Abstract
What drives investment in automation technologies? This paper documents a positive relationship between labor-friendly institutions and investment in industrial robots in a sample of advanced and developing economies. Institutions explain a substantial share of cross-country variation in automation. The relationship between institutions and robots is stronger in sunk cost-intensive industries, where producers are vulnerable to holdup. The result suggests that one reason for producers to invest in automation is to thwart rent appropriation by labor.
1. Introduction
Over the last decade, advances in robotics have generated concerns about labor displacement. While a growing body of literature investigates the economic impact of robots, the equally important question of what drives investment in automation has received much less attention. The main contribution of this paper is making a step toward filling that gap by documenting a positive relationship between labor-friendly institutions and investment in industrial robots. Theoretical arguments and the empirical evidence support a simple underlying mechanism: labor-friendly institutions increase labor bargaining power, providing an incentive to substitute workers with robots.
A simple model of technological choice with wage bargaining is used to guide the empirical analysis at the country–industry–year level. In this model, firms can choose between using a traditional technology employing capital and labor or using robots, which perfectly substitute for labor. Labor-friendly institutions increase workers’ ability to extract rents at the expenses of firms. Thus, when automation is a viable alternative i.e. capital and labor are substitutes, firms increase investment in robots to minimize dependency from labor in production and thwart rent appropriation.
In the model, firms face sunk costs at the moment of hiring. Since part of the initial investment cannot be recovered if workers walk away and production does not take place, workers exploit their bargaining power to extract rents. Thus, the model provides a testable implication: the higher the sunk cost, the higher the rent workers can extract when institutions are labor-friendly, and the higher the incentives to invest in robots.
Controlling for country-year and industry-year characteristics, such as the features of the broader institutional system, human capital endowment, demand and supply shocks, and the task composition of employment1, the paper provides robust evidence that industries characterized by a high incidence of sunk costs are indeed disproportionately automated in countries with labor-friendly institutions.
The second key contribution of the paper is providing evidence that while labor-friendly institutions increase investment in labor-substituting capital—such as robots—it also discourages the use of labor-complementing capital. This finding is rationalized by the model predicting an opposite relationship among institutions, sunk costs, and investment when capital complements labor. The underlying intuition is simple: when labor is essential in production, firms cannot avoid rent extraction and react by investing less. Most capital assets are characterized by some degree of complementarity with labor and hence the negative empirical correlation between aggregate investment and labor-friendly institutions.
A case in point is the motor vehicle industry. Motor vehicles is an industry characterized by large sunk costs, because both suppliers of components and assemblers need specific equipment that has little scope for utilization outside the industry.2 That makes it hard to find an alternative use of capital and fully recover the cost of investment if production does not take place. In countries with high union rates, for instance, motor vehicles tends to be highly automated but with a relatively low aggregate capital to labor ratio.
Although being reasonably robust and grounded in a plausible theoretical framework, the findings of this paper are subject to the important limitation of being based on data aggregated at the country/2-digit industry level. For instance, this might hide relevant firm-level heterogeneity in the type of robots adopted or the strength of workers’ bargaining power, which in turn could affect the relationships of interest. This also implies that while the paper provides empirical evidence supporting the hypothesis that labor-friendly institutions drive automation because they create a holdup problem3, the level of aggregation of the data does not allow to rule out alternative but not necessarily competing explanations.4 As a consequence, the evidence provided in this paper does not necessarily have a causal interpretation. Yet, to the best of my knowledge, there are no other available data sources allowing for a meaningful cross-country–industry–year examination of the relationship between and labor institutions and robot adoption. Indeed, a number of contributions exploit the same data sources on robots as in this paper, either to study automation in an international setting (Graetz and Michaels, 2018; Acemoglu and Restrepo, 2022) or to exploit variation in robot adoption across industries (Acemoglu and Restrepo, 2020; Dauth et al., 2021).
It is also reassuring that the main findings of the paper are consistent with previous research. In particular, Belloc et al. (2022) document a positive correlation between the strength of employee representation and the use of automation technologies at the establishment level.5 The findings of the paper are also consistent with Caballero and Hammour (1998), which are among the first to provide evidence that the tightening of labor institution spurs capital deepening. Exploiting country–industry variation, Acemoglu and Restrepo (2022) provide some evidence that unions are positively related to robot adoption. However, none of these papers explicitly take into account the role of capital–labor substitution and study the implications of holdup using data on robots.
The relationship between holdup and investment is examined in related work, such as Cardullo et al. (2015), Acemoglu and Shimer (1999), and Connolly et al. (1986). The findings in this article are consistent with all such papers, which advocate a negative relationship among labor-friendly institutions, sunk costs, and aggregate investment, which is typically characterized by some degree of complementarity with labor. Jäger et al. (2021) and Jäger et al. (2022) find a limited role for the codetermination of board members in affecting capital investment, but unlike in this paper they focus on a single specific labor market institution.
More broadly, this paper relates to a growing literature studying the impact of robots on economic outcomes (Acemoglu and Restrepo, 2020; Graetz and Michaels, 2018; Dauth et al., 2021; Hirvonen et al., 2022; Battisti et al., 2017). Unlike in these papers, the main contribution of this study is exploring the determinants of investment in automation. Moreover, with the exception of Graetz and Michaels (2018), the latter contributions focus on a single country or a specific industry within a country, while this paper looks at a large number of countries and industries.
The rest of the paper is organized as follows: section 2 presents the data and the descriptive evidence that motivates the study; section 3 presents a model, which is used to guide the empirical analysis; section 4 includes the empirical analysis, including the methodological approach (4.2) and the main results (4.3); and section 5 provides additional results based on alternative samples and levels of data aggregation. Finally, section 6 concludes.
2. Data and descriptive evidence
This section motivates the analysis by presenting the main data and some descriptive evidence based on 53 Organization for Economic Cooperation and Development (OECD) and non-OECD countries from 1993 to 2013. Detailed information on data sources are provided in Supplementary Data Appendix A. Summary statistics of the variables used in this section can be found in Supplementary Appendix Table A1.
Data on shipments of industrial robots are obtained from the International Federation of Robotics (IFR). Data on shipments are used to construct the stock of operational robots in each country–industry–year cell. Industrial robots are defined by the International Organization for Standardization (ISO) 8373:2012 as an automatically controlled, reprogrammable, multipurpose manipulator programmable in three or more axes, which can be either fixed in place or mobile for use in industrial automation applications.
As any other piece of machinery and equipment, industrial robots are included in accounts of aggregate capital.6 However, the definition of industrial robots suggests that they differ in one fundamental dimension from most other categories of capital equipment: they are characterized by a high degree of substitutability with human labor, i.e. they are labor-saving technologies. Unlike industrial robots, most other categories of assets included in capital accounts are characterized by some degree of complementarity with labor. Buildings, (non-autonomous) vehicles, and the vast majority of machine tools are examples of labor-complementing capital. Indeed, estimates from different countries and levels of aggregation suggest that the elasticity of substitution between aggregate capital and labor is generally less than unity (Klump et al., 2012). Sections 3 and 4.4 will study theoretically and empirically the implications that differences in the degree of substitution with labor have on the relationship between labor institutions and investment.
A potential issue of the IFR data is that shipments are counted in “units.” Therefore, in the paper robots are assumed to have a similar impact irrespective of their size or complexity. However, these data are unique in that they allow for a meaningful international comparison, because the IFR has a common protocol to count robots that ensures some consistency across countries, industries, and years.
The data show that there are large differences in adoption of industrial robots, even within the OECD region between countries at similar levels of per capita income and narrowly defined industries. For instance in motor vehicles, which alone accounts for almost half of the total robots usage in the OECD region, the number of robots per thousand employees, “robot density” hereafter, is 5 in Ireland, 40 in the Netherlands, and roughly 100 in Belgium, Korea, France, and Japan. In 2013, the United States used 10 robots per thousand employees less than Italy and 20 less than Germany and Spain. Such heterogeneity is not limited to motor vehicles and it is even more extreme in other industries such as electronics, where Korea and Japan used almost 80 robots per thousand employees in 2013, against 15 or less in other OECD economies.
Differences in adoption are unlikely to be due to differences in robot prices, especially among OECD countries similarly integrated in international markets. Evidence on robot prices for six large economies is documented in Graetz and Michaels (2018), which present very limited cross-country price variation. An alternative explanation for cross-country differences in technology adoption is the presence of frictions. Examples include lack of education (Nelson and Phelps, 1966), organizational capital (Brynjolfsson and Hitt, 2000), credit constraints (Parente and Prescott, 1994), or labor market rigidities (Bartelsman et al., 2016). However, data suggest that frictions are unlikely to explain differences in adoption. Figure 1 shows robot density in OECD countries relative to the United States for the manufacturing industry in 2013. While considered the most innovative country in the world and an efficiency benchmark in comparative macroeconomic studies, the United States uses less robots than most other OECD economies.
Cross-country differences in adoption of industrial robots
Motivated by the wide cross-country heterogeneity in labor market institutions, this paper investigates whether they can explain the differences in robots’ adoption. Data on institutions are taken from Adams et al. (2017), Visser (2015), and Armingeon et al. (2013). The data show that institutions are much more “labor-friendly” in some countries than in others. For instance, the constitutional protection of labor rights and the strength of employee representation tend to be lower in Anglo-Saxon countries than in most countries in Continental Europe. Union coverage is above 50% in most European countries—almost 100% in Spain, France, and Italy, while in the United States and Japan coverage is well below 20%.
In countries with labor-friendly institutions, the cost of labor should be higher for firms. Therefore, due to the high degree of substitution with labor emphasized in the definition of industrial robot, incentives to automating production should be higher in countries with labor-friendly institutions. Descriptive evidence is consistent with the hypothesis. The top panel of Figure 2 depicts the relationship between the 1995–2015 change in the number of robots per thousand workers and the 1994 union membership rate.7 The figure shows that countries with higher union membership adopted a larger number of robot per worker over the period considered. The central panel of Figure 2 displays the correlation between the change in robots’ adoption over the same period and the 1994 value of an index of constitutional protection of labor rights. Again we observe a positive relation between institutions and automation. Constitutional provisions can heavily affect labor bargaining power. For instance, in the United States where the right to collective bargaining is not granted by the constitution, workers need to follow costly and time-consuming procedures in order to join a trade union and be represented in wage negotiations.8 On the contrary, in most European countries with constitutional provisions, employers cannot refuse to engage in collective bargaining. In such countries, workers benefit of a stronger representation and are more likely to obtain higher wage or to win industrial disputes.9 Therefore, strong unions or a legal environment improving the bargaining position of workers should increase employers’ labor costs, thereby creating incentives to invest in automation. According to such a view, countries in which functional income is biased toward labor should automate the most, because producers have greater incentives to redistribute rents from labor to capital. The relationship depicted in the bottom panel of Figure 2 provides some evidence in support of the hypothesis. Countries with higher labor shares in 1994 experienced a larger increase in the adoption of robots. Thus, the descriptive evidence presented so far suggests that investment in automation is at least partially driven by an attempt to redistribute rents from labor to capital.
Industrial robots, labor institutions, and the labor share
3. A model of technological choice with wage bargaining and sunk costs
This section sketches a model of technological choice with wage bargaining and sunk costs. The model serves the purpose of rationalizing the contrasting views expressed by the literature about the impact of institutions on investment. The key result from the model is that labor-friendly institutions encourage investment in labor-saving technology and discourage investment in labor-complementing capital. A detailed description of the model and its solution, as well as additional results, can be found in the Model Supplementary Appendix B.
3.1 The model environment
There is a single final good Y produced by a representative firm in a perfectly competitive final output market. This firm combines an infinity of intermediate goods indexed by i, with aggregate measure 1. The quantity of each intermediate good is denoted by y(i). The final good firms have access to the production function |$ln \, Y = a + \int_0^1 ln \, y(i) \,\, di$|. The final good is taken to be the numeraire and so its price is set to 1.
3.2 Intermediate good firms
There is free entry in the production of each intermediate good variety, which pushes intermediate good producers’ profits down to zero. The timing assumptions are as in Cardullo et al. (2015) and Acemoglu and Shimer (1999). First, firms decide how much to invest in structures and machinery. Only then they hire workers and bargain over wages. The timing assumptions reflect the fact that building a plant and setting up the machinery takes time. In a typical situation, workers are not hired before everything is ready for production. The assumption of ex ante investment and ex post wage bargaining implies that at least part of the investment is sunk at the moment of bargaining on wages. Anticipating that firms would lose (at least part of) their initial investment if production does not take place (e.g. a strike), workers can hold up firms when they bargain, by demanding higher wages.10
Intermediate good varieties can be produced by one of two potential technologies. One is “traditional” and combines labor and capital. Alternatively, intermediate goods can be produced with robots only. The difference between traditional and automated firms is that the capital used by the former is characterized by some degree of complementarity with labor, while the capital used by the latter (i.e. robots) is a perfect substitute for human workers. Crucially, the assumption on the different degree of substitution with labor implies that only traditional firms are vulnerable to holdup.
3.2.1 Traditional intermediate good firms
Traditional firms produce outputs with a constant returns to scale production function combining capital k(i) and labor. Due to the timing assumptions, capital is rented before hiring at the rate r > 1. For simplicity, each firm is assumed to hire only one worker. The output (per worker) is given by |$y(i)= f\big(k(i)\big)$|.
A fraction of capital |$\sigma \in [0,1]$| is lost if production does not take place.11 Therefore, a fraction of the initial ex ante investment |$\sigma r k(i) $| is sunk at the moment of hiring. Assuming a Nash bargaining rule, the wage equation reads:
In (1), p(i) is the relative price of variety i. Equation (1) shows that wages are increasing with sunk costs. Anticipating that the initial investment would be lost if they refuse to provide their services (e.g. by striking), workers hold up the producer by demanding higher wages. The larger the sunk costs, the larger the rent labor can appropriate. However, the extent to which labor is able to extract rents depends on its bargaining power |$\beta \in (0,1)$|.
Since all traditional firms are identical, they earn the same price p, invest the same amount of capital k, and pay the same wage w.
3.2.2 Automated intermediate good firms
Firms produce one unit of variety i with one robot, i.e. automated firms have a linear production technology. Following Alesina et al. (2018) and Zeira (1998), the production of some varieties is harder to automate.12 Without the loss of generality, intermediate good varieties are ordered in such a way that higher is are more costly to automate. This is reflected in the price of robots being equal to |$\frac{r}{1-i}\geq r$|. The equilibrium stock of robots in automated firms is:
3.2.3 Technological choice
Let |$i^*$| be the intermediate good variety for which firms are indifferent to using traditional or automated production technologies. An expression for |$i^*$| is obtained by equating the marginal cost of the two methods of production and rearranging terms:
Equation (3) describes the extensive margin of robots’ adoption and defines a positive relationship between k and |$i^*$|. A large capital stock implies low returns on investment and hence high marginal costs. This implies that a larger share of varieties will be produced with robots. Therefore, the model predicts that the automation is higher (at least on the extensive margin) in highly industrialized countries, a prediction consistent with the data.
3.3 Equilibrium and analysis
Model Supplementary Appendix B shows that for given levels of output and interest rate, the unique equilibrium stock of robots R and aggregate capital k are given by the intersection of two equations:
Equation |$\phi(R,k)$| describes an increasing relationship between R and k, while as long as |$\varepsilon_{f,k} f\big(k\big)$| is non-decreasing, |$\psi(R,k)$| generates a decreasing relationship between the same variables.Figure 3
The relationship between wages, labor bargaining power, and sunk cost intensity
depicts the equilibrium under two different values of β, with high values representing labor-friendly institutions. For β = 0.3, the economy lies at the equilibrium represented by point A. Now suppose that β increases to β = 0.7. In such a case, wages increase and the net value of engaging in production for traditional firms drops. In turn, that generates an incentive to using robots instead, which do not bargain over wages. Both |$i^*$| and R increase, which shifts |$\phi(R,k)$| up. At point Aʹ, however, there are less traditional firms and the stock of aggregate capital k is lower. That increases the marginal product of capital and lowers the cost advantage of automated firms, which mitigates the increase in |$i^*$| and shifts |$\psi(R,k)$| down, up to the new equilibrium B.
The model predicts that economies with low labor bargaining power have a high level of labor-complementing capital and a low stock of robots, while the opposite is true for high values of β. Model Supplementary Appendix B shows that the equilibrium presents similar characteristics when output is determined endogenously, although the existence and uniqueness of the equilibrium cannot be established in general.13
The equilibrium conditions of the model can be used to study how the labor bargaining power and sunk costs interact in determining the technological choice. Figure 4 presents the results of simulating the path of R, k, |$i^*$|, and w as functions of β. Each panel plots two lines, corresponding to the cases of low and high incidences of sunk costs. Solid lines correspond to the case σ = 0.1, while dashed lines correspond to the case σ = 1, i.e. the whole initial investment is sunk. In panel 4a, the stock of robots is an increasing function of labor bargaining power. For any value of β, however, the R is larger when sunk costs are high. An opposite relationship is presented in panel 4b for aggregate capital. Labor bargaining power lowers incentives to invest in labor-complementing capital, disproportionately more in the presence of large sunk costs. Panel 4c shows that with high sunk costs, the share of automated firms increases much more steeply. Finally, panel 4d confirms that higher bargaining power increases wages, disproportionately when sunk costs are large.
The relationship between key variables of the model, labor bargaining power and sunk costs
4. Empirical analysis
This section empirically tests the predictions of the model presented in Section 3. The empirical analysis is based on a sample of 35 OECD economies and 18 two-digit industries, from 1993 to 2015.14 Summary statistics of all variables used in this section can be found in Supplementary Table A2 of Data Appendix.
4.1 Quantifying industry-level incidence of sunk costs
The empirical methodology in this section crucially relies on measuring industry-level sunk costs. The proxies of industry-level sunk costs are computed from data on secondhand capital expenditures by industries, from the US Census Bureau.15 The idea underlying the construction of the proxy is the following.16 When investment is irreversible, firms should rely less on secondhand capital markets. Therefore, in such industries the share of secondhand capital should be lower. The main proxy of sunk cost intensity is then the inverse share of secondhand capital in each 2-digit industry. An alternative proxy of sunk costs used in this paper is simply the industry-level share of gross fixed investment in the total output.17 The indicator is based on data from STAN and the NBER-CES Manufacturing Database.18,19
Supplementary Appendix Figure A3 displays the proxy of sunk cost intensity.20 Motor vehicles and chemicals are the most sunk cost-intensive industries. As noticed in the introduction, in motor vehicles suppliers of components and assemblers use highly specialized equipment that does not have much use outside that industry. In the chemical industry, refining and processing takes place in large plants and requires heavy equipment. That makes investment practically irreversible.21 Capital is thus highly specific in both industries due to the irreversibility of investment, but the source of irreversibility differs. In the former, it arises for the industry specificity of the equipment. In the latter, it is likely to arise from the large size of the equipment, which makes it hard to move it or ship it. Supplementary Appendix Figure A3 suggests that the construction industry is the less sunk cost-intensive. The reason is that most capital assets used in constructions are general-purpose machinery used to handle materials, machine tools, and vehicles. Moreover, in constructions producers make virtually no investment in buildings, which instead constitute an important category of (at least partially) irreversible investment in other manufacturing industries. Therefore, firms in the construction business are more likely to purchase machinery in secondhand markets, which results in a lower measure of sunk costs. Supplementary Appendix Figure A4 plots the industry-average of the alternative sunk cost variable, computed across all countries from which information is available, against the sunk cost measure based on the secondhand capital expenditure. The chart shows that there is a positive correlation between the two variables.
4.2 Empirical methodology
The analysis is based on the following linear model:
The dependent variable in (4) is shipments of new industrial robots per thousand employees to every country, 2-digit industry, and year.22
The choice of the dependent variable in (4) is similar to that of Acemoglu and Restrepo (2022), which in the country–industry–year specification use shipment of new robots, rather than the stock.23 The industry-level measure of sunk costs is σi.
The variable Instct includes different measures of “labor-friendliness”: (i) the constitutional protection of labor rights; (ii) the strength of employees’ representation in industrial relations; (iii) union density, and (iv) union coverage.24 It should be noticed that the former two variables can only be considered de jure institutions. However, in the sample of OECD countries used in this part of the analysis, it is unlikely that weak enforcement or informality would be an issue, which may otherwise lead to a gap between de jure and de facto institutions.
In some specification, the vector Xci includes a number of controls, which are discussed further below. Since Instct varies at the country-year level, the inclusion of country-year effects uct precludes the estimation of the country-average impact of institutions. Including country-year effects is particularly important because it allows to purge the estimated coefficients from the potential correlation between our main independent variables and other institutions. For instance, union rates might be correlated with the generosity unemployment benefits or firing costs, which in turn might have an impact on robots’ investment. The variable uit denotes industry-year fixed effects (FEs). The inclusion of uit aims at controlling for the impacts of industry-specific unobserved characteristics, such as improvements in industry-specific technology and workforce’s differences in human capital endowment and skills.25 Including industry-year FEs helps as well, mitigating the concern that some industry-specific characteristics correlated with sunk costs, such as routine tasks intensity, might be driving the results.26 The error term is denoted by ɛcit. Errors are clustered at the country level, and all estimates are weighted by the base-year industry share of employment in each country.27
In (4), the coefficients of interest are γ1, which quantifies the differential impact of institutions in industries characterized by different levels of sunk costs. The computation of σi is based on 1994 data for the United States, which is then dropped from the sample prior to estimation.28 This strategy mimics Rajan and Zingales (1998) and minimizes the possibility that the impact of institutions would affect industry-level investment in robots, contaminating the proxy of sunk costs. Indeed, in the United States, regulatory frictions are minimal and so the proxy is more likely to be purely determined by industry-specific technological characteristics, which should be common to all countries in the OECD region. Evidence in support of the identifying assumption is given by the fact that the median within-country variation of σi is greater than its cross-country variation for a given industry.
One concern with the specification in (4) is that there might be factors related to sunk cost intensity that disproportionately spur robot adoption in countries with labor-friendly institutions. For instance, robots might be systematically less effective at replacing labor in sunk cost-intensive industries. Therefore, a stronger uptake could mechanically result from the fact that more robots are needed to replace a worker in those industries. While this is a possibility, it is unlikely that this happens in practice, as sunk costs arise from the specificity of investment, which is unrelated to the particular applications performed by robots. Nevertheless, section 4.3.1 presents several robustness checks aimed at mitigating such concerns.
Another potential issue is that robots’ investment in the United States could have affected the share of secondhand capital in 1994, biasing σi. However, that seems unlikely for three reasons. First, robots account for a very small percentage of the aggregate capital stock. For instance, US 6-digit-level industry data include industrial robots in NAICS 33351 Metalworking Machinery Manufacturing. The industry includes power-driven hand tools, welding and soldering equipment, and industrial robots. The share of value added in total manufacturing of the whole industry is just 3.4% in 2013. Second, the definition of robots suggests that they are flexible machines and so it is unlikely that producers would sell them when they face negative demand shocks or related events. Third, in 1994, industrial robots were not yet widespread in US manufacturing. Such arguments mitigate the concern that in 1994, robots’ investment in the United States might have biased σi, the baseline proxy of sunk costs used in the paper. The variable σi is normalized to have zero mean and standard deviation equal to 1 in the weighted sample. Therefore, γ1 measures the differential impact of institutions in industries one standard deviation above the average sunk cost intensity (henceforth, “sunk cost-intensive” industries).
Finally, one might worry that even investment in industrial robots might be sunk, thereby being vulnerable to the same holdup problem characterizing other forms of capital. However, this is unlikely, for two reasons. First, the ISO definition emphasizes two key elements characterizing industrial robots: “reprogrammable” and “multipurpose” (see section 2). Indeed, the most commonly used industrial robots are mechanical arms that can be used for many different applications by adapting the robotic arms. This makes them unlikely to be specific to a particular industry and therefore unlikely to constitute the kind of irreversible investment, allowing workers to hold up the management. This is also reflected in the fact that all major robot manufacturers have dedicated sections in their websites for secondhand robots.29 Moreover, in many cases firms do not purchase industrial robots, but rather rent them from robot integrators (Acemoglu and Restrepo, 2020). Second, and from another perspective, occupations that are likely complement to robots are high-skill, such as engineers or highly specialized blue collars, which are typically less prone to conflict with the management.
4.3 Institutions, sunk costs, and robots: results
Table 1 shows Ordinary Least Squares (OLS) estimates of γ1.30 The coefficients in Table 1 suggest that institutions are associated with higher automation in sunk cost-intensive industries, roughly between 0.2 and 0.4 additional robots per thousand workers. The only coefficient that is not statistically significant is the one associated with union density in column 3. The evidence is consistent with the hypothesis that labor-friendly institutions induce automation more in sunk cost-intensive industries, where workers can hold up the producer and extract rents.
OLS estimates of the impact of institutions on country–industry shipment of industrial robots per thousand employees.
| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| S/L | S/L | S/L | S/L | |
| Labor rights in the constitution × industry sunk costs | 0.233* | |||
| (0.113) | ||||
| Strong employee representation × industry sunk costs | 0.397** | |||
| (0.173) | ||||
| Union density × industry sunk costs | ‒0.075 | |||
| (0.173) | ||||
| Union coverage × industry sunk costs | 0.274* | |||
| (0.146) | ||||
| Observations | 5255 | 5255 | 5162 | 3561 |
| R-squared | 0.597 | 0.603 | 0.581 | 0.599 |
| Industry-year FE | Yes | Yes | Yes | Yes |
| Country-year FE | Yes | Yes | Yes | Yes |
| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| S/L | S/L | S/L | S/L | |
| Labor rights in the constitution × industry sunk costs | 0.233* | |||
| (0.113) | ||||
| Strong employee representation × industry sunk costs | 0.397** | |||
| (0.173) | ||||
| Union density × industry sunk costs | ‒0.075 | |||
| (0.173) | ||||
| Union coverage × industry sunk costs | 0.274* | |||
| (0.146) | ||||
| Observations | 5255 | 5255 | 5162 | 3561 |
| R-squared | 0.597 | 0.603 | 0.581 | 0.599 |
| Industry-year FE | Yes | Yes | Yes | Yes |
| Country-year FE | Yes | Yes | Yes | Yes |
The table presents OLS estimates of the relationship among labor institutions, sunk costs, and annual installations of robots. The dependent variable is the country–industry shipment of industrial robots per thousand employees. The proxy of sunk cost intensity is the inverse share of the secondhand capital expenditure in a given 2-digit industry. Standard errors are clustered at the country level. The coefficients with *** significant at the 1% level, with ** significant at the 5% level, and with * significant at the 10% level.
OLS estimates of the impact of institutions on country–industry shipment of industrial robots per thousand employees.
| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| S/L | S/L | S/L | S/L | |
| Labor rights in the constitution × industry sunk costs | 0.233* | |||
| (0.113) | ||||
| Strong employee representation × industry sunk costs | 0.397** | |||
| (0.173) | ||||
| Union density × industry sunk costs | ‒0.075 | |||
| (0.173) | ||||
| Union coverage × industry sunk costs | 0.274* | |||
| (0.146) | ||||
| Observations | 5255 | 5255 | 5162 | 3561 |
| R-squared | 0.597 | 0.603 | 0.581 | 0.599 |
| Industry-year FE | Yes | Yes | Yes | Yes |
| Country-year FE | Yes | Yes | Yes | Yes |
| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| S/L | S/L | S/L | S/L | |
| Labor rights in the constitution × industry sunk costs | 0.233* | |||
| (0.113) | ||||
| Strong employee representation × industry sunk costs | 0.397** | |||
| (0.173) | ||||
| Union density × industry sunk costs | ‒0.075 | |||
| (0.173) | ||||
| Union coverage × industry sunk costs | 0.274* | |||
| (0.146) | ||||
| Observations | 5255 | 5255 | 5162 | 3561 |
| R-squared | 0.597 | 0.603 | 0.581 | 0.599 |
| Industry-year FE | Yes | Yes | Yes | Yes |
| Country-year FE | Yes | Yes | Yes | Yes |
The table presents OLS estimates of the relationship among labor institutions, sunk costs, and annual installations of robots. The dependent variable is the country–industry shipment of industrial robots per thousand employees. The proxy of sunk cost intensity is the inverse share of the secondhand capital expenditure in a given 2-digit industry. Standard errors are clustered at the country level. The coefficients with *** significant at the 1% level, with ** significant at the 5% level, and with * significant at the 10% level.
The finding of a positive correlation between labor-friendly institutions and robot adoption is consistent with previous studies. For instance, Acemoglu and Restrepo (2022) find a positive association between robot adoption and labor institutions and Belloc et al. (2022) find that the strength of workers representation is positively related to adoption of the establishment level. In contrast, Dauth et al. (2021) find that worker displacement was muted in commuting zones with greater union density—a finding that is difficult to reconcile with the arguments of this paper. However, their study is based on a single country, Germany, which has very peculiar capital–labor relationships. This suggests that their finding might not generalize to the average economy.
4.3.1 Robustness
This section performs a battery of tests to probe the robustness of the main estimates in Table 1.
First, Supplementary Appendix Table C1 shows that running (4) with the stock of robots per thousand workers as the dependent variable yields qualitatively identical results. Additional estimates, available upon requests, show that the results in Table 1 are also robust to assigning equal weight to each industry.
Second, one might be concerned that even in a sample of OECD economies, the technological characteristics of the United States might not necessarily carry over to less developed economies, such as Mexico and Eastern European countries. Therefore, Supplementary Appendix Table C2 presents the results of estimating (4) using an alternative identification strategy, based on proxies of sunk costs that are industry- and country-specific. The alternative proxy is the 2-digit industry-level gross fixed investment share of the total output. Such a variable is instrumented with the base year, the median level of the same quantity computed from 6-digit industries in the United States. Supplementary Appendix Table C2 shows Two Stages Least Squa estimates using this strategy and the results are consistent with those in Table 1, although the number of observations is lower because the NBER-CES dataset includes only manufacturing industries. Importantly, the first-stage F-statistics is high in all specifications (between F = 22 and F = 57), implying that the countries in the sample have similar sunk cost intensities in each industry. This suggests that at least part of the technological characteristics of the United States do carry over to industries in other OECD countries.
Third, unions may favor robot adoption to absorb positive demand shocks in the product market, for instance because of labor shortages. To address this possibility, Supplementary Appendix Table C3 includes an interaction between the institutional variables and, for each country–industry–year cell, the log-yearly change is value added of OECD trading partners. As expected, all the demand proxies have a positive and significant coefficient. However, this does not significantly change the coefficients of interest, which remain similar to the baseline results.
Fourth, Supplementary Appendix Table C4 shows that including an interaction between institutions and physical capital intensity in Equation (1) does not alter the main results. This is consistent with the idea that it is specifically the sunk nature of the assets in the industry to induce robot adoption.31
Finally, Supplementary Appendix Table C5 includes a number of country-level variables—possibly correlated with labor institutions—that might affect robot adoption disproportionately in sunk cost-intensive industries. These are interactions between industry-level sunk cost intensity and country-level base-year values of: (i) human capital, which are measured with the shares of workers with primary, secondary, and higher education separately; (ii) trade openness, measures by the exports and imports over GDP; (iii) the share of manufacturing output; (iv) financial development, measured by the time to cash a bounced check, and (v) expenditure on labor market training policy as percentage of GDP. The interaction between sunk cost intensity and the log of real GDP per capita is also included in order to capture the impact of broad structural differences across countries. The table suggests that the main results of Table 1 are robust to the inclusion of all such variables and thus mitigate the concern that omitted variables drive our conclusions.
4.4 Institutions, sunk costs, and aggregate investment: results
The model of section 3 suggests that the sign of the relationship among labor bargaining power, sunk costs, and investment depends on the capital’s degree of substitution with labor. The underlying reason is that if capital needs labor in order to become productive (i.e. capital and labor are complementary factors), workers can hold up the producer and extract part of the returns on investment. Since most categories of capital assets are complementary to labor, industry-level aggregate investment is likely to be less than perfectly substitute to labor. Therefore, the larger the sunk costs, the more severe the holdup, and the lower are producers’ incentives to invest in aggregate investment.32 This section tests such prediction empirically.
Table 2 shows the results of estimating (4) with the annual aggregate fixed investment as the dependent variable.33 Although only the coefficients in columns 1 and 2 are statistically significant, the negative signs of the estimated OLS parameters support the idea that unlike for robots, there is a negative correlation among institutions, sunk costs, and aggregate investment. The magnitudes of the impact in columns 1 and 2 are substantial. For instance, the coefficient in column 1 suggests that in countries with constitutional provisions on labor rights, aggregate investment is 26% lower in sunk cost-intensive industries. The results in Table 2 are in line with the findings of Cardullo et al. (2015), which show that institutions increasing the bargaining power of labor lower aggregate investment per worker.34
OLS estimates of the impact of institutions on country–industry gross fixed investment per worker.
| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| log(I/L) | log(I/L) | log(I/L) | log(I/L) | |
| Labor rights in the constitution × industry sunk costs | ‒0.259*** | |||
| (0.060) | ||||
| Strong employee representation × industry sunk costs | ‒0.254** | |||
| (0.108) | ||||
| Union density × industry sunk costs | ‒0.065 | |||
| (0.138) | ||||
| Union coverage × industry sunk costs | ‒0.091 | |||
| (0.076) | ||||
| Observations | 4672 | 4672 | 4613 | 3137 |
| R-squared | 0.963 | 0.961 | 0.958 | 0.968 |
| Industry-year FE | Yes | Yes | Yes | Yes |
| Country-year FE | Yes | Yes | Yes | Yes |
| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| log(I/L) | log(I/L) | log(I/L) | log(I/L) | |
| Labor rights in the constitution × industry sunk costs | ‒0.259*** | |||
| (0.060) | ||||
| Strong employee representation × industry sunk costs | ‒0.254** | |||
| (0.108) | ||||
| Union density × industry sunk costs | ‒0.065 | |||
| (0.138) | ||||
| Union coverage × industry sunk costs | ‒0.091 | |||
| (0.076) | ||||
| Observations | 4672 | 4672 | 4613 | 3137 |
| R-squared | 0.963 | 0.961 | 0.958 | 0.968 |
| Industry-year FE | Yes | Yes | Yes | Yes |
| Country-year FE | Yes | Yes | Yes | Yes |
The table presents OLS estimates of the relationship among institutions, sunk costs, and aggregate investment. The dependent variable is the log annual gross fixed aggregate investment per thousand employees. The proxy of sunk cost intensity is the inverse share of secondhand capital expenditure in a given 2-digit industry. Standard errors are clustered at the country level. The coefficients with *** significant at the 1% level, with ** significant at the 5% level, and with * significant at the 10% level.
OLS estimates of the impact of institutions on country–industry gross fixed investment per worker.
| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| log(I/L) | log(I/L) | log(I/L) | log(I/L) | |
| Labor rights in the constitution × industry sunk costs | ‒0.259*** | |||
| (0.060) | ||||
| Strong employee representation × industry sunk costs | ‒0.254** | |||
| (0.108) | ||||
| Union density × industry sunk costs | ‒0.065 | |||
| (0.138) | ||||
| Union coverage × industry sunk costs | ‒0.091 | |||
| (0.076) | ||||
| Observations | 4672 | 4672 | 4613 | 3137 |
| R-squared | 0.963 | 0.961 | 0.958 | 0.968 |
| Industry-year FE | Yes | Yes | Yes | Yes |
| Country-year FE | Yes | Yes | Yes | Yes |
| (1) | (2) | (3) | (4) | |
|---|---|---|---|---|
| log(I/L) | log(I/L) | log(I/L) | log(I/L) | |
| Labor rights in the constitution × industry sunk costs | ‒0.259*** | |||
| (0.060) | ||||
| Strong employee representation × industry sunk costs | ‒0.254** | |||
| (0.108) | ||||
| Union density × industry sunk costs | ‒0.065 | |||
| (0.138) | ||||
| Union coverage × industry sunk costs | ‒0.091 | |||
| (0.076) | ||||
| Observations | 4672 | 4672 | 4613 | 3137 |
| R-squared | 0.963 | 0.961 | 0.958 | 0.968 |
| Industry-year FE | Yes | Yes | Yes | Yes |
| Country-year FE | Yes | Yes | Yes | Yes |
The table presents OLS estimates of the relationship among institutions, sunk costs, and aggregate investment. The dependent variable is the log annual gross fixed aggregate investment per thousand employees. The proxy of sunk cost intensity is the inverse share of secondhand capital expenditure in a given 2-digit industry. Standard errors are clustered at the country level. The coefficients with *** significant at the 1% level, with ** significant at the 5% level, and with * significant at the 10% level.
5. Additional results
This section presents additional results based on two alternative datasets featuring different levels of aggregation.
5.1 Industrial action and automation
This section exploits country–1-digit industry–year variation in robot adoption and industrial action. Strike data are available for a level of industry aggregation higher than in the previous section, but they include the agricultural sector.
The empirical methodology is based on the idea that a fall in robot prices should be associated with more robots in countries and industries characterized by longer or more frequent strikes, which are detrimental to firm profitability. The details of the data and the empirical approach can be found in Supplementary Appendix D.
Such data and approach deliver results that are in line with those of section 4.3. Robot adoption between 1995 and 2013 has been stronger in countries and industries with a higher incidence of industrial action before 1995.
5.2 What proportion of cross-country differences in automation can be explained by institutions?
This section quantifies the contribution of labor institutions to explaining cross-country differences in robot adoption. Using aggregated data present obvious limitations, but it provides insights on why robot adoption is so heterogeneous even for similar economies.
This part of the analysis exploits specifications in long differences for 53 advanced and developing countries. The change in the total number of robots per thousand workers between 1995 and 2013 is regressed on country-specific institutional variables in 1994. The details are presented in Supplementary Appendix E.
The results suggest that labor institutions have a substantial impact on automation. For instance, countries with strong employees’ representation use twice the average number of robots per worker in the sample. Moreover, cross-country differences in labor institutions are found to explain up to one-third of the total variation in robots’ adoption in the sample. The institutional variables have an impact that is slightly lower but of comparable magnitude to demographic trends, which are studied by Acemoglu and Restrepo (2022).
6. Conclusions
This paper documents a positive relationship between institutions increasing the bargaining power of labor and adoption of industrial robots. Cross-country differences in institutions explain up to 34% of the sample variation in adoption of robots, which is comparable to the estimated contribution of demographic trends.
The relationship between institutions and robots is stronger in sunk cost-intensive industries, where producers are vulnerable to holdup. This result lends support to the hypothesis that producers use automation to minimize dependency from workers and thwart rent appropriation. While avoiding holdup does not need to be the only reason to adopt industrial robots, the relationship among institutions, sunk costs, and automation is robust to controls for other potential underlying mechanisms.
The relationship among labor-friendly institutions, sunk costs, and investment is reversed when capital and labor are not perfect substitutes. This is consistent with the idea that if production depends on some degree on human labor, as it is typically the case with most capital assets, the possibility of holdup erodes the returns on capital and decreases investment.
To tackle the disruption caused by new technologies, governments might reform institutions to increase the bargaining power of labor. However, one possible implication of the findings in this paper is that labor-friendly policies might be counterproductive, especially in contexts where automation opportunities are abundant. Testing this hypothesis, which would require a general equilibrium model or a suitable policy shock, is an important task left for future research.
Supplementary Data
Supplementary materials are available at Industrial and Corporate Change online.
Acknowledgements
I thank Frank Levy, David Margolis, Rajesh Ramachandran, Chris Rauh, Ariell Reshef, Gilles Saint-Paul, Thomas Piketty, and all members of the Oxford Martin Programmes on the Future of Work and Technological and Economic Change for helpful comments on the current and early drafts of the paper.
Funding
I thank Citi for generous financial support. I also thank Frank Levy, David Margolis, Rajesh Ramachandran, Chris Rauh, Ariell Reshef, Gilles Saint-Paul, Thomas Piketty, and all members of the Oxford Martin Programmes on the Future of Work and Technological and Economic Change for helpful comments on the current and early drafts of the paper.
Footnotes
Autor et al. (2003) introduced the idea that routine-manual tasks are the easiest to automate, because they can be codified in instructions that can be performed by machines.
Examples include cutting and pressing machines to stamp car bodies.
Holdup arises when a fraction of the returns on an agent’s relationship-specific investment is ex post appropriable by one of the contracting parties (Grout, 1984).
For instance, Belloc et al. (2022) provide evidence that the strength of workers’ representation drives robot adoption more in environments with stronger cooperation between workers and management.
The drawback of their analysis is that they exploit either a cross-section of international firms or a panel restricted to Italian companies.
The International Standard Industrial Classification (ISIC) rev. 4 includes robots in 28 Machinery and Equipment n.e.c. There is no specific category for industrial robots. For instance, robots with applications related to handling materials are classified under 2816 manufacture of lifting and handling equipment.
Each dot in the figure represents the country-average residual from a regression of long-run differences in robots per worker on the explanatory variables, after partialing out the impact of the 1993 stock of robots per worker, economic, and demographic variables.
To join a union, workers must either be given voluntary recognition from their employer or have a majority of workers in a bargaining unit (e.g. the plant or department) vote for union representation. To win representation, in a first stage at least 30% of employees need to give written support. Then, after 90 days a secret ballot election is conducted and representation is certified if a simple majority of the employees is in favor. If a majority is not reached, the National Labor Relations Act allows workers to form a minority-union, which represents the rights of only those members who choose to join. However, the employer does not have the legal obligation to recognize minority-unions as a collective bargaining agent, which limits considerably their power.
One example is a dispute between a private airline company and a trade union in Ireland (Ryanair Limited vs. Labour Court & Impact, 2007). In that occasion, the Supreme court ruled that while the employer was obliged by the constitution to recognize the pilots’ trade union, it had no legal obligation to recognize its role in collective bargaining.
Therefore, it is implicitly assumed that workers can always afford not to work, so that the threat of not producing is credible for firms.
For simplicity, we assume that σ is the same for every variety i.
For instance, as in Autor et al. (2003), the production of some varieties might involve many non-routine tasks, which makes robots less suitable than human workers to produce that variety.
The output is endogenized by embedding the supply side into an overlapping generation model.
Employment by industry is only available for OECD countries. Robots data are not available for Luxembourg.
The proxy uses data for the first available year, 1994, which is then set as the base year in the estimation.
The methodology is borrowed from Cardullo et al. (2015).
Balasubramanian and Sivadasan (2009) discuss different measures of sunk costs used in the literature.
As for the proxy based on the secondhand capital expenditure, the alternative measure of sunk costs is based on 1994 values.
The NBER-CES Manufacturing Database provides 6-digit-level information on gross fixed investment, shipment, and inventories. To construct the proxy, the first output is constructed summing shipments with the change of inventories. Then, the proxy of sunk costs is obtained by dividing the gross fixed investment by the output, converting North American Industry Classification System (NAICS) code into ISIC Rev. 4 and taking the median value within each 2-digit-level industries.
The US Census Bureau does not report information for the agricultural sector and repair and installation.
Cement kilns, which are hundreds of meters long, are one example of large-scale machinery used in chemical manufacturing.
The number of employees per thousand worker in every country, industry, and year is taken from the OECD database STAN.
Supplementary Appendix Table C1 shows that the results are qualitatively identical when using the stock of robots per worker as the dependent variable in (4).
See Supplementary Data Appendix A for details on the variables.
For instance, improvements in machine vision could boost robots’ adoption in the textile industry, where the micro-imperfections of fabrics made it difficult to automate; robots’ adoption might be higher in high-tech industries with a higher number of engineers.
The inclusion of industry-year FEs would account for such confounding effects as long as all countries in the sample have a similar skill content and routine tasks intensity. This seems to be a relatively innocuous assumption in a sample of OECD countries.
The same weighting scheme is used by Graetz and Michaels (2018) and Acemoglu and Restrepo (2022).
Although data on robots and institutions are available from 1993, the US Census Bureau provides the series on the secondhand capital expenditure from 1994 only.
The inclusion of country-year FE does not allow to estimate the country-wide impact of institutions on robots’ adoption.
The capital intensity of an industry is measured with the US net real capital stock from STAN in the base year, divided by the real output (in logs). As for the other interaction variables, I normalized it as to have zero mean and unitary standard deviation in the weighted sample.
Strictly speaking, one should consider the difference between robots and non-robots capital. Unfortunately, such measures are not available. Neither are the appropriate price indexes for robots, which would allow to detract their value from the aggregate capital stock. However, as discussed in section 4.2, the available evidence suggest that robots account for only a small percentage of the aggregate capital stock.
As for Table 1, the inclusion of country-year FE does not allow to estimate the country-wide impact of institutions on aggregate investment.
An interesting special case is collaborative robots, which typically support workers in heavy or hazardous tasks rather than substitute them. These machines are characterized by strong complementarities with labor and so in light of the model of Section 3, firms might be reluctant in investing in them when institutions are labor-friendly.
