The ICT Revolution and Italy's Two Lost Decades∗
Fabiano Schivardi Tom Schmitz LUISS University, EIEF and CEPR Bocconi University and IGIER
May 19, 2017
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Abstract
Since the middle of the 1990s, Italy's catching-up process with respect to other advanced economies
has ended, and output per capita has started to diverge. One potential reason for this divergence is
the failure of Italian rms to take up the ICT revolution. We provide micro-level evidence on low ICT
adoption in Italy, and show how it is linked to ine cient management practices and ampli ed by input-
output linkages. We then build a general equilibrium model with heterogeneous rms, management and
ICT adoption choices, and production networks, and use it to analyse the quantitative importance of the
ICT revolution for Italy's divergence. We nd that the ICT revolution can account for approximately
25% of the divergence between Italy's and Germany's GDP per hour worked between 1995 and 2015, the
largest part being due to ine cient management lowering the adoption rate and the productivity of ICT
technologies. While the best way for Italy to catch up would be to improve management practices, the
fact that production networks create externalities which make ICT adoption ine ciently low creates a
role for subsidy policies to improve aggregate outcomes.
Keywords: Italy, Productivity slowdown, Divergence, ICT, Technology adoption, Management.
JEL Codes: L23, O33
∗Schivardi: Department of Economics, LUISS University, Rome, Italy, [email protected]. Schmitz: Department of Eco- nomics, Bocconi University, Via Roentgen 1, 20136 Milan, Italy, [email protected].
1 1 Introduction
From the end of World War 2 to the middle of the 1990s, Italy had higher or equal GDP growth rates than the United States and Northern Europe. Since then, however, Italian growth has been dismal, driven by exceptionally low productivity growth. Between 1995 and 2015, real GDP per hour worked in Italy grew by just 6%, whereas it increased by 24% in the entire Eurozone, 28% in Germany and 40% in the United
States (see Figure 1). The reasons for this twenty-year long divergence between Italy and other developed economies are still not fully understood.1
Figure 1: Growth and ICT adoption 1.4 5 4 1.3 3 1.2 2 1.1 1 GDP per hour worked, 1995 = 1 1 0
1995 2000 2005 2010 2015 ICT capital services per hour worked, Real Euros 1980 1985 1990 1995 2000 2005 Year Year
USA Italy US ITA Germany GER
GDP per hour worked ICT intensity Note: GDP per hour worked is taken from the OECD (available at http://stats.oecd.org, accessed on May 18, 2017). ICT intensity is measured by ICT capital services per hour worked from the EU KLEMS database. This series is only available up to 2007. Dollar values for the United States are converted into Euros by using the average exchange rate between 1999 and 2007.
In this paper, we analyse and quantify one potentially important reason for divergence: the failure of Italian
rms to take up and e ciently use Information and Communication Technologies (ICT). Indeed, the ICT revolution has been an important driver of productivity growth in other developed countries since the mid-
1990s (Fernald (2014), Gordon (2016)).2 In Italy, however, it has made relatively little headway. In 2007,
Italian rms' ICT capital per hour worked stood at roughly one third of the German and one fth of the
US level (see Figure 1). In the European Commission's 2016 Digital Economy and Society Index, Italy ranks 15th out of 19 Eurozone countries for the integration of digital technology in rms.3 We argue that the low diusion of the ICT revolution and its comparatively small impact on productivity are due to the
1Italy's experience is similar to that of other Southern European countries. For instance, Spanish real GDP per hour worked also increased by only 16% between 1995 and 2015, and Spain's TFP growth was even lower than Italy's. 2In 1987, Robert Solow famously complained that you can see the computer age everywhere, except in the productivity statistics (Solow (1987)). However, Fernald (2014) and Gordon (2016) show that around ten years later, ICT caused productivity growth in the United States to accelerate substantially for about a decade (1994-2004). They also note that growth has slowed down since, and Gordon claims that it will remain low in the foreseeable future. Yet, even the lower growth rate of US productivity between 2005 and 2015 is substantially higher than the Italian one in that same time period. Also, others have been more optimistic about the future productivity-enhancing capacities of ICT (Brynjolfsson and McAfee (2014)). 3Luxembourg, Greece, Latvia and Estonia are ranked lower. See https://ec.europa.eu/digital-single-market/en/desi.
1 lower e ciency of Italian rms' management practices. Building on the widespread empirical evidence on the complementarity between ICT and e cient management (Brynjolfsson and Hitt (2000), Garicano and
Heaton (2010), Bloom et al. (2012)), we show that ine cient management practices have lowered both ICT adoption and ICT productivity. Furthermore, they have skewed the Italian rm size distribution towards small rms, further depressing ICT adoption rates because of xed adoption costs and production network externalities. We argue that these factors can explain a sizeable share of Italy's divergence.
Using micro-level data from the European Union's Community survey on ICT usage and e-commerce in enterprises, we rst provide evidence on ICT adoption rates in Italy and Germany (which we use throughout as a point of comparison). We show that Italian adoption rates are lower for a range of ICT technologies.
This appears to be due to ICT demand rather than ICT supply factors, and in particular, to the ine cient management practices of Italian rms. Finally, we show that production networks matter. Italian adoption rates are particularly lower than German ones for technologies which are useful to rms if others in their production network have adopted them as well, such as software for supply-chain management (SCM).
Furthermore, the SCM adoption choice of rms is positively correlated with the presence of large rms in the same industry and region before the ICT revolution, suggesting that SCM adoption by (large) nal producers spills over to their (smaller) suppliers.
We then build a general equilibrium model with heterogeneous rms, ICT and management adoption choices, and production networks, in order to quantify the importance of the ICT revolution for divergence and to do some counterfactual policy experiments. The basic features of our model are similar to a standard Melitz
(2003)/Hopenhayn (1992) framework. A continuum of nal producers produce a set of dierentiated goods under monopolistic competition. To enter the market, rms pay a xed entry cost and take a productivity draw from an exogenous distribution. After learning the outcome of this draw, they decide whether to stay in the market and produce (in which case they need to pay another xed cost) or to exit. We enrich this standard setting by allowing rms to increase their productivity through management and ICT, and by introducing intermediate inputs. Management and ICT both increase nal producers' productivity, but have a xed adoption cost. Importantly, we assume that rms can only adopt ICT if they also adopt management, in line with the strong complementarity documented by the empirical literature. As adoption bene ts are proportional to productivity, but adoption costs are not, nal producers then sort into dierent categories according to their productivity draws: the rms with the highest draws adopt both management and ICT,
rms with intermediate draws adopt only management, rms with lower draws do not adopt any of the two, and the rms with the lowest draws exit the market. Each nal producer uses labour and a set of rm-speci c intermediate inputs, produced by suppliers. Suppliers are modelled analogously to nal producers, but we
2 assume for simplicity that they produce only with labour and cannot adopt management. However, they can adopt ICT, which helps them to reduce some iceberg coordination costs between themselves and their nal producer, if and only if the latter has also adopted ICT. This strong complementarity captures the network component of technologies such as SCM, and introduces an externality, as rms do not fully internalize the eects of their ICT adoption decision on their production network.
We calibrate this model to the Italian and German economies. Precisely, we compare both countries' equilibria before the ICT revolution (when we assume that the ICT technology is not available) to their equilibria after the ICT revolution (when we assume that it is), assuming they dier in only two parameters, management and ICT productivity. These parameters capture the productivity increases due to the adoption of these two technologies. We calibrate them using microeconometric evidence from Bloom et al. (2012, 2016), and
nd that both are lower in Italy, as ine cient management both directly lowers productivity and reduces the e ciency with which rms use ICT.
We nd that the ICT revolution increases income dierences between Italy and Germany. Low ICT produc- tivity directly lowers aggregate productivity, as less Italian rms adopt ICT and the adopting rms increase their productivity by less. This direct eect is compounded by an indirect selection eect: as the most e - cient rms expand less, ine cient rms can stay in the market. Low management productivity further lowers the bene ts of ICT adoption with respect to its costs. Furthermore, the ICT revolution eventually increases the share of rms using management, and therefore increases the diusion of an ine cient technology in the Italian economy. Finally, production networks add a multiplier eect, as lower ICT adoption by nal producers spills over to suppliers. Jointly, these eects generate a divergence between Italian and German income per capita of 5.5 percentage points, 25% of the actual divergence between 1995 and 2015. The largest share of this divergence is explained by Italy's lower ICT productivity. To close the gap with Germany, our model suggests therefore that Italy needs to improve management practices, the ultimate source of its low
ICT productivity. However, doing so may be complicated and take time. In the short run, ICT subsidies may reduce the gap somewhat, as network externalities make ICT adoption suboptimally low.
Our work is closely related to Bloom et al. (2012) and Pellegrino and Zingales (2014). Bloom et al. (2012) show that the subsidiaries of US multinationals in Great Britain use more ICT, and use ICT more productively than subsidiaries of multinational rms from other countries, or British rms. They interpret this as evidence that the management practices of US rms enhance their e ciency at using ICT, and argue that it can explain growing divergence between Europe and the United States. Similarly, Pellegrino and Zingales (2014) argue that familism and cronyism in Italian rms made them unable to bene t from the ICT revolution.4 While
4Furthermore, they argue that another reason behind Italy's divergence is the greater prevalence of small rms, which may have inhibited a productive response to higher international competition.
3 we also argue that low ICT productivity due to ine cient management is important, our paper puts forward additional divergence channels (such as the fact that the ICT revolution makes ine cient management more widespread, and that adoption by nal producers spills over to their suppliers). More importantly, we provide a full quantitative assessment and counterfactual policy analysis based on a general equilibrium model, while the earlier papers only show microeconometric results.5 Other studies have recently explored the role for dierences in management e ciency in explaining cross-country productivity dierences, but have not linked them to ICT (Guner et al. (2015), Akcigit et al. (2016), Bloom et al. (2016)).
In other related work, Garicano (2015) argues that on top of ine cient management, the prevalence of small
rms in Italy, driven by size-dependent regulations, could explain its low ICT adoption rates. However, while there is evidence that size-dependent regulations are important in other countries such as France (Garicano et al. (2013)), they have only a marginal eect for the Italian rm size distribution (Schivardi and Torrini
(2008)). In our model, the Italian size distribution is also skewed towards smaller rms, but this is an endogenous consequence of low management and ICT productivity, which do not allow the largest rms to expand as much and therefore lower competitive pressures on smaller and less e cient rms. Finally, other studies have emphasized dierent explanations for the Italian productivity slowdown, citing increasing misallocation (Calligaris (2015), Calligaris et al. (2016)), implicit subsidies to low-skilled labour (Daveri and
Parisi (2010)) and worsening governance (Gros (2011)). Certainly, such a long-lasting and deep phenomenon as the Italian slowdown is not monocausal, and we do not claim that the ICT revolution it its only driver.
However, we provide evidence for it being an important factor.
The remainder of the paper is structured as follows. Section 2 presents empirical evidence on the Italian divergence, and on ICT and management adoption at the micro level. Section 3 introduces our model, and Section 4 studies its comparative statics with respect to management and ICT productivity. Section 5 describes the model's calibration, its quantitative predictions and the counterfactual policy exercises.
2 The Italian divergence and ICT adoption
Italy's divergence started around the same time as the ICT revolution (that is, rms' large-scale adoption of ICT) increased productivity growth in most developed economies. There is a consensus that ICT was an important factor for the increase in productivity growth in the frontier economies, particularly the US
Fernald (2014); Gordon (2016).6 The increase has been lower but still substantial in Germany, while it was
5Using Bloom et al's data, Hassan and Ottaviano (2013) also argue that low ICT adoption due to ine cient management could be behind Italy's divergence, but they do not provide a model or a quantitative assessment. 6The literature typically explains the Solow paradox, and the delay of ICT showing up in productivity statistics, with the necessity of implementing long-lasting organizational changes to fully exploit the possibilities of ICT (Brynjolfsson and Hitt, 2000).
4 much more modest in Italy. In 2007, ICT capital services per hour worked in Italy were around one euro, against three for Germany and more that ve for the US (see Figure 1).
Importantly, the Italian slowdown is not due to its sectoral structure: Italian productivity growth has been lower than that of Northern Europe or the United States within virtually every sector (Pellegrino and Zingales
(2014)). Thus, the slowdown cannot be due to Italy being specialized in the wrong sectors, but must be due to more general factors aecting the economy as a whole. So, given that ICT boosted productivity growth in the frontier economies, and Italy appears to have had little ICT penetration, it is reasonable to suppose that the Italian slowdown can be explained at least partially by this fact.
Our key hypothesis is that Italy's low take-up of the ICT revolution is ultimately due to the ine cient man- agement of its rms. This ine ciency aects ICT adoption through two channels. The rst is direct: as management and ICT are complements, lower managerial e ciency lowers the productivity of ICT technolo- gies and thus the incentives to adopt them. Second, lower managerial e ciency results in a size distribution tilted to the left. Smaller rm size reduces ICT adoption, due to the xed cost component of the adoption choice and to the network externalities that characterize some ICTs. In the reminder of this section we oer some empirical evidence to corroborate this hypothesis, before proposing a theoretical model to analyze and quantify it.
2.1 Managerial practices, rm size and ICT adoption
As has been shown by, among others, Bloom et al. (2016), the average quality of managerial practices employed by Italian rms is lower than that of German or American rms. Bloom et al. propose a method to measure the quality of managerial practices and apply it to a large set of rms in dierent countries. They
nd large variations across countries in the average e ciency of the managerial practices. For example, the dierence between German and Italian rms in the average (zero-mean and unit-standard deviation) score of managerial practices is 0.36 (see Table 7 of Bloom et al. (2016)).
One possible explanation for this dierence is ownership and control dierences between Italy and Germany.
Bloom and Van Reenen (2007) show that rms owned and controlled by an individual or a family tend to display management practices of lower quality than rms with other ownership and control mode, such as, with dispersed shareholders, owned by a private equity fund, owned by a family but run by an external CEO.
As it turns out, Italian family rms are reluctant to open up the rm's control to managers external to the
rm. Table 1, taken from Bugamelli et al. (2012) and based on the EFIGE database,7 shows that while
7The EFIGE dataset has been assembled in 2009 as the result of a European eort coordinated by the Bruegel institute (see Altomonte and Aquilante, 2012). The survey covered a representative sample of rms with more than 10 employees in seven European countries (including Italy, Germany, France and Spain), and contained questions both about rms' usage of ICT and about their management structure. Furthermore, through linking the original survey to the Amadeus database, provided by Bureau Van Dijk, the dataset also contains a large number of balance sheet variables, allowing to calculate dierent measures
5 family ownership of rms is very common in most European countries8, Italy stands out for the share of family rms that are fully controlled by the owning family (i.e., that do not have any managers from outside that family). This is the case for two thirds of all Italian rms, whereas in France, Germany and the UK this happens for less than 30% of rms. This striking fact suggests ine ciencies in the managerial delegation process in Italy.
Table 1: Share of rms with family ownership and control (in percentage points)
Family owned rms Within family owned rms: CEO is a All executives are family member family members France 80.0 62,2 25,8 Germany 89,8 84,5 28.0 Italy 85,6 83,9 66,3 Spain 83.0 79,6 35,5 United Kingdom 80,5 70,8 10,4
Source: EFIGE database (see Bugamelli et al. (2012)).
A consequence of lower e ciency and of the reluctance to open up control of family rms should be that
Italian rms in general are less likely to hire external managers. As Figure 2 shows, 77% of German rms hire at least one external manager, while this is the case for only 40% of Italian rms. Furthermore, there are large dierences in the share of managers in the total workforce of rms, going from on average 6.5% in
Germany to 3.1% in Italy. These dierences are large in essentially any size class.
Figure 2: Firms with managers, by size class
Firms with Managers by Size Class Share of Managers by Size Class
GER GER 10−19 employees 10−19 employees ITA ITA
GER GER 20−49 employees 20−49 employees ITA ITA
GER GER 50−249 employees 50−249 employees ITA ITA
GER GER 250+ employees 250+ employees ITA ITA
0 .2 .4 .6 .8 1 0 2 4 6 8 % of firms % of of workers
Source: EFIGE database
Lower managerial e ciency can lead to lower adoption rate of ICT. There is indeed ample evidence that of productivity. 8Ownership and control structure are self-reported.
6 Figure 3: Average rm size 20 15 10 Average Firm Size 5 0 United States Germany Italy Spain
Source: Eurostat Structural Business Statistics
ICT is complementary to skilled labor (Bresnahan et al. (2002); Caroli and Van Reenen (2001)). Typically, managers are highly educated, suggesting that the complementarity is with such workers. Bloom et al.
(2012) directly study the complementarity between management and ICT. They nd that rms with better managerial practices have a higher return from ICT adoption in terms of productivity growth.
While complementarity represents a direct channel through which managerial e ciency can aect ICT adop- tion, the second channel goes through the size distribution. Given that managerial practices aect rms e ciency, they translate into dierences in size: in fact, large institutions need codi ed procedures and prac- tices, so that good managerial practices are an essential ingredient of rm growth. An implication is that average rm size should be larger in countries where rms employ better practices. Indeed, Eurostat's Struc- tural Business Statistics indicate that the average US rm has around 19 employees, the average German
rm has around 12 employees, but the average Italian rm has less than 5 (see Figure 3). The ranking in terms of the size distribution is the same as that of managerial practices.
2.2 Micro-level evidence on ICT adoption
We now document the patterns of ICT adoption in Italy and Germany. To do so, we use the 2014 wave of the European Community survey on ICT usage and e-commerce in enterprises. This survey is coordinated by Eurostat, but run by national statistical o ces, who also regulate their availability to researchers. The survey is based on a representative sample of rms with more than 10 employees,9 strati ed by sector, size
9National statistical institutes can also choose to survey smaller rms, and both the Italian and the German one do so. However, the Italian statistical institute does not make this data available to researchers, so that we choose to ignore rms with less than 10 employees throughout. Furthermore, due to more stringent data protection regulations, the Italian data contains very limited rm-level information apart from ICT adoption. For instance, we cannot observe the actual number of employees
7 and geographical area. It covers 19,000 rms for Italy and around 7,500 for Germany.
As a general indicator of ICT adoption, we consider whether the rm employs ICT specialists, that is, workers with speci c ICT skills, for which ICT and information systems management represents the main occupation.
Table 2 reports the share of rms that employ ICT specialists, in total and by size class (columns [1] and [2]).
Overall, 15% of Italian rms employ ICT specialists, against 23% of German rms, a dierence in adoption rates of 8 percentage points, or more than 50%. The likelihood of employing ICT specialists is strongly increasing in rm size: it goes from 22% in the 10-49 size class in Italy to 81% in the 250+ size class in
Germany. This is expected: ICT technologies are characterized by a xed-cost component that makes larger
rms more likely to adopt them.10 However, the table indicates that this is not the whole story: with the exception of the 10-249 size class, the adoption rate of Italian rms is lower within class, indicating that they have a lower propensity to adopt ICT even when controlling for rm size.
Table 2: ICT diusion and barriers to adoption in Italy and Germany
ICT specialists Di c. in hiring Fixed connect. Max speed
[1] [2] [3] [4] [5] [6] [7] [8] ITA GER ITA GER ITA GER ITA GER Size class 10-49 11 15 33 54 95 94 2,40 2,57 50-99 35 39 22 56 97 96 2,55 2,77 100-249 58 57 24 40 97 97 2,63 2,90 250+ 74 81 28 53 98 98 3,02 3,50
Total 15 23 30 52 95 95 2,43 2,64
Note: Cells in columns [1]-[6] report the share of rms that have aswered yes to the following question: if the rm employs ICT specialists ([1]-[2]); if the rm has encountered di culties in hiring ICT specialists, only for rms that tried to hire ([3]-[4]); and if the rm has a xed internet connection ([5]-[6]). Columns [7]-[8] report the maximum download speed. All statistics use survey weights. For clarity, we report unconditional summary statistics. All results are con rmed when we control for sectoral and geographical dummies.
In this paper, we emphasize the role of low rm demand for ICT to explain lower ICT adoption. However, one could imagine that low supply of ICT-related human capital or infrastructure plays a role, too. Table
2 provides some evidence against this alternative explanation. Columns 3 and 4 display the percentage of
rms that reported di culties in recruiting ICT specialists (among those who were on the market for such workers). While in Italy 30% of rms reported problems, in Germany 52% did so, indicating that scarcity of
ICT-related skills cannot explain the ICT adoption gap between the two countries. Furthermore, there do not appear to be large cross-country dierences in the access to or speed of internet connections (Columns 5 and sales of Italian rms, but only dummies for size classes. 10For earlier studies on ICT adoption also showing a positive correlation between size and adoption see Fabiani et al. (2005) for Italy and Bayo-Moriones and Lera-López (2007) for Spain.
8 through 8). Overall, this evidence suggest that demand factors are key to explain the dierences in adoption rates between Italian and German rms.
2.3 Dierences between ICT technologies and network eects
Having established that Italian rms adopt less ICT in general than German rms even within size class, we now exploit the richness of the Eurostat survey to shed some more light on the possible mechanisms behind these dierences. The expression ICT is used to indicate an array of diverse technologies, such as organizational software, software for supply chain management, online sales, websites and social networks, which serve dierent purposes. In Table 3 we report the adoption rate of four speci c technologies that are likely to have a direct impact on productivity: Enterprise Resource Planning (ERP), Radio-Frequency Iden- ti cation (RFID) for products, Customer Relationship Management (CRM) and Supply Chain Management
(SCM). Broadly speaking, the rst two technologies are used to organize production within the rm while the other two are used to organize the interaction with entities external to the rm, in particular customers and suppliers.
Table 3: Key indicators of ICT adoption in Italy and Germany
ERP RFID CRM SCM
[1] [2] [3] [4] [5] [6] [7] [8] ITA GER ITA GER ITA GER ITA GER Size class 10-49 34 33 3 3 17 25 15 20 50-99 58 60 8 4 27 36 21 33 100-249 70 68 11 8 31 40 23 38 250+ 79 85 12 12 36 48 36 57
Total 38 41 4 4 19 28 16 24
Note: Each cell reports the share of rms that have answered yes to the following questions: if the rm uses enterprise resource planning software (ERP, [1]-[2]); if the rm uses Radio-Frequency Identi cation technology to monitor the production process (RFID, [3]-[4]); if the rm uses Customer Relationship Management software to organize and process information about customers (CRM, [5]-[6]); if the rm uses Supply Chain Management software to communicate and coordinate with customers and suppliers (SCM, [7]-[8]). All statistics use survey weights.
As it turns out, there are some dierences in adoption patters between the two classes of technologies. For
ERP and RFID, total adoption rates are fairly similar between Italy and Germany. In particular, if we compare homogeneous size classes, the adoption rates of Italian rms is very close to that of German rms.
For these technologies, Italian adoption rates are depressed because of the skewed size distribution, but there does not appear to be an eect conditional on size. In the case of CRM and SCM, instead, we nd a country
9 eect above and beyond that of size: adoption rates are lower in Italy, both in total but also comparing rms in the same size class. As we show below, this dierence is possibly related to network externalities. Before doing so, however, we document that ICT adoption and productivity are related.
2.4 ICT and rm productivity
In our dataset, we can verify that ICT adoption increases rm productivity.11 Table 4 reports the results of OLS regressions of log of sales per worker on various indicators of ICT adoption. In column [1] we only control for size dummies, in addition to industry and regional dummies, included in all regressions. As expected, productivity monotonically increases with size: rms with 50-99 employees produce on average approximately 15% more sales per worker than rms with 10-49 employees, those with 100-249 employees
25% more and those with 250 or more employees 30% more. In Column [2] we include a dummy for rms hiring ICT specialists. The dummy is highly signi cant and the eect is substantial: rms with ICT specialists have a productivity that is two thirds higher than rms without them. Interestingly, once we include this variable, the size dummies lose signi cance. Of course, this relationship should not be interpreted as causal.
However, it does indicate that even a simple binary indicator of ICT adoption is strongly correlated with productivity and that, conditional on such indicator, size does not matter anymore. In Column [3] we include an alternative measure of ICT expense, a dummy for rms that oer formal training to ICT specialists (results do not change if we use training for non ICT specialists). The pattern is very similar to that in column [2].
Results are also con rmed when we control for ERP adoption (Column [4]). In the next two columns we include the dummies for adoption of the technologies that we de ned as allowing to manage relationships
external to the rm, that is, Customer Relationship Management /CRM and Supply Chain Management.
We argued that these technologies are less about the internal organization of the rm and more about how the rm relates to customers/suppliers. As such, their eects on e ciency might be not as strong as for the
ERP, that instead allows to organize and manage production processes within the rm. We nd that rms that have adopted these technologies are indeed more productive, but the eect of the size dummies in this case survives, although smaller than in the baseline regression of Column [1]. Of course, as Table 2 shows, the diusion rate of these technologies is lower than that of ERP, which might also explain why the size eect survives their inclusion. This is even more apparent when we consider Radio Frequency Identi cation, that only 4% of rms have adopted (Column [7]). Finally, in Column [8] we perform a horse race and include all the indicators at the same time. Not surprisingly, the eect of each one of regressors is reduced, as dierent measures of ICT adoption tend to be correlated within rms. Even so, the dummies for the presence of ICT
11Unfortunately, we have a (rough) measure of labour productivity for Germany, where we have data on sales and on the number of employees. For Italian rms, we do not observe rm sales or employment. We therefore run this exercise for German rms only.
10 Table 4: Productivity, size and ICT adoption
[1] [2] [3] [4] [5] [6] [7] [8] Size dummies 50-99 emp 0.142*** 0.025 0.021 -0.019 0.074** 0.091*** 0.095*** -0.042 (0.029) (0.029) (0.030) (0.030) (0.030) (0.029) (0.030) (0.032) 100-249 emp 0.229*** 0.014 0.015 0.006 0.134*** 0.153*** 0.171*** -0.076** (0.033) (0.035) (0.035) (0.035) (0.034) (0.032) (0.034) (0.037) 250+ emp 0.272*** -0.062* -0.085** -0.030 0.154*** 0.123*** 0.198*** -0.218*** (0.032) (0.037) (0.039) (0.036) (0.033) (0.033) (0.033) (0.044) ICT specialist 0.513*** 0.082** (0.029) (0.037) Training 0.486*** 0.147*** (0.031) (0.037) ERP 0.499*** 0.269*** (0.029) (0.031) CRM 0.259*** -0.011 (0.025) (0.031) SCM 0.369*** 0.157*** (0.025) (0.027) RFID 0.098* -0.024 (0.052) (0.052)
Cons. 11.277*** 11.291*** 11.381*** 11.240*** 11.293*** 11.248*** 11.377*** 10.916*** (0.085) (0.084) (0.089) (0.085) (0.090) (0.085) (0.090) (0.114) R-sq 0.1057 0.1469 0.1420 0.1487 0.1190 0.1317 0.1071 0.2578 No. Obs 7583 7493 6900 7040 6966 7534 6889 6303
Note: The dependent variable is the natural logarithm of sales per worker. 50-99 emp is a dummy for rms with between 50 and 99 employees, and similarly for the other size dummies, with the excluded category being rms with 10-49 employees. ICT specialists is a dummy equal to one if the rm employs ICT specialists, and Training, ERP, CRM, SCM and RFID are analogously de ned dummy variables. All regressions include 30 industry and 16 regional dummies. Robust standard errors in parenthesis. *** indicates signi cance at 1%, ** at 5%, * at 10%. specialists, training, ERP and SCM are still highly signi cant. With all these controls, the size dummies turn negative, possibly suggesting that, controlling for ICT adoption, the production technology display decreasing returns to scale.
The analysis of this subsection delivers two main results. First, in general ICT is correlated with rms productivity. Second, of the four technologies analyzed in Table 2, those for which the correlation survives in the saturated regression of Column [8] are ERP and SCM. In what follows, therefore, we concentrate on these two technologies.
2.5 Network externalities and rm size distribution
Why do we observe the relative dierences in adoption rates between external and internal technologies documented in Table 2? One possible explanation is related to the network component of some ICT technolo- gies, particularly SCM technologies. In general, SCM refers to the e cient organization of the supply chain
11 from raw materials to nal goods. The production of most goods and services typically entails some form of work division between rms. This division generates transactions costs, such as shipping intermediate inputs between rms, managing inventories, or communicating the features of the required intermediate inputs.
The SCM technologies allow to optimize this process, reducing transaction and coordination costs between
rms. The key aspect is that their usefulness for each rm critically depends on the degree of adoption of other rms along the supply chain. Stated dierently, they are a textbook case of network externality, where
the value [of adopting the technology] is dependent on the number of others using it (Shapiro and Varian
(2013)). It might than be that a system where production is more fragmented among a large number of small producers (Italy) naturally tends to deliver lower adoption rates than one in which there are more medium and large size rms, that operate as a coordination mechanism along the production chain and facilitate the spread of these technologies also among small rms. This is less of an issue for ERP technologies, that allow for a better management of ows internal to the rm, and whose productivity is not subject to the network externality. One possible explanation of the lower adoption of external technologies is therefore a rm size distribution skewed towards small rms.
To empirically test the relevance of this channel, we perform the following exercise on Italian rms. We exploit the fact that, as shown by Guiso and Schivardi (2007), Italian rms tend to be clustered at the geographical-sectoral level, and that geographical and technological proximity foster input-output exchanges.
We therefore test if a rm's probability of adoption of SCM technology depends on the size distribution of
rms in the same area and sector. Adoption data come from the Eurostat survey used before, which reports the region and the two digit sector of each rm.12 We match each region-sector combination with data on
rms size distribution from the 2001 Census, a year in which ICT diusion was still modest (see Figure 1) and therefore unlikely to aect the size distribution much.
We then run probit regressions of the SCM adoption dummy on indicators of the size distribution at the region-sector level for the ERP and SCM technologies. As indicators of the size distribution, we consider three dierent statistics at the regional-sectoral level: the share of small rms (1-10 employees), of medium size rms (50-999), and large rms (1000+). We nd substantial heterogeneity in the size distribution across region-sectors: the average share of small rms is 0.87 with a standard deviation of 0.16, that of medium sized
rms is 0.021 with a standard deviation of 0.038, and that of large rms is 0.001 with a standard deviation of
0.006. To ensure that the results are not driven by the fact that some sectoral characteristic might be driving both size structure and adoption rates, we insert a full set of sector dummies, as well as regional dummies to control for regional eects. We also include 4 rm size dummies for the size categories. The results are
12Guiso and Schivardi (2007) also use two digit sectors, while they use Local Labor Systems as the geographical unit, a substantially ner de nition than regions. Unfortunately, due to con dentiality reasons regions are the smallest geographical unit we have access to.
12 reported in Table 5.
Table 5: Italian rms: Probability of adoption in 2014 and share of rms by size class in 2001
[1] [2] [3] [4] Panel A: ERP Share of rms: Small (1-10) 0.540** 0.695*** (0.236) (0.277) Medium (50-999) -0.0332 0.782 (0.569) (0.624) Large (1000+) -1.183 -0.963 (1.813) (1.865) Obs. 18,824 18,824 18,824 18,824
Panel B: SCM
Small (1-10) -0.940*** -0.888*** (0.265) (0.323) Medium (50-999) 1.342** 0.261 (0.617) (0.755) Large (1000+) -1.182 -1.358 (1.235) (1.195) Obs. 18,824 18,824 18,824 18,824
Note: The table reports the results of probit regressions of the adoption choice of Italian rms of ERP (panel A) and SCM (Panel B), as de ned in the note to Table 3, on the share of rms by size class in each rm's sector-region in 2001. All regressions include size class dummies (4), 2-digit sector dummies (62) and region dummies (20). standard errors clustered at the region-sector level in parenthesis. * p < 0.10, ** p < 0.05, *** p < 0.01.
Panel A reports the regressions for the ERP technology. We nd no evidence of a negative relationship between size and adoption. If anything, a larger share of small rms increases adoption. One possible explanation is that, in the absence of network externalities, a larger share of small rms can increase adoption via competition (Aghion et al. (2005)) and/or information spillover eects (Guiso and Schivardi (2007)).
Instead, neither the share of medium nor of large rms has any eect on the adoption rate.13
Things are dierent for the SCM technology. In this case, the share of small rms has a strong negative impact on adoption, while that of medium rms has a positive impact. This is in line with the idea that a large population of small rms magni es the negative eects of network externalities on adoption rates, while medium rms do the opposite. While we have no information on the position of each rm in the supply chain, one possible interpretation is that medium size rms are more likely to be downstream rms, buying intermediates from local small rms. A larger population of medium sized rms can reduce the extent
13These results are in line with the ones of Fabiani et al. (2005) when studying ICT adoption by Italian manufacturing rms using a dierent data source. In particular, they nd that the number of rms at the local-sectoral level incerases the adoption rate of ICT technologies with no network components, such as PCs or organizational software, while it has a negative eect (although non statistically sifni cant) for netword technologies (B2B, B2C etc).
13 of network externalities. Interestingly, the share of large rms has no signi cant eect on adoption. One possible interpretation is that large rms are less likely to outsource locally, as they can access inputs on a more global scale.14 All in all, the evidence on adoption of dierent technologies by Italian and German rms can be summarized as follows. First, in both countries, adoption rates increase with size for all technologies.
Second, within size class, the adoption of internal ICT technologies is similar for Italian and German rms.
Third, the adoption rate of network technologies is higher for German than for Italian rms, even within size class. Fourth, ICT adoption improves productivity. Fifth, controlling for size, sectoral and regional dummies, the adoption rate of Italian rms in 2015 decreases with the share of small rms at the local-sectoral level in
2001, while the opposite occurs for internal technologies, suggesting a role for network externalities. We now develop a model that can account for these facts.
3 The Model
3.1 Assumptions
Agents and preferences The economy is populated by a mass L of identical consumers, who each inelas- tically supply one unit of labour. They consume an (endogenously determined) mass MF of dierentiated nal goods, and the representative consumer has the utility function
ε MF ε−1 ε−1 C = c (i) ε di , with ε > 1. (1) ˆ F 0
Final producers Each nal good is produced by one nal producer under monopolistic competition. Final producers need to pay an entry cost of fF,E units of labour, which gives them a monopoly for the production of one dierentiated nal good i with the exogenous productivity aF (i), drawn from the cumulative distribution function GF . After learning its productivity, the rm can decide to remain in the market, in which case it needs to pay an additional xed cost of fF units of labour, or to exit. Firms which remain in the market produce with the production function
1M (i) 1M (i)1F,ICT (i) 1−β β yF (i) = aF (i) ξ ϕ (lF (i)) (YS (i)) , with β ∈ (0, 1)
σ (2) σ−1 MS (i) σ−1 where Y (i) = y (i, j) σ dj , with σ > ε. S ˆ S 0
14Anecdotal evidence supports this. For example, it is often argued that the large plants of the car producer FCA in Southern Italy (Lazio, Campania, Basilicata) failed to generate local spillovers, as they do not use local intermediate inputs.
14 Thus, rms use a Cobb-Douglas technology combining labour lF (i) and a continuum of dierentiated inter- mediate inputs indexed by j. Importantly, each rm uses its own set of intermediate inputs, and cannot use inputs produced for other rms. MS (i) stands for the (endogenously determined) mass of inputs available to rm i, yS (i, j) for the amount of intermediate input j that it uses, and σ for the elasticity of substitution between inputs. We assume that intermediate inputs of the same nal producer have a higher elasticity of substitution among each other than nal goods.
Equation (2) shows that rms can upgrade their productivity when they adopt management (captured by the indicator function 1M (i), equal to 1 if rm i adopts management) and when they adopt ICT (captured by the indicator function 1F,ICT (i)). Management represents the adoption of formal and structured management practices, including the hiring of external managers, whereas rms without management can be thought of as run and managed by their owners. A rm that adopts management increases its productivity by a factor
15 ξ > 1, but needs to pay a xed cost of fF,M units of labour. Similarly, ICT adoption raises productivity 16 by a factor ϕ > 1, but also entails a xed cost of fF,ICT units of labour. Equation (2) implies that rms can only adopt ICT if they have adopted management. This follows a large literature showing that ICT enhances productivity only if it is accompanied by e cient management practices (Brynjolfsson and Hitt
(2000), Garicano and Heaton (2010), Bloom et al. (2012)). In our quantitative analysis, we will therefore also assume that the productivity eect of ICT, ϕ, depends itself on management e ciency. ICT adoption does not only increase nal producers' productivity directly, but also enables them to interact more e ciently with their suppliers. To see this point, we now describe these suppliers.
Suppliers Suppliers can enter the market by paying an entry cost of fS,E units of labour. This gives them a monopoly for the production of one input j which can be used by rm i, with an exogenous productivity aS (i, j) drawn from the cumulative distribution function GS. After learning its productivity, the supplier can decide to remain in the market, in which case it needs to pay an additional xed cost of fS units of labour, or to exit. Firms which remain in the market produce with the production function
(3) ybS (i, j) = aS (i, j) lS (i, j) , where stands for the amount of labour hired and for the quantity of the input produced by lS (i, j) ybS (i, j) the supplier. We assume that there are frictions in the relationship between suppliers and nal producers, which represent coordination costs.17 Therefore, the quantity of inputs produced by the supplier is not equal
15There is ample evidence for the fact that adoption of more structured management practices increases rm productivity (see, for instance, Bloom et al. (2016)). 16These modeling choices are similar to Bustos (2011), who studies the eects of technology adoption in a Melitz model. 17We assume that these frictions cannot be overcome by vertical integration, and in general abstract from questions related to rm boundaries.
15 to the quantity of inputs which arrive at the nal producer and can be used for production (denoted yS (i, j)). Precisely, in order to deliver one unit of its input, the supplier must ship τ > 1 units. These costs can be however be reduced by a factor 1/γ ∈ (1/τ, 1) if both the supplier and its nal producer adopt ICT. Thus, ICT has a network component: it is only useful for a supplier if its client uses it as well. Summarizing, the quantity of input j arriving at nal producer i, denoted yS (i, j), is given by
1 1 γ S,ICT (i,j) F,ICT (i)y (i, j) y (i, j) = bS , (4) S τ
where 1S,ICT (i, j) is an indicator function equal to 1 if supplier j of nal producer i adopts ICT. ICT adoption has a xed cost of fS,ICT units of labour for the supplier.
Timing and market structure The model has a single period, which consists of two stages. In the
rst stage, nal producers and suppliers take their investment decisions (entry, exit, management and ICT adoption). In the resulting game between nal producers and their suppliers, we assume that nal producers can move rst. This is a technical assumption which avoids multiple equilibria.
Once all investment decisions are taken, suppliers make their nal producers a take-it-or-leave-it oer for the price of their intermediate input. Thus, nal producers have no monopsony power and take the prices of inputs as given, while suppliers operate in a classical monopolistic competition setting.
Productivity distributions Finally, for simplicity, we assume that productivity, both among nal pro- ducers and suppliers, follows a Pareto distribution with minimum value 1 and shape parameter k (so that −k). Furthermore, we assume (ε−1)(σ−1) which is necessary to ensure that GF (a) = GS (a) = 1 − a k > σ−1−β(ε−1) , expected pro ts are nite. The Pareto distribution's convenient properties18 allow us to solve the model analytically. Furthermore, it has been shown that this distribution matches the real-world productivity dis- tribution quite closely (see, for instance, Chaney (2008) and Melitz and Redding (2014)), so that this choice is also empirically reasonable.
3.2 Solution
In order to solve the model, we proceed backwards through its two stages. That is, we rst consider the pricing and input demand decisions of nal producers and suppliers, taking their investment decisions as given. We then turn to investment decisions, and nally impose free entry and labour market clearing.
18The conditional distribution of a Pareto remains a Pareto distribution with the same shape parameter, and its expectation is a linear function of its lower bound.
16 3.2.1 Demand and price setting decisions
Final producers Final producers rst solve a cost minimization problem: taking wages and intermediate input prices as given, they need to choose labour and intermediate inputs such as to minimize their production costs for any quantity produced. Standard arguments show that this problem yields, for each intermediate input j, the demand function −σ pS (i, j) yS (i, j) = YS (i) , (5) PS (i)
1 1−σ MS (i) where p (i, j) is the price of input j used by rm i and P (i) = (p (i, j))1−σ dj is the price S S ˆ S 0 index for the intermediate inputs used by rm i. The marginal cost of production of rm i is then
1−β β 1 w PS (i) (6) MCF (i) = , eaF (i) 1−β β
1 1 1 where M (i) M (i) F,ICT (i). The marginal cost depends on the rm's productivity and on eaF (i) ≡ aF (i) ξ ϕ a Cobb-Douglas aggregate of wages and intermediate input prices. Finally, the cost shares of labour and intermediate inputs are constant, so that
wl (i) P (i) Y (i) F = S S = MC (i) y (i) . (7) 1 − β β F F
Equations (5) to (7) characterize nal producers' optimal input choices. Next, we can then turn to their pro t maximization problem. Normalizing the CES price index for nal goods PF to 1 and imposing market clearing (cF (i) = yF (i)), demand for nal good i is given by
−ε yF (i) = pF (i) C. (8)
where pF (i) is the price of nal good i. Therefore, each nal producer optimally chooses a price
ε p (i) = MC (i) . (9) F ε − 1 F
As usual, more productive rms have lower marginal costs, and therefore charge lower prices and sell greater quantities. However, as Equation (6) shows, a rm's marginal cost also depends on the price of its inputs.
To determine the latter, we now turn to the problem of suppliers.
17 Suppliers The demand function faced by supplier j selling to nal producer i is given by Equation (5). The supplier thus optimally chooses to charge a constant mark-up over its marginal cost:
σ w pS (i, j) = , (10) σ − 1 eaS (i, j)
1 1 S,ICT (i,j) F,ICT (i) where γ aS (j) . Note that the price of an input depends on the ICT adoption eaS (i, j) ≡ τ decision of both the supplier and its nal producer: if both have adopted ICT, they save on coordination costs and the price is low, but if one of them has not, coordination costs and prices are high.
Variable pro ts Combining Equations (5) to (10), we can now derive an expression for both nal pro- ducers' and suppliers variable pro ts (excluding xed costs). Final producers' variable pro ts are given by β(ε−1) Var ε−1 (11) πF (i) = χ (eaF (i)) AeS (i) B,
1 −ε ε−1 β(1−ε) σ−1 where χ ≡ 1 ε ββ (1 − β)1−β σ is a constant, A (i) = MS (i) (a (i, j))σ−1 dj ε−1 ε−1 σ−1 eS 0 eS ´ is the aggregate productivity of rm i's suppliers, and B ≡ w1−εC is a summary statistic for wages and aggre- gate consumption. Equation (11) shows that nal producer's pro ts are increasing in their own productivity
and in the aggregate productivity of their suppliers, . eaF (i) AeS (i) The variable pro t function of suppliers, in turn, is given by
!σ−1 Var β (ε − 1) eaS (i, j) Var (12) πS (i, j) = πF (i) . σ AeS (i)
Equation (12) shows that a supplier's pro ts depend on its relative productivity with respect to the aggregate productivity of suppliers selling to the same nal producer. Furthermore, supplier pro ts are increasing in the intermediate input share β and decreasing in the substitutability of inputs σ. We are now ready to analyze rms' investment decisions, which shape their productivities , and . eaF eaS AeS
3.2.2 Suppliers' investment decisions
Upon learning its productivity aS (i, j), a supplier to rm i needs to decide whether to remain in the market, and whether to adopt ICT. Its decision problem depends on whether its nal producer has adopted ICT or not, and we therefore consider both of these cases in turn.
Suppliers selling to a nal producer without ICT These suppliers do not adopt ICT, as it would be useless to them. Thus, they only decide whether to remain in the market or to exit. While the pro ts from
18 exit are 0 (abstracting from the sunk entry cost), the pro ts from remaining in the market and producing are !σ−1 β (ε − 1) aS (iNoICT, j) Var (13) πS (iNoICT, j) = πF (iNoICT) − fSw. σ τAeS (iNoICT) Pro ts are increasing in the supplier's productivity draw, and therefore, suppliers follow a cut-o decision rule:19 rms with a productivity draw lower than a cut-o value ∗ exit, while rms with a produc- aS (iNoICT) tivity draw higher than this value remain in the market. The cut-o is given by
1 ! σ−1 ∗ σfS a (iNoICT) = τA (iNoICT) . (14) S eS β(ε−1) Var w πF (iNoICT) Intuitively, an increase in the aggregate productivity of other suppliers lowers supplier j's market share and increases the exit cut-o. An increase in rm i's pro ts, instead, implies that rm i buys more intermediate inputs and therefore decreases the exit cut-o, as pro ts of all suppliers rise.
In order to create an input for rm i, suppliers need to pay an entry cost fS,Ew. There is free entry, and therefore, this entry cost must equal their expected pro t, so that
+∞ 1−σ β (ε − 1) Var σ−1 ∗ wfS,E = τAeS (iNoICT) π (iNoICT) a dG (aS) − (1 − G (a (iNoICT))) fSw σ F ˆ S S ∗ aS (iNoICT) (15)
As G is the cumulative distribution function of a Pareto distribution, we can solve for the integral in Equation (15), and combine the resulting expression with Equation (14) to get
1 k ∗ σ − 1 fS ∗NoICT (16) aS (iNoICT) = ≡ aS . k − (σ − 1) fS,E
This cut-o does not depend on the productivity of the nal producer. Indeed, an increase in nal producer productivity shifts up the demand symmetrically for all suppliers. With CES demand and a Pareto produc- tivity distribution, this is only accomodated by a change in the mass of inputs and does not trigger selection.
Using Equations (14) and (11), we can now nally determine the mass and the aggregate productivity of rm i's suppliers: 1 ∗NoICTσ−1 ε−1 B ! σ−1−β(ε−1) β (ε − 1) χ aS (aF (iNoICT)) w NoICT e (17) AeS (i ) = σ−1 στ fS
!σ−1 k − (σ − 1) τAeS (iNoICT) and NoICT (18) MS (i ) = ∗NoICT . k aS
19This holds under a parameter condition shown in the Appendix, ensuring that a supplier with the lowest possible productivity draw indeed does not want to produce in equilibrium.
19 Both the aggregate productivity of suppliers and the mass of suppliers are increasing in the nal producers' productivity (as σ > ε, σ − 1 − β (ε − 1) > 0). This is a standard consequence of increasing returns to scale (created by xed costs): a larger input market sustains a larger mass of input varieties, and with an elasticity of substitution larger than 1, this increases aggregate production. Therefore, all else equal, our model predicts that more productive rms have more suppliers.
Suppliers selling to a nal producer with ICT When nal producer i has adopted ICT, its suppliers may have an incentive to do so as well. Supplier j's pro ts are now given by
σ−1 β(ε−1) aS (iICT,j) Var without ICT σ πF (iICT) − fSw τAeS (iICT) πS (iICT, j) = . (19) σ−1 β(ε−1) γaS (iICT,j) Var with ICT πF (iICT) − (fS + fS,ICT ) w σ τAeS (iICT) ICT adoption increases suppliers' variable pro ts, but has a xed cost. Therefore, only the most productive suppliers adopt ICT. Precisely, there are now two cut-os ∗ and ∗ , such that all rms aS (iICT) aS,ICT (iICT) with productivity draws higher than that cut-o remain in the market (adopt ICT), while all rms with lower productivity draws exit (do not adopt ICT). When the reduction of coordination costs due to ICT is low enough with respect to its xed costs, not all suppliers adopt ICT, and we have ∗ ∗ . In order aS (i) < aS,ICT (i) to shorten the exposition, we focus on this case and relegate the discussion of the case in which all suppliers adopt ICT to the Appendix. Then, ∗ is still given by Equation (14), and aS (iICT)
1 ! σ−1 ∗ σfS,ICT (20) aS,ICT (iICT) = τAeS (iICT) . β(ε−1) σ−1 Var w (γ − 1) πF (iICT)
∗ aS (iICT) Note that the ratio ∗ does not depend on any endogenous variables, and is one-to-one related to aS,ICT (iICT) the fraction of suppliers which adopt ICT. Denoting this fraction by sS,ICT (iICT), we have
k !k ! σ−1 ∗ γσ−1 − 1 f aS (iICT) S (21) sS,ICT (iICT) = ∗ = . aS,ICT (iICT) fS,ICT We can now solve for all supplier variables exactly as before. The free-entry condition is
∗ aS,ICT (iICT) +∞ 1−σ β(ε−1) Var σ−1 σ−1 wfS,E = τAeS (iICT) π (iICT) a dG (aS) + (γaS) dG (aS) σ F ˆ S ˆ ∗ ∗ aS (iICT) aS,ICT (iICT) ∗ ∗ − (1 − G (aS (iICT))) fSw − 1 − G aS,ICT (iICT) fS,ICT w (22)
20 Together with Equations (14) and (20), this yields
1 σ−1 (f + s f )! k ∗ k−(σ−1) S S,ICT S,ICT ∗ICT (23) aS (iICT) = ≡ aS . fS,E
This exit cut-o is strictly higher than the one for the suppliers of a non-ICT adopting producer. Indeed, as some suppliers now adopt ICT, they trigger a selection eect by expanding their market share and pushing low-productivity suppliers out of the market. As before, the exit cut-o does not depend on the productivity level of the nal producer.
The aggregate productivity of suppliers is still given by Equation (17), just replacing ∗NoICT by ∗ICT. The aS aS mass of inputs is !σ−1 k − (σ − 1) τAeS (i) fS (24) MS (i) = ∗ . k aS (i) fS + sS,ICT fS,ICT As before, both the aggregate productivity and the mass of suppliers are increasing in nal producer produc- tivity.20 Furthermore, aggregate supplier productivity is higher for ICT-adopting nal producers. As nal producers move rst in the investment game, they take this into account, and therefore have an additional incentive to adopt ICT. Nevertheless, their ICT adoption generates some externalities: some of its bene ts accrue to suppliers, and therefore, ICT adoption is ine ciently low. We now consider the investment problem of nal producers.
3.2.3 Final producers' investment decisions
Upon learning their productivity aF (i), nal producers take three decisions: whether to remain in the market, to adopt management and to adopt ICT. When taking these decisions, nal producers know that their choices perfectly determine the aggregate productivity of their suppliers. While the pro ts from exit are 0 (abstracting from the sunk entry cost), the pro ts associated with the rm's other options are obtained by combining Equation (11) with the results from the two previous sections:
βθ βθ Λ a (i) a∗NoICT B σ−1 B − f w w/o management and ICT F S w F θ βθ NoICT β πF (i) = ∗ B σ−1 with management, w/o ICT , Λ ξaF (i) aS w B − (fF + fF,M ) w βθ βθ ∗ICT B σ−1 with management and ICT Λ ξϕaF (i) aS w B − (fF + fF,M + fF,ICT ) w (25)
20Note that all else equal, ICT-adopting nal producers have fewer suppliers. However, in the cross section, this eect may be dominated by the fact that ICT-adopting rms are more productive, and more productive rms have more suppliers.
21 βθ (ε−1)(σ−1) θ β(ε−1) σ−1 ε−1 where θ ≡ and Λ ≡ χ σ−1 . Equation (25) shows that the rms with the lowest pro- σ−1−β(ε−1) στ fS ductivity do not nd it pro table to pay the xed cost and exit.21 Among producing rms, both management and ICT adoption increase rms' variable pro ts, but have a xed adoption cost. Therefore, low-productivity
rms (which make low variable pro ts) do not want to pay that cost, while high-productivity rms do.
It is then easy to show that rms' decisions are again characterized by cut-o rules. Firms with productivity draws above a cut-o level ∗ remain in the market, while rms with lower draws exit. Likewise, there aF are cut-o levels ∗ for management and ∗ for ICT adoption, holding ∗ ∗ ∗ To aF,M aF,ICT aF ≤ aF,M ≤ aF,ICT . shorten the exposition, we focus on the case where not all rms adopt management, and not all rms with management adopt ICT, so that ∗ ∗ ∗ . Intuitively, this occurs when the cost/bene t ratios of aF < aF,M < aF,ICT management and ICT are su ciently high. In our later analysis, we do not impose these restrictions, and we also analyze, for instance, what happens if ICT becomes so productive that all rms with management want to adopt it. The Appendix gives the exact solution of the model for all possible cases. In the case considered here, the three cut-os are given by
1 θ ∗ fF (26) aF = θ , ∗NoICTβθ B ε−1 Λ aS w ,
1 θ ∗ fF,M (27) aF,M = θ , θ ∗NoICTβθ B ε−1 Λ(ξ − 1) aS w
1 θ
f and a∗ = F,ICT . (28) F,ICT θ ! ICT β θ a∗ βθ θ S ∗NoICT B ε−1 Λξ ϕ ∗NoICT − 1 aS aS w
Equations (26) to (28) show that the cut-os only depend on the endogenous summary statistic B and on w the model's parameters. In particular, they allow us to solve already for the fraction of nal producers which adopt management and ICT:
k ∗ICT βθ θ k θ θ aS θ ! θ fF ξ ϕ a∗NoICT − 1 fF ξ − 1 S sF,M = and sF,ICT = . (29) fF,M fF,ICT
In equilibrium, nal producer's entry cost must equal their expected pro ts. Therefore,
21This statement is true under a parameter restriction ensuring that the lowest possible productivity draw is not too high. See the Appendix for details.
22 ∗ ∗ ∗ aF,M aF,ICT aF,ICT θ βθ βθ f = Λ B (ε−1) a∗NoICT aθ dG (a ) + (ξa )θ dG (a ) + a∗ICT (ξϕa )θ dG (a ) F,E w S ˆ F F ˆ F F S ˆ F F ∗ ∗ ∗ , aF aF,M aF,M ∗ ∗ ∗ − (1 − G (aF )) fF − 1 − G aF,M fF,M − 1 − G aF,ICT fF,ICT (30) where we have already divided both sides of the free-entry condition by the wage w. Using Equations (26) to (28) and combining them with the free-entry condition, we get
1 θ (f + s f + s f )! k ∗ k−θ F F,M F,M F,ICT ICT (31) aF = . fF,E
We have now almost completely solved the model: the only things left to determine are the equilibrium level of wages and the mass of nal goods produced.
3.2.4 Closing the model
The national income identity of our economy is C = wL. Indeed, as free entry holds for nal producers and all their suppliers, entry costs must equal expected pro ts. Therefore, in the aggregate, all pro ts are paid out as wages to the workers employed to pay the entry costs. Recalling that we de ned B ≡ w1−εC, we can combine Equations (26) and (31) to get
1 ∗NoICTβθ ! θ 1 Λ aS ε−1 ∗ (32) w = L aF . fF
To determine the mass of nal goods, we need to use the labour market clearing condition, which states that the xed labour supply L must be equal to the labour demand by all nal producers and suppliers. After some computations (shown in the Appendix), this condition yields
θL k − θ L MF,E = and MF = , (33) εkfF,E εk fF + sF,M fF,M + sF,ICT fF,ICT where stands for the mass of nal producers which pay the entry cost (so that ∗ ). MF,E MF = (1 − G (aF )) MF,E
23 MF Finally, we can determine the aggregate mass of suppliers, MS = MS (i) di, and show that ˆ0
∗ICT βθ−k θ aS ϕ NoICT −1 a∗ S f + s f + ICT βθ s f F F,M F,M a∗ F,ICT ICT θ S ϕ NoICT −1 a∗ β (ε − 1) k − (σ − 1) L S MS = . (34) ε kσ f f + s f + s f S F F,M F,M F,ICT ICT
In Section 5, we calibrate this model to the Italian and German economies, and use it to assess the quantitative importance of the ICT revolution for Italy's divergence. Informed by our own empirical evidence and other microeconometric studies, we assume that Italy is characterized both by a lower management productivity
ξ and by lower ICT productivities ϕ and γ (which are ultimately due to ine cient management practices as well). Before doing this, however, we analyze in Section 4 the model's comparative statics with respect to these three parameters. This sheds some light on the underlying mechanics, and helps understanding and interpreting the quantitative results.
4 Comparative statics on management and ICT productivity
4.1 Changes in ICT productivity and a rst divergence channel
We start by analyzing the basic eects of the ICT revolution (de ned as an increase in ICT productivity).
In our model, ICT both increases nal producers' productivity by a factor ϕ, and lowers coordination costs between nal producers and suppliers by a factor γ. While we consider a joint increase in ϕ and γ in our quantitative analysis, we here consider both increases separately, to clarify their conceptual dierences.
Proposition 1. An increase in ϕ, the productivity of ICT for nal producers...
(a) increases the share of nal producers with ICT (sF,ICT ). (b) increases the fraction of suppliers with ICT, through the extensive margin, if and only if γ > 1.
(c) increases the share of nal producers with management (sF,M ) if and only if all nal producers with management also adopt ICT. Otherwise, this share is unchanged.
(d) increases the exit productivity cut-o ∗ and the wage . aF w
(e) decreases the mass of nal producers MF and the aggregate mass of suppliers MS.
Proof. See Appendix.
Figure 4 illustrates these results. In each panel, the leftmost point on the x-axis, ϕ = 1, corresponds to the model's equilibrium before the ICT revolution: as ICT does not improve productivity, no rm adopts it, and
24 it is as if this technology would not exist. Although our model is static, one could therefore interpret these graphs as showing the evolution of steady states over time, as ICT becomes more and more productive.
Figure 4: Comparative statics for ϕ
Wage Percentage of rms with management and ICT
1.6 1 ICT, Final producers 0.9 Management, Final producers 1.5 ICT, Suppliers 0.8
0.7 1.4
rms 0.6 fi
1.3 0.5
0.4
1.2 Fraction of 0.3
0.2 1.1 0.1
1 0 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 ϕ ϕ Exit productivity cut-os Masses of nal producers and suppliers
×10-4 2.8 8 Final producers Mass of final producers 2.7 Suppliers of Non-ICT-adopters 7 Mass of suppliers Suppliers of ICT-adopters 2.6 6 2.5 5 2.4
2.3 4
2.2 3 2.1 2 2 1 1.9
1.8 0 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 ϕ ϕ
Higher ICT productivity makes ICT more attractive, and directly increases nal producers' ICT adoption.
Their choice spills over to suppliers, as the suppliers of the newly adopting nal producers have now an incentive to adopt ICT as well (as long as γ > 1, which we have assumed when drawing Figure 4). For both categories of rms, this triggers a selection eect, as the rms with the highest productivity draws increase their productivity and market shares further through ICT adoption, and thereby push small and less productive rms out of the market.
As a result, the exit productivity cut-o for nal producers increases, and the share of suppliers subject to a higher exit cut-o increases as well. Therefore, the mass of nal producers (equal to the mass of nal goods) and the mass of suppliers both fall. On its own, this fall would have a negative eect on wages, as the elasticities of substitution for nal goods and inputs are larger than 1. However, aggregate productivity rises as well, both through the direct eect of ICT and through higher selection. It is straightforward to show
25 that the latter eect dominates, so that wages (which are equal to income per capita in our model) rise.
Finally, management adoption is driven by opposing forces. On the one hand, higher wages and lower market shares lower the incentives of non-ICT adopting rms to adopt management. On the other hand, higher selection lowers the mass of low-productivity rms which do not adopt management. As long as some rms with management do not have ICT, these two eects exactly cancel out, and the share of management- adopting rms is independent of ϕ. However, when ICT gets so productive that all rms with management adopt it, further increases in ϕ also increase management adoption, as it is a prerequisite for ICT adoption.
Just as increases in the ICT productivity of nal producers spill over to suppliers, decreases in the coordination costs borne by suppliers also spill over to nal producers. Therefore, a decrease in γ, the rate at which ICT lowers coordination costs between nal producers and suppliers, has qualitatively very similar eects to an increase in ϕ, as shown in Proposition 2 and in Figure 5.
Proposition 2. An increase in γ, the rate at which ICT lowers coordination costs,...
(a) increases the share of nal producers with ICT (sF,ICT ). (b) increases the fraction of suppliers with ICT, both through the intensive and the extensive margin.
(c) increases the share of nal producers with management (sF,M ) if and only if all nal producers with management also adopt ICT. Otherwise, this share is unchanged.
(d) increases the exit productivity cut-o ∗ and the wage . aF w
(e) decreases the mass of nal producers MF and the aggregate mass of suppliers MS.
Proof. See Appendix.
An increase in γ stimulates ICT adoption for suppliers selling to an ICT-adopting nal producer. This increases the aggregate productivity of suppliers interacting with an ICT-adopting nal producer, which in turn gives nal producers an incentive for ICT adoption. The eects of higher ICT adoption for these two categories of rms are very similar to the ones discussed above. Again, higher selection leads to a decrease in the mass of nal producers and suppliers, an increase in aggregate productivity, and an increase in wages. The only dierence is that higher ICT adoption and selection for suppliers now occur also through the intensive margin (more suppliers adopt ICT even conditional on producing for an ICT-adopting nal producer), and not only through the extensive margin.
26 Figure 5: Comparative statics for γ
Wage Percentage of rms with management and ICT
1.035 0.4
1.03 0.35
0.3 1.025
0.25 rms
1.02 fi 0.2 1.015 ICT, Final producers 0.15 Management, Final producers Fraction of ICT, Suppliers 1.01 0.1
1.005 0.05
1 0 1 1.1 1.2 1.3 1.4 1.5 1.6 1 1.1 1.2 1.3 1.4 1.5 1.6 γ γ Exit productivity cut-os Masses of nal producers and suppliers
×10-4 2.4 2.4
2.2 2.3
2
2.2 Final producers Suppliers of Non-ICT-adopters 1.8 Suppliers of ICT-adopters 2.1 1.6
1.4 2 Mass of final producers 1.2 Mass of suppliers 1.9 1
1.8 0.8 1 1.1 1.2 1.3 1.4 1.5 1.6 1 1.1 1.2 1.3 1.4 1.5 1.6 γ γ
Unsurprisingly, the ICT revolution increases aggregate productivity and incomes. However, the preceding analysis also indicates a rst channel for divergence. Indeed, if for some reason the increase in ICT produc- tivity associated with the ICT revolution had been lower in Italy than in other developed economies, that could explain that Italian incomes and aggregate productivity have grown less.
This argument has been put forward by Bloom et al. (2012) and Pellegrino and Zingales (2014), who argue that Italy's ICT productivity is lowered by ine cient management practices. It is important to stress that although their argument is based on dierences in management, in the context of our model, it is not captured by dierences in the management productivity parameter ξ. Indeed, these studies argue (and show econometrically) that even when controlling for the direct eect of management practices on productivity,
ICT adoption still has a lower eect on rm productivity for rms with less e cient management. In our model, this implies that the ICT productivities ϕ and/or γ must be lower in Italy than in other countries. We calibrate these dierences in our quantitative analysis, and try to assess their role for the overall divergence.
27 However, this is not the only way in which dierences in management practices can explain divergence. It turns out that direct dierences in management productivity (captured by the parameter ξ in our model) matter as well. Indeed, as management and ICT are complements, the ICT revolution would lead to diver- gence between two countries with dierent management productivity even in the absence of dierences in
ICT productivity. In the next section, we formalize this argument, which to the best of our knowledge has not yet been emphasized by the existing literature.
4.2 Dierences in management productivity and a second divergence channel
To show how dierences in management productivity aect divergence, we start by characterizing the impli- cations of dierences in management productivity for our model's equilibrium.
Proposition 3. A decrease in management productivity ξ...
(a) decreases the share of nal producers with management (sF,M ) and with ICT (sF,ICT ). (b) decreases the fraction of suppliers with ICT, through the extensive margin.
(c) decreases the exit productivity cut-o ∗ and the wage . aF w
(d) increases the mass of nal producers MF and the aggregate mass of suppliers MS.
Proof. See Appendix.
Figure 6 illustrates these results. Lower management productivity directly lowers management adoption by
nal producers. As management and ICT are complements, it also lowers the bene ts of ICT adoption with respect to its xed costs, so that a lower share of nal producers adopt ICT. This spills over to suppliers: conditional on interacting with an ICT-adopting nal producer, suppliers' adoption decisions are unchanged, but as there are now less ICT-adopting nal producers, there are also less ICT-adopting suppliers.
In an economy with lower management productivity, the nal producers with the highest productivity draws adopt less ICT, less management, and less e cient management. Therefore, they cannot expand their production as much, and the exit productivity cut-o for nal producers is lower: less productive rms have higher market shares, and can therefore aord to stay in the market. Lower selection further depresses management and ICT adoption rates, as low-productivity rms are less likely to adopt, and it increases the mass of nal producers and suppliers which produce in equilibrium.22 In sum, an economy with lower management productivity has more rms (and more nal goods), but lower aggregate productivity. It is easy to show that the second eect dominates, so that wages are also lower.
22On the one hand, an economy with low management productivity has more nal producers (suggesting more suppliers), but on the other hand, they are less productive (suggesting less suppliers, as less productive rms have fewer suppliers). Equation (34) shows that these two eects exactly cancel out in an economy without ICT. With ICT, the selection eect for suppliers implies that the aggregate mass of suppliers becomes decreasing in supplier ICT adoption.
28 Figure 6: Comparative statics for ξ
Wage Percentage of rms with management and ICT
1.35 0.9 ICT, Final producers 0.8 Management, Final producers 1.3 ICT, Suppliers 0.7 1.25 0.6 rms 1.2 fi 0.5
1.15 0.4
Fraction of 0.3 1.1 0.2
1.05 0.1
1 0 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 ξ ξ Exit productivity cut-os Masses of nal producers and suppliers
×10-4 2.5 10 Final producers Mass of final producers Suppliers of Non-ICT-adopters 9 Mass of suppliers 2.4 Suppliers of ICT-adopters 8 2.3 7
2.2 6
2.1 5
4 2 3
1.9 2
1.8 1 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 ξ ξ
Thus, modelling Italy as an economy with low management productivity can reproduce a large number of stylized facts: compared to an economy with higher management productivity, the average Italian rm is both smaller and less productive, less rms adopt management and ICT, and income per capita is lower.
Moreover, the preceding analysis suggests that the ICT revolution ampli es these dierences. Indeed, in our model, ICT adoption is depressed in an economy with low management productivity, both through a direct eect (lower management productivity increases the cost-to-bene t ratio of ICT) and through an indirect eect (lower management productivity skews the size distribution towards smaller rms, which are less likely to adopt ICT). As we have shown in Section 2, the empirical evidence suggests that both of these channels are active in Italy. This implies that the ICT revolution would have led to divergence even in the absence of the dierences in ICT productivity that we have considered in Section 4.1.
To make this point more formally, consider two economies which have dierent levels of management pro- ductivity, but are otherwise completely equal. In line with our quantitative analysis, we refer to the low management productivity economy as Italy (I) and to the high management productivity economy as Ger-
29 many ( ). Then, as shown in Proposition 3, we have wD . However, what happens when their common D wI > 1 ICT productivities ϕ and γ increase?
Proposition 4. When , the ratio of wages wD is increasing in both ICT productivities and . ξD > ξI wI ϕ γ
Proof. See Appendix.
This result is due to the complementarity between ICT and management, which explains that ICT adoption increases faster with ICT productivity in an economy with higher management productivity. More formally, as long as not all rms with management adopt ICT, the ratio of German to Italian wages is given by
1 D D D ! k w fF + sF,M fF,M + sF,ICT fICT I = I I . w fF + sF,M fF,M + sF,ICT fICT
The share of management-adopting rms (sF,M ) is independent of ϕ (see Proposition 3), but the share of
∂s ICT-adopting rms (sF,ICT ) is increasing in ϕ, and as one can easily see from Equation (29), F,ICT/∂ξ∂ϕ > 0. Thus, the German ICT adoption rate increases faster in ICT productivity, and therefore German wages rise faster than Italian wages.23
Finally, even when ICT productivity rises so much that all rms with management adopt ICT, we can show that wages continue to diverge. This is due to a slightly more subtle channel: the ICT revolution now starts to increase the share of rms with management in both countries, and therefore the share of rms for which Italy has a productivity disadvantage with respect to Germany. Indeed, if no rm used management in both countries, there would be no productivity and income dierences, but if all rms use management, productivity and income dierences are maximized (and it can be shown that they are exactly equal to the
D ratio ξ /ξI ). Therefore, in the long run, the ICT revolution causes divergence also because it makes Italian ine ciencies for management more salient.24
Summarizing, our model suggests that there are two channels through which the ICT revolution can lead to divergence between Italy and Germany, both linked to ine cient management of Italian rms. First, this ine ciency limits Italy's actual productivity gains from using ICT. Second, ine cient management has further depressed Italy's ICT adoption rates, and is likely to become a more salient problem in an economy in which ICT enhances the macroeconomic importance of management. We are now ready to proceed to a quantitative analysis of these mechanisms.
23Mathematically, of course, this statement is not quite enough. See the full proof in the Appendix. 24For low levels of ICT productivity, ICT can be understood as size-biased technological change: it is adopted only by large rms because of its xed cost, and as large rms are larger in Germany, it is adopted more in Germany. For high levels of ICT productivity, where basically all rms want to adopt ICT, this is not true any more, and divergence is due instead to the fact that rms which want to adopt ICT also need to adopt management, a technology that is less e cient in Italy.
30 5 Calibration and counterfactual exercises
In this section, we use our model to get an idea on the quantitative importance of the ICT revolution for
Italy's divergence with respect to Germany, our comparison country. Our model has 16 parameters, listed in Table 6. We assume throughout that Italy and Germany share the same values for all parameters, except for management and ICT productivity. We do so because we want to focus exclusively on the drivers of divergence we have discussed in this paper, and therefore eliminate all other dierences between the two countries. Of course, this does not imply that these other dierences are not important in practice.
5.1 Calibration
5.1.1 Management and ICT productivity
We calibrate the management and ICT productivity parameters by using the results of two cross-country studies by Bloom, Sadun and van Reenen. In Bloom et al. (2016), the authors estimate the relationship between rms' management scores obtained from their World Management Survey (WMS)25 and rms' total factor productivity. Relying on cross-sectional and experimental evidence, they conclude that on average, a one standard deviation increase in the standardized WMS management score causes a 10% increase in rm productivity. Furthermore, the average WMS management score of Italian rms is 0.36 standard deviations lower than the German one (see Table 7 of Bloom et al. (2016)).26 Given these results, we assume that the eect of management adoption in Germany is equivalent to a two standard deviation increase in the
WMS management score, and therefore increases rm productivity by 20% (ξD = 1.2). Intuitively, as the standardized WMS score is roughly normally distributed, this corresponds to passing from the 5th percentile of management scores (i.e., basically no formal management) to the mean. Furthermore, as the Italian management score is 0.36 standard deviations lower, going from the Italian to the German management increases productivity by 3.6%. Accordingly, we set I ξD ξ = 1.036 ≈ 1.158. In order to calibrate ICT productivities, we rely on Bloom et al. (2012). In this study, the authors show that rms with a better people management score generate higher productivity increases from ICT invest- ment.27 Their measure of a rms' ICT investment is the natural logarithm of computers per worker, and their estimation results imply that a rm with the average German people management score increases its productivity by 16% when doubling its number of computers per worker (which corresponds, when starting
25The WMS is described in greater detail on its website, http://worldmanagementsurvey.org/. 26The dierence between employment-weighted averages is slightly higher. However, for our purposes, the unweighted average appears more relevant, because in our model, the size distribution is an endogenous consequence of management e ciency. This is a conservative choice, as our divergence estimates would be larger when choosing the employment-weighted average. 27The people management score is a subcategory of the general WMS score, which relates to management practices on hiring, ring, promotion and demotion. The gap between the average score of Italian and German rms for this people management score and the general WMS score is virtually identical (see Figure 3 in Bloom et al. (2012)).
31 from the mean value of computers per worker, to an increase of a little more than two standard deviations).
A rm with the average Italian people management score instead increases its productivity by only 10.2% when doubling its numbers of computers per worker.28 Accordingly, we set ϕD = 1.160 and ϕI = 1.102. Of course, it is not clear whether doubling the number of computers per worker is the best proxy for ICT adoption. In particular, its productivity eects appear relatively low when comparing them with our own regression evidence (see Table 4). In our quantitative analysis, we will study how results change when we let
D ICT productivities be larger, while maintaining the same ratio ϕ /ϕI as in the original calibration.
Table 6: Parameter values
Parameter Description Value Source/Target
ξI Italian management productivity 1.158 Bloom et al. (2016)
ξD German management productivity 1.200 Bloom et al. (2016)
ϕI Italian ICT productivity for nal producers 1.102 Bloom et al. (2012)
ϕD German ICT productivity for nal producers 1.160 Bloom et al. (2012) I Italian ICT reduction in coordination costs 1 Simpli cation γ 0.898 D German ICT reduction in coordination costs 1 Simpli cation γ 0.84 β Intermediate input share 0.5 Jones (2011)
ε Elasticity of substitution for nal goods 3 Jones (2011)
σ Elasticity of substitution for inputs 5 -
τ Coordination costs 2 Normalization
k Shape of the Pareto productivity distr. 5.33 Chaney (2008)
fF,E Entry cost for nal producers 0.9 Exit rate of 60% in Germany
fF Fixed cost of production for nal producers 1 Normalization
fF,M Management adoption cost for nal producers 0.886 50% mgmt. adoption in Germany
fF,ICT ICT adoption cost for nal producers 1.9 39% of nal prod. with ICT in Germany
fS,E Entry cost for suppliers 0.99 Exit rate of 60% in Germany
fS Fixed cost of production for suppliers 1 Normalization
fS,ICT ICT adoption cost for suppliers 1.8 32% of suppliers with ICT in Germany L Labour endowment 1 Normalization
Finally, we have no direct evidence on ICT-related reductions in coordination costs. Therefore, we assume that they are exactly symmetric to the increases of nal producer productivity, so that D 1 (i.e., ICT γ = 0.84 28These numbers are calculated using Table 6, Column 3 of Bloom et al. (2012), yielding 14.3 + 0.12 · 14.5 ≈ 16.0 for Germany, and 14.3 − 0.28 · 14.5 ≈ 10.2 for Italy.
32 adoption reduces coordination costs by 16% in Germany) and I 1 . γ = 0.898
5.1.2 Other parameters
Following Jones (2011), we set the elasticity of substitution between nal goods to 3 and the intermediate input share to 1/2, which is in line with the standard values used in the literature. We arbitrarily set the elasticity of substitution between intermediate inputs to 5, which is larger than the elasticity for nal goods without being extreme. The level of coordination costs τ is just a scaling parameter and does not matter for adoption rates or relative wages. We therefore normalize it to 1. The tail of the sales distribution of nal producers generated by our model is Pareto with shape parameter k . To match the shape of real-world sales θ distributions, we set such that k , following Chaney (2008). k θ = 2 This leaves us with eight parameters to calibrate: the seven xed costs and the labour endowment. The labour endowment and the absolute level of the xed costs of production do not matter for adoption rates or relative wages, and we therefore normalize them to 1. The xed costs of entry also do not matter for relative outcomes. We set them in order to generate an exit rate of around 60% for suppliers and nal producers in
Germany, which corresponds to the share of US manufacturing rms which exit the market within ve years of their entry (Dunne et al. (1988)). The xed cost of management is set in order to match the German rate of management adoption. In Section 2, we have shown that 77% of all German rms in the EFIGE database hire external managers. However, as EFIGE oversamples large rms, the true management adoption rate is certainly lower, and we target an adoption rate of 50%.29 Finally, the xed costs of ICT adoption for suppliers and nal producers are set such as to roughly match German ICT adoption rates in 2014. In our empirical analysis, we have considered a variety of relatively advanced ICT technologies, so it is hard to say what a unique target should be. We calibrate the model to get an ICT adoption rate of 39% for nal producers and of 32% for suppliers, which is in the ballpark of the adoption rates shown in Section 2.
5.2 Quantitative results
As stated in the introduction, between 1995 and 2015, German GDP per hour worked has grown by 28%, while Italian GDP per hour worked has only grown by 6%.30 How does this divergence of 22 percentage points compare to the one generated by our model?
Table 7 shows our model's main quantitative predictions. The rst column, entitled Before ICT shows our model's equilibrium in a situation in which the ICT technology is not available (that is, all parameters are set to their values in Table 6, but all ICT productivities are set to 1). This situation represents the situation before
29However, results hardly change when choosing 77% as a target. 30This is virtually unchanged when considering TFP: German TFP grew by 17% and Italian TFP fell by 4%, a divergence of 21 percentage points.
33 the ICT revolution. As German management productivity is higher than Italian management productivity,
German wages are already higher than Italian wages, by 2.6%. The second column shows what happens after the ICT revolution (that is, when going to the equilibrium in which all parameters are set to their values in
Table 6). The ICT revolution triggers divergence: German wages are now 8.1% higher than Italian wages.
Thus, wages have diverged by 5.5 percentage points, which represents 25% of the actual divergence between Italy and Germany. This suggests that the ICT revolution was indeed important.
Table 7 also shows that the ICT revolution exacerbates the dierences between the Italian and the German size distribution: before the ICT revolution, the average German rm was 13% larger than the average Italian
rm, after the ICT revolution, it is 50% larger. Finally, adoption rates in Italy after the ICT revolution are substantially below the German ones, with bigger gaps than the ones indicated in the data.
Table 7: Quantitative predictions
[1] [2] [3] [4] [5] [6]
Before ICT After ICT ϕD = ϕI ξD = ξI No spillovers ϕ → +∞
wD wI 1.026 1.081 1.029 1.052 1.081 1.122 Divergence 5.49 pp 0.4 pp 5.2 pp 5.48 pp 9.6 pp
Share of actual divergence 25.0% 1.6% 23.7% 24.9% 43.7%
D sF,M 50% 50% 50% 50% 50% 100% I sF,M 29% 29% 31% 50% 29% 100% D sF,ICT 0% 39% 39% 39% 17% 100% I sF,ICT 0% 10% 31% 12% 5% 100% Germ. share of suppliers with ICT 0% 32% 32% 32% 46% 46%
It. share of suppliers with ICT 0% 7% 29% 8% 20% 20%
Ratio of rm sizes 1.13 1.50 1.15 1.32 1.26 1.03
Note: all percentages are rounded. Calculations in the main text are done with the unrounded original numbers.
As we have discussed in Section 4, our model generates divergence due to two sources: dierences in man- agement productivity, and dierences in ICT productivity. To assess their relative importance, we do two additional experiments, shown in columns [3] and [4] of Table 7. In column [3], we recompute the equilib- rium after the ICT revolution assuming that Italy has the same ICT productivities as Germany (that is,
I D , and I D 1 ). In column [4], instead, we keep assuming that ICT productivities ϕ = ϕ = 1.16 γ = γ = 0.84 are dierent, but we set Italy's management productivity to the German level (that is, ξI = ξD = 1.2).31
31Note that in this case, both countries have the exact same wage before the ICT revolution.
34 This analysis shows that the main source of divergence are dierences in ICT productivities. Indeed, when only considering dierences in ICT productivities, we still get a divergence of 5.2 percentage points in wages, while when considering only dierences in management productivities, divergence only equals 0.4 percentage points.
Similarly, we can also assess the importance of network externalities for divergence. In our model, suppliers only adopt ICT if their nal producer has adopted ICT as well. Therefore, depressed ICT adoption by nal goods producers in Italy spills over to suppliers, further amplifying the gap with Germany. To analyze the role of these spillovers, we switch them o in Column [5], by assuming that the ability of suppliers to reduce coordination costs through ICT adoption depends only on their own adoption decision, and not on that of
nal producers.32 All parameter values are the ones of Table 6. In the resulting equilibrium, divergence between Italy and Germany is indeed lower than in the baseline case, even though the dierences for relative wages are quantitatively very small. Dierences for adoption rates are larger, however. For nal producers, the German ICT adoption rate is 4.1 times higher than the Italian one in the baseline case with spillovers, but only 3.3 times higher than the Italian one in the case without spillovers. For suppliers, the German adoption rate is 4.3 times higher with and 2.3 times higher without spillovers.33 Thus, our model replicates the stylized facts shown in Section 2: in the presence of network spillovers, dierences in adoption rates get ampli ed.
Finally, the model can also be used to analyze what happens if ICT productivity continues to grow (and adoption costs remain identical). Thus, in column [6], we calculate the limit equilibrium of our model when
D the ICT productivity of nal producers tends to positive in nity (but the ratio ϕ /ϕI remains at its value from the baseline calibration). In this case, German wages become 12.2% higher than Italian wages, representing a divergence of 9.6 percentage points.34 Thus, our model predicts that if ICT and management continue to spread through the economy, Italy will diverge even further. However, note that the rm size distribution of both countries tends to converge again in this extreme case: as all rms adopt both technologies, these no longer trigger dierential selection in both countries.
Our model is very stylized, and the conclusions from its calibrated version should therefore be interpreted
1 S,ICT (i,j) 32That is, we change Equation (4) to γ ybS (i,j) . This alternative model is straightforward to solve. Now, yS (i, j) = τ all suppliers are in the same situation as suppliers to ICT-adopting nal producers in our baseline model. However, switching o these direct spillovers does not completely eliminate network externalities. For instance, part of the bene ts of supplier ICT adoption still arise to their nal producer clients. 33Note that the adoption rates of nal producers are lower than in the baseline case (while the ones of suppliers are higher). This is due to the fact that in the baseline model, nal producers had an additional incentive to adopt ICT, in order to induce their suppliers to do so as well. Now, this is no longer necessary, as suppliers can adopt by themselves. This does not imply, however, that ICT adoption in the baseline case was excessive with respect to the social optimum: here, we are comparing two dierent models. 34We still assume that γ is equal to its values in Table 6. Indeed, γ cannot become in nitely large, as it is bounded above by τ. When we assume that ICT also becomes so productive to eliminate all coordination costs, the divergence in Column [5] falls to 6.5 pp. This is smaller than the number in the main text, because ICT productivity for coordination cost reduction is now exactly the same in Italy and Germany.
35 with care. Nevertheless, it does indicate that dierences in management and ICT productivity, set to levels in line with the microeconometric evidence, have the potential to explain a sizeable part of Italy's divergence during the ICT revolution.
5.3 ICT subsidy policies
[This part is still missing. Our analysis suggests that in order to close the income gap with Germany, Italy needs to improve management practices. However, doing so may be complicated and take time. In the short run, ICT subsidies can reduce the gap somewhat, as network externalities make ICT adoption suboptimally low. In this section, we want to analyze this point, by determining the model's social planner solution and a government's optimal subsidy policy. We can then study how much this optimal subsidy would improve
Italian income, and how much of the gap with Germany it would close. Furthermore, we can study whether subsidies are more e cient when they target nal producers or suppliers.]
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A Theoretical Appendix
A.1 Further details of the model solution
A.1.1 Parameter conditions
Throughout, we assume that both a nal producer and a supplier do not produce if they draw the lowest possible productivity (equal to 1). In order to ensure this, we impose the parameter conditions
σ − 1 f θ f S > 1 and F > 1. k − (σ − 1) fS,E k − θ fF,E
39 Intuitively, as long as xed costs of production are su ciently high, these conditions are satis ed.
A.1.2 Additional equilibrium con guration
As mentioned in the main text, the con guration described there is not the only one: depending on parameter values, all suppliers may adopt ICT, all rms may adopt management and ICT, etc. In each of these cases, some formulas slightly change. In any case, however, Equations (23), (31) and (33) remain valid.
Incomplete adoption of ICT by suppliers To systematically study the dierent equilibria, we start with situations where, as in the main text, not all suppliers of an ICT-adopting rm adopt ICT themselves.
It is easy to show that this is the case if and only if
σ−1 γ − 1 fS < fS,ICT .
Then, there are four possible con gurations for nal producers.
ICT βθ a∗ θ 1. When θ and θ S ξ −1 , we are in the situation fF ξ − 1 < fF,M ϕ ∗NoICT − 1 fF,M < θ fF,ICT aS ξ described in the main text, with ∗ ∗ ∗ . aF < aF,M < aF,ICT ICT βθ θ ICT βθ θ a∗ (ξ −1) a∗ 2. When S and θ S , (ξϕ) ∗NoICT − 1 fF ≤ fF,M + fF,ICT θ fF,ICT ≤ ϕ ∗NoICT − 1 fF,M aS ξ aS then cut-os hold ∗ ∗ ∗ . That is, all nal producers with management also adopt ICT. In aF < aF,M = aF,ICT that case, ∗ is still de ned by Equation (26), but the common cut-o for management and ICT is given by aF
1 ε−1
∗ ∗ fF,M + fF,ICT aF,M = aF,ICT = . ∗ICT βθ βθ θ θ aS ∗NoICT B ε−1 Λ (ξϕ) ∗NoICT − 1 aS aS w
Furthermore, Equation (32) remains valid, so that the full solution of the model can easily be obtained just as in the main text.
ICT βθ ICT βθ θ a∗ a∗ 3. If S and θ S , then fF,M + fF,ICT < (ξϕ) ∗NoICT − 1 fF fF,ICT < ϕ ∗NoICT − 1 (fF + fF,M ) aS aS cut-os hold ∗ ∗ ∗ . That is, all nal producers adopt management and ICT, and the unique aF = aF,M = aF,ICT production cut-o is 1 θ f + f + f a∗ = a∗ = a∗ = F F,M F,ICT . F F,M F,ICT θ θ ∗ICTβθ B ε−1 Λ (ξϕ) aS w
In that case, the wage is given by
1 θ ∗ICTβθ ! θ 1 Λ(ξϕ) a ε−1 ∗ S w = L aF . fF + fF,M + fF,ICT
40 4. Finally, there is one last case, in which all nal producers adopt management, but not all of them adopt ICT. We do not consider this case in detail, because we for all comparative statics and during the entire quantitative analysis that the xed costs of management are high enough for the least productive nal
θ producers not to want to adopt it on its own. For the sake of completeness, this case occurs if ξ − 1 fF > ICT βθ a∗ and θ S , and cut-os then hold ∗ ∗ ∗ . The fF,M fF,ICT > ϕ ∗NoICT − 1 (fF + fF,M ) aF = aF,M < aF,ICT aS common cut-o for exit and management adoption is given by
1 θ ∗ ∗ fF + fF,M aF = aF,M = θ . θ ∗NoICTβθ B ε−1 Λξ aS w
1 θ ∗NoICT βθ θ 1 Λξ (a ) while the cut-o for ICT adoption is still de ned by Equation (28). The wage is given by w = L ε−1 a∗ S . F fF +fF,M
Complete adoption of ICT by suppliers Now, we turn to situations in which all suppliers of an ICT- adopting nal producer also adopt ICT. This happens if
σ−1 γ − 1 fS > fS,ICT .
In that case, Equation (23) remains valid (with sS,ICT = 1). However, the aggregate productivity of suppliers of ICT-adopting rms is now
1 ∗ICTσ−1 ε−1 B ! σ−1−β(ε−1) β (ε − 1) χ γaS (aF (i)) w ICT e AeS (i ) = σ−1 στ (fS + fS,ICT )
Therefore, the pro t of an ICT-adopting supplier also changes: instead of the expression given in Equation
(25), it is now equal to
βθ βθ ! σ−1 σ−1 θ σ−1 γ fS ∗ICTβ B Λ ξϕaF (i) aS B − (fF + fF,M + fF,ICT ) w fS + fS,ICT w
Again, there are four possible con gurations for nal producers. These are exactly analogous to the ones de- βθ ICT βθ ICT βθ a∗ σ−1 σ−1 a∗ scribed in the previous section, just that the term S is replaced with γ fS S , ∗NoICT ∗NoICT aS fS +fS,ICT aS and the de nition for the unique cut-o in Con guration 3 changes.
A.1.3 Labour demands
We start by determining the total labour demand by all suppliers serving a given nal producer i. Writ- ing MS,E (i) for the mass of rms which pay the entry cost to take a productivity draw, the labour
41 demand of all suppliers is for entry costs, ∗ for xed costs and MS,E (i) fS,E MS,E (i) (1 − G (aS (i))) fS ∗ for ICT adoption (if applicable). On top of these xed costs, suppli- MS,E (i) 1 − G aS,ICT (i) fS,ICT (σ−1) ∗ Var 35 ers demand M (i) (1 − G (a (i))) ∗ π (a ) units of labour for nal goods production. S,E w S EaS ≥aS (i) S S Summing up these uses of labour and using the free-entry condition, the total labour demand of suppliers of
nal producer i is
σ ∗ Var ∗ LS (i) = MS,E (i) (1 − G (aS (i))) EaS ≥a (i) πS (aS) . w S
∗ Var Now, we can note that M (i) (1 − G (a (i))) ∗ π (a ) equals the aggregate variable pro t of S,E S EaS ≥aS (i) S S all suppliers of rm . Equation (12) implies that this aggregate pro t is a share β(ε−1) of the variable pro t i σ of nal producer i. Therefore, we have in the end
β (ε − 1) L (i) = πVar (i) . S w F
We are now ready to proceed to the overall labour market clearing condition. Writing MF,E for the mass of nal producers which pay the entry cost to take a productivity draw, the total labour demand is composed of
for entry costs, ∗ for xed costs, ∗ for management MF,EfF,E MF,E (1 − G (aF )) fF MF,E 1 − G aF,M fF,M costs and ∗ for ICT adoption. On top of these xed costs, each nal goods MF,E 1 − G aF,ICT fF,ICT producer demands (1−β)(ε−1) Var units of labour for production, and as we have just shown, all its w πF (i) suppliers jointly demand β(ε−1) Var units of labour. Summing all these uses up and making use of the w πF (i) free entry condition for nal producers, it comes that
∗ ∗ ∗ L = εMF,E fF,E + (1 − G (aF )) fF + 1 − G aF,M fF,M + 1 − G aF,ICT fF,ICT .
Using Equation (31), we directly get Equation (33).
A.1.4 Aggregate mass of suppliers
The aggregate mass of ICT-adopting suppliers is equal to
∗ICT βθ−k! k − (σ − 1) β (ε − 1) a k−θ ICT S θ k MS = MF fF ∗NoICT (ξϕ) sS,ICT (sF,ICT ) . k − θ σfS aS
35This uses the very useful property that Var TCS (i, j) = (σ − 1) πS (i, j) .
42 A.2 Proofs of Propositions
A.2.1 Proposition 1
Part (a) follows directly from Equation (29). Part (c) follows directly from Equations (31) and (32). Finally, for Part (d), the fact that the mass of nal producers increases is a direct consequence of MF,E being independent of and ∗ decreasing, as ∗−k . ξ aF MF = aF MF,E
43