrapolated to e.g. SMEs.

A further limitation of the data used in our study is that R&D Scoreboard data
do not allow us to identify the effect of product and process innovations separately.
However, as discussed in the introduction, the employment effect of innovation can be
very different depending on the nature of innovation. In order to separately identify the
employment effect of the product and process innovation, other sources of data, such as
the Community Innovation Survey (CIS), need to be used, which is a promising area for
the future research.

Lastly, in our study we focus on the snapshot of the economy at one period of
In the longer
time without taking higher-order effects of ﬁrms innovation activity.
run, investing in the innovation activity encourages knowledge-based economy, drives
demand for high-skilled, educated workers and eventually brings a country on the higher
growth path. However, a comprehensive assessment of these effects is only possible
within general-equilibrium models that capture vertical and horizontal linkages between
ﬁrms, which is not possible to account for in micro-econometric studies, such as the one
presented in this paper (Brandsma and Kancs, 2016). Hence aligning our results with
macro results is indeed important for enhancing our understanding of the employment
effect of innovation and it sets a promising avenue for the future research.

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19

ONLINE APPENDIX

Appendix A. Explanatory variables

The following groups of the explanatory variables were used in our analysis in the

main text:

• Net sales, NSALES: In line with the accounting deﬁnition of sales, sales taxes and
shares of sales of joint ventures & associates are excluded. For banks, sales are
deﬁned as the “Total (operating) income" plus any insurance income. For insurance
companies, sales are deﬁned as “Gross premiums written" plus any banking income.

• Operating proﬁt, OP: Proﬁt (or loss) before taxation, plus net interest cost (or minus
net interest income) and government grants, less gains (or plus losses) arising from
the sale/disposal of businesses or ﬁxed assets. Due to the fact that companies
report both positive and negative operating proﬁt, we cannot take a logarithmic
transformation of this variable. In order to do so, we created the following two
variables ln OP+ and ln OP−. The former variable is equal to the log of actual values
whenever a ﬁrm reports positive proﬁt and zero otherwise. The latter variable is
equal to the log of absolute actual values multiplied by minus one whenever a ﬁrm
reports negative proﬁt and zero otherwise.

• Capital expenditure, CAPEX: The expenditure used by a company to acquire or
upgrade physical assets such as equipment, property, industrial buildings.
In
company accounts capital expenditure is added to the asset account (i.e. capitalised),
thus increasing the amount of assets. It is disclosed in accounts as additions to
tangible ﬁxed assets.

• Market capitalisation, MCAP: The share price multiplied by the number of shares
issued at a given date. Market capitalisation data have been extracted from both
the Financial Times London Share Service and Reuters. These reﬂect the market
capitalisation of each company. The gross market capitalisation amount is used to
take into account those companies for which not all the equity is available on the
market.

• Country dummies: There are 36 distinct countries in our sample.

• Industry sector dummies: The industry sectors are based on the ICB classiﬁcation.
The level of disaggregation is generally the three-digit level of the ICB classiﬁcation,
which is then converted to NACE Rev.2.

20

• Sectoral dummies: In order to account for the sectoral heterogeneity with respect to
the R&D intensity, we regroup all ﬁrms into four sub-samples according to the level
of their technological sophistication. Following the OECD classiﬁcation, all ﬁrms in
our sample are regrouped into four 3-digit Industry Classiﬁcation Benchmark (ICB)
groups: high-, medium-high-, medium-low-, and low-tech companies:

– High-tech: Technology hardware & equipment, Software & computer services,
Pharmaceuticals & biotechnology, Health care equipment & services, and
Leisure goods;

– Medium-high-tech: Industrial engineering, Electronic & electrical equipment,
General industrials, Automobiles & parts, Personal goods, Other ﬁnancials,
Chemicals, Aerospace & defence, Travel & leisure, Support services, and
Household goods & home construction;

– Medium-low-tech: Food producers, Fixed line telecommunications, Beverages,
General retailers, Alternative energy, Media, Oil equipment, services & distri-
bution, and Tobacco;

– Low-tech: Gas, water & multi-utilities, Oil & gas producers, Nonlife insurance,
Industrial metals & mining, Construction & materials, Food & drug retail-
ers, Banks, Electricity, Industrial transportation, Mobile telecommunications,
Forestry & paper, Mining, Life insurance.

Appendix B. Veriﬁcation of GPS balancing property

The balancing property of the constructed GPS variable is veriﬁed following the
procedure suggested by Hirano and Imbens (2004). Each covariate is subdivided into
three groups of 553 observations according the tercentiles of the distribution of the
treatment intensity variable. The initial testing of the balancing property amounts to
testing whether the average value of a particular variable in every group is equal to
the average value in the remaining groups. The results of these tests are reported in
Table Appendix B.1. Only for a handful of covariates we cannot reject the tested null
hypothesis at usual signiﬁcance levels, indicating that there is a strong heterogeneity
among covariates belonging to these three groups pertinent to different values of the
treatment intensity. A well speciﬁed GPS should be able to successfully account for these
differences.

Before verifying the balancing properties of the GPS, we impose the so-called common-
support restriction. The purpose of this restriction is to ﬁlter out observations that are
rather dissimilar in their characteristics when used for the GPS computation in the ﬁrst
step, see Equations (1) and (2). As argued by Becker et al. (2012), it is advisable to impose

21

Table Appendix B.1: Covariate balance, t-statistics (Initial data)

dose_group_1 dose_group_2 dose_group_3

ln CAPEX
[ln CAPEX]2
ln MCAP
[ln MCAP]2
ln OP+
(cid:2)ln OP+(cid:3)2
ln OP−
(cid:2)ln OP−(cid:3)2

-18.35
-14.91
-8.93
-8.11
-14.36
-13.13
-5.08
-3.17

-1.86
-0.28
2.01
2.28
-3.91
-1.22
-6.13
-4.62

19.32
17.44
6.19
5.44
15.80
14.03
8.76
6.69

the common-support condition in order to improve the balancing properties of the GPS
and hence achieve more reliable estimation results.

For each treatment group, deﬁned above, k = 1, 2, 3, we evaluate GPS values for

each observation i at the respective median treatment value,

k
i . We determine the
j
i for each j = k with those computed
common support region by comparing values of
for other groups j (cid:54)= k at the median treatment value of the selected group j. Those

(cid:91)GPS

(cid:91)GPS

j(cid:54)=k
i

(cid:91)GPS

that fall outside of the range of

j
observations for which
i are labelled as
those that do not satisfy the common support restriction and therefore are removed from
the analysis. At the ﬁnal step, we retain only observations i that survive the common
support ﬁltering in all treatment groups. In Table Appendix B.2 we report the number of
observations retained in each group that satisfy the common support condition. Taken
together, only 1296 out of 1659 observations can be considered as comparable in terms of
their characteristics and hence are retained for a further analysis.

(cid:91)GPS

Table Appendix B.2: Number of observations in common support

cosu_true_id dose_group_1 dose_group_2 dose_group_3

1296

1651

1430

1411

Table Appendix B.3: Number of observations by dose group and block

m(GPS) = 1
m(GPS) = 2
m(GPS) = 3
m(GPS) = 4
m(GPS) = 5

1:(Total)

738
200
146
112
100

1

68
68
68
68
68

~1

2:(Total)

2

~2

3:(Total)

670
132
78
44
32

492
230
207
184
183

105
104
104
104
105

387
126
103
80
78

776
212
97
110
101

3

87
87
86
87
87

~3

689
125
11
23
14

22

Table Appendix B.4: Covariance balance, t-statistics (GPS-adjusted)

dose_group_1 dose_group_2 dose_group_3

ln CAPEX
[ln CAPEX]2
ln MCAP
[ln MCAP]2
ln OP+
(cid:2)ln OP+(cid:3)2
ln OP−
(cid:2)ln OP−(cid:3)2

-2.43
-1.52
-0.84
-0.70
-0.92
-0.98
0.36
0.35

-0.51
-0.58
0.85
0.82
-0.47
-0.28
-0.87
-0.84

2.12
1.84
0.33
0.18
1.50
1.45
0.06
0.16

In order to check whether the balancing property of the constructed GPS can be
warranted in our data, we subdivide each group into blocs of approximately the same
size corresponding to quintiles of the respective GPS. The resulting cell sizes of each
block are reported in Table Appendix B.3. The testing procedure of the differences in
means for each variables and for each treatment group conditioning on the GPS values
is conducted in the following two steps. In the ﬁrst step, ﬁve tests for the differences in
means are conducted for each block. Then in the second step the computed block-speciﬁc
differences in means are combined using the total number of observations in each block
as weights. The balancing properties of covariates adjusted for the GPS are reported in
Table Appendix B.4. Compared to the results for unadjusted covariates reported in Table
Appendix B.1, a substantial improvement can be observed, as only three test statistics
exceed the nominal 5% signiﬁcance level. Hence, we can conclude that the generalised
propensity scores are appropriately deﬁned.

23

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doi:10.2760/52757 

ISBN 978-92-76-00041-9