Impact of Industrial Robots on Labor Income Share: Empirical Evidence from Chinese A-Listed Companies

Abstract

Based on data from the International Federation of Robotics (IFR) and Chinese A-Share Listed Companies 2011–2019, this paper evaluates how the penetration of industrial robots in China affects the labor income share from both theoretical and empirical perspectives. We first develop a theoretical framework considering robots in the task model, consider different tasks matching different types of labor, construct a labor income share model including robots based on the task model, and perform a theoretical analysis finding that industrial robots can improve labor income. Then, we explore the mechanism of labor price distortion as an intermediate variable that can reduce the labor income share, finding that robots are able to effectively reduce the negative impact of labor price distortions on labor income share. After correcting for potential endogeneity problems, the results confirm a positive, significant, and lasting impact of industrial robot penetration on labor income share, confirming that labor price distortion is the underlying mechanisms through which the robots can effectively reduce the negative impact of labor price distortions on labor income share. At the same time, the impact of robots on firms’ labor income shares varies significantly across different regions, external financial dependence, and skill premiums. Our findings can help the government to provide a decision-making basis for how industrial robots can better serve people in the new century, ensuring that people can share in the achievements of economic development.

1. Introduction

Against the backdrop of the latest round of technological revolution and industrial change, the use of industrial robots has developed rapidly in China. According to the International Federation of Robotics (IFR) “Global Robotics 2023” data, China’s industrial robot ownership average annual growth rate in the period 2010–2021 was more than 35%. In 2021 the stock of industrial robots exceeded one million units, the world’s largest stock of industrial robots, as shown in Figure 1. As a large developing country with economic transformation, China’s use of industrial robots not only plays an important role in economic growth and employment structure [1,2,3,4], it also has a profound impact on the pattern of income distribution [5,6,7]. How to increase labor income in national incomes while achieving a fair distribution between labor and capital is crucial for advancing common prosperity.

China’s initial income distribution pattern at the current stage presents a low labor income share feature. According to calculations based on data from the China Statistical Yearbook, the proportion of labor compensation to GDP declined from 48.71% in 2000 to 39.74% in 2007, a significant decrease of 8.97 percentage points. After reaching a trough in 2007, it then began to show an upward trend. In 2017, China’s labor income share rebounded to 47.51%, showing a U-shaped trend of decline followed by an increase. Compared with other countries in the world, China’s share of labor income remains at a relatively low level [8,9]. A low labor income share not only leads to low consumption, insufficient domestic demand, and a decline in the people’s sense of happiness, it also further widens the gap between the rich and poor, aggravates social contradictions, and constrains the sustainable development of the economy. Therefore, a comprehensive study of the impact of the application of industrial robots on the share of labor income and its mechanism of action can provide new ideas for achieving a more inclusive pattern of income distribution.

Regarding the research on labor income share, scholars have focused on industrial structure adjustment, technological progress bias, globalization, and international trade [10,11,12,13]. In terms of how the use of robots affects labor income shares, scholars have often viewed industrial robots as a capital-biased technological advance, where the use of industrial robots will lead to a decline in the labor income share when the elasticity of substitution between capital and labor is less than one [14]. In addition, robots have the characteristics of a general purpose technology (GPT), and the increase in output and production efficiency of traditional industries fully reflects the spillover characteristics of artificial intelligence [15]. Therefore, robots are regarded as another production factor; it has been found that when the elasticity of substitution between robots and labor exceeds 1.9, industrial robots can reduce the share of labor income [16]. The impact of industrial robots on the labor income share depends mainly on the elasticity of substitution between robots and labor [6]. In terms of empirical research, some previous results suggest that robots can reduce labor income share [17,18], however, other studies suggest that industrial robots increase the labor income share [19]. The current work on the impact of industrial robots on labor income shares is mainly focused on the national macro-level. Micro-enterprise data are concentrated in specific regions and the sample is not representative; thus, a more systematic empirical analysis is needed. Previous scholars have discerned a “polarization” phenomenon regarding the impact of robots on the labor force, and the proposition of the task model can explain this matter [20]. However, studies on how robots influence the labor income share within the task model have not been carried out.

The core issue studied in this paper is how the use of industrial robots affects the labor income share. Theoretically, the labor income share model based on the task model framework remains exploratory. Therefore, theoretically analyzing the role of robots in the labor income share within the task model is one of the main issues studied in this paper. In the empirical aspect, studies on the impact of industrial robots on labor income share mainly focus on the national macro-level. Micro-enterprise data are concentrated in specific regions, and the samples are not representative. Therefore, another main issue is how to systematically construct the penetration of robots at the prefecture-level city, match it with Chinese micro-enterprise data, and conduct an empirical analysis combined with the theoretical model on the impact of robots on the labor income share. The theoretical exploration of labor income share within the task model framework aims to bridge existing gaps in scholarly research, offering a novel perspective to help understand the impact of robotic technology on income distribution. Additionally, this study expects to deliver more precise policy recommendations through rigorous empirical research and meticulous data analysis.

Regarding the above matters, this paper first incorporates industrial robots into the task model, assuming that there is a competitive relationship between labor and industrial robots in each task, and constructs a labor income share model in a perfectly competitive market, which enriches the research on the impact of industrial robots on labor income share in the framework of the task model. Second, at the empirical level, this paper utilizes country–industry industrial robot stock data released by the International Federation of Robotics (IFR) and China’s listed manufacturing firms to empirically analyze the penetration of industrial robots at the firm level in China by constructing a Bartik-type measure [1,21]. This empirical analysis shows that industrial robots significantly increase the labor income share. To address the possible endogeneity of the model, we use robotics data from the USA industry to construct instrumental variables for this paper; the results are consistent with the benchmark regression. There are also significantly different impacts on different regions, external financing dependencies, and skill premiums. Finally, this paper finds that penetration of industrial robots reduces labor price distortions, thereby alleviating the negative impact of labor price distortions on the labor income share.

The present study contributes to the literature in the following ways. First, in contrast to existing studies, this paper introduces industrial robots into the task model, considers different tasks matching different types of labor, and constructs a labor income share model including robots based on the task model. Second, we explore the heterogeneity of the impact of robot penetration on labor income share from multiple dimensions, including regional variations, dependence on external financing, and labor skill premiums. Third, in term of mechanisms, this paper proposes and empirically demonstrates that labor price distortion is the underlying mechanisms through which robots can effectively reduce the negative impact of labor price distortions on labor income share, thereby providing new search ideals for the impact of industrial robots.

The rest of the paper is organized as follows: Section 2 reviews the relevant literature on industrial robots and labor income share; Section 3 provides a theoretical framework with two hypotheses; Section 4 introduces the data and relative variables; Section 5 provides the empirical strategy and robustness tests; and Section 6 presents our conclusions and recommendations.

2. Literature Review

Increasing the proportion of labor income in the national economy is an important way to expand the proportion of middle-income groups and steadily promote the realization of common prosperity. Compared with other countries in the world, China’s labor income share remains at a relatively low level [8,22]. A low labor income share not only lead to low consumption, insufficient domestic demand, and a decline in people’s sense of well-being, it also further widens the gap between the rich and the poor, intensifies social conflicts, and constrains the sustainable development of the economy. Regarding previous research on labor income shares, scholars mainly focus on industrial restructuring, technological progress bias, globalization, international trade, etc. Under China’s unique dual economic structure, with the optimization and upgrading of traditional industries and the advancement of industrial modernization, the share of agriculture, which has the highest share of labor income share in the whole economy, is declining; meanwhile, the share of modernized industrial and manufacturing output is rising and changes in industrial structure have led to a continuous decline in the share of China’s labor income [10,11,23]. With the development of the economy, the change in labor income share shows a U-shaped pattern of initial decline followed by rise. Industrial structure changes can explain the decline of labor income share in China at this stage, but cannot explain the decline of labor income share in the longer term or for developed countries where the industrial structure has reached a stable state [24].

In previous research into the impact of biased technological progress on labor income share, scholars have found that China’s marginal output elasticity of labor is greater than 1 and that the direction of technological progress is capital-biased; empirical evidence has found that capital-biased technological progress significantly reduces the labor income share [25,26]. The model presented by Wang Linhui and Yuan Li shows how biased technological progress affects factor income distribution [27]. At the same time, Wen Yanbing and Lu Xueqin studied China’s labor income share in terms of market competition and institutional quality [28].

Globalization and international trade are also major factors affecting the share of labor income [29,30]. China’s trade liberalization has diminished capital and labor costs, causing a decline in labor income share at the enterprise level [11]. Furthermore, international trade prompts technological progress to be inclined towards capital, resulting in factor income being skewed towards capital [31]. Regarding studies on institutions and market structure, scholars have mainly discussed the effects of monopoly pricing, political relations, labor unions, financing constraints, and taxation on declining labor income shares [32,33,34].

With the development of automation technology, the phenomenon of robots replacing human workers has raised concerns about labor surpluses [35]. However, research on the impact of automation on the workforce continues to be debated. Studies have suggested that the rise of automation puts most jobs in Europe at risk of becoming obsolete [36]. However, some scholars argue that historical technological revolutions have not led to sustained reductions in labor demand, with automation being no exception [37]. Scholars mainly explain this by Skill-Biased Technological Change (SBTC) increasing the demand for skilled workers, including college graduates; that is, there is good complementarity between technological progress and skilled labor, indicating that technological changes do not reduce employment. However, research has found that SBTC struggles to account for the ’polarization’ phenomenon in the labor market. This refers to a rapid increase in both high-skilled and low-skilled labor relative to medium-skilled labor [5]. Zeira proposed a task model that adeptly explains the polarization phenomenon in the labor force [20]. We know that a task is the output of a unit of work activity, whether goods or services. Skills represent the worker’s ability to perform various tasks; workers apply their skills to tasks in exchange for wages while simultaneously actualizing their output within these tasks. When skilled workers can perform multiple tasks, changes in the labor market conditions and technology that alter the tasks performed by workers cause the distinction between skills and tasks to become very important. Therefore, the introduction of the task model can explain the impact of automation technology on the labor market [38]. Yang Guang and Hou Yu introduced the scale effect and pricing behavior of robots into the task model and studied the impact of industrial robots on economic growth [3].

With regard to artificial intelligence research on income distribution, scholars have argued that AI could reduce labor income share. For example, based on Chinese provincial panel data from 2008–2017, Chao Xiaojing and Zhou Wenhui found that artificial intelligence has a negative impact on labor income share [9]. Yu Lingzheng and Wei Xiahaic carried out a theoretical study finding that when robots and labor are substitutes, the application of robots will lead to a decrease in the labor income share. Using enterprise questionnaire survey data from Guangdong Province, they empirically demonstrated that robots significantly reduced labor income share [17]. He Xiaogang and Zhu Guoyue et al. obtained similar research results [18]. However, other studies have argued that AI can increase labor income share. Alai Yeerken and Deng Feng found that digital service trading has a positive effect on labor income share [39]. Jin Chenfei and Wu Yang et al. found that the application of artificial intelligence significantly increased the share of labor income of enterprises based on a database of “machine-for-human“ pilot enterprises in Zhejiang Province from 2015–2017, for which they used the double-differential propensity-matching score method (PSM-DID) [19].

The established literature on the impact of industrial robots on the labor market, labor compensation, and even macroeconomic conditions has been widely discussed in China, providing an important reference for this paper. However, there has not yet been sufficient discussion of how industrial robots affect the labor income share from the perspective of task-biased technology, which forms the starting point of our study.

3. Theoretical Model

3.1. The Impact of Robots on Labor Income Share

Previous theoretical models examining skill premiums have treated technological change as either Factor-Augmenting or Hicks-Neutral, ignoring the fact that a distinguishing feature of automated production is that firms choose whether or not to use machines to replace labor in different production tasks. Autor and Levy et al. pioneered the distinction between labor inputs that perform routine and non-routine tasks, and incorporated work tasks into their theoretical framework [40]. Yu Lingzheng and Wei Xiahai et al. further developed a simplified “robot–work task“ theoretical model based on the foundational concepts of the ALM model [41]. This model assumes a fixed elasticity of substitution between routine and non-routine tasks as well as between technologies. It examines technological progress as task-biased (TBTC), analyzing the impact of robots on wages for workers engaged in different studies. In this paper, we draw on the ideas and assumptions of the ALM model to construct a brief theoretical model on the “robot–task” foundation.

Consider a firm with four factors of production: robots, construction equipment, workers performing routine tasks, and workers performing non-routine tasks. The general production function is presented as follows:

$$Y=f(K_S,K_A,l_R,l_N,{\phi }_R,{\phi }_N)$$

(1)

where Y denotes the total output, $K_S$ and $K_A$ represent construction equipment and robots, respectively, $l_R$ represents workers engaged in routine tasks, and $l_N$ denotes the workers engaged in non-routine tasks. we denote the input efficiency of routine tasks by ${\phi }_R$ and the input efficiency of non-routine tasks by ${\phi }_N$.

To more precisely detail the effects of various tasks on the distribution of labor income, a two-layer nested Constant Elasticity of Substitution (CES) production function is utilized. This approach draws on the capital–skill complementarity hypothesis [42] and incorporates the core hypothesis of the task model [41]. The production function is defined as follows:

$$Y=K_S^{\alpha }{\left\{{\left({\phi }_R{l}_R\right)}^{\sigma }+{\left[K_A^{\rho }+{\left({\phi }_N{l}_N\right)}^{\rho }\right]}^{{\displaystyle \frac{\sigma }{\rho }}}\right\}}^{{\displaystyle \frac{1-\alpha }{\sigma }}}$$

(2)

where $\sigma ,\rho \in (-\infty ,1)$ indicate the constant elasticity of the substitution coefficients, which represents the elasticity of substitution between robots and workers provided with routine and non-routine tasks; the elasticity of substitution between robots and workers engaged with routine tasks is $1/(1-\sigma )$, while the elasticity of substitution between the robot and workers engaged with non-routine tasks is $1/(1-\rho )$.

The production function (2) should satisfy the following two assumptions [41]: (1) there is strong substitutability between robots and workers engaged in routine tasks, i.e., $0<\sigma <1$; and (2) there is a complementary relationship between robots and workers engaged in non-routine tasks, i.e., $\rho <0$. Equation (2) is then expressed as the “robot–task“ model, which is also the key assumption of the ALM task model.

Assuming that the final product’s price is normalized to 1, under conditions of perfect competition and market clearing the price of factors equals their marginal output, equating the wages of workers performing different tasks to their marginal labor output. Consequently, the wages of workers engaged in non-routine $\left({\omega }_N\right)$ and routine tasks $\left({\omega }_R\right)$ are expressed as follows.

$${\omega }_N=(1-\alpha )K_s^{\alpha }·Y^{{\displaystyle \frac{1-\alpha -\sigma }{1-\alpha }}}·{\left[K_A^{\rho }+{\left({\phi }_N{l}_N\right)}^{\rho }\right]}^{{\displaystyle \frac{\sigma -\rho }{\rho }}}·{\phi }_N^{\rho }·l_N^{\rho -1}$$

(3)

$${\omega }_R=(1-\alpha )K_s^{\alpha }·Y^{{\displaystyle \frac{1-\alpha -\sigma }{1-\alpha }}}·{\phi }_R^{\sigma }·l_R^{\sigma -1}$$

(4)

To further analyze the impact of robots on the share of labor income in the task model, we can define the labor income share $\left(LS\right)$ as the proportion of total labor income in the total output of a firm. Based on the specific expressions of ${\omega }_N$ and ${\omega }_R$, in this study we represent the total labor remuneration as $WL={\omega }_N{l}_N+{\omega }_R{l}_R$. Hence, the labor income share can be expressed as follows.

$$LS={\displaystyle \frac{WL}{Y}}={\displaystyle \frac{{\omega }_N{l}_N+{\omega }_R{l}_R}{Y}}=(1-\alpha ){\displaystyle \frac{{[K_A^{\rho }+{\left({\phi }_N{l}_N\right)}^{\rho }]}^{\frac{\sigma -\rho }{\rho }}·{\left({\phi }_N{l}_N\right)}^{\rho }+{\left({\phi }_R{l}_R\right)}^{\sigma }}{{[K_A^{\rho }+{\left({\phi }_N{l}_N\right)}^{\rho }]}^{\frac{\sigma }{\rho }}+{\left({\phi }_R{l}_R\right)}^{\sigma }}}$$

(5)

The level of labor income share is the combination of $K_A$, i.e., the robot change, with $\sigma$ and $\rho$ being the elasticity of substitution between robots and workers provided with routine and non-routine tasks, respectively. Additionally, ${\phi }_N{I}_N$ and ${\phi }_R{I}_R$ represent the input efficiency of the labor force engaged in non-routine tasks and routine tasks, respectively. Their changes also affect the labor income share. The introduction of the $K_A$ change affects the labor income share only when all of these variables assume the appropriate size and sign.

To more straightforwardly understand the impact of robots on the labor income share, we compute the partial derivative of Equation (5) concerning $K_A$. The result is shown as follows:

$${\displaystyle \frac{\partial LS}{\partial K_A}}={\displaystyle \frac{(1-\alpha )U^{\frac{\sigma -2\rho }{\rho }}}{{[U^{\sigma /\rho }+{\left({\phi }_R{l}_R\right)}^{\sigma }]}^2}}·[-\sigma ·{\left({\phi }_R{l}_R\right)}^{\sigma }{K}_A^{\rho }-\rho ·{\left({\phi }_N{l}_N\right)}^{\rho }]·[U^{\sigma /\rho }+{\left({\phi }_R{l}_R\right)}^{\sigma }]$$

(6)

where $U=K_A^{\rho }+{\left({\phi }_N{l}_N\right)}^{\rho }$.

It can be known from Equation (6) that determining the influence of robots on the labor income share is contingent upon the relationship between $\sigma ·{\left({\phi }_R{l}_R\right)}^{\sigma }{K}_A^{\rho }$ and $-\rho ·{\left({\phi }_N{l}_N\right)}^{\rho }·[U^{\sigma /\rho }+{\left({\phi }_R{l}_R\right)}^{\sigma }]$. Based on the prevailing hypotheses, robots and workers involved in routine tasks are in a substitution relationship, that is, $0<\sigma <1$, whereas robots and workers engaged in non-routine tasks are in a complementary relationship, that is, $\rho <0$. When the labor input efficiency of performing routine tasks and non-routine tasks is approximately equal, ${\left({\phi }_R{l}_R\right)}^{\sigma }\approx {\left({\phi }_N{l}_N\right)}^{\rho }$. With the extensive use of industrial robots, it is evident that $\sigma ·{\left({\phi }_R{l}_R\right)}^{\sigma }{K}_A^{\rho }\le -\rho ·{\left({\phi }_N{l}_N\right)}^{\rho }·[U^{\sigma /\rho }+{\left({\phi }_R{l}_R\right)}^{\sigma }]$. Thus, it can be seen from Equation (6) that the increase of $K_A$ with respect to robots can increase the labor income share. To elaborate further on the economic significance, it can be discerned from Equations (3) and (4) that in contrast to the labor force involved in routine tasks, the extensive utilization of robots has a pronounced boosting impact on the wages of the labor force engaged in non-routine tasks. Meanwhile, the substitution of robots and labor force engaged in non-routine tasks leads to an eventual increase in the labor income share through the use of robots.

We develop and discuss a simple and stylized model of labor income share and its response to robots. This model yields the following theoretical results: when robots and workers engaged in non-routine tasks are in a complementary relationship ($\rho <0$) and robots and workers performing routine tasks are in a substitutive relationship ($0<\sigma <1$), the use of robots increases labor income share at stationary equilibrium. As a result, we propose Hypothesis 1.

Hypothesis 1. 

(H1) Robots $K_A$ have a positive impact on labor income share $LS$.

H1 provides important theoretical support for understanding how robots affect labor income share, and forms the theoretical basis for constructing the empirical model in this paper.

3.2. The Impact of Robots on Distorted Labor Prices

In traditional labor markets, employers have more bargaining power and workers are in a relatively disadvantaged position, resulting in asymmetric labor negotiations and the inability to achieve effective resource allocation and transactions in the market. Employers are unable to accurately assess the value of workers, which may lead to employers being willing to pay wages higher or lower than their value, resulting in distorted labor prices. Labor price distortions reduce the share of labor income. Yu and Wu [43] have observed that the digital economy leverages data as a production factor to mitigate resource mismatches and market distortions. The advancement of digital technology has enhanced the transparency and symmetry of labor market information, facilitating easier access for workers to details of job opportunities, salary structures, and company practices. This not only lowers the costs associated with job searches but also maintains the negotiating power of workers during wage discussions. Furthermore, the evolution of digital technology has empowered workers to organize themselves into more influential trade unions and labor associations. This organizational strength enhances the bargaining position of labor, leading to a more equitable negotiating environment with employers and reducing the extent of labor price distortions.

Robots, as a representative form of automation technology, have been shown to have a crowding-out effect on low-skilled labor while having no meaningful effect on high-skilled labor [4]. With the wide application of robots, low-skilled laborers have to transfer to better-matching tasks through skill retraining, effectively alleviating the distortion of labor pricing and solving the mismatch problem in market-based allocation of labor. This improves the marginal productivity of laborers and increases labor income share; hence, we propose Hypothesis 2:

Hypothesis 2. 

(H2) Robots can effectively reduce the negative impact of labor price distortions on labor income share.

3.3. Theoretical Framework

Figure 2 below presents a graphical representation of the theoretical framework. In the following section, we use this framework to empirically examine the relationships between the robots and labor income share.

4. Empirical Strategy

4.1. Data Sources

The robots used in the empirical analysis provided in this paper mainly refer to industrial robots. The data are taken from the IFR, which is the most authoritative database on industrial robots, providing data on both stock and incremental industrial robots on a country–industry–annual basis. While existing studies focus on the industry level and provincial macro-level, this paper focuses on the micro-level, drawing on Acemoglu and Restrepo’s measure of robot exposure in commuting areas in the US to measure the penetration of industrial robots at the regional level in China [1]. Simultaneously, the dataset of Chinese A-share listed companies is exceptionally comprehensive, encompassing basic company information, stock market transaction dynamics, detailed financial statements and their indicators, corporate governance structures, the nature of equity, executive compensation, research and development innovations, as well as litigation and arbitration records, among other aspects. Utilizing these detailed data resources, our study combines the data of Chinese A-share listed companies from 2011 to 2019 with data on penetration of industrial robots, focusing on the micro-level of firms to further analyze how the penetration of industrial robots affects the labor income share in China. This analysis aims to provide deeper insights into the specific impacts of technological advancement on the labor market.

4.2. Model

To identify the causal impact of penetration of industrial robots on the labor income share of enterprises, we construct the baseline estimating equation as follows:

$$L{S}_{isrt}={\alpha }_0+{\alpha }_{1}AP{R}_{rt}+{\alpha }_2^{\prime }{X}_{isrt}+{\psi }_r+{\varphi }_i+{\phi }_t+{\epsilon }_{isrt}$$

(7)

where i is a firm, s is an industry, r is a prefecture-level city, t is a year, $L{S}_{isrt}$ is the labor income share of industry s in prefecture-level city r by firm i in year t, $X_{isrt}$ represents the corresponding control variables, ${\psi }_r$ stands for the regional fixed effects, ${\varphi }_i$ stands for the firm-level fixed effects, ${\phi }_t$ stands for the year-level fixed effects, and ${\epsilon }_{isrt}$ refers to the error term. In Equation (7), ${\alpha }_1$ measures the overall impact of penetration of industrial robots on the labor income share of enterprises.

4.3. Measurement of Labor Income Share

For the labor income share ${LS}_{isrt}$, we adopts the value-added method, as follows: labor income share = cash paid to employees, and for employees/(cash paid to employees and for employees + operating profit + depreciation and amortization + various taxes paid), where cash paid to employees and for employees includes wages, bonuses, allowances, and social security contributions [13,34].

4.4. Measurement of Penetration of Industrial Robots

Acemoglu and Restrepo constructed the robot exposure in the USA commuting areas based on a Bartik-type measure to study its impact on the USA labor market [1]. Wang and Dong argued that robot penetration is a better indicator than robot stock for measuring the actual level of robot adoption in a region [14]. This paper draws on their methodology to construct the penetration of industrial robots at the regional level in China. The specific measures are as follows.

Industry-level industrial robot penetration indicator, denoted as ${\mathit{PR}}_{s,t}$:

$$P{R}_{s,t}={\displaystyle \frac{Ro{b}_{s,t}}{Em{p}_{s,t=2010}}}$$

(8)

where $Ro{b}_{s,t}$ represents the industrial robot stock of industry s in year t and $Em{p}_{s,t=2010}$ indicates the number of persons employed in industry s in 2010 (the base period).

The penetration of industrial robots in region r in year t is $AP{R}_{r,t}$:

$${APR}_{r,t}={\sum }_s\frac{Em{p}_{r,s,t=2011}}{Em{p}_{s,t=2011}}\times P{R}_{s,t}$$

(9)

where ${\displaystyle \frac{Em{p}_{r,s,t=2011}}{Em{p}_{s,t=2011}}}$ represents the share of industry s in prefecture-level city r of the total employment in industry s for the whole country.

We decompose the penetration of industrial robots at the industry level to the prefecture-level in order to investigate the impact of industrial robots on the share of labor income at the micro-level.

Table 1. Changes in the penetration of industrial robots in China.

Regions	The Penetration of Industrial Robots		Regions	The Penetration of of Industrial Robots
	2011	2019		2011	2019
National (average)	0.1389	1.5452	Henan	0.0609	0.6901
Beijing	0.9169	8.3326	Hubei	0.0801	0.9511
Tianjin	0.5158	6.3329	Hunan	0.0544	0.6123
Hebei	0.0669	0.7482	Guangdong	0.1157	1.4059
Shanxi	0.0397	0.4229	Guangxi	0.0294	0.3197
Inner Mongolia	0.0267	0.2937	Hainan	0.0254	0.2410
Liaoning	0.0621	0.7269	Chongqing	0.3821	4.3641
Jilin	0.0423	0.4791	Sichuan	0.0412	0.4726
Heilongjiang	0.0369	0.4172	Guizhou	0.0345	0.3662
Shanghai	0.9466	10.9783	Yunnan	0.0342	0.3684
Jiangsu	0.1228	1.5297	Tibet	0.0277	0.2408
Zhejiang	0.1555	1.9189	Shanxi	0.0500	0.5429
Anhui	0.0365	0.3928	Gansu	0.0172	0.1852
Fujian	0.1328	1.7131	Qinghai	0.0473	0.5153
Jiangxi	0.0422	0.4896	Ningxia	0.0157	0.1689
Shandong	0.1030	1.2533	Xinjiang	0.0422	0.4275

reports robot penetration by province in China in 2011 and 2019. In terms of average, the penetration of industrial robots in the country increased from 0.14 in 2011 to 1.55 in 2019, and the penetration of industrial robots in various provinces had a significant growth. However, there are obvious regional differences, with the highest penetration in eastern China, the second-highest in central China, and the lowest in western China. In terms of the average annual growth rate, the eastern, central, and western regions are the same, showing that industrial robots are in a stage of rapid development.

4.5. Other Variables

In this paper, we refer to the research literature on the factors affecting labor income shares [11,12,13] to adopt seventeen distinct control variables $X_{isrt}$: (1) corporate accounting performance (roa), which is calculated by the enterprise net profit/total assets; (2) total debt ratio (debate), calculated by total debt/total assets; (3) company growth (growth), calculated by the rate of change in total assets; (4) ownership concentration (Cr5), specified as the sum of the squares of the shareholdings of the top five largest shareholders; (5) industry concentration (HHI), specifically the Herfindahl–Hirschman Index, is the sum of the squares of the percentage of the total revenue of each market competitor in an industry; (6) the number of managerial shareholdings (mngshrs), specified as the logarithm of the sum of managerial shareholdings; (7) the capital output ratio (k/y), expressed by the net fixed assets/main business income; (8) invention patent applications (patent), expressed as the logarithm of the total number of invention patents; (9) income tax (income_–tax), calculated based on tax/total profits; (10) company stock performance (bm), expressed using the book value of the enterprise at the end of the period; (11) the cash holding level (cash), expressed using (monetary funds+trading securities)/total assets; (12) nature of the equity (soe), which takes a value of 1 if the actual controller is state-owned and 0 otherwise; (13) capital intensity (ci), expressed using the firm’s total assets/operating revenues; (14) board independence (bodindept), specified as independent directors/board members; (15) enterprise asset size (size), expressed as the logarithm of total enterprise assets; (16) regional export share (export), expressed by regional exports/regional GDP; and (17) government expenditures (govexp), expressed by local government general budget expenditure/regional GDP, where export and govexp serve as macro-level control variables. The descriptive statistical results of the main variables are shown in

Table 2. Descriptive statistics of the variables.

Variables	N	Mean	Std. dev.	Min	Max
LS	24,965	12.9734	9.3175	0.1451	97.1412
APR	24,965	0.7669	0.6127	0.0038	2.2479
roa	24,965	0.0392	0.1102	−6.776	8.4414
debrate	24,965	0.4244	0.242	0.0071	10.4953
growth	24,964	0.2293	0.6873	−0.929	41.4625
Cr5	24,965	0.5134	0.1997	0.2	0.9939
HHI	24,965	0.0955	0.1036	0.0156	0.7762
mngshrs	19,457	15.5371	3.6127	0	21.9304
k/y	24,464	0.4635	0.4929	0.0061	3.6495
invention	11,979	2.4215	1.769	0	10.3739
income–tax	24,408	0.1658	0.1313	−0.5148	0.7837
bm	24,356	0.625	0.2456	0.0098	6.5459
cash	24,965	0.198	0.1457	0.0002	0.9804
soe	24,965	0.1281	0.3343	0	1
ci	17,264	2.3545	1.6724	0.3894	12.0143
bodindept	24,936	0.3746	0.0559	0	0.8
size	24,965	22.1266	1.3261	17.7564	28.6365
export	24,965	0.0407	0.0292	0.001	0.1092
govexp	24,405	0.154	0.051	0.0763	0.2909

.

4.6. Correlation Analysis between Robots and Labor Income Share

Based on measurements of the penetration of industrial robots (APR) and enterprise labor income share (LS) in China, in order to align with the level of robot penetration in prefecture-level cities, we compute the labor income share of prefecture-level cities in light of the locations of enterprises in these cities on the basis of the labor income share at the enterprise level. Scatter diagrams and the fitted straight lines, shown in Figure 3, depict the relationship between APR and LS. The results reveal a significant positive correlation between penetration of industrial robots and labor income share. This indicates that the utilization of robots contributes to increasing the labor income share. To validate the stability and reliability of this relationship, the subsequent section presents the results of strict empirical testing and analyses based on Equation (7).

5. Empirical Results

5.1. Baseline Regression

Table 3. Baseline regression results.

Variables	(1)	(2)	(3)	(4)
APR	0.1948 ***	0.0459 ***	0.1678 ***	0.0470 **
	(0.0128)	(0.0193)	(0.0154)	(0.0220)
roa	−0.2782 ***	−0.2942 ***	−0.2997 ***	−0.3010 ***
	(0.0915)	(0.0459)	(0.0921)	(0.0460)
debrate	−0.2507 ***	−0.0045	−0.2561 ***	−0.0041
	(0.0451)	(0.0252)	(0.0457)	(0.0254)
growth	−0.0959 ***	−0.0763 ***	−0.0971 ***	−0.0803 ***
	(0.0126)	(0.0058)	(0.0128)	(0.0060)
Cr5	−0.0094	−0.0721 *	−0.0170	−0.0932 **
	(0.0407)	(0.0379)	(0.0416)	(0.0390)
HHI	−0.7546 ***	−0.0301	−0.7950 ***	−0.0301
	(0.0626)	(0.0882)	(0.0646)	(0.0890)
mngshrs	−0.0080 ***	−0.0027	−0.0073 ***	−0.0031
	(0.0024)	(0.0026)	(0.0025)	(0.0027)
k/y	0.1511 ***	0.1393 ***	0.1534 ***	0.1327 ***
	(0.0215)	(0.0172)	(0.0219)	(0.0176)
invention	0.0287 ***	0.0022	0.0286 ***	0.0023
	(0.0040)	(0.0023)	(0.0040)	(0.0023)
income–tax	−0.2584 ***	−0.0384	−0.2787 ***	−0.0414
	(0.0622)	(0.0274)	(0.0636)	(0.0280)
bm	−0.3831 ***	0.0768 ***	−0.3711 ***	0.0734 ***
	(0.0344)	(0.0252)	(0.0353)	(0.0256)
cash	0.2637 ***	−0.1443 ***	0.2535 ***	−0.1710 ***
	(0.0627)	(0.0354)	(0.0643)	(0.0364)
soe	0.0619 **	0.0476 ***	0.0682 **	0.0522 ***
	(0.0269)	(0.0140)	(0.0273)	(0.0142)
ci	0.1223 ***	0.1513 ***	0.1221 ***	0.1532 ***
	(0.0069)	(0.0056)	(0.0071)	(0.0057)
bodindept	0.2492 **	−0.0405	0.2758 **	−0.0509
	(0.1216)	(0.0815)	(0.1233)	(0.0826)
size	−0.1192 ***	−0.2278 ***	−0.1211 ***	−0.2280 ***
	(0.0075)	(0.0110)	(0.0077)	(0.0113)
export			0.0322 **	0.0208
			(0.0127)	(0.0394)
govexp			0.0832 ***	-0.0231
			(0.0263)	(0.0385)
Constant	4.9176 ***	7.0597 ***	4.6929 ***	7.1262 ***
	(0.1644)	(0.2369)	(0.1791)	(0.2680)
Firm FE	NO	YES	NO	YES
Region FE	NO	YES	NO	YES
Year FE	NO	YES	NO	YES
N	6309	5865	6097	5645
$R^2$	0.2772	0.9385	0.2810	0.9396

Note: Standard errors clustered at the at the region level in parentheses. ***, ** and * indicate statistical significance at 1%, 5% and 10% levels, respectively.

reports the results of the benchmark regressions. Column (1) examines the impact of industrial robot penetration on labor income share with, where the control variables contain mainly firm-level information. Column (2) builds on column (1) by fixing firm, region, and year fixed effects. Column (3) adds two prefecture level city macro-level control variables, exports (export) and government expenditure (govexp). Column (4) builds on column (3) by fixing firm, region, and year fixed effects. The all results show that the estimation coefficient of the main explanatory variable (APR) is positive and statistically significant at the 5% level, indicating that the penetration of robots can effectively increase the labor income share. The results in column (4) show that for 1% increase in APR, LS will increase by 0.047 percentage points. The regression results are consistent with the theoretical model, thus verifying Hypothesis 1. The research conclusion of this paper is consistent with that of Jin et al. [19], the author empirically-found that the application of artificial intelligence significantly increased the labor income share of enterprises based on the database of “machine replacement“ pilot enterprises in Zhejiang Province from 2015 to 2017. However, the result is contrary to that of Cheng et al. [17], who found that industrial machines reduce the labor income share at the 10% significance level. Possible reasons for this could be that Cheng et al. utilizes the China Enterprise General Survey (CEGS) database, which may have a sample selectivity bias compared to Chinese A-share firms, and that the sample size is only three consecutive years of data from 2015–2017. The robot data is a dummy variable formed based on whether firms adopt robots for production in the questionnaire survey, but Wang and Dong [4] point out that the penetration of robots is more reflective of the actual level of robot adoption in a region.

Taking the estimated results of Column (4) as an example, we find that roa, debrate, growth, Cr5, cash, size have a significantly negative effect on the labor income share, while k/y, bm, soe, ci have a significantly positive effect. Capital output ratio (k/y) significantly raises the labor income share, suggesting that firms with higher net fixed assets are more likely to transfer investment income to workers. Firms with higher company stock performance (bm) are more inclined to increase workers’ income. Nature of equity (soe) may affect the level of compensation and benefits for employees, and indirectly impact the share of labor income. An increase in capital intensity (ci) may lead to an increase in labor productivity and thus an increase in the share of labor income. The above results are consistent with the conclusions of Bai and Qian [10], Luo and Zhang [11], and Wen and Lu [28].

5.2. Endogeneity Concerns

To address the bias of regression results caused by endogeneity, this paper uses the USA industry-level data on the stock of industrial robots and the number of people employed by sub-industry to calculate the USA industry-level industrial robot penetration [4]. The specific calculation of the instrumental variables of robot penetration is given by

$$AP{R}_{r,t}^{IV}={\sum }_j\frac{Em{p}_{r,s,t=2011}}{Em{p}_{s,t=2011}}\times \frac{Ro{b}_{s,t}^{US}}{Em{p}_{s,t=2010}^{US}},$$

(10)

where $Ro{b}_{s,t}^{US}$ represents the stock of industrial robots in the USA industry s in year t, and $Em{p}_{s,t=2010}^{US}$ indicates the employment in the USA industry s in 2010 (the base period). The $t=2011$ mainly refers to the lagged period of one year from the base year (t = 2010) adopted in this paper. We contend that there exists a lag in the application of automation technology, and the robots utilized in the current year will exert an influence on the labor income share in the subsequent year.

We use the USA industrial robots as the instrumental variable in this paper, because the USA industry-level industrial robots penetration on China’s labor market is reflected in the technological characteristics of similar industries, which satisfies the correlation of instrumental variables, while it is not related to other factors affecting China’s industrial robots, and meets exclusion constraints, and that ${\mathrm{APR}}^{IV}$, as an instrumental variable for China’s region-level industrial robots penetration, can better solve the model’s endogeneity problem. Meanwhile, we analyze the lagged period of robots penetration (L.APR) as an instrumental variable as well.

To address the bias of regression results caused by endogeneity, we select ${\mathrm{APR}}^{IV}$ and L.APR as IVs to construct two-stage least squares (2SLS) regressions.

Table 4. Regression results using instrumental variables.

Variables	(1)	(2)	(3)	(4)
${\mathrm{APR}}^{IV}$	0.1502 ***	0.0437 *
	(0.0176)	(0.0242)
L.APR			0.1477 ***	0.0828 ***
			(0.0163)	(0.0258)
Control   Variable	YES	YES	YES	YES
Firm FE	NO	YES	NO	YES
Region FE	NO	YES	NO	YES
Year FE	NO	YES	NO	YES
N	6097	5645	5363	4844
$R^2$	0.2809	0.3497	0.2860	0.3646
First-statge F statistic	19,662.01	20,796.58	$2.3\times {10}^4$	28094.32

Note: Standard errors clustered at the at the region level in parentheses. ***, and * indicate statistical significance at the 1% and 10% levels, respectively.

shows the regression results in columns (1)–(4), where columns (1) and (2) are regression results for ${\mathrm{APR}}^{IV}$, and columns (3) and (4) are regression results for L.APR.

The F-statistics of the weak instrumental variables in all first-stage regressions are much larger than the empirical value of 10, suggesting that APR is correlated with the endogenous explanatory variables. The estimation results presented in column (2) show that the estimated coefficient of the penetration of robots (${\mathrm{APR}}_{r,t}^{IV}$) is 0.0437, which is significantly positive at the 10% level. The estimation results in column (4) reveal that the estimated coefficient of the lagged one period of the penetration of robots (L.APR) is 0.0828, which is significantly positive at the 1% level. This suggests that the penetration of robots has significantly increased the labor income share. The other control variables remain consistent with the results in Table 3, demonstrating the robustness of the instrumental variable regression results and better control of omitted variable bias.

5.3. Robustness Check

Next, we conducted robustness estimation based on different scenarios, mainly the transformation of the dependent variable, changing the measurement method of the main explanatory variables and sub-sample regression.

(1)

Alternative measures of the dependent variable to overcome the possible bias of the indicator are shown in Table 3. Referring to the existing literature that examines the labor income share at the micro-level, this paper measures employee income share in the following four ways: referring to Chang and Wang [44], the employee income share is the ratio of the compensation of workers to the sum of the compensation of laborers and the capital income, in which the compensation of laborers is measured by the payment of cash to and for the employees and the capital income is measured by the sum of the profit from the main business and the depreciation of the fixed assets, denoted by LS1. As the share of employee income fluctuates in the range of $(0,1)$, referring to Li et al. [23] and Wei et al. [32], we apply logistic transformation for adjustment to LS/(1-LS), then take the logarithm, denoted by LS2. Referring to Hu and Maimaitiyiming [45], the share of employee income is the ratio of laborers’ remuneration to the firm’s total assets at the end of the period, denoted by LS3. Moreover, LS4 is calculated by referring to Fang [46], i.e., the share of employee income of a listed company = cash paid to and for employees/(operating income − operating costs + cash paid to and for employees + depreciation of fixed assets). From the regression results in columns (1)–(4) of

Table 5. Robustness test: changing the measurement of labor income share.

Variables	(1)	(2)	(3)	(4)
	LS1	LS2	LS3	LS4
APR	0.1018 ***	0.0112 ***	0.0903 ***	0.0950 ***
	(0.0379)	(0.0033)	(0.0236)	(0.0260)
Control   Variable	YES	YES	YES	YES
Firm FE	YES	YES	YES	YES
Region FE	YES	YES	YES	YES
Year FE	YES	YES	YES	YES
N	2696	2736	2736	2722
$R^2$	0.8731	0.9268	0.9416	0.8746

Note: Standard errors clustered at the at the region level in parentheses. *** indicates statistical significance at the 1% levels.

, the regression coefficients of LS1, LS2, LS3, and LS4 are 0.1018, 0.0112, 0.0903, and 0.0950 respectively, all of which are significantly at the 1% level. It can be seen that APR and the share of labor income share remain significantly positively correlated with each other, which is consistent with the conclusions of this paper.

(2)

Alternative measures of the main explanatory variables: (I) according to the calculation method in Equation (9), we use the change of ${\mathrm{APR}}_{r,t}$ − ${\mathrm{APR}}_{r,t-1}$ to represent the industrial robots penetration degree in year t and region r, obtaining the change in the permeability of industrial robots at the regional level from 2011 to 2019. (II) Through an advanced search on the official Patent Gateway website, we obtained the number of patents related to “robot” and “intelligence” disclosed between 2011 and 2019 for each of the 288 prefecture-level cities in order to show the level of robotics usage at the regional level. From the regression results in columns (1)–(3) of

Table 6. Robustness test: changing the measurement of APR.

Variables	(1)	(2)	(3)
	The Change of “APR”	Number of “Robot” Patents	Number of “Intelligence” Patents
APR	0.0872 **	0.0198 **	0.0219 *
	(0.0366)	(0.0101)	(0.0131)
Control   Variable	YES	YES	YES
Firm FE	YES	YES	YES
Region FE	YES	YES	YES
Year FE	YES	YES	YES
N	5378	5645	5645
$R^2$	0.9424	0.9396	0.9396

Note: Standard errors clustered at the at the region level in parentheses. **, and * indicate statistical significance at the 5% and 10% levels, respectively.

, the regression coefficients of APR in columns (1) and (2) are 0.0872 and 0.0198 respectively, which are significantly positive at the 5% significance level. The regression coefficient of APR in column (3) is 0.0219, which is significantly positive at the 10% significance level. It can be seen that APR and the share of labor income share remain significantly positively correlated with each other, which is consistent with the conclusions of this paper.

(3)

Sub-sample regression. To further verify the impact of industrial robots penetration on labor income share, the data were regressed on the full sample for the 2011–2019 balanced panel and the year interval was divided into 2011–2015 and 2016–2019 for subsample regressions. The specific results are shown in

Table 7. Robustness test: subsample regression.

Variables	(1)	(2)	(3)	(4)
	Full Sample	2011–2019 Year Balance Panel	2011–2015 Year	2016–2019 Year
APR	0.0470 **	0.0687 *	−0.0686	0.0470 **
	(0.0220)	(0.0384)	(0.0584)	(0.0220)
Control   Variable	YES	YES	YES	YES
Firm FE	YES	YES	YES	YES
Region FE	YES	YES	YES	YES
Year FE	YES	YES	YES	YES
N	5645	3279	1990	5645
$R^2$	0.9396	0.9668	0.9680	0.9396

Note: Standard errors clustered at the at the region level in parentheses. **, and * indicate statistical significance at the 5% and 10% levels, respectively.

, the column (1) shows the regression results of the full sample. In column (2), when the sample is adjusted to the balanced panel data from 2011 to 2019, the regression coefficient of APR is 0.0687, which is significant at the 10% level. In column (3), when the sample interval is selected as 2011–2015, the APR on the labor income share is not significant. In column (4), when the sample interval of 2016–2019 is selected, the regression coefficient of APR is 0.047, which is significant at the 5% level. A possible reason for this is that the application of industrial robots in China only started around 2011, The impact of the initial stage of robots use on the labor income share is not statistically significant. However, with wide application of robots, the number of robots tends to complement workers performing non-routine tasks, which is expected to significantly increase the labor income share.

5.4. Heterogeneity Analysis

(1)

Regional heterogeneity. According to the descriptive statistical analysis in Table 1, there are differences in robots penetration among different regions, which may lead to heterogeneity in the impact effect on labor income share. Therefore, to further study the impact of robots penetration on the share of labor income in each region, China’s economic regions were first divided into the eastern, central, western, and northeastern regions according to the division method used by the Bureau of Statistics. As shown in

Table 8. Heterogeneity analysis of different regions.

Variables	(1)	(2)	(3)	(4)
	Eastern Region	Central Region	Western Region	Northeast Region
APR	0.0631 **	0.1713 *	0.0699	−0.3480
	(0.0261)	(0.0938)	(0.0952)	(0.3157)
Control   Variable	YES	YES	YES	YES
Firm FE	YES	YES	YES	YES
Region FE	YES	YES	YES	YES
Year FE	YES	YES	YES	YES
	4193	766	488	173
$R^2$	0.9437	0.9280	0.9377	0.9646

Note: Standard errors clustered at the at the region level in parentheses. **, and * indicate statistical significance at the 5%, and 10% levels, respectively.

, the (1), (2), (3), and (4) columns represent the eastern region, the central region, the western region, and the northeastern region respectively. The regression results show that APR significantly increases the labor income share in the eastern region (Beijing, Tianjin, Hebei, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan) and central region (Shanxi, Anhui, Jiangxi, Henan, Hubei, and Hunan). For the western region (Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang) and Northeast region (Liaoning, Jilin, and Heilongjiang), the effect of APR on labor income share is not significant. There are significant differences between the regions.

(2)

Heterogeneity in external financing dependence. When a country’s financial markets are less developed, the cost of external financing for firms is higher. In this case, the higher the dependence on external financing, the more enterprises need to rely on internal funds to alleviate external financing constraints. When robots are employed for production, firms allocate more of their profits to scarce resources, and have limited funds for raising labor income; on the contrary, external financing constraints due to underdeveloped financial markets have less impact on firms with lower reliance on external financing. Thus, under the same conditions, these firms can allocate more funds to laborers and increase their labor income share while using robots for production to increase output. As shown in

Table 9. Heterogeneity analysis for external financing dependence.

Variables	(1)	(2)
	High Dependence on External Financing	Low Dependence on External Financing
APR	0.0435	0.0624 *
	(0.0336)	(0.0325)
Control   Variable	YES	YES
Firm FE	YES	YES
Region FE	YES	YES
Year FE	YES	YES
N	2999	1999
$R^2$	0.9435	0.959

Note: Standard errors clustered at the at the region level in parentheses. * indicate statistical significance at the 10% levels.

, columns (1) and (2) are the regression results of APR on the labor income share of companies with High Dependence on External Financing and Low Dependence on External Financing respectively. The results show that APR increases the labor income share of firms with Low Dependence on External Financing (the regression coefficient is 0.0624, and the significance level is 10%) more significantly than that of firms with High Dependence on External Financing.

(3)

Heterogeneity of skill premiums. Robots improve technological progress and labor skill premiums, leading to the high-skilled labor force exerting a “skill crowding-out effect” on the low-skilled labor force. High-skilled workers are more likely to see improved labor productivity due to technological progress, which in turn promotes the relative demand for high-skilled workers in order to achieve the optimization and upgrading of human capital structure and increase the share of enterprise labor income. When the wage level of high-skilled workers rises, the income gap between them and low-skilled workers widens, causing a skill premium. The influence of robots on the labor income share may vary depending on the skill premium. In order to verify this conclusion, we assessed the impact of robots on labor income share by dividing our sample into low skill premium and high skill premium groups according to the measurement method of Chen and Guo [47]. In this method, the skill premium is the difference between the wage paid for high-skilled labor and the wage paid for low-skilled labor; the sample was divided into high skill premium and low skill premium according to the median of the skill premium, while the impact of robots on the labor income share is discussed separately. As shown in

Table 10. Heterogeneity analysis for skill premium.

Variables	(1)	(2)
	Low Skill Premium	High Skill Premium
APR	0.0583	0.0504 **
	(0.0407)	(0.0249)
Control   Variable	YES	YES
Firm FE	YES	YES
Region FE	YES	YES
Year FE	YES	YES
N	1404	3903
$R^2$	0.9624	0.9432

Note: Standard errors clustered at the at the region level in parentheses. ** indicate statistical significance at the 5% levels.

, columns (1) and (2) are the regression results of APR on the labor income share of companies with Low Skill Premium and High Skill Premium respectively. The results show that APR increases the labor income share of firms with High Skill Premium (the regression coefficient is 0.0504, and the significance level is 5%) more significantly than that of firms with Low Skill Premium.

5.5. Mechanism Analysis

To further discuss the impact of robots on labor price distortion, we refer to Sheng and Xu [48] for their research methodology and use the C-D production function method to measure labor price distortion. The core idea of this method is to first determine the marginal output of a factor by estimating the production function:

$$\begin{array}{c}\hfill Y=A{K}^{\alpha }{L}^{\beta }\end{array}$$

where Y is the gross output, A is the technological progress, K is the capital stock, L is labor, $\alpha$ is the elasticity of capital output, and $\beta$ is the elasticity of labor output.

Then, the marginal output of labor is

$$\begin{array}{c}\hfill M{P}_L=A\beta K^{\alpha }{L}^{\beta -1}=\beta Y/L.\end{array}$$

Comparing the resulting marginal output of labor $M{P}_L$ with the real price of labor w yields the price distortion of labor ($distL$):

$$\begin{array}{c}\hfill distL=M{P}_L/w.\end{array}$$

When industrial robots (APR) affect the labor income share (LS), if APR can affect LS by affecting distL, then distL is said to be the mediator variable, APR can either affect LS either directly or indirectly through distL. The mediation effect model of this paper is constructed as follows:

$$L{S}_{isrt}={\beta }_0+{\beta }_{1}AP{R}_{rt}+{\beta }_2^{\prime }{X}_{isrt}+{\psi }_r+{\varphi }_i+{\phi }_t+{\epsilon }_{isrt},$$

(11)

$$dist{L}_{isrt}={\lambda }_0+{\lambda }_{1}AP{R}_{rt}+{\lambda }_2^{\prime }{X}_{isrt}+{\psi }_r+{\varphi }_i+{\phi }_t+{\epsilon }_{isrt},$$

(12)

$$L{S}_{isrt}={\gamma }_0+{\gamma }_{1}AP{R}_{rt}+{\gamma }_{2}dist{L}_{isrt}+{\gamma }_3^{\prime }{X}_{isrt}+{\psi }_r+{\varphi }_i+{\phi }_t+{\epsilon }_{isrt},$$

(13)

with the interpretation of the parameters shown in Equation (7).

According to Hypothesis 2, if there is a mediating effect of labor price distortions, then the coefficient ${\beta }_1$ in Equation (11) should be significant, as should the coefficients ${\lambda }_1$ in Equation (12) and the coefficients ${\gamma }_1$ and ${\gamma }_2$ in Equation (12). As shown in

Table 11. Robots, labor price distortion, and labor income shares.

Variables	(1)	(2)	(3)
	LS	distL	LS
APR	0.0470 **	−0.0381 **	0.0037 *
	((0.0220)	(0.0193)	(0.0022)
distL			−1.1361 ***
			((0.0018)
Control   Variable	YES	YES	YES
Firm FE	YES	YES	YES
Region FE	YES	YES	YES
Year FE	YES	YES	YES
N	5645	5644	5644
$R^2$	0.9396	0.9384	0.9994

Note: Standard errors clustered at the at the region level in parentheses. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively.

, the columns (1), (2), and (3) present the regression results of Equations (11), (12), and (13), respectively. In column (1), the estimated coefficient of APR is about 0.047, indicating that robots significantly increase the labor income share of firms. In column (2), the estimated coefficient of APR is significantly negative at the 5% level, with a regression coefficient of −0.0381, suggesting that robots can reduce the distortion of the labor price of the firms. From column (3), it is possible to find the coefficient of distL. The estimated coefficient of distL is significantly negative at the 1% level, with a coefficient of −1.1361, while the estimated coefficient of APR is significantly positive at the 10% level and the estimated coefficient of APR decreases compared with column (1). This indicates that labor price distortion has a partial intermediary effect between robots and labor income share; that is, with the widespread use of robots, the labor price distortion will decrease, then the labor income share will increase to a certain extent, verifying Hypothesis 2.

5.6. Discussion

This paper primarily investigates the influence of industrial robots utilization on labor income share. Based on the task model, it is proposed that employing robots will enhance the labor income share. The primary reason for this is that using robots exerts a crowding-out effect on the labor force engaged in routine tasks, but offers complementary utility for the labor force involved in non-routine tasks. Meanwhile, in contrast to the labor force engaged in routine tasks, the extensive application of robots has a marked boosting effect on the wages of the labor force undertaking non-routine tasks. Concerning the distortion of labor price, with wider implementation of robots low-skilled laborers are compelled to transfer to better-matching tasks through skill retraining, effectively alleviating the distortion of labor prices and resolving the mismatch issue of labor in market-based allocation. This has the effect of boosting the marginal productivity of laborers and raising the labor income share.

The results of this study are consistent with the discoveries of Jin Chenfei and Wu Yang et al. [19], who also documented an increase in labor share attributed to automation in the manufacturing sector. Nevertheless, our study extends this work by delving into Chinese A-share listed companies, providing theoretical evidence based on the task model. Similar to the outcomes achieved by Xin Baogui and Ye Xiaopu, we find that although the utilization of industrial robots has broadened the income gap, it has augmented labor incomes [49].

While our findings offer valuable contributions to the economics of automation, several limitations should be recognized. Concerning the data, our robots adoption data were restricted to specific industries and countries, possibly biasing our comprehension of global trends. Regarding the causal issue, although advanced statistical methods were utilized to address endogeneity concerns, the observational nature of the data restricted our capacity to firmly establish causality between robots adoption and changes in income distribution. Additionally, it is challenging to distinguish between routine tasks and non-routine tasks within existing enterprises at the micro-level, making it difficult to conduct further detailed empirical analyses based on the task model.

6. Conclusions

Although China has become used to a supercharged rate of expansion, its economy faces many challenges, such as income imbalance and low remuneration for labor. This paper systematically investigates the impact of industrial robots on labor income share through both theoretical models and empirical analyses. Our basic conclusions can be summarized as follows: in terms of theoretical analysis, this paper introduces industrial robots into the task model, considers different tasks matching different types of labor, and constructs a labor income share model including robots based on the task model. The theoretical analysis finds that industrial robots can improve labor income share. We exploit the mechanism of labor price distortions as an intermediate variable that can reduce the labor income share, finding that robots can effectively reduce the negative impact of labor price distortions on labor income share. In the empirical analysis, this paper constructs the penetration of industrial robots at the regional level using the stock of industrial robots in industry and matching this with Chinese industrial data from 2011 to 2019. Based on the causal strategy of using Bartik-style instrumental variables to solve the endogeneity problem in the regressions, the results show that penetration of industrial robots has a positive effect on labor income share and that the conclusions remain consistent. In a robustness test, replacing the labor income share and industrial robots penetration indicators in the construction of industrial robots penetration in industry produced estimation results that remained robust.

In terms of heterogeneity at different regional levels, this study found that the penetration of industrial robots has a greater positive effect on the labor income share in the eastern and central regions compared with the western and northeast regions. In addition, the positive impact of industrial robots penetration on the labor income share of enterprises with low external financing dependence is obviously greater than that of enterprises with high external financing dependence. The reason for this might be that enterprises with low dependence on external financing are more willing to choose industrial robots with lower costs for production, which helps enterprises to save costs, improve production efficiency, product quality, and technical level, and increase their labor income share. In terms of skill premiums, we find that robots have a positive effect on high skill premiums, as high-skilled workers are more likely to improve their labor productivity thanks to technological progress, which in turn promotes the relative demand for high-skilled workers to achieve optimization and upgrading of human capital structure and increases the share of enterprise labor income.

Our results provide useful insights into ways of promoting labor income share. Combined with China’s income distribution policy, the findings presented in this paper bring forward the following related policy suggestions.

First, although China has introduced many income distribution policies, it has not yet formed a set of mature and effective mechanisms for Chinese enterprises, and the incentive effect of robots is not yet significant. While industrial robots can effectively improve labor income share, there is a short-term crowding-out effect on the labor force. Therefore, it is necessary for policymakers to further strengthen employment security policies and cultivate professional and skilled talents, especially in skills training for emerging industries. At the same time, it is necessary to improve the unemployment insurance system and strengthen social security for unemployed workers, and more effective subsidy policies should be considered to guide enterprises in providing security measures around labor income.

Second, policymakers should focus on protecting labor income and raising people’s incomes through multiple channels. At the enterprise level, the western and northeast regions should invest in high-tech industries and the government should reduce the construction costs around such industries through policies such as financial subsidies and tax and fee reductions. In addition, enterprises should actively introduce senior technological talents to match the structure of labor demand with the industrial structure of the market and further balance the structure of income distribution under the new development pattern.