Analytical framework

Drawing upon the existing body of literature and recognized stylized facts, this study formulates an economic model to investigate the impact of sectoral linkages on structural change within the Chinese economy.

The model consists of two types of agents: household and firms. In the goods market, there are three distinct types of final goods derived from the agricultural, manufacturing, and services sectors, while the factor markets are characterized by a single type of factor, labor. All markets are perfectly competitive. A representative household supplies labor to firms in three sectors, which compensate the household with wages in the factor market. The output produced by firms in three sectors can be either consumed by the household or utilized as intermediate goods input in production within the goods market. The intermediate goods input by firms across different sectors establish a production network within this economic framework, thereby inducing the significance of sectoral linkages and the underlying mechanisms that affect structural change within the economic system. This analytical framework is depicted in Fig 3 below.

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Fig 3. Analytical framework.

The figure illustrates the fundamental structure of the economic system, along with its connection with the input-output analysis through the application of structural decomposition analysis (SDA).

https://doi.org/10.1371/journal.pone.0330908.g003

The potential pathways through which sectoral linkages impact the structural change process can be discerned from Fig 3. Variations in the input of sectoral intermediate goods will influence the production processes of firms, subsequently leading to adjustment in their output levels. These changes in output will, in turn, affect the supply to satisfy household's demand as well as the demand from firms for intermediate inputs. Ultimately, all of these variations will propagate throughout the structural change process. The aforementioned analyses establish a connection between production networks and structural change.

The right-hand side of Fig 3 illustrates the connection of structural decomposition analysis (SDA) with the economic system. The labor factor is identified as the primitive input. The output employed by firms as intermediate goods in the production process is identified as the intermediate input. Additionally, the output consumed by household is identified as final demand. Collectively, these three components constitute the primary driving forces within SDA. The SDA procedure part outlines the specific methodology of SDA and elucidates the roles of these three components.

Utilizing this analytical framework, we first develop a general equilibrium model related to the economic system depicted above. Subsequently, we calibrate the model parameters in accordance with the data, which is elaborated upon in the benchmark calibration part. Following the model specification and benchmark calibration, we conduct simulations using our baseline model and compare the results of these simulations with the observed data dynamics. To explore the roles of sectoral linkages and productivity as pivotal factors driving structural change in China, we perform a counterfactual analysis. Additionally, we adjust the preference and production function specification within our model to check its robustness. Drawing upon the results from these three procedures, we examine the underlying mechanisms from the perspective of production network. Finally, we integrate the model with SDA to identify and elucidate the roles of various components within the economic system. In conclusion, this section will encompass a discussion on model specification, benchmark calibration, counterfactual analysis and robustness check design, mechanism test design, structural decomposition analysis procedure literally.

Model specification

As most literature argues and defines [37–39], structural change, or structural transformation, is often associated with the dynamics of three broad sectors. Informed by this body of literature, our model is constructed within the framework of a static, perfectly competitive open economy that encompasses three sectors: agriculture (denoted as a), manufacturing (denoted as m), and services (denoted as s).

Firms.

Goods and labor are freely mobile between sectors. Within each sector, there exists a representative firm that employs labor and intermediate inputs to produce final goods. We adapt the Cobb-Douglas production function as referenced in [6,40]. The production function is as follows:

(1)

The term , i, j{a, m, s} is the intermediate input from sector j that is utilized by sector i in the production process. is the corresponding labor input. Exponential is the share of nominal value-added relative to total output in sector i. Exponential is the share of sector j's goods in sector i's total intermediate input, and . The term represents the total factor productivity. All information presented in this section holds for a given period t. To avoid needless notation, for the remainder of this section I will not use the t subscript.

Household.

In the economy, there exists an infinitely living representative household endowed with L units of labor per period. This household supplies labor inelastically to all firms.

At each period, the household purchases final goods from three sectors using its labor earnings. C represents the aggregate consumption of final goods from these three sectors. In addition, the definition of consumption that we refer to here should be more precisely defined as final absorption. This includes consumption, investment, government purchases, and exports. For convenience, we denote it with the letter “C”. The utility function is expressed in the Stone-Geary form, as described in [37]:

(2)

is the level of subsistence consumption for agricultural final goods and can be interpreted as the household's own production of services. These two variables cannot be zero simultaneously so as to keep preference non-homothetic.

The budget constraint is represented as follows: , i. is the price for the consumption of final goods in sector i. is the nominal wage in the labor market.

Equilibrium.

In a competitive equilibrium, the following conditions are satisfied: (1) given the prices of goods, the household maximizes its utility under budget constraint; (2) given the prices of factors, firms maximize their profits under the production function; and (3) all markets for goods and factor clear.

1. (1). By solving the household's optimization problem, we obtain:

(3)(4)

P is defined as the price of aggregate consumption C. for i=a, m, s, and .

1. (2). By solving firms' optimization problems, we obtain:

(5)(6)

So, the dual equation for (6) is:

(7)

is defined as the intermediate input from sector j that is utilized by sector i. According to the definitions of exponential  and , and can be regarded as the sectoral value-added; therefore, they can be denoted as and . Consequently,

1. (3). The market clearing condition satisfies:

(8)(9)

Using the equilibrium equations presented above, sectoral shares in value-added can be expressed as follows^.. More details can be found in Appendix A in S1 Appendix.

(10)

, and are corresponding entries in the matrix Ω, where . Each entry in the matrix is denoted as , for i, j=a, m, s. is the diagonal matrix of . Equation (10) exhibits the formulation of sectoral value-added shares within a general equilibrium model, as well as their relationship to the sectoral linkages and prices.

Benchmark calibration

This subsection appliesdata to calibrate the aforementioned model to the Chinese economy for the period spanning from 1978 to 2014. Prior to the calibration process, we outline the data we utilize.

The data is collected from the World Input-Output Database (WIOD) [14]. For the years 1978–2000, the data is sourced from the Long-run WIOD [36], specifically the time series of the National Input-Output Tables (NIOT). For the subsequent years from 2001 to 2014, the data is sourced from the 2016 release version of WIOD. The subindustries are categorized into three broad sectors—agriculture, manufacturing, and services—according to the International Standard Industrial Classification of All Economic Activities, Rev. 3 (ISIC). The category of manufacturing encompasses not only itself but also includes other subindustries, as outlined in the following paragraph. For the sake of brevity, we collectively refer to these as manufacturing. This terminology is commonly used in relevant literature. The classification is widely used by researchers in the field of structural change [37,38].

In the Long-run WIOD, agriculture is classified under subindustries labeled by code AtB, manufacturing is classified under subindustries with codes C to F, and services is classified under codes G to LtQ. In the 2016 release version of WIOD (hereafter referred to as WIOD 2016), agriculture is classified under subindustries with codes A to B, manufacturing is classified under subindustries with codes C to F, and services is classified under subindustries with codes G to U. A notable distinction from conventional literature is our classification of construction within the manufacturing sector, which is consistent with the sector classification employed by the National Bureau of Statistics in China. Conversely, the International Standard Industrial Classification (ISIC) categorizes construction within the services sector.

Utilizing the classification mentioned above and data from WIOD, we construct the panel for calibration. The annual sectoral value-added, intermediate inputs and outputs are presented directly in the table. We aggregate them in accordance with the aforementioned classification. Since we assume that the output produced by firms is either utilized as sectoral intermediate inputs or consumed by the household as final goods, and all markets are perfectly competitive, so we aggregate the final absorption items in the table, which encompass consumption, investment and export, to match with our model.

The calculation of sectoral prices is conducted as follows. Given that WIOD provides sectoral final absorption data in both current and previous year prices, we can calculate the sectoral price deflator for each period. This is achieved by dividing the final absorption at current prices by the final absorption at the prices of the previous year. We designate 1978 as the base year, normalizing the price for each sector in that year to one. Subsequently, we derive the prices for subsequent years by dividing the growth factor of nominal final absorption by the growth factor of the price deflator.

We now proceed to the calibration procedure. The parameters and can be calculated directly from the data in the model specification. The parameters need to be calibrated are the preference parameters: , , , and . We take the nonlinear least square (NLS) method [6] for calibrating these parameters. Using sectoral prices and total value-added, we select the manufacturing sector as a reference sector. The objective function for calibration aims to minimize the sum of squared distances between the actual sectoral final absorption, denoted as , obtained from WIOD, and its corresponding values derived from the first-order conditions implied by Equations (4): . Through calculation and simplification, we get the final expression for the objective function, which is presented below. Additional information regarding the derivation of this equation can be found in Appendix B in S1 Appendix.

(11)

The calibration results are reported as follows in Table 1.

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Table 1. Calibration results for parameters.

https://doi.org/10.1371/journal.pone.0330908.t001

Sectoral productivity is defined as the residual in the production function, which can be calculated as follows:

(12)

The nominal wage W is derived from the expression: . To accomplish this calculation, it's necessary to gather data on total labor input. We utilize data from the National Bureau of Statistics (NBS) and adjust it in accordance with the clarification proposed by Holz [41] to ensure consistency. It is noteworthy that the NBS of China revised its employment series data to correspond with the population censuses conducted in 2000 and 2010; however, data prior to 1990 remains unadjusted. Holz (2006) identified this discrepancy and addressed it by employing sectoral employment shares reported by the NBS, which were anchored to the population censuses of 1982 and 1990. As a result, this study integrates Holz's data for the years preceding 1990 with the NBS's data for the subsequent years.

Counterfactual analysis and robustness check design

It can be deduced from Equation (10) that sectoral linkages and prices serve as the primary determinants influencing the dynamics of sectoral value-added shares. Furthermore, the forces that underlie sectoral prices are linked to sectoral productivities. Therefore, we employ the methodology presented in reference [29] for our counterfactual analysis to evaluate the impact of sectoral linkages and productivity. We analyze the former firstly. In this analysis, the parameters related to sectoral linkages are held constant at their initial values throughout all years, while all other parameters and variables remain unchanged. The differences observed between the results of this counterfactual analysis and the baseline will reflect the effects we seek to investigate.

To examine the second potential channel through which these factors operate, it is essential to analyze the relationship between sectoral prices and their corresponding productivity, as articulated in Equation (13) of our basic model as below.

(13)

This equation demonstrates that sectoral productivity has a significant influence on the equilibrium prices of final goods, which subsequently affects final absorption. We apply the same methodology previously discussed to analyze this relationship. In this case, sectoral productivity are held constant at its initial values from 1978 for all subsequent years, while other parameters and variables remain unchanged. The differences between the results obtained from this counterfactual analysis and the baseline will reflect the effects attributable to sectoral productivity.

In order to check the robustness of our model specification and the outcomes of the baseline simulation, we examine it from two dimensions: (1) alternative preference specification and (2) alternative production function specification.

Initially, we adopt a homothetic Constant Elasticity of Substitution (CES) utility function to characterize the preferences of a representative household, as exhibited in Equation (14).

(14)

The parameters and variable values are maintained in accordance with the baseline model. We simulate the dynamics and conduct counterfactual analyses utilizing the methodology previously outlined.

Subsequently, we replace the Cobb-Douglas production function with a generalized CES production function, as referenced in [42–44]. The functional form is articulated in Equation (15).

(15)

For this production function, we apply the same methodology as previously described to derive the calibration functions for the two elasticity parameters, as well as the general equilibrium functions. We then simulate the dynamics of value-added shares and conduct the counterfactual analysis as previously indicated.

Mechanism test design

In order to further elucidate the underlying mechanisms, this study refers to existing literature on production networks [7,9].

For the equilibrium equations previously articulated, we apply logarithmic transformation to both sides followed by total differentiation. This approach yields the subsequent equation (More details can be found in Appendix C S1 Appendix):

(16)

In the Equation (16), and . Each diagonal entry of the matrix is and each off-diagonal entry is . . Each entry of matrix is denoted as , for i, j=a, m, s. The matrix dlnRW is the differentiation of market real wage, with all components expressed as dlnW-dlnP uniformly.

Given that , it follows that . Equation (16) exhibits the relationship between variations in total output or value-added and fluctuations in sectoral productivity and real wages. In a perfectly competitive factor market, there exists no sectoral heterogeneity regarding changes in real wages. Variations in sectoral productivity will propagate across all sectors via sectoral linkages, as represented in matrix . According to reference [40], changes in sectoral productivity can be decomposed into intra-sectoral and inter-sectoral variations, denoted . is the indicator function for j = i. The latter part illustrates how one sector may be influenced as a consumer of other sectors, which is characterized as the downstream network effect. In this context, sector linkages can act as a significant driving force.

In the mechanism test and SDA, we select the United States, Japan and South Korea as reference countries within the same time window. The United States has passed through the second phase of transformation and become service-oriented at the beginning of this period. The rapid growth of producer services, especially high R&D intensive services, has come to dominance the economy. Meanwhile, manufacturing production has largely been outsourced abroad to other countries. Japan has passed through the second phase of transformation in the mid-1970s, but its manufacturing sector also experienced rapid growth, which continues to play a substantial role in its economy until the economic bubble in the 1990s. It establishes tight connection with the services sector during this time. South Korea has completed its first phase of transformation during the earlier part of this period and passed through the second phase in the 1990s. In contrast with the United States and Japan, South Korea has relied on capital-intensive manufacturing sectors to complete its industrialization process and then developed services that are closely connected to support its manufacturing sector. These three countries have passed through the second phase of structural transformation process at varying points within the same period, resulting in diverse significance and developmental patterns within their manufacturing and services sectors. The distinct characteristics of structural change processes in these countries may offer valuable insights for the Chinese economy, particularly in terms of comparing the intersectoral linkages among different sectors. Additionally, all three countries—China, Japan, and South Korea—are situated within the East Asia region, where geographical proximity, cultural similarities, and comparable development patterns may yield analogous outcomes across these nations.

In order to compare the strength of linkages as a driving force across different sectors in China and three additional countries, we conduct a counterfactual analysis. In this analytical framework, we compare the downstream network effect coefficient after assigning a value of 1 to all .

Structural decomposition analysis method

Structural Decomposition Analysis (SDA) is a widely used method employed to elucidate the channels through which each component operates within the input-output framework, applicable to both sectoral output and value-added metrics. This study applies SDA to identify the potential channels that drive structural change across three broad sectors.

From Equation (10), it indicates that . This equation can be expressed in matrix form as follows:

Therefore, . To derive the matrix form for value-added shares, we divide the total value-added V across the three sectors. This can be articulated as: , where and ; represents the total value-added driven by sectoral final absorption.

Within the SDA framework, the variations of can be decomposed into changes across its three components L, and f. Given the discrepancies in the reference system, two distinct decomposition approaches are outlined below:

An alternative approach can be expressed as:

These two separate decomposing approaches ultimately yield the same outcome, as evidenced in the existing literature. Dietzenbacher and Bart [45] investigate these two approaches and contend that employing the average of the results derived from both approaches is an acceptable strategy, which is frequently utilized in literature. Consequently, we adopt the averaging approach and reformulate it to derive the final decomposition expression.

The aforementioned expression suggests that changes in sectoral value-added shares can be ascribed to the changes in primitive inputs, the structure of intermediate inputs, and final demand, referred to as primitive, intermediate and final respectively. Corresponding with the model we specify aforementioned, these three components are matched with labor input and intermediate goods input in production by firms, final output consumed by the household. Therefore, we build the bridge between model framework and SDA method, so as to underline the microeconomic mechanism for SDA method.

Baseline

Equation (10) demonstrates that both sectoral linkages and final absorption influence the value-added shares. In this study, we employ the aforementioned decomposition results to simulate the structural change occurring in China. The outcomes of this simulation are presented below and compared with the previously discussed data in Fig 4.

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Fig 4. Sectoral value-added shares: Baseline vs data.

The panels arranged from left to right illustrate the annual variations in sectoral value-added shares for agriculture, manufacturing and services. The dashed line depicts the model specified above, which is labeled as the baseline. The solid line depicts the actual data, which is calculated from WIOD.

https://doi.org/10.1371/journal.pone.0330908.g004

It can be found that the model successfully replicates the trend of structural change in China from 1978 to 2014. Fig 4 depicts a decline in the agricultural sector, a modest decline in manufacturing, and an increase in the services sector. This observation is consistent with the data. The model demonstrates a close correspondence with the data across all three sectors, with discrepancies in value-added shares between the simulated results and the actual data remaining within a margin of 1.5 percentage points throughout the entire period. Specifically, compared to 1978, the value-added share of agriculture has diminished by 17.38 percentage points, while the actual data indicate a reduction of 18.69 percentage points. In the manufacturing sector, the share has decreased by 1.94 percentage points, whereas the data reflect a decrease of 2.65 percentage points. The services sector has seen an increase of 19.32 percentage points, compared to the data showing a rise of 21.33 percentage points. Consequently, the basic model effectively captures the characteristics of structural change in China. It also highlights the significant role of sectoral interconnections in production and other contributing factors in this transformation process.

Counterfactual analysis

The basic model effectively captures the dynamics of sectoral shares in value-added, allowing us to identify the effects of input-output linkages and final absorption. We utilize the aforementioned methodology to conduct the counterfactual analysis. First, we will examine the former. Fig 5 presents the results of this analysis.

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Fig 5. Sectoral value-added shares: Constant linkages vs baseline.

The panels arranged from left to right illustrate the annual variations in sectoral value-added shares for agriculture, manufacturing and services. The dashed line represents a scenario in which the linkage parameters are set to their initial values, while all other parameters and variables remain constant. The solid line is depicted from the baseline model.

https://doi.org/10.1371/journal.pone.0330908.g005

The findings indicate that the sectoral shares in value-added exhibit only minor fluctuation when sectoral linkages are maintained at their initial levels, a trend that is less pronounced than that observed in the baseline scenario. Specifically, Fig 5 illustrates a slight reduction in the share of agriculture, while the shares of manufacturing and services remain relatively stable. The changes in value-added shares for agriculture, manufacturing, and services from 1978 to 2014 are recorded as −11.35, 7.91, and 3.45 percentage points, respectively, compared to −17.38, −1.94, and 19.32 in the baseline. This suggests that sectoral linkages contribute to a 34.68% (6.03/17.38) decline in the agricultural share and an 82.15% (15.87/19.32) increase in the services sector. Notably, the manufacturing sector displays a slight upward trend, diverging from the decline indicated in the baseline scenario. This distinction is critical for comprehending structural changes within this sector.

In summary, sectoral linkages exert a significant influence on structural change arising from the intermediate absorption of production process across sectors. What cannot be overlooked is that the importance of input-output linkages for manufacturing development.

Next, we investigate the impact of final absorption on this issue. We employ the same methodology previously discussed. Fig 6 illustrates the results.

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Fig 6. Sectoral value-added shares: Constant productivity vs baseline.

The panels arranged from left to right illustrate the annual variations in sectoral value-added shares for agriculture, manufacturing and services. The dashed line represents a scenario in which sectoral productivity is set to their initial values, while all other parameters and variables remain constant. The solid line is depicted from the baseline model.

https://doi.org/10.1371/journal.pone.0330908.g006

The counterfactual analysis reveals that sectoral shares in value-added vary differently when their productivity remain constant. Specifically, there is a slight decline in the agricultural sector, a pronounced decline in the manufacturing sector, and an increase in the services sector, as depicted in Fig 6. The changes in value-added shares for these three sectors from 1978 to 2014 are −11.71, −15.34, and 27.27 percentage points respectively, compared to −17.38, −1.94 and 19.32 in the baseline. This evidence further supports the notion of Baumol's cost disease affecting the manufacturing and services sectors, which can be attributed to their initial productivity gaps. This analysis indicates that, in the absence of technological advancements in sectoral productivity, the manufacturing share would experience a significant decline, while the services sector's share would see a substantial increase. In conclusion, sectoral productivity is crucial in affecting the final absorption through the pricing of final goods during the structural change, thereby highlighting their importance for industrial development.

Robustness check

In this section, we employ the methodology mentioned above to check the robustness of our model specification results from two distinct dimensions: (1) different preference specification and (2) different production function specification.

Initially, we modify the preference specification and then simulate the dynamics and conduct the counterfactual analysis. The results from this preference specification indicate no obvious differences in the dynamics of sectoral value-added shares and the counterfactual outcomes when compared to the baseline model. Specifically, the changes in the three sector shares from 1978 to 2014 are recorded as −17.23, −2.07, and 19.31 percentage points from 1978 to 2014, compared to −17.38, −1.94, and 19.32 in the baseline. This suggests that sectoral linkages and productivity continue to be vital factors driving structural change. When the sectoral linkage parameters are set to their initial values, the observed changes in shares are −11.22, 7.79, and 3.44 percentage points, compared to −11.35, 7.91, and 3.45 in the baseline. Furthermore, when adjusting the sectoral productivity to its initial values, the changes in shares are −11.59, −15.4, and 27.21 percentage points, compared to −11.71, −15.34, and 27.27 in the baseline. Overall, the analysis reveals no significant differences between the two driving forces examined within this preference specification.

Subsequently, we replace the Cobb-Douglas production function with an alternative specification. The same methodology as described above is employed to derive the calibration function for the two elasticity parameters and corresponding general equilibrium functions. We then simulate the dynamics of value-added shares and conduct the counterfactual analysis as previously described. Under this new production function specification, the simulation results indicate that the value-added shares of the three sectors have changed by −18.67, −5.43, and 12.32 percentage points from 1978 to 2014, compared to −17.38, −1.94, and 19.32 in the baseline. Additionally, when the sectoral linkage parameters are set to their initial values, the changes in shares are reported as −11.15, 8.5, and 4.78 percentage points, in contrast to −11.35, 7.91, and 3.45 in the baseline. Moreover, when the sectoral productivity is adjusted to its initial values, the changes in sector shares are −12.73, −18.06, and 22.22 percentage points, compared to −11.71, −15.34, and 27.27 in the baseline. The specification of the CES production function similarly yields no significant differences between the two driving forces.

In summary, we conduct robustness checks by altering the preference and production specifications. There are no significant differences between these specifications and the baseline model in terms of simulation and counterfactual analysis. This finding reinforces our assertion about the functions of sectoral linkages and productivity in the structural change.

Mechanism test

The counterfactual analysis and robustness checks presented above substantiate the significance of sectoral linkages. To further investigate the underlying mechanism, we take the methodology employed from the mechanism test design. The results are depicted in Fig 7 below.

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Fig 7. The Downstream network effect on three sectors.

The panels arranged from left to right illustrate the annual variations of downstream network effect on agriculture, manufacturing and services for four countries mentioned above.

https://doi.org/10.1371/journal.pone.0330908.g007

Fig 7 demonstrates that sectoral linkages can bring in sectoral value-added growth through downstream network effect, given equivalent sectoral productivity growth. This phenomenon is pronounced in the agricultural sector within China and South Korea, where agricultural development increasingly relies on productivity growth in the other two sectors. In contrast, the manufacturing sector does not show an evident upward or downward trend and remains stable across these four countries. However, it exhibits a higher absolute value in China, indicating that the Chinese manufacturing sector constructs stronger interconnections with the other two sectors. The services sector displays varied dynamic patterns across these four countries. Notably, the Chinese services sector demonstrates the most substantial downstream network effect. This suggests that productivity growth in the other two sectors, particularly in manufacturing, can propagate downward to the services sector, with this effect being magnified through the established sectoral linkages.

In summary, we examine the underlying mechanism of sectoral linkages, represented as downstream network effect, in the dynamics of sectoral value-added shares. The decomposition of sectoral value-added is made within a general equilibrium framework utilizing mathematical tools, followed by a counterfactual analysis. Our findings highlight considerable sectoral heterogeneities through cross-country comparisons. Specifically, in the context of China, all three sectors demonstrate stronger interconnections, whereby sectoral productivity growth exerts a more pronounced amplifying effect through these connections.

Detecting driving forces via SDA

In this section, we analyze the function of different components of sectoral value-added shares through SDA method, which is based on input-output analysis. The decomposition approach previously described is applied to the sample data, allowing for an evaluation of the contributions of three distinct factors. The findings are summarized in Table 2.

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Table 2. Factor contributions for structural change in China, The United States, Japan and South Korea^a.

https://doi.org/10.1371/journal.pone.0330908.t002

Firstly, this study examines the individual impacts of these three factors. In comparison to the beginning of Chinese economic reforms in 1978, the contribution of primitive inputs has markedly decreased, particularly in comparison to three other countries. This decline reflects, to a certain extent, the industrial upgrading across three sectors. The reallocation of resources along both sides of the product chain at a micro-level induces the macro-level downward trend of primitive inputs. Meanwhile, sectoral linkages, represented by intermediate inputs, are increasingly critical. This finding supports our previous assertions of sectoral linkages, particularly within the manufacturing and services sectors. Furthermore, although final demand remains relatively stable, its significance should not be overlooked throughout this process.

Lastly, this study examines the impacts of these three factors within the sector. In the agricultural sector, the changes of these three factors occur simultaneously with its value-added share. This phenomenon is observable in both the Japanese and South Korean agricultural sectors. It is apparent that the final demand exerts the greatest influence, followed by the primitive inputs. This finding is closely associated with the production characteristics inherent to this sector. Agricultural production begins with the input of various resources to organize the production process, and the products are primarily sold directly to households and enterprises, both within and outside the sector. Consequently, there are relatively few interconnections with other sectors, which may explain why the intermediate inputs contribute a minimal amount.

In contrast, the manufacturing sector has witnessed a significant reduction in primitive inputs since 1978, as evidenced by the data presented in the table. During this period of development in China, it is widely recognized that Chinese manufacturing sector has become increasingly integrated into global production networks. Enterprises have engaged more with one another throughout the industrial upgrading process, both within the sector and outside. As a result, there has been a substantial increase in intermediate inputs, which counters the trend in value-added share and enhances its importance within the production framework.

Similarly, South Korea has also undergone more pronounced structural change compared to the United States and Japan during the same period. The data indicates that the intermediate inputs function like China during its manufacturing expansion. The final demand also holds considerable importance. As China's GDP per capita rises alongside its economic growth, a growing number of households are able to access a wider variety of products from the manufacturing sector. This trend is a natural consequence of the demand-driven effect associated with structural change. In contrast, the final demand exhibits a declining trend in the other three countries. Given their transition towards more service-oriented economies, the importance of manufacturing has become somewhat less significant.

The services sector is heavily dependent on sectoral linkages, as demonstrated by the dynamics of intermediate inputs. It is well established that services production require the exchange of substantial goods and information both within the sector and externally, thereby relying on sectoral linkages. Additionally, certain subindustries of this sector are directly connected to households, which amplifies the impact of final demand. When comparing China to other countries, it becomes apparent that intermediate inputs are more important in the growth of Chinese services sector, whereas the influence of final demand is more pronounced in the other three countries. This observation suggests distinct patterns of sectoral development. The growth of services in China demonstrates a high degree of reliance on sectoral linkages, while the other three countries exhibit a stronger connection to final demand.

The results of the structural decomposition analysis are consistent with our findings in the baseline. The intermediate inputs across three broad sectors exhibit similar patterns to their value-added shares within an economy throughout different stages of the structural change process. The growth and expansion of China's manufacturing and services sectors increasingly rely on sectoral linkages, thereby enhance their workforce in China's structural change process.