Analysis of the status of the division of labor in global value chains based on data empowerment

Assume that there are only two production sectors, intermediate and final, and that the final product is produced by feeding only intermediate goods. Each of these two intermediate goods production sectors is denoted by subscript k = {1, 2}. On the supply side, production using the constant elasticity of substitution technique is modeled as: 4Qt=[ ω11αQ1tα−1α+ω21αα−1αα ]α/(α−1)$${Q_t} = {\left[ {\omega _1^{{1 \over \alpha }}Q_{1t}^{{{\alpha - 1} \over \alpha }} + \omega _2^{{1 \over \alpha }}{{\alpha - 1} \over {{\alpha \over \alpha }}}} \right]^{\alpha /(\alpha - 1)}}$$ where Q_t represents the quantity of final finished goods, Q_kt represents the quantity of inputs of intermediate goods, and subscript t represents time. Parameters ω₁, ω₂ ∈ (0,1) and ω₁ + ω₂ = 1. Parameter α ∈ [0,∞) represents the elasticity of substitution in the intermediate goods production sector.

Meanwhile, on the demand side, a monopolistic competition model with fixed elasticity of substitution is constructed: 5Dn=(pn−σGVCnσ−1(P°)1−σ)×E$${D_n} = \left( {{{p_n^{ - \sigma }GVC_n^{\sigma - 1}} \over {{{\left( {P^\circ } \right)}^{1 - \sigma }}}}} \right) \times E$$ where D_n represents the demand for the n product; p_n represents the price of the n product, p is the price index; GVC_n represents the index of the international division of labor position in the global value chain of the n product; σ represents the elasticity of substitution between products, and σ ∈ (1,+∞), E are exogenous consumption expenditures. And where P° is satisfied: 6P°=[ ∫pn1−σλGVCnσ−1dn ]1/(1−σ)$$P^\circ = {\left[ {\int {p_n^{1 - \sigma }} \lambda GVC_n^{\sigma - 1}dn} \right]^{1/(1 - \sigma )}}$$

To simplify the analytical results, here let P = (P°)^1–σ, then D_n can be expressed as: 7Dn=(pn−σGVCnσ−1P)×E$${D_n} = \left( {{{p_n^{ - \sigma }GVC_n^{\sigma - 1}} \over P}} \right) \times E$$

It can be seen that the demand for product n is positively correlated with the GVC position index GVC_n of that product, i.e. the higher the GVC position index of product n, the relatively higher the demand for product n. The GVC international division of labor position index is related to the export domestic value added of the product and the export complexity of the product. Production in the two sectors is assumed to be differentiated, resulting from production efficiency and technology level T. Production efficiency is expressed in terms of marginal cost of production, which is inversely correlated, and the two are specifically expressed as follows: 8MC(GVC,ξ)=(cξ)×GVCγmc$$MC\left( {GVC,\xi } \right) = \left( {{c \over \xi }} \right) \times GV{C^{{\gamma _{mc}}}}$$

Where c is a constant, γ_mc represents the elasticity of marginal cost, and T represents the technological level of the sector. The higher the technological level of the sector’s production, the higher the output obtained for the same cost; in other words, the higher the technological level of the sector’s production, the lower the cost of its inputs for the same output. Thus, the cost of fixed inputs required for the production of a product is denoted by λ: 9FC(GVC,T)=(fT)×GVCγfc+FC0$$FC(GVC,T) = \left( {{f \over T}} \right) \times GV{C^{\gamma fc}} + F{C_0}$$ where f is a constant, γ_fc represents the elasticity of fixed production costs, γ_fc ∈ (0,∞); FC₀ represents the initial cost of production.

Combining the above formulas, the position of the international division of labor in the global value chain can be expressed as: 10GVC(ξ,T)=[ 1−γmcγfc×Tf×(1−1σ)σ×(ξc)σ−1×EP ]1//γfc−(1−γmc)(σ−1) }$$GVC\left( {\xi ,T} \right) = {\left[ {{{1 - {\gamma _{mc}}} \over {{\gamma _{fc}}}} \times {T \over f} \times {{\left( {1 - {1 \over \sigma }} \right)}^\sigma } \times {{\left( {{\xi \over c}} \right)}^{\sigma - 1}} \times {E \over P}} \right]^{\left. {1//{\gamma _{fc}} - \left( {1 - {\gamma _{mc}}} \right)(\sigma - 1)} \right\}}}$$

Eq. γ_fc–(1–γ_mc)(σ–1) > 0. rrom the expression, it can be found that product productivity and product production technology have a direct impact on the international division of labor status. And the industry will improve the allocation efficiency of all kinds of factor resources because of the penetration of its digital technology, and then enhance the production efficiency. This paper establishes a model of the impact of digital economic development on production: 11ξ=(∫01XIρdi)1/ρ$$\xi = {\left( {\int_0^1 {X_I^\rho } di} \right)^{1/\rho }}$$

Where X represents the factors of production to be invested to improve productivity, ρ represents the alternative parameters of factors of production, ρ ≤ 1 and ρ ≠ 0. There are various factors affecting productivity, and in this study, the factors affecting productivity are classified into two main categories, one from digitization technology and one from non-digitization technology. ξ Where X = A denotes the portion of productivity increase made possible by digitization technology and X = NA denotes the portion of productivity increase not made possible by digitization technology, there are: 12X={ AUpgradedbydigitaltechnologyNAUpgradedbynon-digitaltechnology$$X = \left\{ {\matrix{ A & {Upgraded{\rm{ }}by{\rm{ }}digital{\rm{ }}techno\log y} \cr {NA} & {Upgraded{\rm{ }}by{\rm{ }}non - digital{\rm{ }}techno\log y} \cr } } \right.$$

According to equations (11) and (12), the productivity ξ function is expressed as: 13ξ=[ θ(Aθ)ρ+(1−θ)(NA1−θ)ρ ]1/ρ$$\xi = {\left[ {\theta {{\left( {{A \over \theta }} \right)}^\rho } + (1 - \theta ){{\left( {{{NA} \over {1 - \theta }}} \right)}^\rho }} \right]^{1/\rho }}$$

Similarly, the theoretical model that portrays the impact of digital development on the level of technology: 14T=(∫01XIμdi)1/μ$$T = {\left( {\int_0^1 {X_I^\mu } di} \right)^{1/\mu }}$$ where μ represents the substitution parameter of the factors of production, μ ≠ 1 and μ ⊕ 0. rurther the function of productivity ξ is expressed as: 15T=[ φ(Aφ)μ+(1−φ)(NA1−φ)μ ]1/μ$$T = {\left[ {\varphi {{\left( {{A \over \varphi }} \right)}^\mu } + (1 - \varphi ){{\left( {{{NA} \over {1 - \varphi }}} \right)}^\mu }} \right]^{1/\mu }}$$

Combining the above equations while assuming that both ρ and μ converge infinitely to 0, we have: 16GVC(A)={ 1−γmcγfc×(1−1σ)σ×(NA)μA1−μf×[ [ (NA)ρA1−ρ C ]σ−1EP }1γfc−(1−γmc)(σ−1)$$GVC\left( A \right) = {\left\{ {{{1 - {\gamma _{mc}}} \over {{\gamma _{fc}}}} \times {{\left( {1 - {1 \over \sigma }} \right)}^\sigma } \times {{{{(NA)}^\mu }{A^{1 - \mu }}} \over f} \times {{\left[ {{{\left[ {{{(NA)}^\rho }{A^{1 - \rho }}} \right.} \over C}} \right]}^{\sigma - 1}}{E \over P}} \right\}^{{1 \over {{\gamma _{fc}} - \left( {1 - {\gamma _{mc}}} \right)(\sigma - 1)}}}}$$ From Eq. ∂GVC(A)/∂A > 0. Based on the above quantitative derivation, it can be found that the development of digital economy helps to advance the climb of the international division of labor position in the global value chain, which will be verified in the research of this paper.

The ADB-MRIO database [19] is an important tool for the study of global value chains constructed by the Asian Development Bank and contains input-output data for 35 production sectors in 62 major global economies. Since the database does not publish the latest data for 2024, the value added decomposition data based on ADB-MRIO calculations from the UIBE database is used in this part. In this paper, data cleaning and sectoral merging are carried out, on the basis of which the GVC forward participation index, GVC backward participation index and GVC division of labor status index of different types of industries are measured, and the data year interval is 2010-2023. The countries studied mainly include China, Japan, South Korea, New Zealand, Australia, Indonesia, Singapore, Thailand, Malaysia, Vietnam, the Philippines, Brunei, Laos, Myanmar, and Cambodia. ADB-MRIO does not list the input-output data of New Zealand and Myanmar individually, so New Zealand and Myanmar are not included in the research scope of this paper.

This section measures the digital economy development level of 13 countries from 2010-2023, and the overall measurement of the digital economy development level is shown in Figure 2. Singapore’s digital economy development level is basically stable at the forefront, followed by South Korea, but the gap gradually widens after 2015, gradually stabilizing Singapore’s leading position in the world in terms of digital economy development capability. Among the 13 sample countries, 5 countries (China, Singapore, Australia, Japan, and South Korea) have a digital economy development level index that exceeds the sample average (0.332) by 2023. Among them, except for China (0.587), which is a developing country, the other four countries (0.675, 0.396, 0.446, 0.591) are developed countries, while the level of digital economy development in developing countries (0.160-0.275) are below the average. As a result, it is evident that the level of development of the digital economy varies significantly from country to country. However, as a whole, the level of development of digital economy in all countries is showing a clear upward trend, indicating that there is a large potential for the development of the digital economy in all countries, but there are significant differences in the level of development of the digital economy between different countries, in particular, the contrast between the top and latecomer economies is still large.

Figure 2.

Digital economic development level index