metadata: authors: 0: author: Brambilla,Irene
count: World
docna: 0: docna: Digital technology adoption and jobs : a
            model of firm heterogeneity
docty: Policy Research Working Paper
abstracts: cdata!: This paper develops a theoretical
            framework that expands the task-based models of technical
            progress and labor markets to allow for firm heterogeneity
            and wages that vary across firms. The model is compatible
            with the empirical observation that more productive firms
            are larger, are more skill intensive, and pay higher wages
            across skill categories. The model predicts that the
            decision to invest in information and communications
            technology depends on firm size and labor market
            characteristics. As a result of investment in information
            and communications technology firms grow, become more
            intensive in complex tasks, become more skilled intensive,
            and employ more skilled workers as long as skilled labor is
            complementary to information and communications technology.
            Employment of unskilled workers increases as well, provided
            that firm output growth is sufficiently high to overcome the
            negative substitution effect. Workers who remain employed
            are better off because their wage increases with information
            and communications technology. To the extent that skilled
            workers have more bargaining power than unskilled workers,
            or that their wage scheme is more tied to firm performance,
            wage inequality at the firm level increases with information
            and communications technology.
repnme: repnme: Digital technology adoption and jobs : a
            model of firm heterogeneity
display_title: Digital technology adoption and jobs
            : a model of firm heterogeneity
listing_relative_url: /research/2018/01/29550749/digital-technology-adoption-jobs-model-firm-heterogeneity
topicv3: ICT Impact on Jobs m1503943 2684,Labor Force m1504054 2750,Labor Productivity m1504060 2756
publishtoextweb_dt: 2018-01-31T00:00:00Z
no_of_pages: 35
model_extractions: WPS8326 Policy Research Working Paper 8326 Digital Technology Adoption and Jobs A Model of Firm Heterogeneity _Irene Brambilla_ Finance, Competitiveness and Innovation Global Practice Group January 2018
Policy Research Working Paper 8326

# **Abstract**

This paper develops a theoretical framework that expands the task-based models of technical progress and labor markets to allow for firm heterogeneity and wages that vary across firms. The model is compatible with the empirical observation that more productive firms are larger, are more skill intensive, and pay higher wages across skill categories. The model predicts that the decision to invest in information and communications technology depends on firm size and labor market characteristics. As a result of investment in information and communications technology firms grow, become more intensive in complex tasks, become more skilled intensive, and employ more skilled workers as long as skilled labor is complementary to information and communications technology. Employment of unskilled workers increases as well, provided that firm output growth is sufficiently high to overcome the negative substitution effect. Workers who remain employed are better off because their wage increases with information and communications technology. To the extent that skilled workers have more bargaining power than unskilled workers, or that their wage scheme is more tied to firm performance, wage inequality at the firm level increases with information and communications technology.

This paper is a product of the Finance, Competitiveness and Innovation Global Practice Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at irene.brambilla@econo.unlp.edu.ar.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Digital Technology Adoption and Jobs:**

**A Model of Firm Heterogeneity**<sup>**1**</sup>

Irene Brambilla<sup>2</sup> Universidad Nacional de La Plata and CONICET JEL codes: J24, J31 Keywords: ICT, jobs, labor demand, firm heterogeneity, rent-sharing, tasks

> 1 I thank Rita Almeida, Mark Dutz, Truman Packard, Daniel Lederman, Robert Willig and seminar participants at the World Bank’s Workshop on Digital Technology Adoption, Skills, Productivity and Jobs in Latin America, LACEA and AAEP for their comments and suggestions. The views expressed in this paper are those of the author.

> 2 Department of Economics, Universidad Nacional de La Plata. Email: Irene.brambilla@econo.unlp.edu.ar
# **1. Introduction**

The relation between the adoption of digital technologies, its impact on productivity, and the consequences on employment and labor markets has been the subject of much study in the last three decades. Investment in information and communication technologies (ICT) has been credited with the increase in US productivity in the second-half of the 1990s and the increasing productivity gap between the US and the EU. Skill-biased technological change is argued to be one of the main reasons behind the steady increase in the demand for skilled labor, wage inequality and job polarization since the 1980s.

Two main strands of literature have studied the labor market impacts of technological progress: the early literature on skill-biased technological change of Katz and Murphy (1992), Bound and Johnson (1992), Goldin and Katz (1998), among others, and the tasks approach to labor demand of Autor, Levy and Murnane (2003) and Acemoglu and Autor (2011). The literature on skill-biased technological change assumes that technology is complementary with skilled labor, therefore positively affecting the relative demand and wage of skilled workers. The tasks approach argues that the complementarity or substitutability between technology and labor does not occur at the worker category but rather depending on how susceptible different tasks are for automatization. They conclude that tasks performed by workers in the middle of the skill distribution are more likely to be substitutable by machines. Almost all of these papers describe general equilibrium models and use data on wage and employment aggregated up to the district, industry or country level.

Most notably the bulk of the literature in skill-biased technological change and the tasks approach to labor demand features homogeneous firms and competitive labor markets. While these are useful assumptions when studying employment and wages in general equilibrium, the model descriptions miss out on predictions at the firm-level. Firmlevel studies have consistently shown that there is high variance in labor force composition and wages across firms. A higher skill share and higher wages are associated with larger, more productive firms that engage in complex activities such as innovation, quality upgrading, and exporting.<sup>3</sup> Moreover, the extent to which investing in ICT boosts firm productivity has also been shown to depend on firm characteristics denominated under the umbrella term of organizational capacities.<sup>4</sup> In this paper we extend the tasks model of Acemoglu and Autor (2011) to allow for firm heterogeneity in technology and non-competitive labor markets with firm-level wages, in order to study the effects of investment in ICT on firm-level outcomes. We start by describing

> 3 Bernard and Jensen (1999), Verhoogen (2008), Kugler and Verhoogen (2012), Aw et al (2011).

> 4 Machin and Van Reenen (1998), Bloom, Sadun and Van Reenen (2012).

2
a situation in which firm heterogeneity is Hicks-neutral as in Melitz (2003) and then allow for differences in the relative efficiency with which firms use skilled and unskilled labor. We further allow wages to differ across firms due to rent-sharing as in Amiti and Davis (2011). The product market is monopolistically competitive and thus firms with different price and profit levels co-exist. Firms operate using skilled and unskilled labor, and may additionally use ICT capital. Investing in ICT capital involves paying a fixed adjustment cost given by installation costs, on-the-job training and firing costs. As a result not all firms choose to invest in ICT. As in Acemoglu and Autor (2011), skilled and unskilled labor are perfect substitutes in the production of tasks of different levels of complexity. ICT capital is also a substitute for unskilled labor, whereas the degree of complementarity with skilled labor depends on their elasticity of substitution.

Our model aims to be flexible enough to accommodate several micro-level empirical facts. Namely, that firms make different decisions. They differ in size, in the skill ratio, in wages, and on whether they invest or not in ICT. It also allows for wage differences across workers that are otherwise alike except for which firm they work for. Our model predicts that as a result of ICT firms grow, pay higher wages, become specialized in more complex tasks, and employ more skilled workers and become more skilled intensive as long as skilled labor and ICT are complements. Employment of unskilled workers increases, though not as much as employment of skilled workers, if firm output growth due to ICT investment is sufficiently high to overcome the negative substitution effect. It also predicts that workers that remain employed at the original firm experience an increase in wage.

The model is of partial equilibrium in the sense that we consider one industry and fixed wages, and that we do not model firm entry. Our model is static, however, we loosely interpret predictions of scenarios with and without ICT as changes in firm behavior due to adoption of ICT.

The paper is organized as follows. Section 2 describes the background literature on the impact of technological progress on labor outcomes and productivity. Section 3 discusses the model of firm heterogeneity. Section 4 concludes.

# **2. Background**

In this section we briefly review the literature on technology adoption and its impact on labor markets, including the early literature of skill-biased technological change as well as the more recent tasks approach to the demand for skills. We end with a discussion of the impact of investment in ICT on productivity.

3
# _Skilled-biased technological change_

The rise in the skill premium, and especially the college premium, during the 1980s and 1990s motivated a large literature that pointed towards skill-biased technological change as a driving force behind this phenomenon.<sup>5</sup> Several early papers such as Katz and Murphy (1992), Bound and Johnson (1992), and Berman, Bound and Griliches (1994) show that the college premium grew significantly in the US during the 1980s (Berman et al, 1994, estimate the increase in the college premium in 10 percentage points). They argue that while the supply of college graduates did not grow as fast during the 1980s as it did during the 1970s, it still grew significantly. To account for the rise in the skill premium substantial growth in the demand for skills must have taken place. Berman, Bound and Machin (1998) find similar results for OECD countries.

Katz and Murphy (1992), Card and Lemieux (2001), Autor, Katz and Krueger (1998), among others, use a demand and supply framework in which the demand for skilled and unskilled labor is based on a production function that allows for factor augmenting technological progress. The output production function takes the form where �� is output and �� and �� are skilled and unskilled labor. The time-varying parameters �� and �� are factor augmenting technological change. Based on an assumption of inelastic short-run supply and competitive labor markets, Katz and Murphy (1992) derive an estimable equation linking the skill premium to the relative supply of skills and a trend representing skill augmenting technological change. They estimate the increase in the demand for skills to be of 3.3 percent annually. Card and Lemieux (2001b) find that it is relevant to define the supply of skills by age cohort, as workers of different age and experience are not interchangeable.

Krussell et al (2000) Interpret skill-biased technological change as a complementarity between capital and skilled labor. They argue that skill-biased technological change is treated in previous papers as a latent unobserved variable. They instead work with a production function in which capital is introduced explicitly as complementary to skilled workers. The function takes the form where �� is output, �� and �� are skilled and unskilled labor, and �� is capital. The complementarity between capital and skilled labor is modeled with a smaller elasticity of

> 5 De‐unionization, International trade, and more recently offshoring of manufacturing jobs have been pointed out as alleged culprits as well.

4
substitution than between capital and unskilled labor ( ���� . They use national accounts data to build a time series of infrastructure and capital equipment from 1962 to 1993 and data on labor supply from CPS surveys. Their estimates are consistent with capital skill complementarity. Additionally, they find that capital grew more rapidly after 1975, when the skill premium started to rise more sharply. Their results indicate that after accounting for the capital-skill complementarity most of the changes in skill premium become accounted for.

Goldin and Katz (1998) study the complementarity of capital and skilled labor from a historical perspective using US Census of Manufacturers for 1909, 1919, 1929, and the NBER Manufacturing Productivity Database for later time periods. They argue that the complementarity between capital and skills is not a recent phenomenon and that it goes back to the beginning of their sample period.

More specifically related to the use of digital technology, Krueger (1993) finds that workers who use computers at work earn a wage premium of 10% to 15% and estimates that about one-third of the rise in skill premium is due to increased computer use. DiNardo and Pischke (1997), however, cast doubt on these findings by estimating substantial wage returns to the use of pencils, telephones, and working in a sitting position as well. Autor, Katz and Krueger (1998) use CPS data sets to assess how on-the-job computer usage varies across industries and argue that the rise in the demand for skills is actually increased demand for computing skills.

# _The tasks approach_

Autor, Levy and Murnane (2003) introduce a tasks approach to labor demand. The tasks approach emphasizes the role of automatization of tasks in relation to technological progress and labor markets. Autor et al (2003) state that computers can substitute workers who perform cognitive and manual tasks that can be accomplished by following an explicit set of rules (routine tasks), while computers complement workers performing non-routine and problem-solving and complex tasks. They model these ideas with a production function that takes the form where �� and �� are routine and non-routine workers and � are computers. Computers are perfect substitutes for routine labor and have a declining price. They use data on information on the task composition of jobs from 1960 to 1998 and find that computer usage is linked to a reduction of employment in routine tasks and with an increase in demand for college graduates.

A following strand of literature argues that the patterns of wage inequality and the demand for skills have been shifting since the 1990s towards an increase in polarization (i.e.

5
a fall in demand for middle-skill workers). Autor, Katz and Kearney (2008) find that wage inequality at the bottom half of the income distribution has not increased since the 1980s and that, instead, wage inequality has risen in the upper tail. Goos and Manning (2007) and Goos, Manning and Salomon (2014) show that there has been a decrease in the share of middle-skill occupations in total employment in the UK and in 16 European countries. The unifying idea behind these findings is based on the tasks approach: occupations in the middle of the skill distribution are more susceptible to automatization than occupations at the lower and upper tails.

Acemoglu and Autor (2011) develop a more sophisticated model of the task content of jobs in which output is produced by a continuum of tasks and where each task can be performed by low, medium or high-skill workers, or by technology. Their model can account for job polarization, as tasks performed by middle-skill workers are subject to be substituted by technology. This is the mechanism that drives the concentration in high and low pay occupations. The model that we develop in Section 3 is loosely based on Acemoglu and Autor (2011).

Autor and Dorn (2013) study the impact of computerization on the demand for lowskilled labor. They use district-level data for the US and show that areas with high levels of routine tasks have experienced greater adoption of ICT, greater reallocation of workers from routine tasks to the service sector, wage polarization, and large inflows of high and low skilled workers.

Michaels et al (2014) study whether ICT has contributed to the rise in polarization. They put together a comprehensive industry-level data set on 11 advanced countries from 1980 to 2004. Their findings indicate that the industries which invested more heavily in ICT demanded more highly qualified workers in detriment of workers with intermediate education. Additionally, the estimated effect is quantitatively large, and can explain onequarter of the college wage bill in the economy as a whole.

The firm-level evidence on skilled-biased technological change, occupations and tasks, and labor outcomes is scarce. One example is Akerman et al (2014). They study skill complementarity of broadband internet in Norway and show that access to broadband internet improves the labor market outcomes and the productivity of skilled workers.

# _Labor market institutions_

To the extent that digital technology is a substitute for certain types of workers or tasks, investment in ICT is associated with employment reallocation. Employment protection laws that make labor adjustment costly, such as firing costs, are expected to negatively affect the adoption of ICT. This effect is larger the larger the substitutability between ICT and certain types of workers.

6
Gust and Marquez (2004) present empirical evidence that across industrialized countries there is a negative correlation between ICT investment and employment protection laws. They develop a dynamic model of vintage capital and skilled-biased technological change. In each period a firm decides whether to upgrade technology, which in turn requires to upskill the labor force. Firing costs delay or prevent firm decisions to adopt the latest technology.

Employment protection legislation can also be viewed as discouraging to undertaking risky activities such as investment in innovation and in ICT-intensive sectors, as in Bartelsman, Gautier and de Wind (2016), Saint Paul (2002), Koeniger (2005), Bartelsmand and Hinloopen (2005), and Samainego (2006). Bartelsman et al (2016) argue that, because of the experimentation and changes required in organizational structure, the outcome of investment in ICT is highly uncertain. This is supported by the empirical finding that productivity is more dispersed in ICT-intensive sectors (Brynjolfsson et al., 2008). If for a given firm investment in ICT is unsuccessful, the firm might be forced to exit the market because it cannot break even. Thus, incentives to invest in ICT depend on exit costs, with higher exit costs being detrimental to investment in ICT. In this scenario, firing costs are a barrier to investment in ICT.<sup>6</sup> Using a cross-industry and cross-country panel dataset of the US and the EU (EUKLEMS), Bartelsman et al (2016) show that high-risk ICT-intensive sectors are smaller in terms of employment in countries with stricter labor regulations. These empirical facts hold when comparing the EU to the US, where labor regulations are more flexible, and when comparing countries within the EU. Further, the effect of labor regulations is increasing in the risk of the investment. The paper also develops and calibrates a model and their simulations show that, due to lower investment in ICT, aggregate productivity in the US would be 10 percent lower if severance payments in the US were similar to the average cost in Europe.

# _Digital technology adoption and productivity_

Empirical studies find that ICT is important in explaining productivity differences across countries, across sectors, and across firms. Treating ICT as an input that enters into the production function, a large group of papers has focused on studying the role of ICT in the resurgence in labor productivity in the US during the 1990s, from the growth accounting and cross-industry econometric perspectives. Jorgenson, Ho and Stiroh (2008) and Oliner, Sichel and Stiroh (2007) argue that the ICT producing sectors have been responsible for the increase in productivity from 1995 to 2000, whereas after 2000 further growth in investment

> 6 Acharya, Baghai and Subramanian (2013) make the opposite argument that stricter labor laws work as a commitment device by preventing firms from dismissing workers after short‐run failures and thus encouraging employees to engage in risky innovative activities that are profit maximizing in the long‐run.

7
in ICT has not occurred in ICT producing sectors but rather in ICT using sectors. In contrast, both investment in ICT and productivity improvements have been much more moderate in the EU during the same period (von Ark et al, 2008). For comprehensive surveys see Draca, Sadun and Van Reenen (2007) and Syverson (2011).

Firm level studies are scarcer, partly due to the endogeneity in input choice that arises in the estimation of production function, and also due to the difficulty in measuring ICT capital at the firm level. In particular, one potential problem is that the direct cost of purchase of ICT does not fully represent the cost of adjusting the organization of the firm to deal with the new technology. To address this issue several firm level studies have highlighted the complementarities between ICT, organizational capacities, and human capital. Bresnahan, Brynjolfsson and Hitt (2002) run their own survey and find that ICT is complementary to decentralized decision making, self-managing teams, worker autonomy, broader responsibilities of workers, and skills. They attribute part of the large estimated returns to ICT to be derived from the change in organizational capacities. Further support for the organizational capacities hypothesis is provided by Brynjolfsson and Hitt (2003). They study investment in computers and find that the explanatory power of computers on firm output growth is substantially larger in the medium run than in the shorter run, suggesting that ICT capital becomes more productive as firms have time to adjust their labor force, managerial practices, and overall firm capabilities.

Bloom, Draca and Van Reenen (2016) apply the organizational capacities hypothesis to explain the differences in the contribution of ICT to productivity growth between the US and Europe. Using a panel of firms they show that US multinationals operating in Europe obtain larger productivity gains from ICT compared to European firms. They further find evidence that the productivity advantage of ICT in US firms is due primarily to different management practices.

# **3. Model**

In this section we describe a partial equilibrium model of firm heterogeneity and investment in ICT. We start describing a situation in which firms produce using skilled and unskilled labor. We then allow for investment in ICT. The model is based on the task production function of Acemoglu and Autor (2011), extended to allow for firm heterogeneity as in Melitz (2003) and rent-sharing wage schedules as in Amiti and Davis (2011).

# _Products and preferences_

In a given industry there is a continuum of product varieties, each variety indexed by � , with the total mass of varieties given by � . Varieties are horizontally differentiated and enter 8
= [[ ore x(v) v E E =(" ~~P)~~ “ ~~ep~~ <u>5</u> p(v) v P p= leg rom 1-€ 0 6G F V x t(i) i € [0,1] 1 x(0) = Oexp iI0 Int@i) ail.

0 6
x(@) 6 t(i,0) = a, (i, 0) LG, 8) + ay (i, 9) H(i, 4).

ay (i, 0) a, (i,9) i 6.

H(i, @) LCi,@) 1 ay (i, 8)/a,(i, A) i (H) (L) 6 a Wy (70) w_ (7) ue Wy (at) > w,(m) Vr ~~Wy~~ = Wy(0) ~~wy,~~ = w,(0) <u>Wu WL</u> 1>00 Wy (1t) = <u>Wy</u> 120 w(t) = <u>W,</u>
Wy (70) w_<sup>(1)</sup> <!-- Start of picture text --> Wy<br>Wy<br><!-- End of picture text --> <!-- Start of picture text -->
|<br><!-- End of picture text -->

<!-- Start of picture text -->
|<br>(z) wy, (1)<br>uw<br>WH VQ<br>Wr’ os<br>ror a,(0,0 < —wy< ay(1,0)<br><!-- End of picture text -->

<!-- Start of picture text --> ; Wu(t) _<br>WL ;<br><!-- End of picture text --> ay (i,0) Wy (70) w_<sup>(7)</sup> WH (9) w, (0)
<u>wu(@)</u> <u>w1(9) wu(@)</u> 1 - <u>Ww1i@)</u> l <u>az(i,@)</u> ay(i,0) (0,1) i<i (6) i>i (0) 1 w,(@) <u>wy</u> (0) _ a,(i (0),6) ay (@),8) az (i,é) ay(i,8) c(@) ~~19)~~ oy 16) ifi<i (6) | ~~8H)~~ gy (ay ifizi (6) ~~wi)~~ c(@)x ifizi .

J i i J i<i (0) i>i (0) _ c(@) = <u>5 exp fl‘OO a,</u> ~~wi@)(8)~~ di +| © f* <u>a,</u> ~~wn)(8)~~ ul

0 ay ay if) 0
<!-- Start of picture text -->
| eta<br>a,(i,@)<br>wu (8)<br>w,(@)<br><!-- End of picture text -->

i (L) i H <!-- Start of picture text --> tv.0 )| w,(9) ayG,<br>9)<br>Wy(@) a, (i, 8)<br>a<br><!-- End of picture text -->

t(i,0) j
<!-- Start of picture text --> c(@)<br><!-- End of picture text --> 0.

<!-- Start of picture text --> H(@) 1-i (6)<br>=) c(@)x(8),<br>1) =7 w,(8) . eayx(a)* ;<br><!-- End of picture text --> <!-- Start of picture text --> H(@ )_ w,(8)1-i (@)<br>L(@) wy(@) i ()<br><!-- End of picture text --> <!-- Start of picture text --> i (0)<br><!-- End of picture text --> m(0) = max(p(4) —c(@)) x(p(@)) — F. E p(@) = ~~7~~ fo ): (0) = Ac(@)"-®) — F =e &(e-1)€-VE 6, 0 0.
same across firms. Firms produce if indirect profits (net of fixed costs) are zero or strictly positive. Firms that do not break even exit the market.

Notice that due to the rent-sharing wage schedules, the variable unit cost ���� depends on profits. Solving the firm profit maximization problem involves finding an equilibrium in which maximized profits predict a given marginal cost through the rent-sharing constraints, and that same marginal cost generates the same level of maximized profits when the CES pricing rule is applied. As shown by Amiti and Davis (2011), because for a given � the dependence of costs on profits is monotonically increasing, the CES pricing rule holds.<sup>7</sup> This is also a property of Nash bargaining solutions.

# _The role of firm heterogeneity_

The firm heterogeneity parameter � affects firm decisions of price, relative labor demands, and wages. There are two different channels through which the heterogeneity parameter operates: it enters the upper-tier Cobb-Douglas production function multiplicatively, and it affects the inverse labor requirements in the lower-tier production function. In what follows we describe the role of each channel separately.

We start by considering a situation in which technology differences (captured by � ) do not affect the ratio of inverse input requirements. The objective of this exercise is to describe a scenario in which the only channel of technological firm heterogeneity is the Hicks-neutral multiplicative component of the upper-tier production function, as in Melitz (2003), and in which wages vary by firm as in Amiti and Davis (2011).

# **Proposition 1** . _Productivity, size and wages._

Because the relative efficiency and the relative cost of skilled to unskilled labor are the same across firms, the assignment of each type of worker to tasks is also the same (Figure 4), as is the relative production of tasks (Figure 5), and total relative labor demand. Firm heterogeneity only predicts differences in scale and in wages across firms. The scale of firms both in terms of units of production and skilled and unskilled employment depends

> 7 Costs are increasing in wages, which in turn are increasing in profits.

15
w,(@) <!-- Start of picture text --> ay (i)<br>f a, (i)<br><!-- End of picture text --> 0.

tG, 9) <!-- Start of picture text --> w,(9) ay)<br>Wy (8) a, (i)<br>|<br><!-- End of picture text -->

t(i, 0) 0.
positively on the Hicks-neutral productivity � . Scale differences across firms unfold from ���� and therefore ���� being decreasing in �. The cross sectional prediction is that more productive firms are larger and pay higher wages, and that skill intensity is the same across firms.

We now turn to a situation in which there is a complementarity between total factor productivity and skilled labor, modeled as differences in Hicks-neutral productivity as well as input requirements across firms. The objective of this scenario is to study conditions under which the ratio of skilled to unskilled workers varies across firms.

# **Proposition 2** . _Complementarity between productivity and skilled labor._

Assume that ����,�� is increasing in �, then, ����,��

- (i) ����, �����, ����� are increasing in �;

(ii) �<sup>∗</sup> ��� is decreasing in �; ���� (iii) is increasing in �. ���� Intuitively, differences in technology that are not Hicks-neutral generate differences in relative factor demands. The situation is depicted in Figures 6 and 7. In Figure 6, the inverse relative input requirements of the more efficient firm (green line) lie above the inverse relative input requirements of the less efficient firm (blue line). As a result, the more productive firms allocate a larger number of tasks to skilled workers. In Figure 7, the more efficient firm faces lower relative costs for skilled tasks (green line) compared to the less efficient firm (blue line). The most efficient firm is more intensive in skilled tasks per unit of output. The cross sectional prediction of this scenario is that more productive firms are larger, pay higher wages, and are more skill intensive. All firms pay the same relative wage.

# _Investment in ICT_

We now assume that firms have the option to invest in ICT. We denote the stock of ICT with �. Each unit of � has a unit cost of ���� . A positive investment in ICT also implies paying a fixed cost �. The fixed cost represents the adjustment costs of adopting the new technology, given by the installation of the new technology itself, training of the labor force, and firing costs of displaced workers. Because of the fixed cost, not all firms invest in ICT in equilibrium.

ICT capital is applied to tasks in the same manner as skilled and unskilled labor, with the caveat that it is combined with skilled labor. The upper-tier production function remains unchanged, as output is obtained with the same combination of tasks as without ICT. The 17
<!-- Start of picture text --> ay (i, O,)<br>w,(@)<br>wi®) aa<br>i (0 ) i(@@ )<br><!-- End of picture text --> 0, % <!-- Start of picture text --> tG, 9)<br>w,(@) ayG, 01)<br>\\ wy(@) a, Gi, 81)<br>i, Q . w, (8) ay (i, 9)<br>aN Wy (8) a, (i, Ao)<br>. |<br>0, 9<br>j i<br><!-- End of picture text -->

t(i, 6)
T ti, ~~o-1 o-1 =~~ 0) = a,(1,8) L(G,@) + ay(i,0) [H0) ~~j~~ <u>=</u> +7 0 ~~)e~~ |", o>1.

o o o> 0 i sTM(0) = (wy (8)1? + Wier7) 0 wi (8) T.

wi (8) WicT sTM(@) o->1 g—- 00 sTM(0) wi (8) WicT a7 i*7(@) ~~wi (8)~~ _ ~~sTM(@)~~ a,(i*7(@),0) ay(i*"(@),8)
OA). _ ~~GO)se~~ L onOO) cutif i<i°TM(6) c’ (6) = <u>A exP ifi*T(@) a,(.,8)w! (0)</u> di+ Dono1 <u>a,sTM(0)(i, 8)</u> a cTM(@) < c(0), VO c'(@) c(0) w,(@)) — (wy(8) — wh()); (sTM(6) — wy(6)) (s"(@) - (w7 (6) — w.(6)); i(@) i*7(@) sTM (0) wi (8) wy (8) — wi (@) <0 w,(@) — wi (8) < 0 i (0) sTM(0) — wy(0) < 0.

WV wy m' (6) m(0).

g*T 1’ (9*7) = aC) 6>07 g*t WicT g*T
Recall that unit variable costs are constant in output and that they decrease with ICT for all firms. Firms with larger � are able to diffuse the fixed cost � over a larger base of units of output that are produced at a lower variable cost, until reaching a critical point �<sup>∗�</sup> (point i). The critical point is achieved for larger levels of firms productivity as the unit cost ���� or the adjustment cost become larger Ψ (points ii and iii).

For an intuition see Figure 8. The blue curve represents profits without ICT. The red curve represents profits with ICT. The dotted red line represents hypothetical profits with ICT if the adjustment costs of ICT were zero and lies above the blue line for all � , implying that all firms would invest in ICT without adjustment costs. Increases in ���� reduce the slope of the red line, whereas increases in Ψ shift the curve downwards. The implication of this result is that more productive larger firms invest in ICT whereas less productive smaller firms are not able to cover the adjustment costs of investment and produce applying a less efficient combination of inputs. The result creates cross-sectional correlation between investment in ICT and size, task complexity, wages, and skill intensity, as per Proposition 2. It also highlights that investment in ICT depends on market conditions represented by the price of ICT and the costs of adjustment.

Proposition 3 refers to firm-level variables that are predictors of investment in ICT. We now turn to describing changes in firm behavior due to ICT.

# **Proposition 4** . _Within firm changes due to ICT_

Assume that for a given �, �<sup>�</sup> ��� > ���� , then Firms invest in ICT when profits are larger compared to a situation of no ICT. The increase in profits is derived from a reduction in costs. The lower variable unit cost implies a lower price and higher quantity of output (i). The increase in profits that results from the ICT investment is shared with workers through the fair-wage schedules, and thus wages go up for both � skilled and unskilled workers (ii). We have that �<sup>�</sup> ��������� and that �� ���������; as a result, a smaller share of tasks is assigned to unskilled labor (iii) (Figure 9).

Regarding production of tasks, for the same reason as point (iii) above the participation of tasks carried out with the combination of skilled labor and ICT increases (Figure 10). These are the more complex tasks. Conditional on output, there is a substitution effect whereby the production of complex tasks increases and the production of noncomplex tasks decreases. Total production of tasks depends on output. Production of complex tasks 21
# **Figure 8. The Decision to Invest in ICT**

<!-- Start of picture text --> � � ����Ψ<br>� � ���<br>����<br>� ∗<br>� ∗� �<br>��<br>���Ψ<br><!-- End of picture text --> The solid blue curve represents profits with no ICT. Firms with productivity below �<sup>∗</sup> do not break even and exit the market. The solid red curve represents profits with ICT. Firms with productivity below �<sup>∗�</sup> are efficient enough to cover the adjustment cost of investment Φ and choose to invest in ICT. Firms with productivity between �<sup>∗</sup> and �<sup>∗�</sup> stay in the market but do not invest in technology.

unambiguously increases, while production of non-complex task increases only if the increase in output is sufficiently high to compensate the negative substitution effect.<sup>8</sup> This proposition provides predictions for within-firm variation due to ICT. Firms that invest in ICT experience a reduction in variable costs, become larger in terms of sales, pay higher wages to both skilled and unskilled workers, perform a larger share of tasks with a combination of skilled labor and ICT, and increase the relative production of complex tasks.

> 8 In Figure 10, point A represents a scenario in which ICT is not available. When ICT is available the firm chooses point C. The movement from A to B, which is a movement along an isoquant, is a substitution effect, whereas the movement from B to C, which is a movement along a ray through the origin (not shown), is an output effect. Production of complex tasks unambiguously increases, whereas the direction of change in production of non‐complex tasks depends on the opposing forces of the substitution and output effect.

22
<!-- Start of picture text --> ay (i,A)<br>a, (i,8)<br>w,(@)<br>Wy (0)<br>wi (9)<br>i*T (0) i (6)<br>N\<br><!-- End of picture text --> <!-- Start of picture text --> tG,9)<br>\ \ w,(@) ay, 8)<br>@)<br>N<br>\ sTM(@) a,(i,<br>N<br>—<br><!-- End of picture text --> <!-- Start of picture text --> t(i, 0)<br><!-- End of picture text --> j i
oO HTM(0) _ (sTM(@)\° <u>wi (@) 1-70) LT(6)</u> ~~(aa) wy~~ <u>(0) i*7(@)</u> i*TM(0); ~~(Go)~~ <u>sT(@)\"</u> Wy (8) < Wier sooo!(9) = H(8) pool’(9) = L(8) wy (8) > Wier Oe a veal’”(8) < L(8)
(iii) lim �→�<sup>������0</sup> A lower elasticity of substitution represents a situation in which skilled labor and ICT are better complements. The stronger the complementarity between skilled workers and ICT, the larger the savings in costs and the larger the share of tasks that are produced with the skilled labor-ICT combination. Given that lim �→�<sup>������</sup> 0 , there is no employment of unskilled workers in the limit.

Summing up Proposition 5. As complementarity between skilled labor and ICT increases (lower �� , the share of skilled labor in total firm employment becomes increasing in ICT. For a given � , the share of skilled labor further depends (negatively) on the wage of skilled labor � � ����� relative to the price of technology � ��� ; this effect is magnified by �.

Regarding the absolute level of employment by worker type, the effects of ICT are ambiguous as well. We start by discussing unskilled employment. Conditional on a given level of output, unskilled workers are replaced by the CES combination of skilled workers and ICT. The substitution of unskilled workers takes place through two channels: a smaller set of tasks is assigned to unskilled labor (as argued in Proposition 4 and depicted in Figure 9); and the participation of unskilled tasks on output decreases (Figure 10). These effects work in the direction of reducing the demand for unskilled workers. At the same time, the output expansion due to the reduction in variable costs works in the direction of increasing the demand for unskilled workers. The overall effect of ICT adoption on employment of unskilled workers is positive if the output effect dominates the substitution effects.

In the case of skilled employment both the output effect and the two substitution effects mentioned above increase the demand for skilled workers through an increase in the demand for the CES skilled workers-ICT combination. There is however the issue of whether skilled labor and ICT are substitutes or complements. If their elasticity of substitution � is sufficiently small, employment of skilled workers increases with ICT. Notice that regardless of whether the absolute levels of skilled and unskilled employment increase or decrease, firm-level wages of both worker types increase due to rent-sharing. This implies that while some workers may be displaced by ICT, other workers in the same firm are better off after ICT due to the increase in wages.

# _Wage inequality_

So far we have assumed that the skilled to unskilled ratio is constant in firm profits. This needs not be so. In this section we assume that the rent-sharing schedules are relatively 25
<!-- Start of picture text --> :<br><!-- End of picture text --> Wy (7) wz (11) <!-- Start of picture text --> (89) (8) 7" (64)<br><!-- End of picture text --> 1 Wy (it) w,(x1) Wy (1) /w, (10) <u>wy (1)</u> wi (1) a ~~wy (8)~~ 0. w(0) ~~wH(9)~~ T _ ~~wyH()~~ ‘T ~~wi)~~ > <u>wi (6) ,VvO>0</u>
This scenario represents a situation in which the skill premium is larger in more productive larger firms, and in which the skill premium increases with investment in ICT. Point (ii) is derived from the fact that profits increase due to investment in ICT. Figure 11 represents this scenario. The blue and green dotted lines represent the difference in skill premium between a small and large firm, while the green and red lines show the skill premium for the same large firm after investment in ICT.

Notice that as firms become more productive, the increase in the relative efficiency in the use of skilled labor (ratio of inverse unit requirements) makes skilled workers more cost effective and firms more skill intensive. The increase in the relative wage of skilled workers works in the opposite direction and partially offsets the increase in their relative efficiency. Empirically it is usually found that larger, more productive firms are on average more skill intensive, which suggests that as firms become more productive the relative efficiency in the use of skilled labor increases at a larger rate than the relative wage of skilled workers.

_Industry-level outcomes after adoption of ICT_ Differences in productivity across firms lead to different firm-level outcomes that we have discussed in the previous sections. In our previous description, we have considered the decisions faced by small firms and the within-firm changes after investing in ICT. We now turn to comparing industry-level equilibria without and with investment in ICT.

Investment in ICT presents to firms as an opportunity to reduce variable costs, reduce prices, increase output, and is thus in principle profit enhancing. For some firms, however, the news is not so good. Low-productivity firms are not able to afford the fixed costs of ICT and choose not to adopt new technology. High-productivity firms, on the other hand, do adopt ICT and increase output. The increase in competition reduces the residual demand for low productivity firms, and their output and profits fall. The firms with lowest productivity are pushed out of the market.

This mechanism is depicted in Figure 12. There is an initial situation in which investment in ICT is not available. Profits under the initial situation are plotted with a dashed blue curve and denoted by �<sup>�</sup> ���. The cutoff productivity in the initial situation is �<sup>�</sup> . Firms with productivity below �<sup>�</sup> exit the market. We now turn to a second situation in which firms have the option to invest in ICT. The solid red and blue curves represent profits for firms that choose to invest and not to invest in ICT, respectively denoted by �<sup>�</sup> ��� and ����. The parameters �<sup>∗�</sup> and �<sup>∗</sup> are the cutoffs for investing in ICT and exiting the market. Consider the difference between ���� and �<sup>�</sup> ���. The curve �<sup>�</sup> ��� lies above the curve ���� because under ���� firms that do not invest in ICT face a more intense competition from firms that do 27
# **Figure 12. Industry equilibrium with and without ICT**

<!-- Start of picture text --> � � ���<br>� � ���<br>����<br>� �<br>� ∗ � ∗� � � �<br>��<br>���Ψ<br><!-- End of picture text --> The dashed blue curve represents profits in an initial situation “0” in which firms do not have the option to invest in ICT. The parameter �<sup>�</sup> is the productivity cutoff, so that firms with productivity below �<sup>�</sup> exit the market because they do not break even. The solid blue and red curves represent profits in a situation in which ICT is available. As before, the solid blue curve represents profits for a firm �<sup>∗�</sup> that does not invest in ICT, given the equilibrium response of all other firms, and the red curve represents a similar profit curve for a firm that does invests in ICT.

invest in ICT. The cutoff �<sup>∗</sup> is therefore larger than the cutoff �<sup>�</sup> , that is, more firms choose to exit the market in a situation in which ICT is available.

Firms that remain in the market can be classified in three groups. First, low productivity firms, with productivity parameter between �<sup>∗</sup> and �<sup>∗�</sup> , which do not invest in ICT and for which output and profits are lower than under the initial situation with no ICT. Second, medium-productivity firms, with productivity parameter between �<sup>∗�</sup> and �<sup>�</sup> (see Figure 12), which do invest in ICT, but for which the reduction in variable costs is not high enough and their output and profits are lower than under the initial situation. Finally, highproductivity firms, with productivity parameter above �<sup>�</sup> , which choose to invest in ICT and for which output and profits are higher than under the initial situation. Summing up, the availability of ICT concentrates production around high productivity firms. The lowest productivity firms exit the market; low and medium-productivity firms become smaller; whereas high-productivity firms become larger. Further, the availability of ICT may induce entry of new firms.

28
G H(@) L(@) e*T et 00 H(@) =|6 H(@)dG(@) +|eTHTM(6)dG(@) +{61 HTM(@)dG(@) ert gt co L(@) -|0 L(@)dG(@) +{Q*TLTM(6)dG(@) +{g1 LTM (@)dG(@)

L(@) G.

H(@) G
skilled and unskilled, affect wage schedules in cases of large industries or industries with specific factors or mobility costs. These effects have been studied theoretically and empirically, without considering wage heterogeneity, by a large share of the tasks-approach literature of labor markets and technology adoption. In this paper we abstract from general equilibrium wage effects while instead focusing on firm-level outcomes and allowing for imperfect competition in labor markets.

# **4. Conclusions**

We develop a theoretical framework that expands the task-based models of technical progress and labor markets to allow for firm heterogeneity and wages that vary across firms. Our model is compatible with the empirical observation that more productive firms are larger, are more skill intensive, and pay higher wages across skill categories. Regarding investment in ICT, our model predicts that the decision to invest in ICT depends on firm size and labor market characteristics. As a result of investment in ICT, firms grow, become more intensive in complex tasks, and become more skilled intensive as long as skilled labor is complementary to ICT. Even if firms become more skilled intensive, the overall effect of ICT adoption on employment of unskilled workers could be positive if the increase in output due to the reduction in variable costs is sufficiently high. At the aggregate level, changes in employment depend on the distribution of firm productivity and the resulting concentration of production, as output effects become largest for the highest productivity firms. The changes in skill intensity and the absolute level of employment by worker type are questions open for empirical research. Workers who remain employed are better off because their wage increases with ICT. To the extent that skilled workers have more bargaining power than unskilled workers, or that their wage scheme is more tied to firm performance, wage inequality at the firm-level increases with ICT.

# **References**

Acemoglu D. and D. Autor (2011): “Skills, Tasks and Technologies: Implications for Employment and Earnings”. _Handbook of Labor Economics_ , vol. 4b, pp. 1044—1166.

Acharya, V., R. Baghai, and K. Subramanian (2013): “Labor Laws and Innovation,” _Journal of Law and Economics_ , vol. (56), pp. 997—1037.

Akerman, A., I. Gaarder, and M. Mogstad (2015): “The Skill Complementarity of Broadband Internet,” _The Quarterly Journal of Economics,_ vol.130(4), pp. 1781—1824.

Amiti, M. and D. Davis (2011): “Trade, Firms, and Wages: Theory and Evidence,” _Review of Economic Studies,_ vol. 79, pp. 1—36.

Autor D. H., and D. Dorn (2013): “The growth of low-skill service jobs and the polarization of the US labor market,” _The American Economic Review_ vol. 103(5), pp. 1553—1597.

30
Autor, D.H., L.F. Katz and M.S. Kearney (2008): “Trends in U.S. Wage Inequality: Revising the Revisionists,” _The Review of Economic and Statistics_ , vol. 90(2), pp. 300—323.

Autor, D. H., L. F. Katz, and A. B. Krueger (1998): “Computing Inequality: Have Computers Changed the Labor Market?," _Quarterly Journal of Economics,_ vol. 113(4), pp. 1169—1213.

Autor, D. H., F. Levy, and R. J. Murnane (2003): “The Skill Content of Recent Technological Change: An Empirical Exploration,” _The Quarterly Journal of Economics_ , vol. 118(4), pp. 1279—1333.

Aw, B.Y., M. J. Roberts, and D.Y. Xu (2011): “R&D Investment, Exporting, and Productivity Dynamics,” _The American Economic Review,_ vol. 101(4), pp. 1312—1344, June.

Bartelsman, E., P. Gautier and J. de Wind (2016): “Employment Protection, Technology Choice, and Worker Allocation,” _International Economic Review_ , vol. 57(3), pp. 787—826, August.

Bartelsman, E.J. and J. Hinloopen (2005): “Unleashing Animal Spirits: Investment in ICT and Economic Growth”, in L. Soete and B. ter Weel (eds.), _The Economics of the Digital Society_ , Edward Elgar, pp. 272 – 304.

Berman, E., J. Bound, Z. Griliches (1994): “Changes in the Demand for Skilled Labor within U.S. Manufacturing: Evidence from the Annual Survey of Manufactures,” _The Quarterly Journal of Economics,_ vol. 109(2), pp. 367—397.

Berman, E., J. Bound, S. Machin (1998): “Implications of Skill-Biased Technological Change: International Evidence,” _The Quarterly Journal of Economics,_ vol. 113(4), pp. 1245—1279, November.

Bernard, A. and B. Jensen (1999): “Exceptional Exporter Performance: Cause, Effect, or Both?,” _Journal of International Economics,_ vol. 47, pp. 1—25.

Bloom, N., R. Sadun, and J. Van Reenen (2012): “Americans Do I.T. Better: US Multinationals and the Productivity Miracle,” _American Economic Review,_ vol. 102(1), pp. 167—201.

Bound, J. and G. Johnson, “Changes in the Structure of Wages in the 1980’s: An Evaluation of Alternative Explanations,” _The American Economic Review,_ vol. 82(3), pp.371—392.

Bloom, N., M. Draca, and J. Van Reenen. (2016): “Trade induced technical change? The impact of Chinese imports on innovation, IT and productivity.” _The Review of Economic Studies_ , vol. 83(1), pp. 87—117.

Bresnahan, T., Brynjolfsson, E. and M.L. Hitt (2002) “Information Technology, Workplace Organization, and the Demand for Skilled Labor: Firm-Level Evidence,” _The Quarterly Journal of Economics,_ MIT Press, vol. 117(1), pp. 339—376, February.

Brynjolfsson, E., and L.M. Hitt (2003): “Computing productivity: Firm-level evidence,” _Review of Economics and Statistics,_ vol. 85(4), pp. 793—808.

Card, D. and T. Lemieux (2001): “Dropout and Enrollment Trends in the Postwar Period: What Went Wrong in the 1970s?,” in J. Gruber ed., _Risky Behavior among Youths: An Economic Analysis_ , University of Chicago Press for the NBER.

Card, D. and T. Lemieux (2001b): “Can Falling Supply Explain the Rising Return to College for Younger Men? A Cohort-Based Analysis,” _The Quarterly Journal of Economics,_ vol. 116(2), pp. 705—746.

31
Di Nardo, J., and J.P. Pischke (1997): “The Returns to Computer Use Revisited: Have Pencils Changed the Wage Structure Too?," _Quarterly Journal of Economics,_ vol. 112(1), pp. 291—303.

Draca, M., R. Sadun, and J. Van Reenen (2007): “Productivity and ICT: A Review of the Evidence”, in Avgerou, Mansell, Quah, and Siverstone, eds., _Handbook of Information and Communication Technologies,_ 100-147, Oxford, UK. Oxford University Press.

Koeniger, W. (2005): “Dismissal costs and innovation,” _Economics Letters_ , vol. 88(1), pp. 79—84, July.

Goldin, C., and L. Katz (1998): “The Origins of Skill Capital Complementarity,” _Quarterly Journal of Economics,_ vol. 113(3), pp. 693—732.

Goos, M. and A. Manning (2007): “Lousy and Lovely Jobs: The Rising Polarization of Work in Britain,” _Review of Economics and Statistics,”_ vol. 89, pp. 118—133.

Goos, M., A. Manning, A. Solomons (2014): “Explaining Job Polarization: Routine-Biased Technological Change and Offshoring,” _The American Economic Review,_ vol. 104(8), pp. 2509—2526, August.

Gust, C., and J. Marquez (2004): “International Comparisons of Productivity Growth: The Role of Information Technology and Regulatory Practices”, _Labour Economics_ , vol. 11(1), pp. 33—58, February.

Jorgenson, D.W., M.H. Ho, and K.J. Stiroh (2008): “A Retrospective Look at the U.S. Productivity Growth Resurgence,” _Journal of Economic Perspectives_ , vol. 22(1), pp. 3–24.

Katz, L. F., and K. M. Murphy (1992): “Changes in Relative Wages, 1963-1987: Supply and Demand Factors,” _The Quarterly Journal of Economics_ , vol. 107(1), pp. 35—78.

Krueger, A. B. (1993): “How Computers Have Changed the Wage Structure: Evidence from Microdata,” _The Quarterly Journal of Economics_ , vol. 108(1), pp. 33—60.

‐ Krusell, P., L. Ohanian, J. V. Ríos-Rull, G. L. Violante (2000): “Capital Skill Complementarity and Inequality: A Macroeconomic Analysis," _Econometrica_ , vol. 68(5), pp. 1029—1053.

Kugler, M. and E. Verhoogen (2012): “Prices, Plant Size, and Product Quality,” _Review of Economic Studies,_ vol. 79(1), pp. 307—339, January.

Machin, S. and J. Van Reenen (1998): “Technology and Changes in Skill Structure: Evidence from Seven OECD Countries, _The Quarterly Journal of Economics,_ vol. 113(4), pp. 1215—1244.

Melitz, M. (2003): “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” _Econometrica,_ vol 71., pp. 1695—1725.

Michaels, G., A. Natraj, and J. Van Reenen (2014): “Has ICT Polarized Skill Demand? Evidence from Eleven Countries over Twenty-five Tears,” _Review of Economics and Statistics_ , vol. 96(1), pp. 60—77.

Oliner, S.D., D.E, Sichel, and K.J. Stiroh (2007): “Explaining a Productive Decade,” _Brooking Papers on Economic Activity,_ (1), pp. 81—137.

Saint-Paul, G. (2002), “Employment Protection, International Specialization, and Innovation,” _European Economic Review,_ vol. 46(2), pp. 375—395.

32
Samaniego, R. (2006): “Employment Protection and High-Tech Aversion,” _Review of Economic Dynamics,_ vol. 9(2), pp. 224—241.

Syverson, C. (2011): “What Determines Productivity,” _Journal of Economic Literature,_ vol. 49(2), pp. 326–365.

van Ark, B., M. O’Mahoney and M. Timer (2008): “The Productivity Gap between Europe and the United States: Trends and Causes.” _Journal of Economic Perspectives_ , vol. 22(1), pp. 25—44.

Verhoogen, E. (2008): “Trade, Quality Upgrading, and Wage Inequality in the Mexican Manufacturing Sector,” _The Quarterly Journal of Economics,_ vol. 123(2), pp. 489—530.

33