Economic Modelling 128 (2023) 106524

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Economic Modelling
journal homepage: www.journals.elsevier.com/economic-modelling

Digital technologies and productivity: A firm-level investigation☆

Francesco Nucci a, *, Chiara Puccioni b, Ottavio Ricchi c
a
Sapienza University, Italy
b
Confindustria, Italy
c
Italian Ministry of Economy and Finance, Treasury Department, Italy

A R T I C L E I N F O A B S T R A C T

Handling editor: Sushanta Mallick We characterize the process of digital transformation of Italian firms and the impact on TFP. Using information of
unusual breadth on different types of investments in digital technologies, we consider various dimensions of
Keywords: digital adoption such as whether firms invested in advanced domains (like AI) or bundles of more than one
Firm adoption of digital technologies technology. We investigate the effects of digital technologies on productivity using alternative criteria to classify
Firm productivity
firms as digital adopters. With our baseline definition, the estimated effect on the percentage change in TFP
between 2015 and 2018 is about one percentage point (0.97). With more restrictive definitions of digital
adoption, the estimated impact is found to be larger, and it is largest when digital adoption is associated with
investments in at least one AI-related technology. We also show that, in general, the effect of digital adoption is
more sizeable in the service sector, in larger firms and in older firms.

1. Introduction Yet, the rapid diffusion of digital technologies has coincided with a
protracted slowdown of aggregate productivity growth since the mid-
The rise of the New Digital Economy represents a major shift in the 2000s (see, e.g., Cette et al., 2016). Indeed, despite the unprecedented
way firms operate. Digital technologies imply an overall reduction in pace of digital adoption in the business sector, the gains in terms of faster
firm’s costs, such as those for information search and processing and for productivity growth at the economy level have not been visible. Among
coordination and communications, and enable firms to substantially the explanations for this seeming productivity paradox, Van Ark (2016)
transform their production processes and business models (Goldfarb and argues that the new digital economy is still in its “installation phase”,
Tucker 2019). Brynjolfsson et al. (2017) emphasize that economies have while Brynjolfsson et al. (2017, 2021) state that the measured produc­
been experiencing a continuing progress of information technologies in tivity gains from digital investments do not materialize immediately and
many domains, from further technology advances in computer power to most of them are still to come. On the other hand, a wide dispersion has
a large diffusion of investment in innovative technologies, like cloud been documented in the extent to which firms are embracing the digital
infrastructure, and to advances in artificial intelligence and machine transformation (Andrews et al., 2018) and, according to Sorbe et al.
learning. (2019), this heterogeneity across firms and industries contributes to

☆
We are grateful to the Editor, Sushanta Mallick, the Associate Editor and two anonymous referees for very useful comments. We also thank Fabio Bacchini,
Federico Belotti, Mirko Menghini and Sandro Montresor for insightful suggestions, Patrizia Cella, Maria Carla Congia and Caterina Viviano for helpful guidance on
the Istat databases, and Giuseppe Nicoletti, Brindusa Anghel and participants at the Annual Conference of the Global Forum on Productivity (Venice), the 14th
National Statistical Conference (Turin) and the Fondazione Tor Vergata-MEF-DT workshop on the Italian production system (Rome) for their comments. The project
is part of a broader research collaboration between Italy’s Department of the Treasury at the Ministry of the Economy and Finance (MEF-DT) and ISTAT, Italy’s
National Statistical Institute.
* Corresponding author.
E-mail address: francesco.nucci@uniroma1.it (F. Nucci).

https://doi.org/10.1016/j.econmod.2023.106524
Received 1 August 2022; Received in revised form 21 July 2023; Accepted 4 September 2023
Available online 13 September 2023
0264-9993/© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
F. Nucci et al. Economic Modelling 128 (2023) 106524

explain why aggregate productivity gains from digitalization are not so remains the same.
evident. In estimating the effects of digital adoption on a measure of firm
A variety of empirical studies, both at the industry and the firm level, performance we focus on total factor productivity (TFP) and employ the
have investigated the effects of investments in digital technologies on propensity score matching (PSM) methodology combined with a
the productivity performance. In general, the existing evidence indicates difference-in-differences (DiD) analysis. This should allow us to mitigate
a positive and statistically significant association between digital- the well-known problems of self-selection into treatment, endogeneity
technology adoption and productivity using different measures and and reverse causation that may affect the estimation of the
different approaches (see Bloom et al., 2007; Draca et al., 2006; Syver­ digitalization-productivity relationship. Thus, we focus first on
son, 2011 for a review of the evidence).1 However, there are several numerous characteristics, evaluated before the treatment, that are likely
studies that reach a different conclusion. For example, Acemoglu et al. to affect firms’ adoption of digital technologies. Among firms with these
(2014) show that the intensity of information technologies does not characteristics, some have adopted digital technologies in the
affect labor productivity in the US manufacturing sector outside the 2016–2018 period while some others have not. Second, we match firms
computer producing sector. DeStefano et al. (2018) document no effects that have invested in digital technologies with their corresponding
of ICT on productivity for UK firms and other existing studies on the ‘‘twins’’ that have not and then compare the variation in productivity
impact of broadband adoption on productivity find no significant impact over the period 2018–2015 between the two groups of firms.
(see Haller and Lyons, 2015 and the references therein). We find that investments in digital technologies have discernible and
Against this background, this paper seeks to investigate how in­ statistically significant effects on firm productivity. Our estimation
vestments in digital technologies impinge on firms’ productivity. Pre­ findings indicate that firms that have invested in at least one type of
liminary to this, we characterize the process of firm’s digitalization in digital technology over the 2016–2018 period have a rate of variation of
Italy and the multiple dimensions though which digital adoption can TFP, between 2015 and 2018, which is 0.97 percentage points higher, on
occur, shedding light on the heterogeneity across firms in the way they average, than that of similar firms with no digital adoption. Not sur­
rely on new technologies. We document who invests in digital tech­ prisingly, when we focus on the alternative definitions of treatment
nologies and how by examining numerous firm characteristics. We then presented earlier, from those based on the adoption of more advanced
evaluate the effects of digital adoption on productivity focusing on technologies (e.g., AI) to those based on bundles of more than one
different types of investment in digital technologies and considering that technology, the estimated effects are larger in size and statistically sig­
digital technologies are often used in bundles. nificant. For all the criteria to classify firms as treated with digital
In our empirical investigation we use high-quality, firm-level on adoption, we supplement our findings with several evidence on the
digital adoption of unusual breadth. Indeed, a Survey by the Italian quality of the matching, the existence of common trends before the
Statistical Institute (Istat) in the 2019 Permanent census of enterprises treatment and the robustness of the results to alternative matching
has a detailed section on firms’ use of digital technologies. Among methods.
numerous questions, the Survey has asked firms to report whether, in the Moreover, we detect heterogeneity in the productivity gains from
period 2016–2018, they have invested in each of nine different types of digital adoption not only regarding the way we measure the firm pro­
digital technologies (Istat, 2020a). The types of digital technologies are pensity to invest in digital technologies but also in reference to various
grouped in three domains. The first (Internet-based technologies) com­ firm characteristics. We show that the estimated effect of digital adop­
prises specific digital investments which refer to optic-fiber ultra-­ tion on TFP varies in strength between different groups of firms and is, in
broadband connection, mobility connection (4G and 5G) and internet of general, stronger in firms operating in services, in larger firms and in
things. The second domain (Areas of application of artificial intelli­ older firms.
gence, AI) encompasses investments in immersive technologies, big The remaining of the paper is organized as follows: in Section 2 we
data, and automatization, robotics, and smart systems. The third domain provide a background discussion of the relevant issues, with an overview
(Other technological areas) includes investments in 3D printing, simu­ of the related literature; Section 3 describes the data and especially the
lation of interconnected machines and cyber-security. measures of digital adoption; Section 4 illustrates the empirical meth­
Based on firms’ responses to these questions, we have first singled odology; Section 5 presents the baseline econometric results, while
out the group of firms that did not invest in any digital technology in the Section 6 focuses on some extensions. Section 7 concludes.
period 2016–2018 and the group of those which have invested in at least
one of the nine types of digital technologies. Then, to capture the 2. Background and related literature
different domains of digital adoption and the different ways in which the
propensity to invest in digital technologies can be characterized, we Significant advances in information technologies have taken place,
have used various alternative classification criteria to allocate the firms ranging from further progress in computer power to adoption of inno­
into the group of digital adopters. Our first alternative to the baseline vative technologies like cloud infrastructure and those associated with
group identifies firms as ‘digital’ if they have invested in at least one new artificial intelligence and machine learning (see, e.g., Brynjolfsson et al.,
technology in the second and third domains, which are likely to 2017). The adoption of digital technologies induces a substantial decline
comprise more advanced technologies (e.g., big data, advanced auto­ of firms’ costs along several domains and prompt innovation in their
mation, 3D printing, augmented and virtual reality) compared to those production processes and business models enhancing the flexibility of
included in the first domain. Other criteria to define digital adopters are the firm organization (Goldfarb and Tucker, 2019). As shown by Bartel
based on whether firms have invested in a bundle of more than one et al. (2007), the use of new computerized technologies can increase the
digital technology. Thus, one group includes firms which have invested customization of firms’ products, induce faster machine setup times, and
in a bundle of at least two types of new technologies, while another one reduce the run time during production.
includes firms that have invested in a bundle of at least three types. Parallel to this, however, measured productivity growth has shown a
Finally, given the specificities of the second technological domain, we large deceleration over the 2005–2015 period and low productivity
experiment with a definition of digital adopters that includes in this growth rates have been recorded in that period in almost all developed
group only the firms with at least an investment in the areas of appli­ economies, especially in the euro area. Labor productivity growth rates
cation of AI. In all cases, the reference group of the “non adopters” in a broad group of developed countries declined in the mid-2000s and
have remained low since then. As Van Ark (2016) reports, the slowdown
in global total factor productivity growth has been even more dramatic,
1
Previous contributions include, among others, Brynjolfsson and Hitt (2003), moving down from 1.3 per cent from 1999 to 2006 to 0.3 per cent from
Bloom et al. (2012), Gal et al. (2019) and Anderton et al. (2023). 2007 to 2014. This amounts to a “productivity paradox”, that is the

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F. Nucci et al. Economic Modelling 128 (2023) 106524

coexistence of advances in ICT with a protracted slowdown in produc­ may require time to implement (see Brynjolfsson et al., 2021).
tivity growth, and Brynjolfsson et al. (2017) reformulate the original Focusing on patterns before mid-2000s, Bloom et al. (2012) use
Solow paradox as follows: “we see transformative new technologies microeconomic data on establishments in Europe owned by US multi­
everywhere but in the productivity statistics”.2 nationals vis-à-vis establishments in Europe owned by non-US multi­
Several empirical studies, both at the firm and the industry level, nationals or purely domestic establishments. IT related productivity is
investigate the relationship between the adoption of digital technologies derived through the control function approach introduced by Olley and
and productivity. In their survey, Draca et al. (2006) note that several Pakes (1996) with several refinements. Specifically, they estimate an
studies at the industry level detect significant productivity gains from IT augmented Cobb-Douglas production function where both IT and non-IT
capital over the 1987–2000 period. As for firm-level investigations, capital inputs are separately considered, so that IT capital is taken as a
Draca et al. (2006) state that most of them find a positive and significant state variable and its potential endogeneity is controlled for. They pro­
association of IT with productivity. Similarly, if we focus on more recent vide estimates for the productivity of IT capital and document differ­
surveys the empirical evidence points, in general, to a positive associa­ ences across US and European firms in IT-related productivity. Their
tion between digital adoption and productivity (Syverson, 2011; Bloom empirical results point to US people-management practices as a driver of
et al., 2012) and this is confirmed in Gal et al. (2019), who provide an the productivity premium, owing to a superior ability in IT exploitation.
updated and comprehensive literature review. There are, however, Similarly, Caroli et al. (2001) show that information technologies
contributions to the literature that reach a different conclusion. For induce productivity gains in firms characterized by decentralized ar­
example, Acemoglu et al. (2014) provide evidence for the US that, if the chitectures, higher levels of human capital and team-based production.
computer-producing industries are excluded from the sample, then the At the same time, Tambe et al. (2012) argue that firms endowed with
intensity of use of IT investments has no effect on productivity. Simi­ proper organizational structures, processes and skills can enjoy larger
larly, DeStefano et al. (2018) find no significant impact of ICT on pro­ benefits from digital technologies, because the interplay of technological
ductivity.3 As for the impact of firms’ broadband adoption on and organizational innovations can induce productivity enhancements
productivity, Haller and Lyons (2015), Bertschek et al. (2013) and through greater product customization and increased product variety.
Colombo et al. (2013) do not detect significant effects, contrary to other Garicano (2010) emphasizes the relevance of complementarities be­
contributions, such as for example Akerman et al. (2015) and Grimes tween information and communication technology (ICT) and organiza­
et al. (2012), who reach a different conclusion. tional design. He shows that: a) the required adaptation and refocusing
Gal et al. (2019) use data on digital technology adoption at the in­ of firms’ organizational practices differ depending on the type of ICT
dustry level and estimate total factor productivity at the firm level using investments; b) the impact of ICT on productivity might be negligible
the control function approach to mitigate the endogeneity of input without organizational changes because complementarities between
choices in the production function. They find that the impact of digital organization and ICT are important.4
adoption on productivity increases can be sizeable, especially for firms Other authors, such as Bloom et al. (2007), detect a positive effect of
that already enjoyed high level of productivity, and their results hold for ICT on firm productivity in Europe at the macro level (average effect)
various technologies (high-speed broadband access, simple and complex but it is heterogeneous across firms and positively depends on factors
cloud computing, CRM, and ERP software). Moreover, they show that such as the quality of practices in human resources management and the
productivity gains from digital technologies are larger in manufacturing degree of decentralization in firms’ organizational structure.
than in services and, in general, in industries with a high reliance on Anderton et al. (2023) use a large European panel dataset at the firm
streamlined or automated routine tasks. level and show that digitalization accelerates firms’ TFP growth on
Using a panel of US establishments, Jin and McElheran (2019) pro­ average, although its impact is very heterogeneous. According to their
vide evidence that recent dramatic increases in firms’ ability to access findings, only firms operating in some sectors seem to benefit from
information technologies as a service are conducive to positive effects on digital adoption, only the 30% most productive laggard firms benefit
productivity of young establishments and that performance gains from from digitalization, and intangible assets act as a complement, as their
new IT services are disproportionately detected among young firms. A presence amplifies the effect of digital adoption on firm’s TFP growth.5
firm-level study on the effects of computerization on productivity is due Cusolito et al. (2020) estimate the effects of adopting digital business
to Brynjolfsson and Hitt (2003), whose results indicate that, over short solutions on TFP focusing on firm-level data for 82 developing econo­
horizons (one year), computerization does not significantly affect pro­ mies over the period 2002–19 drawn from the World Bank’s Enterprise
ductivity growth. Conversely, however, as the time horizon increases, Survey (WBES). The latter collects information on technology adoption
computerization does impinge on productivity. They interpret this result
by emphasizing the role of computers as a general-purpose technology
(GPT), so that adoption of digital technologies is not simply about
4
purchasing capital in the form of computers of other machinery. It also Brynjolfsson and Hitt (2003) also lend support to the view that the
contribution of information technology to firm’s productivity hinges crucially
involves a host of complementary investments and innovations which
on organizational complements such as new business processes and work
practices, new skills and new organizational and industry structures. These
complementary investments on innovation, although often hard to measure,
2
There can be non-negligible lags between the implementation of digital can be larger than the investments in digital technologies themselves. Draca
technologies and their full operationalization, so that productivity enhance­ et al. (2006) argue that measured ICT can be seen as only the tip of the iceberg,
ments can take time to materialize. Van Ark (2016) argues that the New Digital as a successful realization of an ICT project requires a reorganization of the firm
Economy is still in its installation phase and productivity gains are yet to come. around the new technology. These reorganization costs may be interpreted
According to Brynjolfsson et al., 2021, when new technologies are introduced, simply as adjustment costs, but they can be particularly substantial in the case
productivity growth is initially underestimated because capital and labor are of ICT.
5
used to accumulate unmeasured intangible assets but, eventually, as growing To measure digitalization, they rely on two variables at the country, sector,
intangible stocks begin to contribute to production, measured productivity and year level. One of them is the ratio between the real investment in Com­
growth will rise. At the same time, there is a wide dispersion across firms in the puter Software and Databases, ICT and R&D as a share of total real investment.
diffusion of digital technologies and the obstacles to it provide another expla­ The second variable of digitalization uses information on prices of digital in­
nation of the slowdown of aggregate productivity (Andrews et al., 2016). vestment and measures the extent to which the digital investment intensity
3
Gordon (2000, 2003) challenges the view that ICT use played an important exceeds, or falls short of, what would be expected from the relative price of
role in post-1995 productivity growth. He asserts that, if the IT-producing in­ digital technologies. They estimate firm-level TFP using the method proposed
dustry were leaving aside, then observed productivity growth in the US econ­ by Gandhi et al. (2020), which has the benefit of imposing less restrictions on
omy was simply a cyclical phenomenon. the functional form of gross output production functions.

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F. Nucci et al. Economic Modelling 128 (2023) 106524

as firms are asked whether they have a business website for carrying out 3. The data
their operations or use a business email to communicate with clients and
suppliers. They estimate firms’ TFP from a log-linearized Cobb-Douglas 3.1. The firm-level databases
production function relying on the Olley and Pakes (1996) approach,
with the extensions proposed by Levinsohn and Petrin (2003) and In our empirical study we use information from four different data­
Ackerberg et al. (2015). Differently from them, however, Cusolito et al. bases at the firm level. Three of them are maintained, and suitably in­
(2020) endogenize TFP by setting it as a function of the adoption of tegrated, by Italy’s National statistical institute (Istat). The first database
digital business solutions in addition to other variables affecting per­ is the Permanent Census of enterprises, which gathers information about
formance. They find that the (probability adjusted) median TFP pre­ the Italian productive system on issues such as firms’ organization and
mium associated with the adoption of a business website for firm business development, competitiveness and environmental sustainabil­
operations is 2.2 per cent and it is higher than the TFP premiums asso­ ity (see Istat, 2020; Monducci, 2020; Costa et al., 2020). We employ data
ciated to other variables that affect performance. from the first permanent census that took place in 2019 and covered the
Bugamelli and Pagano (2004) use firm-level data drawn from a large whole population of Italian enterprises with at least 20 employees, while
sample of Italian manufacturing firms and estimate a marginal product the enterprises with the number of employees comprised between 3 and
of ICT much higher than its user cost. Their empirical findings point to 19 have been properly sampled. The Permanent Census is a sample
an increase in the share of skilled workers and an extensive reorgani­ survey that mainly gathers qualitative information. The latter, however,
zation of the workplace as preconditions for enjoying productivity gains can be suitably integrated with information from statistical registers of
from ICT adoption. Indeed, reorganization costs act as capital adjust­ enterprises and employees. Thus, we combine information from the
ment costs, with a sizeable fixed-cost component, and, therefore, small permanent census with data from the other sources. First, we rely on the
and medium firms have extra difficulties in paying them. They provide Statistical register of active enterprises (ASIA - Enterprises), a business
firm-level evidence on a lack of these complementary investments register developed at Istat covering all enterprises conducting economic
whose cost have acted as a barrier to investment in ICT. Calvino et al. activities in the fields of industry, commerce and services that contribute
(2022) discuss how the weak diffusion of digital technologies in Italy to gross domestic product. We use ASIA register of enterprises to obtain
among smaller and less productive firms has dragged down Italian information on structural characteristics of the firms, such as, for
productivity growth. Their empirical analysis has highlighted three example, the main economic activity (industry), size, legal form, age,
main determinants of the subdued digital diffusion among small firms: i) and turnover. We also rely on the SBS Frame (Structural Business Sta­
lack of complementary skills among workers, ii) low capabilities of tistics), a statistical register on the economic accounts of Italian enter­
managers, and iii) low investments rates in R&D and other intangible prises. From the SBS Frame we obtain information on some firms’
capital. economic variables, such as, for example, the value of production, costs
Hall et al. (2012) investigate the role of ICT investments and R&D of different type and employment. Moreover, in estimating total factor
jointly as an input to innovation rather than simply as an input of the productivity we also use data from Orbis, a well-known data source with
production function. They also allow for measures of organizational longitudinal firm-level information drawn from annual balance sheets
innovation to take into account the interaction among all these factors. and income statements collected by Bureau van Dijk. The final database
Using a complex model, estimated on a large sample of Italian that is employed in the empirical analysis refers to about 68,000 firms.
manufacturing firms, they find that R&D and ICT both contribute to
innovation, even though to a different extent. Importantly, ICT and R&D 3.2. The characterization of firms’ digital adoption
affect productivity both directly and indirectly through the innovation
equation. Each of them individually, however, has large impacts on The Survey of the 2019 Permanent census of enterprises has been
productivity and this suggests some firms’ underinvestment in these conducted from May to October 2019, with 2018 as the reference year.
activities.6 Importantly for our purposes, that survey features a detailed section on
Whilst our paper relates to several contributions surveyed in this firms’ reliance on digital technologies. The survey focusing on this
section, there are, however, three distinctive elements. First, we use specific issue has been conducted among enterprises with at least ten
firm-level, high-quality information of unusual breadth on digital employees in the year 2017. The Survey collects information on several
adoption that allows us to characterize the process of digital trans­ aspects pertaining to digitalization (see Istat, 2020a) and we focus on
formation of Italian enterprises and the different dimensions of the firm investments made in different types of digital technologies. In section
propensity to invest in the new technologies. Second, we rely on a X.5.12, the Survey has asked firms to report whether, in the period
methodology that seeks to establish more directly the impact of digital 2016–2018, they have invested in each of the following nine types of
adoption on productivity and, to tackle the complexity of digitalization, digital technologies that Istat grouped in three different domains (Istat,
we use a variety of alternative criteria to allocate firms in the group of 2020a).
digital adopters. Third, we pay attention to the heterogeneity in the
estimated effects and investigate whether they vary in strength A) Internet-based technologies
depending on a variety of firm’s characteristics. We now turn to our 1) Optic-fiber ultra-broadband connection
empirical investigation and first describe the data that we employ in the 2) Mobility connection (4G and 5G)
analysis. 3) Internet of things
B) Areas of application of artificial intelligence (AI)
4) Immersive technologies
5) Elaboration and analysis of big data
6) Advanced automatization, collaborative robots, and smart
systems
C) Other technological areas
6 7) 3D printing
Pellegrino and Zingales (2017) find that TFP growth was faster in
ICT-intensive sectors in those countries where firms have good practices in the 8) Simulation of interconnected machines
selection and rewarding of managers. Schivardi and Schmitz (2018) calibrate a 9) Cyber-security.
general equilibrium model with firm-level evidence and find that inefficient
management practices limit the productivity gains of firms from their IT In Fig. 1, for every single type of investments in digital technologies,
adoption. we report the percentage of firms which have made these investments in

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F. Nucci et al. Economic Modelling 128 (2023) 106524

Fig. 1. Percentage of firms which made investments in digital technologies in the period 2016–2018 for every single type of investment
Legend: Our calculations on Istat data.

the period 2016–2018. Firms’ purchases of Internet-based technologies if it has invested in a bundle of two or more digital technologies, while
that refer to connectivity, such as optic-fiber ultra-broadband connec­ the third alternative criterion establishes that a firm is considered as
tion and mobility connection (4G and 5G), have been made by a sig­ treated if it has invested in a bundle of at least three types of digital
nificant fraction of firms (respectively, 46 and 34 per cent). Investments investments. Our fourth alternative criterion to define treatment with
in more advanced digital technologies are in general much less diffuse. digital adoption is that the firm has made at least one investment in AI.
For example, in the areas of application of AI, investments in immersive In all five classification criteria to assign firms to the treatment group,
technologies have been made by slightly less than 2 per cent of firms, the control group remains the same. This implies that, only for the
while those in big data and in automatization, robotics and smart sys­ baseline definition of treatment, the number of firms in the treated and
tems are reported in, respectively, 6 and about 7 per cent of the firms. A untreated (control) groups amounts to the number of firms in the whole
roughly similar incidence characterizes firm investments in both 3D sample. Conversely, when the alternative ways to define treatment are
printing and simulation of interconnected machines (equal to about 5 used, the number of firms in both the treated and the control group is
and 8 per cent, respectively). One third of the firms in our sample have lower than the number of firms in the whole sample. In Table 1 we
made investments in cyber-security. The overall picture from Fig. 1 document the composition of the group of treated firms for all the
points to a rather limited diffusion of digital adoption among firms, alternative classification criteria we use. Firms in the baseline treatment
especially with reference to more advanced technologies. group (group A) are 68 per cent of firms in the sample. The first alter­
In Fig. 2 we document other dimensions of digital adoption by native treatment group (group B) includes 40.2 per cent of firms, while
reporting the distribution of firms per number of types of digital in­ the second (group C), third (group D) and fourth (group E) alternative
vestments made in the 2016–2018 period. 32 per cent of firms in the treatment groups refer, respectively, to 43.4, 21.7 and 11.3 per cent of
sample have made no digital investments in any of the nine alternative the firms in the sample.
types, while firms that made only one type of investments in digital Before turning to the empirical methodology and the results, let us
technologies represent about 25 per cent of the sample. Hence, the firms provide information on the other variables, especially productivity, and
that have invested in the 2016–2018 period in bundles of digital tech­ present some descriptive statistics.
nologies are about 43 per cent, of which about 22 per cent have invested
in two types of digital technologies and about 13, 5 and 2 per cent have 3.3. Productivity, other variables, and descriptive statistics
invested, respectively, in three, four and five types. Only a handful of
firms have invested in six or more types of digital technologies (1.7 per We use total factor productivity (TFP) as measure of firm perfor­
cent of the sample). mance in the empirical analysis. Firm-level TFP is obtained through the
The group of firms with no investments in digital technologies is our estimation of production functions separate for each macro-sector
control group. To assign firms to the group of those “treated” with digital relying on the Levinsohn and Petrin (2003) methodology (LP)
adoption we rely on alternative criteria. Our baseline criterion is to augmented with the Ackerberg et al. (2015) corrections (ACF). They are
define a firm as treated if it has invested in at least one of the nine types both semi-parametric algorithms building on the original method pro­
of digital technologies. The alternative criteria are the following. First, posed by Olley and Pakes (OP; 1996) which controls for the correlation
firms are defined as treated if they have invested in at least one digital between the unobservable productivity shocks and the input levels using
technology in the second or third domain, which refer to the “Areas of firm investments as a proxy variable for productivity. The LP method
application of artificial intelligence” and “Other technological areas”, seeks to overcome the issue of a significant number of zero investment
respectively, and typically encompass more advanced technologies values in the data by using intermediate inputs, instead of investment, as
compared to the first domain. Second, a firm enters the treatment group a proxy variable. The Ackerberg et al. (2015) method puts into questions

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F. Nucci et al. Economic Modelling 128 (2023) 106524

Fig. 2. Distribution of firms per number of types of investment in digital technologies made in the period 2016-2018
Legend: Calculations on Istat data.

Table 1
– Mean values of variables across different groups in terms of types of investment in digital technologies (Values are in thousands of Euro).
Year 2018 All sample Control Group Baseline treated Alternative treated Alternative treated Alternative treated Alternative treated
Group A Group B Group C Group D Group E

(1) (2) (3) (4) (5) (6) (7)

Revenues 14610 8966 17270 21930 21010 28110 32740

Gross production 15230 9348 18010 22900 21930 29340 34380
Value added 3664 2337 4289 5398 5205 6872 8214
Number of workers 59.4 42.8 67.2 79.1 78.9 99.4 116.9
Purchases 7852 4764 9305 11890 11310 15300 17520
Labor costs 2391 1587 2769 3434 3344 4388 5258
Age (years) 24.1 23.4 24.5 25.6 24.8 25.2 25.7
Labor productivity 276.7 234.8 296.4 321.0 314.9 349.9 344.3
log (TFP) 5.242 5.228 5.249 5.253 5.256 5.264 5.259
Number of firms 67925 21740 46185 27333 29450 14736 7699
Incidence of firms (%) 100.0 32.0 68.0 40.2 43.4 21.7 11.3

Year 2015 All sample Control Group Baseline treated Alternative treated Alternative treated Alternative treated Alternative treated
Group A Group B Group C Group D Group E
(1) (2) (3) (4) (5) (6) (7)

Revenues 12450 7930 14570 18550 17760 23650 27250

Gross production 13310 8233 15700 20240 19360 26430 32030
Value added 3057 2005 3552 4483 4303 5676 6706
Number of workers 50.72 38.0 56.7 66.9 66.2 82.5 95.9
Purchases 6966 4162 8286 10800 10280 14420 17720
Labor costs 1999 1370 2295 2856 2760 3613 4302
Age (years) 21.13 20.4 21.5 22.6 21.8 22.2 22.7
Labor productivity 285.7 239.7 307.3 339.4 330.5 385.1 414.2
log (TFP) 5.289 5.278 5.294 5.296 5.299 5.305 5.301
Number of firms 67925 21740 46185 27333 29450 14736 7699
Incidence of firms (%) 100.0 32.0 68.0 40.2 43.4 21.7 11.3

Legenda: Calculations on data drawn from Istat and Orbis’s Bureau Van Dyck.

the hypothesis in both the OP and LP method that labor is a fully As we elucidate below, our variable of interest is the log change in
adjustable input. Rather, labor is seen as a state variable because of firm TFP between 2015 and 2018. In Table 1 we report the mean value
significant hiring and firing costs and it should therefore be an argument for several firms’ variables in both 2015 and 2018. We provide distinct
of the demand function for the proxy variable (for an insightful review of figures for the whole sample (column 1), the control group (column 2),
the state of the art in firm-level TFP estimation, see Bournakis and the baseline treatment group (column 3) and each of the other alter­
Mallick, 2018).7 native treatment groups (column 4 through 7). The variables refer to
gross production, revenues, value added, number of workers, purchases
of intermediate goods and services, labor costs as well as labor pro­
ductivity (gross output per employee) and the log of TFP. In Table 2 we
7
We thank Federico Belotti for useful insights on these methodologies and for provide information on the percentage distribution of firms by several
sharing his Stata code to estimate TFP through the LP and ACF algorithms.

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F. Nucci et al. Economic Modelling 128 (2023) 106524

Table 2
Incidence (%) of the treatment groups (vs. the control group) for different definitions of treatment with digital investments.
Incidence of groups: Control Baseline treated Alternative treated Alternative treated Alternative treated Alternative treated All sample
Group Group A Group B Group C Group D Group E

(1) (2) (3) (4) (5) (6) (7)

by Macro area (%)

North 57.4 62.8 67.4 64.5 66.4 68.7 61.1
Center 20.9 18.8 17.4 18.3 17.9 16.3 19.5
South 21.7 18.4 15.2 17.3 15.7 14.9 19.4
Total: 100 100 100 100 100 100 100
by Size class (%)
0-10 workers 6.2 4.8 3.9 4.4 3.9 3.4 1.9
11-20 workers 33.3 26.6 23.2 23.9 20.8 18.0 27.7
21-50 workers 43.9 43.8 43.4 43.2 41.5 40.3 46.2
51-100 workers 10.8 14.6 16.7 16.2 18.2 20.0 14.6
101-250 workers 4.5 7.2 8.9 8.5 10.4 12.2 7.0
>250 workers 1.3 2.9 3.9 3.8 5.2 6.2 2.7
Total: 100 100 100 100 100 100 100
by Sector (%)
High-tech (Manufacturing) 0.9 1.6 2.1 1.9 2.4 2.6 1.4
Medium high-tech (Manufacturing) 9.2 11.3 13.9 12.1 14.3 16.5 10.6
Medium low-tech (Manufacturing) 14.3 14.2 16.8 14.7 15.5 19.3 14.3
Low-tech (Manufacturing) 16.4 13.9 14.8 13.2 12.8 13.6 14.7
Knowledge-intensive services 9.6 13.7 14.9 15.1 16.5 19.0 12.4
Less Knowledge-intensive services 37.3 35.2 29.5 33.7 30.6 24.5 35.8
Others 12.2 10.2 8.0 9.3 7.9 4.4 10.8
Total: 100 100 100 100 100 100 100

Legenda: Calculations on Istat data Column (1) provides the percentage distribution of firms by macro area, size class and sector of activity for the control group;
columns (2)–(6) provide the same information for each of the treatment group. Column (7) refers to all sample.

characteristics: geographic macro-area, size, and sector of activity. In so firms that invested in digital technologies in the 2016–2018 period as
doing, we consider not only the whole sample (column 7) but also focus those in the treated group (T=1) and then focus on numerous observable
separately on the control group (column 1), the baseline treatment characteristics, evaluated before treatment, that may introduce hetero­
group (column 2) and each of the alternative treatment groups (column geneity across firms in their propensity to invest in digital technologies.
3 through 6). The evidence in the table indicates that, if the treatment Among firms exhibiting these characteristics, some have invested in
group is characterized for investments in more advanced technologies, i. digital technologies while some have not. Put it differently, the assign­
e. moving from the baseline treatment group (A) towards group (E), then ment of treatment (i.e. digitalization) is not random in our framework, as
the percentage incidence of firms located in the North of Italy, of larger the latter is not based on experimental data. Second, we match firms that
size and operating in more technology-intensive sectors tends to in­ did invest in digital technologies with their corresponding ‘‘twins’’ that,
crease. We now illustrate the estimation methodology that we employ albeit showing similar characteristics, did not adopt these technologies
on our data. and then compare the variation over time in productivity between the
two groups of firms.
4. The empirical methodology Establishing which individual units are similar conditioning on a
vector of variables, Xi, is a challenging task (curse of dimensionality).
Our goal is to evaluate the impact of firm investments in digital Rosenbaum and Rubin (1983) show that independence conditional to
technologies on its productivity. In so doing a proper methodology the set of control variables, Xi, continues to hold if the latter are sum­
ought to be utilized. Firms that adopt digital technologies have char­ marized by one single variable: the propensity score, P(Ti = 1|Xi). The
acteristics that are likely to differ from those of firms that do not (self- propensity score for an individual firm is the estimated conditional
selection into treatment). Hence, a difference in productivity outcome probability that it is included in the treatment group, P(Ti=1|Xi). Thus,
between firms that have invested in digital technologies and those that firms are matched according to their propensity to be treated, P(Ti=1|
have not cannot be seen as the actual effect of digitalization. Firm pro­ Xi), and the approach therefore requires that there be firms with similar
ductivity is affected by a variety of other factors beyond digital tech­ propensity scores in both groups so that the matching occurs within a
nologies, some of which are observed in the data, such as, for example, common support, i.e. within the range of propensity scores for which
size, age, sector of activity and human capital, while some others are there are firms in both the treatment and control groups.
not. Moreover, we also face the endogeneity problems that may affect Our first step is then to estimate a probit model on our sample where
our empirical findings and try to distinguish between the effects of the dependent variable is a binary variable, treatment (Ti), and the
digitalization on productivity and the influence that the latter, in turn, explanatory variables are the set of variables, Xi, that are evaluated
may have on the adoption of digital technologies. Indeed, reverse before treatment (in 2015) and are likely to influence the probability of
causation may be at work in the relationship between digitalization and being treated (in the period 2016–2018). Then, for each firm in the
productivity as, for example, higher productivity may reduce firm’s unit treated group (T=1) we construct a “counterfactual”, by focusing on
costs and thereby make digital investments more affordable for the en­ similar firms that are in the untreated group and compare the rate of
terprise. Moreover, idiosyncratic, and often unobservable, firms’ fea­ change in productivity between the two groups of firms (Stuart and
tures may impinge on both their use of digital technology and their Rubin, 2008; see Duhautois et al., 2020 for an application on the impact
productivity performance. of innovation on job quality). Propensity score matching creates
To partially deal with these issues, we employ the propensity score equivalent (balanced) treatment and control groups in terms of con­
matching (PSM) approach and combine it with a difference-in-difference founding variables.
(DiD) analysis (see, among others, Heckman et al., 1997, 1998; Blundell Several matching algorithms are available, such as, for example, the
and Costa Dias, 2009). We first identify (with alternative criteria) the nearest-neighbor matching, the radius and caliper matching, the

7
F. Nucci et al. Economic Modelling 128 (2023) 106524

stratification and the kernel matching. Whilst they are all based on the corroborative evidence of this. Let us now turn to the empirical findings.
distance between estimated propensity scores, they differ in how many
units to match and how to do it. In our baseline analysis, we rely on 5. The results
radius matching, with which every treated unit is matched with the
control units whose propensity scores fall in a predefined neighborhood The first step in our modelling approach is that of estimating the
(the caliper) of the propensity score of the treated unit. By employing all probability of being digital adopter. In our probit model the dependent
available comparison observations within a predefined distance around variable is a dummy variable taking the value of one if the firm is
the propensity score of the respective treated, this method allows for the “treated” with digital adoption and zero otherwise. As discussed earlier,
use of more untreated units when good matches are available and fewer we consider a baseline criterion to define treatment plus various alter­
units when they are not. Radius match is therefore a one-to-many native criteria. Conversely, the group of untreated firms is univocally
matching algorithm. One possible drawback is the difficulty of defined as the set of firms that made no investments in any digital
knowing a priori what radius is reasonable. As in Duhautois et al. technology. We estimate a probit model for each alternative definition of
(2020), in our baseline estimations we rely on a caliper vaue of 0.00001, the treatment variable, and the set of covariates refer to observable
which is small and implies a precise matching between the treated and characteristics that may introduce a degree a difference among firms in
control firms. There is a trade-off between the size of the matching group their propensity to invest in digital technologies. These variables deal
and the reduction of the bias between the treated and untreated firms. A with the following aspects: size, industry, geographical location, age, the
small value of the caliper implies that more firms drop out of the com­ share of firm expenditure in services to the value of its production and
mon support (i.e., ‘‘off-support’’ firms), as their degree of specificity is the share of labor costs to the value of production. For industry classi­
too high for counterfactuals to be found. In our empirical analysis, the fication, we use Eurostat indicators on high-tech industry and knowl­
number of treated firms dropping out of the common support varies edge–intensive services (High-tech aggregation by NACE Rev.2). In
across the definition of treatment but is, in general, relatively low. particular, the classification of manufacturing industries according to
However, we also check the robustness of our findings using other technological intensity distinguishes between high-technology, me­
matching algorithms, such as the kernel matching and the radius dium-high-technology, medium-low-technology and low-technology.
matching with a different (larger) caliper value. Following a similar approach, Eurostat classifies service sectors as
An important condition for the PSM approach to be valid is that no
systematic differences should exist among firms in the treated and
control groups in terms of unobserved characteristics that may affect the Table 3
outcome variable. This assumption is unlikely to hold as several unob­ Determinants of Firm Digital Adoption: the results of a probit model with the
served factors may well introduce heterogeneity across firms in the baseline definition of treatment (A).
adoption of digital technologies. To tackle this issue, we use the time Dependent variable: Estimated Marginal effects dy/dx
dimension of our data and resort to first difference for washing out Digital adoption (Baseline Coefficients
unobserved sources of firms’ heterogeneity in the outcome variable. treatment A)
This is the difference-in-difference (DiD) approach that computes the Size (ref. under 10 employees)
change in (the log of) TFP between two periods of time (the first dif­ 10–19 0.059*** (0.019) 0.021*** (0.007)
ference) and compares this variation between treated and untreated 20–49 0.179*** (0.019) 0.063*** (0.007)
50–99 0.339*** (0.023) 0.118*** (0.008)
firms (the second difference). In practice, our baseline estimate with the
100–249 0.446*** (0.029) 0.156*** (0.010)
radius matching model of the average treatment effect on the treated 250 and over 0.655*** (0.042) 0.229*** (0.015)
(ATT) is8 Age (ref. lowest quartile)
2nd quartile 0.048*** (0.014) 0.017*** (0.005)
1 ∑N TR
( C) 3rd quartile 0.043*** (0.014) 0.015*** (0.005)
ATT = 100* TR Δlog (TFP)Ti − Δlog (TFP)i , (1) Top quartile 0.035** (0.015) 0.012** (0.005)
N i=1
Labor cost per unit of output (ref. lowest quartile)
2nd quartile − 0.102*** (0.015) − 0.036*** (0.005)
where NTR is the number of treated firms that have been matched, 3rd quartile − 0.187*** (0.015) − 0.065*** (0.005)
Δlog (TFP)Ti is the change between 2015 and 2018 in the log of TFP for Top quartile − 0.336*** (0.016) − 0.117*** (0.005)
C
Sector by level of technology (ref. high-tech manuf.)
the i-th treated firm and Δlog (TFP)i is the average value of the change Medium high-tech − 0.203*** (0.049) − 0.071*** (0.017)
between 2015 and 2018 in the log of TFP for the untreated firms (Manufacturing)
Medium low-tech − 0.289*** (0.049) − 0.101*** (0.017)
matched with the i-th firm.9 In using the estimator in Eq. (1) we assume
(Manufacturing)
that, before treatment, the outcome variables in the treated and un­ Low-tech (Manufacturing) − 0.405*** (0.049) − 0.141*** (0.017)
treated firms are characterized by the same trend (the common-trend Knowledge- intensive services − 0.005 (0.050) − 0.002 (0.017)
assumption). Using firm-level data over periods of observation prior to Less Knowledge- intensive − 0.280*** (0.048) − 0.098*** (0.017)
treatment, we verify that the common-trend assumption is satisfied as services
Others − 0.351*** (0.049) − 0.122*** (0.017)
the effect of treatment on the outcome variable is not a figment of pre- Geographical area (ref. North)
existing differences in the productivity performance. Center − 0.084*** (0.013) − 0.029*** (0.005)
In the empirical analysis, we rely on several criteria for assessing the South − 0.089*** (0.013) − 0.031*** (0.005))
quality of the match. Indeed, since we condition on the propensity score, Service costs per unit of output (ref. lowest quartile)
2nd quartile 0.096*** (0.015) 0.033*** (0.005))
rather than on the set of covariates, Xi, one needs to verify whether the
3rd quartile 0.158*** (0.015) 0.055*** (0.005))
matching can balance the distribution of the relevant covariates in the Top quartile 0.187*** (0.015) 0.065*** (0.005))
treatment and the control group, and we do so by providing Constant 0.611*** (0.052)

Number of observations 67925

Wald test χ2 1811.5
(with p-value) 0.000
8
In our empirical work, we have employed, among others, the user-written Pseudo R2 0.022
Stata command psmatch2, developed by Leuven and Sianesi (2003). Log likelihood − 41648.1
9
See Lechner (2002) on how the identification of ATT can be affected under Robust standard errors in parentheses.
heterogeneous treatments and Zhou and Xie (2020) for treatment effect het­ *p < 0.10, **p < 0.05, ***p < 0.01.
erogeneity with selection bias.

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F. Nucci et al. Economic Modelling 128 (2023) 106524

knowledge-intensive services (KIS) and less knowledge-intensive ser­ technology, such as, for example, training, consulting, testing and pro­
vices (LKIS). cess engineering and this would contribute to explain our empirical
In Table 3 we report the estimation results of the probit model with result. Finally, the estimation findings reported in Table 3 indicate that
reference to the baseline definition (A) of treatment with digital adop­ firms with a higher share of labor costs to the value of production are,
tion. We report both the estimated coefficients and the marginal effects. ceteris paribus, less likely to adopt digital technologies. A possible
Our estimation findings suggest that a marked digital adoption occurs explanation is that this covariate somehow approximates the degree of
more in larger firms. We consider six size classes and find that, compared labor intensity in the firm production structure and therefore, perhaps
to the lowest size class (the reference category), the magnitude of the not surprisingly, more labor-intensive firms are less likely to rely
estimated coefficients progressively increases for higher size classes, as markedly on digital technologies. It is important to emphasize that all
expected. As for the sector of economic activity, compared to high- variables included in the probit model refer to the year 2015 and are
technology sectors in manufacturing (the reference category), digital therefore evaluated before the possible participation into treatment, i.e.,
adoption is found to be less likely in all other industries, both in before the 2016–2018 period during which firms have (or have not)
manufacturing and in services, as highlighted in previous literature. In invested in digital technologies.
line with other scholars’ findings, even in knowledge-intensive services, In Tables 4a and 4b we report the results from estimating the probit
an extensive digital usage is less likely than in high-tech industries. The model using each of the four alternative definitions of treatment with
effect of age is also positive as, compared to firms with age that lies in digital technologies (definition (B) through (E)). We report only the
the lowest quartile (up to ten years in 2015 since firm establishment), estimated marginal effects and their standard errors. The picture that
older firms are more likely to rely extensively on digital technologies. emerges from the estimation with the baseline treatment definition
Not surprisingly, compared to firms in the North of Italy, the other firms (Table 3) is broadly confirmed in all cases. Not surprisingly, however,
are, ceteris paribus, less likely to adopt digital technologies, with the the estimated effect of each covariate on the probability of treatment
divergence being larger with respect to the South than to the Centre. We varies from one definition of treatment to another. For example, oper­
also find that firms with a higher share of service purchases to the value ating in a large firm (with at least 250 workers) has a marginal effect on
of production are more likely to adopt digital technologies. Arguably, the likelihood of treatment which is larger if the definition of treatment
this expenditure may include services that are complementary to is having invested in AI (definition (E)) and not simply in at least one of

Table 4a Table 4b
Determinants of Firm Digital Adoption: the results of a probit model with Determinants of Firm Digital Adoption: the results of a probit model with
alternative ways to define treatment: definitions of treatment (B) and (C). alternative ways to define treatment: definitions of treatment (D) and (E).
Dependent variable: Marginal effects dy/ Marginal effects dy/ Dependent variable: Marginal effects dy/dx Marginal effects dy/
Digital adoption dx (B) dx (C) Digital adoption (D) dx (E)
Alternative treatment (B) & (C) Alternative treatment (D) &
(E)
Size (ref. under 10 employees)
10–19 0.035*** (0.009) 0.025*** (0.008) Size (ref. under 10 employees)
20–49 0.102*** (0.009) 0.093*** (0.008) 10–19 0.026*** (0.010) 0.011 (0.010)
50–99 0.191*** (0.010) 0.176*** (0.010) 20–49 0.109*** (0.010) 0.095*** (0.010)
100–249 0.252*** (0.012) 0.234*** (0.012) 50–99 0.222*** (0.011) 0.202*** (0.011)
250 and over 0.357*** (0.017) 0.339*** (0.017) 100–249 0.295*** (0.013) 0.265*** (0.012)
Age (ref. lowest quartile) 250 and over 0.428*** (0.018) 0.388*** (0.016)
2nd quartile 0.034*** (0.006) 0.021*** (0.006) Age (ref. lowest quartile)
3rd quartile 0.035*** (0.006) 0.017*** (0.006) 2nd quartile 0.027*** (0.007) 0.021*** (0.007)
Top quartile 0.030*** (0.006) 0.012** (0.006) 3rd quartile 0.017** (0.007) 0.008 (0.007)
Labor cost per unit of output (ref. lowest quartile) Top quartile 0.007 (0.007) − 0.001 (0.007)
2nd quartile − 0.054*** (0.006) − 0.048*** (0.006) Labor cost per unit of output (ref. lowest quartile)
3rd quartile − 0.101*** (0.006) − 0.092*** (0.006) 2nd quartile − 0.052*** (0.007) − 0.054*** (0.007)
Top quartile − 0.178*** (0.007) − 0.162*** (0.006) 3rd quartile − 0.108*** (0.007) − 0.100*** (0.007)
Sector by level of technology (ref. high-tech manuf.) Top quartile − 0.198*** (0.007) − 0.182*** (0.007)
Medium high-tech − 0.099*** (0.020) − 0.105*** (0.020) Sector by level of technology (ref. high-tech manuf.)
(Manufacturing) Medium high-tech − 0.119*** (0.021) − 0.088*** (0.020)
Medium low-tech − 0.134*** (0.019) − 0.142*** (0.020) (Manufacturing)
(Manufacturing) Medium low-tech − 0.177*** (0.021) − 0.115*** (0.020)
Low-tech (Manufacturing) − 0.207*** (0.019) − 0.211*** (0.020) (Manufacturing)
Knowledge- intensive services − 0.030 (0.020) − 0.011 (0.020) Low-tech (Manufacturing) − 0.262*** (0.021) − 0.209*** (0.020)
Less Knowledge- intensive − 0.203*** (0.019) − 0.153*** (0.019) Knowledge- intensive − 0.031 (0.022) − 0.011 (0.020)
services services
Others − 0.244*** (0.020) − 0.190*** (0.020) Less Knowledge- intensive − 0.213*** (0.021) − 0.222*** (0.019)
Geographical area (ref. North) services
Center − 0.054*** (0.006) − 0.039*** (0.006) Others − 0.263*** (0.022) − 0.310*** (0.021)
South − 0.071*** (0.006) − 0.043*** (0.006) Geographical area (ref. North)
Service costs per unit of output (ref. lowest quartile) Center − 0.041*** (0.006) − 0.047*** (0.006)
2nd quartile 0.053*** (0.006) 0.047*** (0.006) South − 0.053*** (0.007) − 0.039*** (0.007)
3rd quartile 0.082*** (0.007) 0.077*** (0.006) Service costs per unit of output (ref. lowest quartile)
Top quartile 0.099*** (0.007) 0.097*** (0.006) 2nd quartile 0.056*** (0.007) 0.057*** (0.007)
3rd quartile 0.090*** (0.008) 0.073*** (0.007)
Number of observations 49073 51190
Top quartile 0.110*** (0.008) 0.090*** (0.008)
Wald test χ2 3443.6 2693.1
(with p-value) 0.000 0.000 Number of observations 36476 29439
Pseudo R2 0.055 0.041 Wald test χ2 3269.8 3322.6
Log likelihood − 31851.9 − 33470.2 (with p-value) 0.000 0.000
Pseudo R2 0.073 0.114
Robust standard errors in parentheses. Log likelihood − 22806.1 − 14988.7
*p < 0.10, **p < 0.05, ***p < 0.01.
Robust standard errors in parentheses.
*p < 0.10, **p < 0.05, ***p < 0.01.

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F. Nucci et al. Economic Modelling 128 (2023) 106524

Table 5
The effect of adoption of digital technologies on productivity (Effects on percentage variation of TFP).
Baseline (A) and alternative definitions of treatment with digital adoption (B), (C), (D) and (E)

Baseline Alternative Alternative Alternative Alternative

Treatment Treatment Treatment Treatment Treatment
Group (A) Group (B) Group (C) Group (D) Group (E)

Outcome variable:
Percentage variation of TFP between 2015 and 2018 0.97*** (0.376) 1.59*** (0.428) 1.60*** (0.421) 2.13*** (0.515) 2.20*** (0.64)
Number of “on-support” (“off-support”) untreated firms 21,371 (369) 20,838 (902) 20,860 (880) 19,425 (2,315) 16,755 (4,985)
Number of “on-support” (“off-support”) treated firms 43,446 (2,739) 25,365 (1,968) 27,275 (2,175) 13,331 (1,405) 6,910 (789)

Notes: The coefficients represent the estimated difference in the 2015 to 2018 log-change in TFP between treated and control firms. Robust standard errors in pa­
rentheses. For each definition of treatment, we report in each column the number of “on-support” untreated and “on-support” treated firms. The number in parenthesis
below it is the corresponding number of “off-support” untreated and treated firms (i.e. those that drop out of the common support).
As illustrated in the text, treatment group (A) comprises firms that invested in at least one type of digital technologies; Group (B) comprises firms that invested in at
least one type of digital technologies in the of “Areas of application of artificial intelligence” or “Other technological areas”; Group (C) comprises firms that invested in
a bundle of at least two types of digital technologies; Group (D) comprises firms that invested in a bundle of at least three types of digital technologies; Group (E)
comprises firms that invested in at least one AI technology.
***p < 0.01; **p < 0.05; *p < 0.10.

the nine types of digital technologies (baseline definition (A)): the Table 6
marginal effects are 0.339 and 0.229, respectively (and are both statis­ The extent of balancing between the two groups (treated and control) after
matching: the case of the baseline treatment group (A).
tically significant).
After estimating the probability that a firm adopts digital technolo­ Matched variables: Mean
gies conditional on observed characteristics, we proceed with the match Treated Control % bias t-stat
of treated to untreated units based on the estimated propensity score. In Size (ref. under 10 employees)
the third step, we compare variation over the 2015–2018 period in the 10–19 0.292 0.292 0.1 0.11
log of TFP between firms with digital adoption (treated) and those 20–49 0.434 0.433 0.1 0.15
without it (control). In Table 5, we report the estimation results for the 50–99 0.128 0.128 − 0.1 − 0.17
100–249 0.052 0.052 0.3 0.38
baseline (A) definition of treatment as well as for the alternative defi­
250 and over 0.015 0.015 0.1 0.08
nitions ((B) through (E)). We find a positive and statistically significant Age (ref. lowest quartile)
impact of digital adoption on firm productivity. The positive effects 2nd quartile 0.263 0.263 0 − 0.04
reported in the table amount to the percentage difference in the varia­ 3rd quartile 0.229 0.230 − 0.1 − 0.18
tion over time of the log of TFP between digital and non-digital firms. Top quartile 0.229 0.229 − 0.1 − 0.1
Labor cost per unit of output (ref. lowest quartile)
Our estimation findings indicate that firms that invested in at least one 2nd quartile 0.258 0.258 − 0.1 − 0.12
type of digital technologies (baseline definition (A) of treatment) have a 3rd quartile 0.251 0.252 − 0.2 − 0.25
rate of change of productivity, between 2015 and 2018, which is 0.97 Top quartile 0.215 0.216 − 0.2 − 0.28
percentage points higher, on average, than that of firms with no in­ Service costs per unit of output (ref. lowest quartile)
2nd quartile 0.244 0.243 0.2 0.24
vestments in new technologies. When we define treatment with invest­
3rd quartile 0.254 0.255 − 0.2 − 0.35
ment in at least one more advanced type of digital technologies Top quartile 0.268 0.268 − 0.1 − 0.08
(definition (B)), the estimated effect is larger and equal to 1.59 per­ Sector by level of technology (ref. high-tech manuf.)
centage points. A similar effect (1.60) is uncovered when we consider as Medium high-tech (Manufacturing) 0.108 0.109 − 0.2 − 0.3
treated the firms that invested in a bundle of at least two types of digital Medium low-tech (Manufacturing) 0.142 0.142 − 0.1 − 0.12
Low-tech (Manufacturing) 0.140 0.139 0.3 0.53
technologies (definition (C)). The estimated effect is larger (2.13 per­ Knowledge- intensive services 0.133 0.135 − 0.4 − 0.54
centage points) if the treated firms are considered those that invested in Less Knowledge- intensive services 0.369 0.368 0.1 0.19
a bundle of at least three types of digital technologies (definition (D)). Others 0.100 0.099 0.1 0.1
Finally, if we restrict the definition of treatment only to firms that have Geographical area (ref. North)
Center 0.179 0.178 0.1 0.2
invested in at least one technology related to artificial intelligence, then
South 0.181 0.181 − 0.1 − 0.11
the effect of treatment is the largest one (2.20 percentage points). In all Pseudo R2 0.000
cases, the estimated effect is statistically significant at the one per cent LR test χ2 (with p-value) 1.89 (0.99)
level.10 Rubin’s B statistic 0.9
We now assess the quality of the matching. Put it simply, we need to Rubin’s R statistic 1.01

compare the picture before and after the matching and verify if there
remain any differences once we condition on the propensity score. To do While significant differences are expected before the matching, after it
this, we first use a two-sample t-test to verify if there are statistically the covariates should be balanced in the two groups and no significant
significant divergences in the means of covariates of the two groups. differences should therefore be detected. In Table 6, we focus on the
baseline definition of treatment (A) and report the mean in the treated
and control groups for each of the covariates. The two groups seem to be
10
In Table 5, for each definition of treatment, we report the number of “on- very similar for all the observables and the assumption of the equality of
support” untreated and “on-support” treated firms. We also report (in paren­ means is always satisfied in some cases.11 Since the t-test requires
thesis) the corresponding number of “off-support” untreated and treated firms, controversial assumptions, such as normal distribution of covariates,
i.e. those that drop out of the common support. Reassuringly, although we use a
small caliper value to ensure a precise matching between treated and control
firms, the number of treated firms dropping out of the common support is rather
11
low: for the baseline definition of treatment, the “off-support” units are 369 As reported in the table, the pseudo-R2 after matching is estimated to be
untreated and 2739 treated firms, while the “on-support” units are, respec­ rather low, Rubin’s B statistic is far less than 25 and Rubin’s R statistic lies
tively, 21,371 and 43,446. between 0.5 and 2.

10
F. Nucci et al. Economic Modelling 128 (2023) 106524

Fig. 3. Assessing balancing properties after matching: % standardised bias (Treatment group with the baseline definition (A) of treated firms).

Fig. 4. Matching Share by Propensity Score (Treatment group with the baseline definition (A) of treated firms).

and is sensitive to sample size, several studies cast doubt on comparisons inspection of Fig. 4 we assess the extent to which the distributions of
after PSM that are based on t-tests (see e.g. Ho et al., 2007, and reference propensity scores in treatment and control groups overlap, providing
therein). Thus, we also use another approach for assessing the difference evidence that, in our analysis, the range of common support between
in marginal distributions of the covariates: the standardised bias. The treated and untreated firms is adequate.12
latter is the difference of sample means in the treated and matched We also verified that the significant effect on productivity of the
control groups as a ratio to the square root of the simple average of the treatment with digital adoption is not simply a figment of diverging
sample variances in the two groups. In Fig. 3, we focus again on the
baseline definition of treatment and report the % standardised bias for
each covariate, and, in all cases, it is far below 3 per cent in the matched
12
samples, which is considered as a satisfactory outcome in most empirical All these balancing tests have been conducted also for each of the alter­
studies (see Caliendo and Kopeinig, 2008). Finally, from a visual native definitions of treatment and they confirm the picture emerging from the
inspection made for the baseline definition of treatment.

11
F. Nucci et al. Economic Modelling 128 (2023) 106524

Table 7
Testing for common trends before the treatment (Effects on percentage variation of TFP over the period 2013–2015).
Baseline (A) and alternative definitions of treatment with digital adoption (B), (C), (D) and (E)

Baseline Alternative Alternative Alternative Alternative

Treatment Treatment Treatment Treatment Treatment
Group (A) Group (B) Group (C) Group (D) Group (E)

I) First test

Dependent variable: Regressors:

Percentage variation of TFP between 2013 1) Treatment dummy variable − 0.16 − 0.27 − 0.24 0.59 0.24
and 2015 (0.331) (0.364) (0.360) (0.589) (0.537)
2) Other controls Yes Yes Yes Yes Yes
(size, age, labor and services cost per unit of output,
sector, area)
Number of observations 64,069 46,508 48,279 25,927 27,739

II) Second test

Outcome variable:
Percentage variation of TFP between 2013 and 2015 − 0.30 − 0.53 − 0.62 0.34 − 0.33
(0.375) (0.424) (0.414) (0.705) (0.635)
Number of “on-support” 60,793 43,566 45,180 19,207 22,366
(“off-support”) untreated and treated firms (3,276) (2,942) (3,099) (6,720) (5,373)

Notes: The two tests are described in the text. Robust standard errors are reported in parentheses. For test II, we report, for each definition of treatment, the number of
“on-support” and (in parenthesis) “off-support” firms (i.e. those that drop out of the common support). As illustrated in the text, treatment group (A) comprises firms
that invested in at least one type of digital technologies; Group (B) comprises firms that invested in at least one type of digital technologies in the of “Areas of
application of artificial intelligence” or “Other technological areas”; Group (C) comprises firms that invested in a bundle of at least two types of digital technologies;
Group (D) comprises firms that invested in a bundle of at least three types of digital technologies; Group (E) comprises firms that invested in at least one AI technology.

patterns in productivity dating back before the treatment. To test for the match, although with different weights; thus, all available infor­
these common trends before the treatment we could use information mation is exploited, as every firm is included in the estimation. The
back to 2013 and performed the following two tests. First, we regressed effect on the outcome variable estimated with the kernel matching
the log variation in TFP between 2013 and 2015 on the treatment model is the following:
dummy variable as well as on all the covariates used earlier for the ( )
NT NC
probit analysis but evaluated in 2013. In the second approach for testing 1 ∑ ∑
ATT = 100* T Δlog (TFP)Ti − wij Δlog (TFP)Cj , (2)
common trends before treatment, we replicated the PSM analysis com­ N i=1 j=1
bined with DiD as follows: first, in the probit analysis the treatment
dummy variable was regressed on all covariates documented before for where NT and NC are the number of, respectively, treated and control
the main analysis but referred to 2013. Then we matched treated and firms, and Δlog (TFP)Ti and Δlog (TFP)Cj are the values of the outcome
untreated firms using the propensity score from this estimation and variables for the i-th treated and the j-th control (untreated) firm,
computed the ATT using the log variation in TFP between 2013 and ∑ C
respectively. The term, Nj=1 wij Δlog (TFP)Cj , is the weighted average of
2015 as the outcome variable. In Table 7 we first report the estimated
coefficient of the dummy variable for the ‘fake’ treatment using the the outcome variables for all untreated firms.13
baseline and all the alternative definitions of ‘fake’ treatment. In all In Table 8 we report the estimated effect of treatment on the dif­
cases, the estimated coefficient is not statistically significant, and this ference in the log variation of TFP over the 2015–2018 period between
lends support to the hypothesis of common trends before the treatment. treated and control firms. For each matching method, we separately
Moreover, in the same table we document the estimated ATT using the consider each definition of treatment. When the larger caliper value is
PSM analysis described earlier. Again, no matter what the definition of used with radius matching, the estimated effects continue to be positive
treated firms are, no statistically significant effects of being in the and statistically significant as those reported in Table 5. With the
treatment group are detected in the TFP (log) variation between 2013 baseline definition of treatment, the estimated effect is almost identical
and 2015. We now turn to a robustness analysis and some extensions. to the corresponding one reported in Table 5 (0.92 vs. 0.97 per cent). For
the alternative definitions of treatment, the estimated effects are a little
6. Robustness and extensions bit smaller in size compared the those documented in Table 5 but their
profile across measures of treatment is qualitatively very similar. When
6.1. Other matching methods the kernel-based matching method is used, the estimated effects are
statistically significant and larger in size than those obtained with the
In our baseline analysis we have used the radius matching method radius matching. In general, however, their distribution across different
with a caliper value of 0.00001. Here we replicate the analysis using measures of treatment is like the one obtained with the other methods:
different approaches. First, we continue to use radius matching but with the smallest effect is found with the baseline definition of treatment and
a larger caliper value (0.001) and second, we employ the kernel-based
matching. As for radius matching, a larger value of the caliper value
implies that less firms drop out of the common support, as the re­ (p−π)
K i j
13
quirements for counterfactuals to be found become less stringent than in The expression for the weight, wij , is the following: wij = ∑NC (h pi − πj ), where
j=1
K h
the case with a smaller caliper value. The kernel matching associates to K(⋅) is the kernel function (widely used kernels are the gaussian and the
the outcome variable of a treated firm, i, a matched outcome given by a Epancehnikov), with K reaching its highest value of one when the untreated
kernel-weighted average of it for all untreated firms, where the weights firm, j, has the same propensity score of the treated firm, i (pi = πj ). h is the
are inversely proportional to the distance in the propensity scores of bandwidth (or smoothing parameter) that governs the pace at which the
firms i and j. With kernel-based matching all untreated firms are used in weights decline as distance increases (the higher is h, the lower is the pace).

12
F. Nucci et al. Economic Modelling 128 (2023) 106524

Table 8
The effect of digital adoption on productivity using other matching methods (Effects on percentage variation of TFP).
Baseline (A) and alternative definitions of treatment with digital adoption (B), (C), (D) and (E)

Baseline Alternative Alternative Alternative Alternative

Treatment Treatment Treatment Treatment Treatment
Group Group Group Group Group
(A) (B) (C) (D) (E)

I) Radius matching with a caliper value of 0.001

Outcome variable:
Percentage variation of 0.92*** 1.22*** 1.28*** 1.48*** 1.40**
TFP between 2015 and 2018 (0.350) (0.407) (0.392) (0.483) (0.602)
Number of “on-support” (“off-support”) untreated and treated firms 67,881 48,987 51,113 36,379 29,281
(44) (86) (77) (97) (158)
II) kernel-based matching

Percentage variation of 2.22* 2.81** 2.76** 3.20*** 3.32**

TFP between 2015 and 2018 (1.189) (1.211) (1.200) (1.237) (1.373)
Number of untreated 67,925 49,073 51,190 36,476 29,439
and treated firms

Notes: The coefficients represent the estimated difference in the 2015 to 2018 log-change in TFP between treated and control firms. Robust standard errors in pa­
rentheses. For the Radius matching (I), we report, for each definition of treatment, the number of “on-support” and (in parenthesis) “off-support” firms (i.e. those that
drop out of the common support).
As illustrated in the text, treatment group (A) comprises firms that invested in at least one type of digital technologies; Group (B) comprises firms that invested in at
least one type of digital technologies in the of “Areas of application of artificial intelligence” or “Other technological areas”; Group (C) comprises firms that invested in
a bundle of at least two types of digital technologies; Group (D) comprises firms that invested in a bundle of at least three types of digital technologies; Group (E)
comprises firms that invested in at least one AI technology.
***p < 0.01; **p < 0.05; *p < 0.10.

Table 9
Heterogeneity across Firms in the Effect of Digital adoption on Productivity Sample splitting analysis – Outcome variable: percentage variation of TFP between 2015
and 2018.
Manufacturing Service firms Younger firms Older firms Smaller firms Larger firms
Firms

Baseline 0.99* (0.527) 1.42** (0.586) 0.79 (0.615) 2.13*** (0.493) 0.86* (0.523) 1.63*** (0.554)
Treatment Group (A)
N. obs. 27,777 32,798 32,695 35,230 33,571 34,354
Alternative 1.54*** (0.571) 1.83*** (0.648) 1.00 (0.729) 2.12*** (0.543) 0.93 (0.615) 2.09*** (0.613)
Treatment Group (B)
N. obs. 21,895 22,160 22,902 26,171 23,298 25,775
Alternative 1.38** (0.584) 1.85*** (0.657) 2.16** (1.255) 1.91*** (0.497) 1.38** (0.598) 1.89*** (0.602)
Treatment Group (C)
N. obs. 21,212 24,582 24,586 26,604 24,640 26,550
Alternative 1.48** (0.684) 2.34*** (0.809) 1.20 (0.779) 2.05*** (0.604) 1.58** (0.778) 2.22*** (0.703)
Treatment Group (D)
N. obs. 15,498 17,156 17,596 18,880 17,706 18,770
Alternative 2.03** (0.804) 1.83** (1.062) 2.81*** (0.964) 0.95 (0.760) 2.24** (1.018) 2.02** (0.868)
Treatment Group (E)
N. obs. 12,880 13,565 14,361 15,078 14,665 14,774

Notes: In splitting the sample according to firm age, the threshold was the median across firms, calculated in 2015, in their years of activity since establishment. When
size is considered, the threshold was the median across firms in 2015 in their number of employees. The coefficients represent the estimated difference in the 2015 to
2018 log-changes in TFP between treated and control firms.
Robust and clustered standard errors in parentheses. For each definition of treatment and each sub-sample, the number of observations refers to both “on-support” and
“off-support” firms. As illustrated in the text, treatment group (A) comprises firms that invested in at least one type of digital technologies; Group (B) comprises firms
that invested in at least one type of digital technologies in the of “Areas of application of artificial intelligence” or “Other technological areas”; Group (C) comprises
firms that invested in a bundle of at least two types of digital technologies; Group (D) comprises firms that invested in a bundle of at least three types of digital
technologies; Group (E) comprises firms that invested in at least one AI technology. ***p < 0.01; **p < 0.05; *p < 0.10.

the effects increase when the definitions of treatment refer to more firm size and age, for example, as pointed out by many scholars, en­
advanced technologies or to bundles of at least two investments. We now terprises often need to supplement digital technologies, especially in the
investigate whether and how the estimated effect of digital adoption Industry 4.0 area, with complementary investments to effectively
varies across firm characteristics. embrace digital transformation and enjoy productivity gains (Bryn­
jolfsson et al., 2017). These complementary investments often imply
6.2. heterogeneous effects across firms significant upfront fixed costs, so that small firms, that are also more
likely to be financially constrained than larger firms, may face serious
The adoption of digital technologies can have idiosyncratic effects on obstacles in accumulating these assets and this may prevent them from
firms due to their characteristics, which can lead to different opportu­ reaping the benefits of digital transformation.
nities and challenges when digital investments are made. In terms of On the other hand, because smaller and younger firms may have a

13
F. Nucci et al. Economic Modelling 128 (2023) 106524

Table 10
The Effect of Digital adoption on other firm variables (Effects on percentage variation of the firm variable over the period 2015–2018).
Baseline Alternative Alternative Alternative Alternative
Treatment Treatment Treatment Treatment Treatment
Group (A) Group (B) Group (C) Group (D) Group (E)

I) Employment

Outcome variable
Percentage variation of employment between 2015 and 2018 4.79*** (0.418) 5.79*** (0.474) 6.10*** (0.470) 7.57*** (0.568) 9.90*** (0.708)
Number of “on-support” (“off-support”) firms 69,596 (3,178) 49,369 (3,168) 51,774 (3,091) 35,352 (3,813) 25,627 (6,020)

II) Revenues

Outcome variable:
Percentage variation of revenues between 2015 and 2018 5.97*** (0.435) 7.44*** (0.501) 7.51*** (0.488) 9.64*** (0.608) 11.47*** (0.742)
Number of “on-support” (“off-support”) firms 69,660 (3,058) 49,325 (3,171) 51,859 (2,960) 35,359 (3,770) 25,673 (5,945)

Notes: The two tests are described in the text. Robust standard errors are reported in parentheses. For each definition of treatment, we report the number of “on-
support” and (in parenthesis) “off-support” firms (i.e. those that drop out of the common support).
As illustrated in the text, treatment group (A) comprises firms that invested in at least one type of digital technologies; Group (B) comprises firms that invested in at
least one type of digital technologies in the of “Areas of application of artificial intelligence” or “Other technological areas”; Group (C) comprises firms that invested in
a bundle of at least two types of digital technologies; Group (D) comprises firms that invested in a bundle of at least three types of digital technologies; Group (E)
comprises firms that invested in at least one AI technology.
***p < 0.01; **p < 0.05; *p < 0.10.

very low level of digital adoption and some technologies significantly significant for all definitions of treatment. Interestingly, the only
reduce the costs of transporting and transmitting data (Goldfarb and exception of a stronger effect for smaller, rather than larger, firms is
Tucker, 2019), we might also expect digital adoption to increase value again the case in which digital treatment is defined through investments
creation in these firms more than in the others. made in AI technologies.16
For all these reasons, in an extension of the analysis, we investigate
the degree of difference (if any) in the estimated effect of digital adop­
6.3. Digitalization and other firm variables
tion on productivity that depends on specific firms’ structural charac­
teristics. We address this issue by applying our methodology on different
Whilst this paper focuses more on productivity, it might also be
sub-samples of data that separate firms according to their sector, the age
important to shed some light on how other dimensions of firm’s
and the size. The results are reported in Table 9. First, we split the whole
behavior are affected by the digital transformation. Therefore, we
sample based on whether a firm operates in the manufacturing or the
investigated how the adoption of digital technologies affects other firm
service sector.14 The estimated effect of digital adoption on productivity
variables in addition to productivity. In so doing, we rely on the same
variation is found to be slightly stronger in firms in the service sector
methodology used thus far, and conduct this further analysis with
than in manufacturing firms. This holds true using the baseline defini­
reference again to all our five measures of the firm propensity to invest
tion (A) of treatment as well as the alternative definitions, with one
in digital technologies. The other firm variables we focus on are
exception only. With definition (A) of treatment, the effect in services is
employment and revenues. In Table 10, we document the effect of the
1.42 per cent vs. 0.99 in manufacturing. However, when we turn to
treatment with digital technologies on the percentage variation of each
investments made in AI technologies, the effect is much stronger in
of these variables over the period 2015–2018.
manufacturing than in services (2.03 vs. 1.83 per cent, respectively). In
We detect a positive and statistically significant impact of digital
all cases the estimated effects are statistically significant whilst with
adoption on the percentage change between 2015 and 2018 of both
different confidence level. Second, we consider firm age and distinguish
employment and revenues and this holds true across all measures of
between younger and older firms. The criterion for splitting the sample
treatment. The estimated effect tends to be larger as we consider more
is the median, in 2015, of the number of years since establishment and
stringent definitions of the treatment with digital adoption that involve
the threshold age is 18 years. The effect on productivity of adopting
investing in more advanced technologies (like AI) or in bundles of more
digital technologies is found to be larger in older than in younger firms
than one technology.
when the baseline definition of treatment is used and in three cases out
of five. The case of treatment with investments made in AI is one of the
7. Concluding remarks
two exceptions for which the effect is stronger in younger than in older
firms. Third, we focus on size and distinguish between smaller and larger
Using firm-level information of high quality drawn from differences
firms. The splitting criterion is based on the median of the number of
sources we first characterize the process of digital transformation of
workers in 2015 and the threshold number is 26.1 workers.15 In general,
Italian firms using information of unusual breadth. We focused on
the impact of digital technologies on productivity change is estimated to
numerous types of investments in digital technologies that firms have
be stronger in larger than in smaller firms and the effect is statistically
(or have not) made in the period 2016–2018 and we identified differ­
ences across firms in the propensity to adopt digital technologies. We did
14 so by considering various dimensions of digital adoption, such as
The number of observations in these two sub-samples is lower than the
whether investments in technologies have been made in more advanced
corresponding number of observations in the whole sample considered so far
for each distinct definition of treatment. The reason is that in our sample split
domains (like AI) or in bundles of more than one type of new technol­
we have distinguished between manufacturing vs. service firms and have ogies. We therefore used a variety of alternative criteria to classify firms
therefore excluded firms operating in the following sectors: Electricity, Gas,
Steam and Air Conditioning supply; Water supply, Sewerage, Waste Manage­
16
ment and Remediation Activities; Construction. While these findings unveil a discernible and significant degree of hetero­
15
In the Istat registers, the number of workers reported for each firm in a geneity in the estimated effects, we are aware that a split of the sample to zoom
given year is the yearly average. Hence, the information on the number of in on specific classes of firms, by reducing the number of observations, may
workers in a firm can well be a non-integer number. reduce the ability of the PSM methodology to find good matches.

14
F. Nucci et al. Economic Modelling 128 (2023) 106524

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