WAGE INEQUALITY AND DIRECTED TECHNOLOGICAL
CHANGE: IMPLICATIONS FOR INCOME DISTRIBUTION
1Cristiano Antonelli, Dipartimento di Economia e Statistica Cognetti de Martiis Università di Torino and BRICK (Bureau of Research in Innovation, Complexity, Knowledge), Collegio Carlo Alberto
and
Giuseppe Scellato, Politecnico di TorinoDipartimento di Ingegneria Gestionale e della Produzione, and BRICK (Bureau of Research in Innovation, Complexity, Knowledge), Collegio Carlo Alberto
ABSTRACT. Large evidence confirms substantial wage differences between small and large firms. The paper contributes the extant literature by discussing two competing hypotheses behind the higher average wage observed in large firms. According to the first line of analysis the wage premium reflects substantial differences in the bargaining power of unionized workers in large and small firms. According to the second, the joint presence of higher unit wages and higher skills in large firms is the consequence of the endogenous capital-intensive direction of technological change. The paper articulates and tests the hypothesis that wage inequality is at the same time a cause and a consequence of the direction of technological change. The empirical evidence based on a large sample of Italian manufacturing firms during years 1996-2005 confirms that the factor intensity of the production process is endogenous to firm size: small firms with lower unit wages rely on more labour-intensive production processes while large firms with higher unit wages and lower user capital costs adopt more capital intensive ones. Results confirm that the size of firms and the average wage account for the larger capital intensity of the production processes and average wages are themselves determined by the capital intensity.
KEYWORDS: WAGE INEQUALITY; SIZE OF FIRMS; DIRECTED TECHNOLOGICAL CHANGE; TECHNOLOGICAL CONGRUENCE; INCOME DISTRIBUTION.
JEL Code: O30
1 The authors acknowledge the support of the Collegio Carlo Alberto, the University of Torino and the Politecnico di Torino. The comments of the referees and of the editor are acknowledged. The usual disclaimers apply.
WAGE INEQUALITY AND DIRECTED TECHNOLOGICAL
CHANGE: IMPLICATIONS FOR INCOME DISTRIBUTION
1. Introduction
Large empirical evidence confirms the high levels of wage inequality associated with the size of firms. This evidence about the wage premium and the differences in terms of unit wages between small and large firms have stirred an intense debate about its determinants. Two schools of thought contrast each other: according to the first the wage premium reflects substantial differences in the bargaining power of workers, respectively weaker in small firms and stronger in larger ones. Workers in large firms have higher levels of unionization and can bargain higher wages. The alternative approach suggests to pay attention to the direction of technological change at the firm level. Large firms use more capital intensive techniques and consequently pay higher wages to their more skilled employees. The matching of higher unit wages and higher skills in large firms is the consequence of the endogenous direction of technological change.
The paper contributes this debate along the following dimensions.
First, it provides a critical review of the relevant literature and highlights the two contrasting hypotheses according to which wage differential between large and small firms is: i) the consequence of the introduction of capital intensive technological change by large firms, or ii) the consequence of the bargaining power of workers that induce the introduction of directed technological change biased in favor of capital intensive technologies. Second, building on the induced technological change approach and the notion of technological congruence, the paper develops the hypothesis that the technological choices of firms are at the same time the explanation and the result of wage differentials. Third, the paper presents the evidence from a set of econometric models aimed at assessing the endogenous nature of the relationship between wage differentials and technological choices for a panel of firms observed over a 10 years period. Finally, the paper explores the implications of the empirical results for understanding the dynamics of income inequality.
2. The research framework
The empirical evidence about the wage premium is strong and persistent across time, regions, industries and is mainly if not exclusively associated to the size of firms. It has been the object of repeated empirical investigations that have confirmed the significant differences between the average levels of unit wages in large and small firms. This evidence has been interpreted as the consequence of alternative mechanisms. We can classify the contrasting hypothesis in two bundles: the pathological and the physiological causes, according to their coherence with the basic assumption of the necessary matching between factor costs and their marginal productivity.
According to the pathological bundle set of hypotheses, wages are larger in larger firms because: i) workers in large firms are better able to organize and enforce their bargaining power and managers are confronted with more powerful unions that are able to extract higher wages; ii) large firms enjoy larger markups and are able to share them with unionized workers; iii) monitoring activities increase more than proportionately with the size of firms with additional layers and higher wages.
According to the core of the physiological bundle of hypotheses, wages increase with the size of firms because of higher levels of labor productivity. This in turn implies that large firms use more capital-intensive techniques than small firms because of higher wages. The physiological bundle of hypotheses include: i) the obvious complementarity between the skills of workers and the capital intensity of the production process (Griliches, 1970); ii) the use of more knowledge intensive technologies by large firms (Dunne & Schmitz, 1992; Reilly, 1995); iii) large firms offer more stable jobs with lower risks so as to attract more skilled workers (Mayo and Murray, 1991); iv) large firms pay efficiency wages to deter shirking and to stir the active participation of workers to learning processes (Oi and Todd, 1999; Stiglitz and Greenwald, 2014) and increase worker participation (Schmidt and Zimmerman, 1991; v) large firms are able to increase the skills of their employees with formal training (Troske, 1999); v) working conditions in large firms are actually harder and higher wages compensate for the inferior conditions (Paez, 2003); vi) higher levels of human capital of workers employed in large firms (Lluis, 2009; Gibson and Stillman, 2009; Galliè and Legros, 2012).
The empirical evidence has not been able to exclude either contrasting hypothesis. Econometric analyses have applied different empirical approaches and typologies of data: firm level data, workers-level data, linked employer-employee data (HongYe, GiSeung, 2014; Lallemand, Plasman, Rycx, 2005; Belfield and Wei, 2004). The results confirm that both the bargaining power and the skill hypotheses find substantial support. Recent Italian evidence fully confirms these results. Scoppa (2014) uses longitudinal data 1985 to 2002 and finds that larger firms pay significantly higher wages, although the individual “unmeasured ability component” accounts for about one half of the uncovered size–wage premium2. The use of a
sample of workers displaced by firm closures to reduce potential self-selection problems arising from endogenous job changes confirms that the wage premium is accounted both by unmeasured workers’ abilities and firm size effects. Bottazzi and Grazzi (2014) confirm that, in the period 1989-2004, after taking into account the inter-sectoral variance, the differences of labor productivity and labor costs among Italian manufacturing firms are strongly associated with the differences in the size of firms. Yet the differences of labor productivity are not able to account for all the differences in labor costs: the wage levels are influenced by the size of firms after taking into account the differences in labor productivity. Leonardi (2007) provided additional evidence confirming the higher levels of capital-output ratios in large firms.
The hypothesis that the higher levels of skill intensity, labor productivity and capital intensity of large firms – all documented by the literature - may stem from the effects of the differences of internal labor markets on the direction of technological and technical choices has received far less attention. In this literature, technological change is regarded as exogenous, rather than the consequence of the creative response of firms that try and cope with differentiated factor costs. As soon as both technical and technological choices are regarded as endogenous, it is possible to articulate the hypothesis that larger firms -facing higher wages- are induced to increase the capital intensity of their production process. Large firms do try to cope with the higher levels of wages stemming from the stronger bargaining power of trade unions increasing the capital intensity of their production process both -with an adaptive response- moving on the existing map of isoquants and -with a creative response- changing the slope of isoquants by means of technological changes directed towards the increase of the output elasticity of capital.
The integration of the analysis of technological congruence and the wage premium debate enables to reconcile the two conflicting approaches identified in the wage premium literature showing that the differences in skills, human capital and worker participation are endogenous. Higher skills are necessarily associated with the more capital intensive technologies that characterize the production process of large firms that have been induced to introduce directed technological changes, biased towards the use of more capital and skill intensive technologies, in order to cope with the higher levels of wages. The skill differentials are endogenous, as they stem from the endogenous introduction of innovations induced by the actual conditions of internal and external labor markets and product markets where winners take all (Autor, Dorn, Kats, Patterson, Van Reenen, 2017).
The latter line of interpretation stems directly from the microeconomic extension of the induced technological change approach: firms have a clear incentive to direct technological change towards the more intensive use of the factors that become relatively cheaper.
The induced technological change approach has been revived by a new wave of contributions that confirm its role at the aggregate level. According to Acemoglu (2015) the relative increase of the wage of blue collars, experienced in the US economy in the last decades of the XX century, pushed firm to introduce new technologies that were both more capital-intensive and skilled-labor intensive than the previous. The skill intensive direction of technological change is a direct consequence of the large increase in the supply of skilled labor and consequent decline in relative terms of their wages with respect to blue-collars’. The dynamics of skilled labor costs added on to the secular decline of capital user costs (Acemoglu, 1998; 2002; 2003; 2010).
Antonelli (2016a) elaborates the notion of technological congruence: with a given budget, output is larger, the larger is the output elasticity of the cheaper input. Hence there is a clear incentive to bias the factor intensity of the production process towards the most intensive use of the inputs that are locally more abundant so as to substitute them to the more expensive and less accessible ones. The search for technological congruence takes place both at the aggregate and the firm level. Directed technological change enables in fact firms to increase the matching between the factor intensity of the production process and the relative availability of inputs in local factor markets. The better is the matching, the larger is output and the lower are production costs and hence the larger are the levels of total factor productivity (Antonelli and Scellato, 2015; Feder, 2018).
The application of the notion of technological congruence at the microeconomic level enables to appreciate the heterogeneity not only of firms, but also, and most importantly, of factor markets and its implications in terms of heterogeneous direction of endogenous technological change. Factor markets are far from homogeneous as the prices of inputs differ widely according to the characteristics of firms and the working of their internal factor markets. Within the same economic system, there is substantial heterogeneity of wage levels associated with the size of firms. This heterogeneity triggers the introduction of heterogeneous directions of technological change. The factor intensity of the production process is twice determined by the relative input cost: i) the search for technical efficiency on the existing map of isoquants that leads to increasing the capital intensity of the production process with the increase of the relative level of wages; ii) the search for technological congruence that induces firms to change the map of isoquants with the introduction of biased technological change directed to increase the output elasticity of cheaper inputs.
3. The hypothesis
The factor intensity of the production process is influenced by the relative costs of inputs and the specific conditions of firms when their heterogeneity is taken into account. The review of the literature on the wage premium has confirmed the strong differences of wages with respect to firm size. Small firms pay lower wages than large ones. This heterogeneity at the firm level is likely to have direct effects on the factor intensity of the production process. According to the technological congruence approach, firms have an incentive to introduce labor saving technologies and techniques so as to increase the capital intensity of their production processes when their wages are larger than the average. On the opposite, firms will increase the labor intensity of their production process when and where, in their specific internal factor markets, labor is cheaper.
The application of the induced technological change approach to the microeconomic level of investigation helps reconciling the two contending hypotheses on the
determinants of the wage premium. The evidence confirms that unit wages are significantly larger in large firms than in small ones. As a consequence, large firms have been forced to: i) introduce technical change consisting in the substitution of capital to labor so as to moving in the existing isoquants map, and ii) introduce new technologies, with a larger output elasticity of capital thus changing the isoquants map; iii) increase the demand for more skilled workers able to command higher levels of capital intensity of the production process. Both technical change and technological change are endogenous and are determined by the wage premium. The induced technological change approach asserts the tight relationship between the relative costs of production factors and the factor intensity of the production process. It holds at the system level with a representative agent as well as at the micro level assuming the heterogeneity of firms. The evident heterogeneity of firms enables to overcome the standard applications at the system level of the induced technological change based upon the representative agent (Samuelson, 1965; Ruttan, 1997 and 2001) and to apply it at the microeconomic level of analysis.
In an economic system characterized by the heterogeneity of firms and factor markets with differentiated factor costs, determined by the characteristics of the firms, the substantial wage differential associated with the size distribution of firms has powerful effects on the factor intensity of the production process3.
Both technical and technological changes are endogenous. The factor intensity of the production process is twice influenced by the relative input cost. Large firms with higher unit wages (and lower user capital costs) have a clear incentive to use a more capital intensive production process than small firms that experience lower unit wages (and higher capital user costs). Directed technological change and standard technical choice account for the higher levels of capital intensity in large with respect to small firms. In turn higher levels of capital intensity of the production process command higher levels of skills, human capital and participation by workers. The notion of efficiency wages applies. Large firms pay higher unit wages that induce and enable the search of more capital intensive technologies and more capital intensive techniques (Akerlof and Yellen, 1986; Aghion, 2015). More capital intensive production processes require higher levels of skills. The factor intensity of the production process is expected to play a strong role in accounting for the wage premium.
There is a bidirectional relationship between wage inequality and the variety of directions of technological change within the very same economic system: the wage premium of workers in large firms is the cause and the consequence of a higher capital intensity of their production process.
According to our hypotheses, the factor intensity of production processes is heterogeneous across firms both across and within sectors as it reflects the heterogeneity of the matching between factor markets and firms size. Our hypothesis contrasts the standard assumption that the factor intensity of the production process is homogeneous across firms that belong to the same system and the same industry. Quite on the opposite, we argue in fact that the factor intensity of the production process varies across firms –even within industries- as it reflects the economic advantages stemming from technological congruence that are differentiated across firms because of the intrinsic heterogeneity of their participation to factor markets. More specifically, we expect that the factor intensity of the production process both across and within each industrial sector is more labor intensive in small firms with lower wages than in large firms with high wages.
4. Empirical analysis 4.1. Dataset
The dataset includes financial accounting data for a large sample of Italian manufacturing companies, observed along the years 1996-2005. The data have been extracted from the AIDA database provided by Bureau Van Dick, which reports accounting information for public and private Italian firms. The companies included in the analysis have been founded before year 1996, they are registered in a manufacturing sector according to the Italian ATECO classification, they are still active by the end of year 2005 and have at least 15 employees at the end of fiscal year 1996. In order to drop outliers due to possible errors in the data source, we computed a set of financial ratios and yearly growth rates of employees, sales and fixed capital stock and we then dropped evident cases of outliers due to errors in the data source4.
The final dataset is a panel of 6204 firms for which we have been able to collect all required financial accounting data. Financial data have been deflated according to a sectoral two-digit deflator using year 2000 basic prices. Tables 1 and 2 provide the summary statistics of the variables used in the econometric analyses and a description of the size distribution of firms in the sample. Average wage (AVGWAGE) is computed as the log of the ratio of labor costs to total number of employees. The log of total assets (SIZE) measures the size of firms. Profitability is defined as the ratio of EBITDA to total assets (ROA). Capital intensity (KL) is measured as the log of the ratio of total assets to total number of employees. Financial leverage is defined as the ratio of net financial debt to total assets (Leverage). The variable Intangible is computed as the ratio of the book value of intangible assets to total assets and can be regarded an indicator of the knowledge intensity of the production process and itself a proxy of the levels of competence and skills of workers.
4 We have computed a set of financial ratios and yearly growth rates of assets and employees. We have then manually screened the top and bottom centile of the related distributions. The manual procedure led to the exclusion of 35 firms.
Table 1 - Variables and summary statistics
Variables Mean Std dev Median
AVGWAGE 10.303 0.240 10.228 KL 9.865 1.083 9.995 SIZE 14.299 1.339 14.332 ROA (%) 5.865 6.338 4.781 Leverage 0.773 0.305 0.791 Intangible 0.141 0.177 0.071
Table 2 - Firm size distribution by size class
Incidence in the sample
Small firms (< 50 employees) 38.41%
Medium firms
(50>= employees <500) 54.42%
Large firms
(>=500 employees) 7.17%
Capital intensity reflects the combined effect of the choice of technologies and techniques. A large capital intensity in fact is the consequence of both the selection on a given map of isoquants of more capital-intensive techniques, and of the introduction of more capital intensive technologies. At the firm level, the direction of technological change is itself both endogenous and heterogeneous and reflects the intrinsic heterogeneity of firms and factor markets. In this perspective, it becomes relevant to assess whether and to what extent the variance of the capital intensity is associated with the actual levels of wages at the firm level.
The firm size distribution in the sample is fully consistent with the Italian evidence at the country level. This is most important when it is matched with the distribution of the employment that applies labor contracts at the firm and the industrial and national level respectively. Almost all the workers in firms with more that 250 employees apply labor contracts both at the firm and the industrial and national level. The share of employment in small and medium firms for which labor contracts are implemented at the firm level is negligible. The bargaining power of trade-unions is weak in small and medium size firms, and much stronger in firms with more than 250 employees. In
these firms, in fact, the implementation of labor contracts at the firm level enables workers to participate into the profits of their firms. In small and medium size firms labor contracts are implemented mainly at the national and industrial level assuming average performances that are well below the levels enjoyed by larger firms. International evidence confirms the strong role of bargaining power of unionized labor (Farber et al. 2018).
4.2. The econometric model
The analysis builds on the assumption that the factor intensity of the production process is the result of intentional strategies implemented at the firm level to take advantage of their specific and idiosyncratic sources of competitive advantage while reducing the factors that undermine it. More specifically, we test the hypothesis that the factor intensity of the production process is influenced by the size of firms that experience substantial differences in their internal factor markets. Factor intensity of the production process reflects and is a reaction to the specific conditions of firms’ internal factor markets. Small firms have an incentive to introduce -more- labor-intensive production processes in order to take advantage of the specific conditions of the factor markets into which they are based. The factor intensity of the production process is the result of intentional strategies aimed at taking advantage of the cheaper cost of labor. For the same token, we expect that large firms with higher wages select more capital-intensive production processes. Accordingly, the econometric models investigate the role of the size of the firm, in accounting for the factor intensity of the production process.
We investigate this issue through a set of models that analyse the endogenous role of the capital intensity of the production process. Table 3 provides the results of a two-stage instrumental variables estimation where in the first two-stage (Model I) the capital intensity of the production process (K/L) is the dependent variable while the one-year lagged levels of average wages (AVGWAGE) and size (SIZE) are the independent variables. In the second stage, the current average wage is the dependent variable and the capital intensity is the independent IV one. The capital intensity is endogenous as it has been estimated, in the first stage, as the dependent variable of the past size of firms and their average wage levels. Table 3 presents also the results of the Model II that includes among covariates the share of intangible capital on total asset (Intangible) as a proxy of the skill intensity of workers engaged in the production process and additional control variables related to the capital structure of firms (Leverage) and their operative profitability (ROA). Results indicate, as expected, a positive association between capital intensity and the variable Intangible, that can be intended as a proxy of the knowledge intensity of the production process of the firm and of the degree of competence and skills of workers. Table 4 provides the two stages models of the IV regressions on the sample split in high-tech and low-tech sectors.
Table 3 - Instrumental variable fixed effects estimates with year dummies.
MODEL I II
First stage Second stage First stage Second stage
Dependent Variable K/L AVGWAGE K/L AVGWAGE
K/L 0.0322*** 0.0321 *** (0.0024) (0.0024) AVGWAGE t-1 0.2491*** 0.2493*** (.0129) (0.0129) SIZE t-1 0.6610*** 0.6668*** (0.0048) (0.0050) ROA t-1 0.0037*** -0.0004* (0.0007) (0.0002) Leverage t-1 0.0146 -0.0101*** (0.0105) (0.0035) Intangible t-1 0.0930*** 0.0200*** (0.0188) (0.0063)
Year dummies Yes Yes Yes Yes
Const -2.4233*** 10.1801*** -2.5380*** 10.1799*** (0.1518) (0.0238) (0.1529) (0.0242) Observations 55,808 55,808 55,793 55,793 Number of id 6,206 6,206 6,206 6,206 R-Sq. Within 0.3165 0.3265 0.3172 0.3268 R-Sq. Overall 0.5012 0.1568 0.4963 0.1599 F-Stat 2296.36*** 1771.71***
Wald-Chi2 2.72e+08*** 2.72e+08***
Table 4 - Instrumental variable fixed effects estimates with year dummies. Sample split between high-tech and low-tech sectors.
HI-TECH SECTORS LOW TECH SECTORS
MODEL I II
First stage Second stage First stage Second stage
Dependent
Variable K/L AVGWAGE K/L AVGWAGE
K/L .02844*** 0.0366*** (0.0043) (0.0030) AVGWAGE t-1 0.2342*** 0.2552*** (0.0212) (0.0164) SIZE t-1 0.6585*** 0.6776*** (0.0084) (0.0063) ROA t-1 0.0015 -.0012*** 0.0095*** 0.0016*** (0.0009) (0.0003) (0.0014) (0.0004) Leverage t-1 0.0386** -0.0097 -0.0002 -0.0099** (0.0180) (0.0061) (0.0129) (0.0042) Intangible t-1 0.0799** 0.0335*** 0.1053*** 0.0117 (0.0313) (0.0106) (0.0236) (0.0077) Year dummies Y Y Y Y Const -2.3382*** 10.2503*** -2.7118*** 10.1151*** (0.2529) (0.0419) (0.1926) (0.0296) Observations 20,544 20,544 35,249 35,249 Number of id 2,285 2,285 3,916 3,916 R-Sq. Within 0.3064 0.3290 0.3254 0.3303 R-Sq. Overall 0.4951 0.1537 0.4994 0.1691 F-Stat 620.06***
Wald-Chi2 8.93e+07*** 1.86e+08***
***Significant at the 1% level, **significant at the 5% level, *significant at the 10% level
The estimates of the first stage indicate that the capital intensity of the production process is positively correlated to the past levels of firms’ size and average wages. At the same time, in the second stage current average wages are positively associated to the instrumented capital intensity of the production process. Technical and technological choices that cause the factor intensity of the production process of firms are endogenous as they have been affected by the differences in factor costs. Indeed, average wage is accounted by the endogenous capital intensity of the production process, which in turn is affected by the past size and capital intensity of
their production process. The size of firms exerts positive effects directly on the factor intensity of the production process and indirectly on average wages.
The models based on sub-samples reported in Table 4 indicate that the results hold both in low and high tech sectors, supporting the bidirectional relationship between wages differential and directed technologies where the size of firms, rather than the type of industry, is the key determinant of wage inequality and of the heterogeneous direction of technological change.
The positive and significant role of the share of intangibles on total assets, after taking into account the levels of total capital intensity, confirms that the levels of knowledge intensity contribute to explain the variance of wage levels. Workers in firms with higher levels of intensity of intangible asset are characterized by higher levels of skills. Interestingly the effect of the variable Intangibles in the second stage equation is no longer significant in the subsample of firms operating in low-tech sectors.
The results of the control variables about the financial structure of the firms lead to a mixed evidence. According to the theory, the larger is the leverage, i.e. the share of liabilities on total assets, and the heavier the financial burden and more selective the filtering procedures of bankers and providers of external funds at large and the lower is the capital intensity of the production process. Firms with a larger share of liability on total assets are less likely to use capital-intensive production processes (Magri, 2009 and 2014). However, in the analyzed sample, we do not find robust evidence of a negative association between leverage and capital intensity. Still, we do find a negative association between leverage and average wage, particularly for the firms operating in low-tech sectors.
The overall evidence is consistent with the both the contrasting interpretations of the wage premium. Two forces are simultaneously at work in accounting for the wage premium: i) the physiological selection of the factor intensity of the production process according to the intrinsic heterogeneity of the cost of labor in internal factor markets. Large firms facing higher wages react by changing the factor intensity of their production process. Larger wages act as efficiency wages that enable corporations to increase the participation of workers and their contribution to more sophisticated production processes. Wage inequality reflects the heterogeneity of the skills of workers; ii) the pathological effect of the changing bargaining power of workers according to the size of firms. Workers in small firms are less able to influence the levels of wages. The small size of firms limits the role of trade unions that are instead far more effective when the size of firms is large. Smaller firms take advantage of their bargaining role, pay lower wages and use more labor intensive production processes.
These results confirm that the capital intensive direction of technological change of large firms exerts an important role in the changing distribution of income at the
system level with a twin powerful effect. First, it increases the output elasticity of capital and accounts for the increasing share of income paid to capital with direct effects on rent inequality. Second, it increases the levels of wage inequality with relevant effects on the levels of income distribution. Wage levels are strongly associated to the size of firms. Employees in large firms benefit of an important wage premium. The wage premium is a consequence of both a stronger bargaining power and skill intensity of the employees of large firms that can benefit from higher levels of unionization, and of the induced introduction of more capital intensive technologies. The introduction of biased technological change directed to substitute more expensive labor with more capital intensive production processes is itself a consequence of the increased levels of wages in large firms. The lower levels of bargaining power and skills of the employees of small firms induce them towards a less capital intensive direction of technological change. The increasing levels of wage inequality are the ultimate consequence of these two nested dynamics.
The results of our analysis suggest that the increasing levels of income inequality at the system level are influenced by the capital intensive direction of technological change augmented by the skewed distribution of wages that reflect the unequal levels of unit wages across firms: wage inequality is a key component of income inequality together and beyond the effects of wages on the direction of technological change. In turn, the induced introduction of directed technological change biased towards more capital intensive technologies has the additional effect to increase the flows of rents paid to the owners of capital. For given levels of wealth inequality, the introduction of capital intensive technologies with a larger capital output elasticity, triggered by wage inequality between large and small firms, increases rent inequalities and adds on to increasing income inequality.
5. Wage inequality and income distribution
The analysis of wage inequality has important implications for the study of income inequality. Increasing levels of income inequality have been identified and regarded as a negative aspect of the changing structure of advanced economic systems since the end of the XX century (Piketty, 2014). The raising levels of income inequality have called increasing attention to try and understand its effects and determinants (Farber et al. 2018). In this context much attention has been paid to the increasing share of rent inequalities (Aghion et al. 1999; Piketty and Saez, 2003). For given – high- levels of wealth inequality, the raising share of income paid to capital does increase the levels of income inequality (Atkinson and Piketty, 2007 and 2009; Kaplan and Rauh 2010). The review of the literature by Franzini and Pianta (2016) identifies a strong consensus about the negative effects of the raising levels of income inequality in terms of falling rates of increase of demand and output. Among other determinants, the literature has focused on the direct effects of the raising levels of profit margins.
As a matter of fact, however, the levels of income inequality are determined by two distinct components: rent inequalities and wage inequalities (Aghion and Bolton, 1992). Wealth inequalities affect income distribution via the distribution of the changing levels of rents paid to capital owners. The literature has much explored the role of rent and wealth inequalities associated with the increase of the share of income paid to capital. The literature has paid less attention to the trends and determinants of the changing levels of wage inequalities and ignored the strong effects that wage inequalities exert on income inequality.
Quite surprisingly, even lesser attention has been paid to appreciating the role of the rate and the direction of technological change in influencing the dynamics of income distribution between capital and labor. Antonelli and Gehringer (2017) have revived the debate on the Schumpeterian hypothesis about the role of the rate of technological change and explored the effects of the rate of technological change in changing the levels of income distribution (Kuznets, 1955).
Acemoglu (1998, 2002, 2003, 2010 and 2015) has much contributed to calling attention on the direction of technological change, its long term bias in favor of the introduction of capital intensive technologies and the central role of the changing relative factor costs (Antonelli, 2016a). The increasing size of the stock of capital that stems from the accumulation of savings exerts negative effects on the levels of capital user costs that in turn are most likely to bias technological change towards a capital intensive direction (Antonelli, 2016b). According to this approach the introduction of new capital intensive technologies, induced by the relative decline of capital user costs, accounts for the increase of the share of capital in income distribution with mechanisms that play a role not only at the macro but also at the micro level (Karabounis, Neiman, 2013; 2017).
The appreciation of the changing levels of income inequality should take into account the effects of wage inequality combined with the endogenous capital intensive direction of technological change. This paper contributes the analysis of income inequality focusing on the effects of the bidirectional relationship between directed technological change and wage inequality and showing that wage inequality affects income inequality both directly and indirectly via its effects on the capital intensive direction of induced technological change that augments the levels of rent inequality.
6. Conclusions
The application of the induced technological change approach at the microlevel of analysis enables to appreciate the substantial heterogeneity across firms. Technological change is viewed as a meta-substitution process that takes place with differentiated effects and intensity at the firm level and consists in reshaping the production function so as to increase the output elasticity of production factors that are cheaper and to reduce the output elasticity of production factors that are locally less abundant and more expensive. Wage premium is an efficiency wage paid by large firms that have higher profitability to attract skilled workers and motivate their
participation to sophisticated production processes. At the same time, higher wages stir large firms to matching the factor costs they actually experience by means of new -more capital intensive- technologies and techniques. Size differences among firms have strong effects not only on unit wages, but also, on the levels of the capital intensity of the production process.
Small firms with lower wages have much a stronger incentive to introduce labor intensive technological innovations rather than capital intensive ones. On the opposite larger firms that experience higher wages but lower capital user costs direct their technological change towards the introduction of more capital intensive innovations. As a consequence, large firms use more capital intensive production processes that make labor more productive and require more skilled workers with higher levels of human capital and participation. Higher wages and skills are complementary aspects of the same endogenous search for technological congruence.
The analysis of the microeconomic determinants of factor intensity of the production process sheds new light not only on the wage premium debate but also upon the role of the characteristics of firms in explaining the introduction of new biased technologies. These results confirm that the direction of technological change at the firm level is far from invariant and exogenous. Actually, its microeconomic variance is likely to affect the aggregate level when the composition of the economic system in terms of firm size and heterogeneity of factor markets changes with direct and indirect effects on income in equality.
Wage inequality is at the same time the cause and the consequence of the introduction of directed technological change biased towards capital intensive technologies when wages are high and labor intensive directions when wages are low. Wage inequality reinforces the levels of income inequality with two mechanisms: i) the between effects that consist in increasing the share of income paid as rents to the increasing size of capital used in the production processes and ii) the within effects that consist in raising the levels of wage inequality that account for a large part of the increasing levels of income inequality.
The policy implications of the analysis are quite important: wage inequality has important twin negative effects on income inequality. Efforts should be made to better balance the asymmetric effects of trade-unions in the bargaining process of wage levels. The concentration of attention of trade-unions on large firms should be counterweighted by stronger mechanisms able to favor the increase of wages in smaller firms. Employment contracts at the national and industrial should be better integrated with employment contracts at the firm level so as to favor the eventual generalization at the system level of the benefits gained at the firm level.
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APPENDIX. The basic model of induced technological change
The standard Cobb-Douglas production function is a suitable and effective starting point as it accommodates explicitly, with and the output elasticity of the production factors and enables to analyze their changes. The standard Cobb-Douglas takes the following format:
Y= K L (1)
where K denotes the amount of capital and L the amount of labor. The cost equation is:
C = rK + wL (2)
Firms select the traditional equilibrium mix of inputs according to the slope of the isocosts given by ratio of labor costs (w) and capital rental costs (r) and the slope of isoquants. The equilibrium condition is:
w/r = () (K/L) (3)
In standard textbooks the output elasticity of inputs is given or exogenous. In the technological congruence approach the output elasticity of inputs is endogenous. Following the Kennedy-von Weiszacker-Samuelson tradition we rely upon a Frontier of Possible Innovations (FPI) that considers the negative relationship between attainable levels of output elasticity, respectively of capital and labor, assuming that firms are able to shape them, as it follows
= g (
The isorevenue is identified by the substitution of the equilibrium condition (3) into the production function (1), as it follows:
Y = L (w/r (5)
Equation (5) makes clear the interaction effects between the bias of the technology as identified by the ratio of the output elasticity of capital and the output elasticity of labor and the ratio of factor costs on the levels of output. Output is larger, the larger is the output elasticity of capital (or labor) the lower is the user cost of capital (or wages). The Cobb Douglas specification in fact makes clear that it is convenient to use more intensively the production factor that is cheaper: clearly the output gets larger, for a given budget, the larger is the intensity of the factor that is locally more abundant and hence cheaper. This static condition becomes a powerful incentive to direct technological change so as to take advantage of the matching between the relative cost of an input and its output elasticity. The differentiation of equation (5) with respect to the w/r enables to identify the effects of the slope of the isocost, and hence of the isorevenue in this context, for given levels of and
Yw/r) r/w) Y
The maximization of output requires that andare chosen so that the slope of the FPI equals the slope of equation (5):
g’(r/w) Y (7)
According to equilibrium condition (7) the output elasticity of capital will be larger, the lower are the relative capital rental costs with respect to wages. When wages (capital rental costs) with respect to capital rental costs (wages) are high, firms have a clear incentive to select a mix of output elasticity where When wages (capital user costs) increase, the incentives to increase the output elasticity of capital (labor) also increase.
