Does the Adjustment of Industrial Structure Restrain the Income Gap between Urban and Rural Areas

2.1 Family Sector

It is assumed that all families have the same risk preference characteristics and the utility function is a function with a relative risk aversion coefficient of 1.

Suppose that there is no population growth in the economy and the population size is unitized. The maximization of family utility includes the following:

where C t and C t + 1 are the first and second consumption, respectively, W t is the wage income obtained for the first period of supply labor; r t + 1 represents the real interest rate level, and δ represents the discount factor.

We introduce the budget constraint formula into the utility function and obtain the unconstrained utility function as follows:

Formula (2) applies to the first consumption ( C t ) and the second consumption ( C t + 1 ) to obtain the following:

2.2 Industrial Sector

The national economic sector is divided into the traditional agricultural production sector and the nonagricultural production sector. It is assumed that the traditional agricultural sector inputs the only factor of production (labor force L a ), while the nonagricultural sector inputs the factors of production (labor force L b ), material capital ( K ), and technological progress ( A ). Technological progress applies to the industrial structure ( φ ). Assume that there is no capital adjustment cost or depreciation. The agricultural sector usually absorbs low-skilled or unskilled labor for employment, with diminishing returns to scale. However, the nonagricultural sector absorbs relatively highly skilled and skilled labor for employment, and the return on the scale remains unchanged. Set the production functions of two production departments as follows: Y b = A ( φ ) K 1 − β L b β ; Y a = L a α , where σ and b are the output elasticity of labor forces.

Assuming that manufacturers compete freely in the labor market, capital market, and product market, then maximizing the profits of manufacturers is equivalent to maximizing their output. Therefore, when the output is maximized, the optimal material capital quantity input selected by the two production departments makes the marginal output of capital equal to the marginal cost (i.e., market interest rate). The optimal quantity of labor is that the marginal output of labor is equal to its marginal cost (wage level); therefore, it is as follows:

where W a ,   W b are the average income level of the agricultural sector and nonagricultural sector, respectively, and r represents the return on capital. The average wage in the agricultural sector is a decreasing (increasing) function of the labor force in the agricultural sector (or the labor force in the nonagricultural sector). The average wage of the non-agricultural sector is a function of the industrial structure of material capital and human capital. According to formulas (5) and (7), the derivative of material capital (K) is obtained:

Equations (8) and (9) show that ∂ R / ∂ K < 0 and ∂ W b / ∂ K > 0 . That is, with the development of the economy, capital accumulation in the nonagricultural sector increases, and the marginal output of capital decreases. The marginal output of labor is increasing, and the relative shortage of highly skilled labor in nonagricultural sectors leads to labor mobility.

In the same way, based on formula (6) of the wage level of the labor department and formula (7) of the wage income level of the labor department, the input of the factor labor force (L _b ) in the nonagricultural department is derived.

In formulas (10) and (11), ∂ W a / ∂ L b > 0 explains the mobility of the nonagricultural labor force ( L b ) and the increasing function of the average wage of the agricultural sector ( W a ) while ∂ W b / ∂ L b < 0 indicates that the wage level ( W b ) of nonagricultural production is a decreasing function of the flow of the nonagricultural labor force (L _b ).

2.3 Equilibrium

When workers can make cross-sectoral choices, rational workers will meet with two choices. First, they will continue to engage in the original agricultural sector, and their utility function is ln C at + ln C a , t + 1 . Second, the labor force is transferred from the agricultural sector to the nonagricultural sector for production activities, and its utility is as follows: ln C bt + δ ln C b , t + 1 − D t ( φ t ) , where D t ( φ t ) is the flow cost of labor engaging in production in the traditional agricultural sector and flowing to a nonagricultural sector.

Because of the transfer cost of labor mobility, whether labor mobility across departments depends on the utility level in both cases. Therefore, when the system is balanced, the resource allocation utility of the labor force in the two departments is equal:

When the utility is maximized, the consumption of the first stage and the second stage is substituted into formula (12), and it is obtained as follows:

The wage level of the nonagricultural production department in period T can be obtained:

where T = W bt / W at ; t represents the income level gap between urban and rural areas and is associated with labor transfer costs; and D t ( φ t ) indicates the change in the industrial structure ( φ ). The transfer cost and industrial structure function of the income gap are derived as follows:

In formula (15), d T / d D ( φ t ) > 0 , which shows that the transfer cost of labor from the agricultural sector to the nonagricultural sector is an increasing function of the urban–rural income gap; that is, the greater the transfer cost of labor is, the greater the income gap between urban and rural areas. The size of the income gap between urban and rural areas caused by changes in the industrial structure depends on the transfer cost ( D ( φ t ) ) of the industrial structure ( φ t ) partial derivation.

2.4 Urban–Rural Income Gap

To better describe how industrial structure adjustment and labor mobility under microscopic conditions affect the income gap behavior of urban and rural residents, we obtain the ratio of (6) and (7) of urban and rural average wages when the output of the production department is maximized:

Take the logarithm on both sides of the equation:

The two sides of formula (18) are related to L _b . The derivative is determined, and the formula is simplified as follows:

In equation (19), ∂ T / ∂ L b > 0 indicates the ratio of urban and rural income ( T ) with the expansion of nonagricultural labor mobility. Changes in industrial structure in the urban–rural income gap ( φ ) derivative lead to the following:

To simplify:

In summary, the micro mechanism of the urban–rural income ratio in formula (21) mainly includes two aspects. First, the change in industrial structure makes the labor force in the traditional agricultural sector flow to the non-traditional agricultural sector, and the change in absolute income of urban and rural residents will have an impact on the relative income between urban and rural areas. Second, the influence of technological progress brought about by industrial restructuring on the urban–rural income ratio.

3.1 Explanatory Variables

3.2 Explained Variable

Two primary methods for measuring the income gap between urban and rural areas are the Gini index and the Theil index. However, the Gini coefficient has some inherent flaws in its calculation method. Specifically, if two countries have the same Gini coefficient, the underlying meanings may differ, suggesting potential errors when comparing the degree of income distribution inequality across different countries or regions. Additionally, the Gini coefficient is not sensitive enough to accurately reflect significant improvements in the situation of low-income groups, nor can it precisely capture changes affecting high-income groups. Consequently, the Gini coefficient may overlook the interests of low-income populations and struggle to fully explain the characteristics of income inequality.

where Thi is the Theil index; I uit and I rit are the disposable income of towns and villages in period T in area I, respectively; P uit and P rit represent the population of towns and villages in period t in area i ; and I it represents the total regional income of region i during period t . Obviously, the Theil index of income not only considers the population structure but also the relative changes of residents’ income and at the same time reflects the realistic background of the dual economic structure between urban and rural areas; therefore, it is more in line with the current situation of the income gap between high- and low-income groups on the macrolevel of measuring urban and rural income.

3.3 Control Variables

This study includes the following control variables: Urbanization level (urb): The relationship between urbanization and urban–rural income distribution is not linear but exhibits an inverted U-shaped pattern (Anand & Kanbur, 1993). The urbanization level is measured as the ratio of the urban population to registered population. Government scale (gov): The government plays a key role in income redistribution through taxation and the provision of public goods, as well as by protecting grassroots workers through the social security system. The government scale is measured as the ratio of fiscal revenue to expenditure. Unemployment rate (une): An increase in the unemployment rate, as per Okun’s Law, indicates an economic recession, which can lead to a decrease in residents’ wage income due to a shrinking market. Human capital (edu): Human capital is a crucial factor affecting economic development, as workers can change their income levels through learning and cross-regional mobility. The average years of education serve as a proxy variable for human capital. Transport infrastructure convenience (tra): The construction of transportation infrastructure not only reflects the convenience of regional transportation but also expands the circulation of goods. A more developed infrastructure can attract investment and employment, leading to a spillover effect that enhances market potential (Bronzini & Piselli, 2009). This variable is measured as the ratio of the sum of railway and highway mileage to the regional area. Ownership structure of employment (own): The employment ownership structure has a dual effect on urban–rural income. First, the mobility of grassroots laborers intensifies competition in the urban labor market, reducing urban wages. Second, labor mobility has improved the efficiency of human resource allocation during employment restructuring. The employment share of state-owned enterprises is used to represent the ownership structure.

3.4 Data Source and Description

This study examines a sample of 30 provincial units in mainland China from 1990 to 2019 for the following reasons: China’s Gini coefficient hovered around 0.3 in the 1980s, indicating a relatively reasonable income gap. The urban–rural income gap began to expand rapidly in the mid-to-late 1990s. Data availability and statistical consistency: Hainan and Chongqing had missing variables prior to 1990, so the study period was limited to 1990–2019. Additionally, due to a severe lack of data, Tibet was excluded from the sample.

The data sources for this study include the Statistical Yearbooks, China Rural Statistical Yearbooks, China Population and Employment Statistical Yearbooks, and China Township Enterprise Yearbooks. Some provincial data were missing and were supplemented through interpolation.

3.5 Econometric Model

Based on the above theoretical basis, we establish the following basic models:

where it stands for the variable in period t and region i , Thi stands for the Theil index, which is used to measure the income gap between urban and rural areas, Lab stands for labor mobility (net inflow and net outflow), ind stands for the industrial structure adjustment (adjustment range and adjustment quality), X stands for the control variable set, α 0 is the intercept term, and ε it is a random error term.

Actually, adjusting the industrial structure and labor mobility are continuous processes, and the income gap between urban and rural areas will not only be affected by their current levels but also by the early stage level. Therefore, the lag period of the industrial structure adjustment belt and labor mobility on the urban–rural income gap is taken as the explanatory variable, and the lag period is selected to control and eliminate endogeneity. The following dynamic panel model is constructed:

With the strengthening of the industrial association and personnel mobility between regions, there is not only a significant path dependence in economic development between regions but also a strong spatial linkage effect in the income gap between urban and rural areas. If only the ordinary panel model is considered and the spatial correlation between variables is ignored, the result will be biased. Therefore, a spatial econometric model is selected to study the problems in this article. Commonly used spatial econometric models include the spatial autoregressive model (SAR) and spatial error model (SEM). When the spatial dependence among variables plays a decisive role in the model and leads to spatial autocorrelation, the SAR model is chosen, whereas when the error term of the model is spatially autocorrelated, the SEM is selected. The two models are expressed as follows:

In formulas (27) and (28), Y and X represent dependent variables and independent variables, respectively; α j , ρ , and λ are coefficients of the variable, ε and μ are error terms that obey a normal distribution; other variables are the same as in the above formula, and W is the spatial weight matrix. Considering that an important factor of labor mobility is the difference in regional economic development level, when choosing the spatial weight matrix, the weight of the economic distance ( w 1 ) can reflect the difference of economic development between different regions. The structure takes the reciprocal of the absolute value of the difference in the per capita GDP between the two regions during the investigation period as the weight, namely w ij = 1 / | X ̅ − Y ̅ | , where X ̅ indicates the regional per capita GDP and Y ̅ indicates the per capita GDP of the region.

Because the labor mobility caused by adjusting the industrial structure in different regions is a continuous process, the resulting income gap depends not only on the current factors but also on the previous factors; that is, the income gap may have dynamic effects. This article will use the dynamic spatial panel model to test the impact of industrial structure adjustment and labor mobility on the income gap. The following model is obtained:

where α it , ν it , ε it are the regional effect, time effect, and random disturbance, respectively; ρ and λ are the spatial lag coefficient and spatial error coefficient, respectively; and other explanatory variables are the same as in the above formula.

4.1 Spatial Correlation Test

Table 1 shows the Moran’s I test results of the urban–rural income gap from 1990 to 2019. The Moran test of the urban–rural income gap under the weight of economic space passed the 1% significance test except in certain years. Generally, the income gap between different regions does not show completely random characteristics, with a very obvious spatial correlation observed between the urban and rural income gaps, especially since 2005.

Before parameter estimation, it is impossible to judge the spatial dependence characteristics of variables according to experience. First, the model that meets the actual requirements must be selected. According to the criterion proposed by Anselin and Florax (1995), the LM-test value of the SAR model is significantly better than that of the SEM model under the economic weight matrix, R-LMERR is significant, but R-LMLAG is not significant. Therefore, the spatial error SAR model is superior to the spatial lag SEM model.^[1]

4.2 Basic Regression

This study first analyzes the estimated results of the urban–rural income gap under the combined effects of industrial restructuring and labor mobility (Table 2). To ensure the robustness of the regression results, core explanatory variables were incorporated into the models. Model (1) and Model (2) examine the effects of the adjustment range and quality of the industrial structure, respectively, on the urban–rural income gap. Model (3) considers the combined impacts of the adjustment range and quality of the industrial structure on the urban–rural income gap. Finally, Model (4) accounts for the dynamic effect of the income gap over a lagged period.

The estimation results across the different models with varying core explanatory variables remain robust (Table 2). From Model (1) to Model (4), it is evident that the adjustment of the overall industrial structure nationwide does not have a significant impact on the urban–rural income gap. However, the quality of industrial structure adjustment has indeed widened the income disparity between urban and rural residents. This study posits that the quality of industrial adjustment represents the progression from low-level to high-level processing and intelligent production of commodities, thereby indicating the developmental trajectory of the entire industrial system. Across the industrial structure, the quality of industrial adjustment typically evolves from agriculture to manufacturing and finally to the service sector. Correspondingly, the industrial focus has shifted from labor-intensive to capital-intensive and technology-knowledge-intensive industries, as China’s industrialization has transitioned from the high-speed development stage to the later phase. Existing research (Luo et al., 2021; Sharon et al., 2020) has concluded that a larger share of the secondary industry or manufacturing sector in GDP is associated with a narrower urban–rural income gap, while a greater proportion of the tertiary industry or service sector corresponds to a wider income disparity. From a micro-perspective, the process of industrial structure adjustment involves a complex evolution from low-tech to high-tech enterprises. If local governments excessively pursue industrial upgrading or “deindustrialization,” it may lead to an increased unemployment rate among low-skilled rural workers, thereby reducing the overall income of low-income groups. However, the upgrading of industries can also result in higher income levels for high-skilled urban residents, further exacerbating the widening urban–rural income gap.

The findings further indicate that labor mobility has narrowed the overall income gap between urban and rural residents (Table 2). Since the 1980s, China’s rural areas have implemented the household contract responsibility system, and the urban food rationing system has gradually disintegrated. These changes have resulted in a substantial increase in agricultural output and the emergence of an agricultural surplus. Consequently, a surplus labor force in the agricultural sector was observed, leading to a continuous large-scale migration of rural workers to cities in search of employment. The transfer of these rural laborers to urban areas has enabled farmers to obtain wage income outside of agriculture, thus increasing the overall income of the rural workforce. Concurrently, the large-scale adoption of agricultural mechanization has greatly improved agricultural productivity, reducing the demand for agricultural labor. However, this has not compromised agricultural production efficiency or crop yields and has instead led to increased operational income for farmers’ households. Additionally, the Chinese government has implemented a series of policies aimed at benefiting rural residents. Collectively, these factors have directly or indirectly promoted the rise in household incomes of rural populations.

4.3 Differentiating the Impact of Labor Mobility Direction

On the basis of the above analysis, we further control the inflow and outflow of the labor force and investigate its impact on the income gap between urban and rural areas. Because the unbalanced panel data cannot be used for spatial measurement, time and regional data are deleted and retained as synchronously balanced panel data, and then, the spatial measurement analysis is carried out (Table 3).

The analysis of labor mobility patterns in Table 3 suggests that the adjustment of industrial structure, whether through net labor inflow or outflow, does not have a significant effect on the income gap between urban and rural areas. However, the quality of industrial restructuring in areas with net labor inflow tends to exacerbate the urban–rural income gap (Model (1) and Model (2)). This observation can be attributed to the fact that net labor inflow typically occurs in the relatively developed southeastern coastal regions of China. During the rapid period of political construction and development, when urban infrastructure was still being established, the demand for grassroots labor was substantial. However, as cities have become more advanced, the economies of these developed areas have undergone a transformation towards science- and technology-driven industries. The strategic shift towards capital- or technology-intensive sectors, such as high-end and knowledge-based industries, has often led to the exclusion or relocation of labor-intensive enterprises. Consequently, workers in the developed regions are frequently employed in labor-intensive industries. Therefore, in the process of upgrading the industrial structure in these developed areas, a large number of laborers are prone to lose their jobs, resulting in a decrease in the overall income of low-income groups (Neves & Silva, 2014; Phan & Coxhead, 2010).

In contrast, the analysis reveals that in areas with net labor outflow (Model (3) and Model (4)), the quality of industrial structure adjustment has had a restraining effect on the income gap between urban and rural areas. Compared to the net labor inflow regions, the net labor outflow areas are predominantly located in central and western China, where the industries tend to be either labor-intensive or capital-intensive. The industrial restructuring in these net labor outflow areas has primarily involved the transfer of labor-intensive and resource-intensive industries from the more developed regions. This process has absorbed a significant number of workers and increased the wage income of the rural labor force as a whole. Consequently, the adjustments to industrial structure in net labor outflow areas have provided more marginal benefits to rural grassroots workers than the changes in the urban industrial structure. Furthermore, the analysis suggests that the net outflow and net inflow of labor have opposing effects on the urban–rural income gap in this region. While the labor flow in net inflow areas suppresses the income disparities between urban and rural areas, the labor outflow in net outflow areas tends to widen the urban–rural income gap. This observation aligns with the general pattern that the income gap between urban and rural areas is typically larger in less developed regions. In other words, the more equitable the distribution of social wealth in the developed areas, the higher the overall well-being of the population (Cremer & Roeder, 2019). Importantly, the spatial spillover effect appears to constrain the urban–rural income gap in the neighboring areas, but exacerbate the gap in the net labor inflow regions.

4.4 Heterogeneity Analysis

4.5 Robustness Test

Considering that there may be some errors in the model setting and variable selection processes, which may affect the reliability of the regression results, to further test the robustness of industrial structure adjustment and labor mobility on the income gap between urban and rural areas, the Theil index of urban and rural income is replaced by the Theil index of urban and rural residents’ consumption (Cthi) and the per capita income ratio of urban and rural residents (Dthi) in this article. Meanwhile, the transportation distance weight matrix ( w 2 ) is used instead of the economic distance weight matrix ( w 1 ) to re-examine the above empirical results, and the inspection results are shown in Table 7.

Table 7 shows the estimation results of the robustness test under the condition of a full sample and differentiated labor flow direction. Under the condition of a full sample (Model (1)∼Model (2)), it can be found that the explained variables lag by one period, and the core explanatory variables are basically consistent with the regression results in Table 2, although the significance of the control variables and the positive and negative directions of the regression coefficients are slightly different. Under the condition of distinguishing the direction of labor mobility, the robustness test in the area of net labor inflow shows that the regression results of the urban–rural income ratio are consistent with the benchmark regression results in Table 3 and the Theil index of the core explanatory variables on urban–rural consumption is slightly different from the explanatory variables in Table 3; however, the regression results of the other variables are basically consistent, which is why they are not repeated here.