Digitalization and economic growth in the new classical and new structural economics perspectives

Abstract

This paper introduces ‘data elements’ into a neoclassical general equilibrium model and the new structural general equilibrium model to study the choice of economic growth paths for developing countries. It derives and compares a general expression for the economic growth rate in equilibrium within the two analytical frameworks following the introduction of digital development comprising primarily the data elements. Additionally, the optimal economic growth path for developing countries before and after the introduction of data elements under both frameworks is identified with important policy implications regarding direct technological progress with respect to the two alternative general equilibrium frame works. This study finds that: (1) No matter what kind of general equilibrium corresponding economic growth path the developing countries choose, the economic growth rate after the introduction of data elements will always be higher than before. (2) Developing countries find the optimal path of economic growth by comparing the different results of economic growth rates under the two analytical frameworks. This paper aligns with a view that when developing countries choose the path of economic growth, they need to combine their own endowment conditions and choose a new structural economics analysis framework for decision-making.

1 Introduction

Economic growth is a prerequisite for development. Therefore, governments of all countries attach great importance to economic growth. The neoclassical growth model and the new structural growth model are tools for exploring the sources of economic growth. The neoclassical growth model is the mainstream method, However, it has shortcomings in setting the production structure and in explaining the economic growth of developing countries. For example, the logic system of explaining economic growth by assuming the exogenous optimal structure, or taking the structure of developed countries as the only structure, has been criticized; The economic data of developed countries support the conclusion that the technological progress gap emphasized by the neoclassical growth model is the cause of the transnational income gap, However, the economic data of developing countries do not support the conclusion that the technological progress gap emphasized by the neoclassical growth model is the cause of the transnational income gap, which contributed to the emergence of the new structural growth theory. According to the new structural growth theory, structural change will lead to the upgrading of any factor endowment structure and promote economic transformation and economic growth.

While the new structural economics growth model has been newly developed based on the experiences and practices of some late-coming economies such as China. In the process of economic growth, the choice of economic growth path will inevitably affect the speed of economic growth, and different economic growth paths will generate different effects. These matters are explored formally in this paper with appropriate consideration of digital development featuring with big data.

With the rapid development of the digital economy, the input of new production factors – ‘data factors’ will cause changes in the production process driven by differentiated technological innovations. How does this feature of economic growth affect the determination of general equilibrium in the neo classical economics model and the general equilibrium in the new structural economics model? What kind of analytical framework is preferred in the digital economy era? To answer these problems, this study introduces the data elements into the two above-mentioned economic growth frameworks, and compares the impact of two economic growth paths—neoclassical and new structural general equilibria. In the case of the neo classical model economic growth rate is accelerated by improving total factor productivity, and in the case of the new structural economics model economic growth rate is improved through boosting total factor productivity in combination with structural changes driven by country-specific natural resource endowments. More specifically, we study the factors influencing economic growth rate under two general equilibrium frameworks by introducing digital development comprising primarily the data elements, to obtain the optimal choice under a balanced economic growth path.

At present, most of the literature on the source of economic growth is based on a neoclassical economics theoretical perspective, and most of the empirical research is based on the premise of expanding input factors and improving the level of technology, and it ignores that structural change is the core issue of developing countries. There are far fewer contributions on (i) the use of a general equilibrium model in a new structural economics setting and (ii) comparisons of neoclassical and new structural analytical frameworks to analyze the sources of economic growth. This study contributes to this gap in the extant literaturein three specific respects: (1) the key production factors in the digital economy era are introduced into a general equilibrium model in the neoclassical economics tradition and the general equilibrium model of new structural economics. This enables us to obtain a more general result in line with economic growth in the digital economy era. (2) the impact of data elements on economic growth is studied under two analytical frameworks. (3) comparing the optimal economic growth path choice of developing countries under different analytical frameworks and discussing the applicability of findings from the model under the conditions of biased technological change progress. The results suggest that there are some considerable advantages in using the new structural economics general equilibrium model as compared to the traditional neoclassical model. Additionally, this study seeks to help to clarify some possible misunderstandings in the use of the new structural economics general equilibrium model which may help support its wider application.

2 Background literature

The model in this study is based on a general equilibrium model of new classical economics, taking the Ramsey-Cass-Koopmans model as an example, and a general equilibrium model in the new structural economics tradition. The mainstream body of modern economic growth theory is neoclassical growth theory and endogenous growth theory. This body of work fuses contributions by Harrod (1939), Domar (1946), Solow (1956), Romer (1986) and Lucas (1988) which offer explanations on the sources of economic growth and the differences in economic development levels between different countries. At its origin lies the work of Ramsey (1928) who proposed the idea of ‘endogenous savings’. It was Cass (1965) and Koopmans (1965) who modeled Ramsey’s thinking building on the Solow (1956) growth model. Thus, the benchmark analytical framework of modern economic growth theory is described as the Ramsey-Cass-Koopmans (RCK) model. The RCK model aroused strong debate in the academic community. Diamond (1965) broke through the infinite period assumption of the RCK model and proposed an overlapping generations model (OLG); Brock and Mirman (1972), Merton (1975) relaxed the underpinning deterministic growth hypothesis and proposed a stochastic growth framework. Some scholars have also expanded the two sector model to include a third government sector in the model. Krugman (1979), Grossman and Helpman (1991) relaxed the closed economy assumptions and expanded into an open economy framework model.

Fu (2017) proposes a new structural economics general equilibrium model with time-varying shares of capital output based on the characteristics of economic development for developing countries such as China. In the digital economy era, what changes might be expected from the RCK model outcomes as well as the new structural economics general equilibrium models? How might a country like China select its economic growth path? These matters are explored within this study. More recently, Jones and Tonetti (2020) constructed a benchmark model composed of consumers and enterprises, and analyzed and compared the equilibrium impacts on consumers’ equivalent welfare. It does so by introducing the data ownership of consumers, data intermediary enterprises and government bans on sales of data. Cong et al. (2021) considered the characteristics of endogenous consumption of data elements and the dynamic noncompetitive characteristics of data in the general equilibrium model composed of consumers, final product producers and intermediate product producers. On this basis, Cong et al. (2022) introduced data intermediaries and innovation departments, examined the multiple use of data, and finally concluded that the increase in data volume can achieve production growth. Tang et al. (2022) constructed a general equilibrium model including data elements to explain the relationship between digital economy development, market structure and innovation performance. Xu and Zhao (2020) introduced data capital into the supply side, built an economic growth model including data capital, ICT capital and traditional material capital, and analyzed the relationship between economic growth and data capital under a general equilibrium path for the two sectors. Cai et al. (2022) established a general equilibrium analysis framework incorporating data elements based on the generalized value theory. The above scholars have all discussed based on the general equilibrium model of new classical economics. Hitherto only Liu and Jia (2022a, b) has introduced data elements based on a general equilibrium model of new structural economics. This enabled study of the theoretical mechanism by which data elements drive economic growth. In addition to the above body of work, there are relatively few studies discussing data elements in a general equilibrium model setting.

Jones and Tonetti (2020) contends that data has a particular relationship with machine learning, privacy economics, and information economics. Cong et al. (2021) also believed that data has a relationship with information and privacy, such that it is difficult to characterize data. Even if the equilibrium solution for one country and two sectors is calculated, changes in a variable will also cause state changes, which are difficult to calculate. Further and more problematic is the fact that the current system of national accounts (SNA2008) does not specifically study the accounting of ‘data elements’ or ‘data assets’. It faces problems such as insufficient statistical indicators, lack of relevant basic data, and lack of effective measurement of data capital or digital investment. This makes it difficult to estimate the capital stock and scale of data elements and calibrate them according to real data. Therefore, the extant literature either adopts their own methods to measure or synthesize, or adopt existing exploratory methods for measurement. For example, Xu and Zhao (2020) selected a “data value chain” approach employed by the Canadian National Bureau of Statistics in 2019 to estimate China’s data capital stock in 2016–2019. Their result sare consistent with some subsequent numerical simulations. Cai et al. (2022) set different parameter values in line with theoretical assumptions, and simulated the contribution of different initial stock sizes of data to the absolute productivity of each time period. Li and Wang (2021) and Wang (2022) both built a data elements indicator system to verify the relationship between the development level of data elements and the development level of manufacturing industry. However, there is no (to our knowledge) relevant research on the estimation of the capital stock of the data elements included in the production function.

In addition to the general equilibrium framework, there are also a large number of studies on data elements and economic growth. In theory, Farboodi and Veldkamp (2021) built a data economy growth model and found that when an economy only accumulates data, the overall growth economics is similar to that of an economy that only accumulates capital. Although the income decreases, the income is bounded. Acemoglu et al. (2019) modeled the data market under the condition of platform sharing, proving that the data price is depressed due to their externalities in equilibrium, and further indicating that closing the data market improved (utilitarian) welfare conditions. This result can be extended to markets with multiple platforms. Liu and Jia (2022a, b) analyzed and compared the neoclassical growth (development) accounting and the new structural growth (development) accounting methods based on the neoclassical new production function and new structural production function that introduced data elements. Yang et al. (2021) uses mathematical analysis and empirical test methods to demonstrate that data elements can not only have a multiplier effect on other production factors, but also promote the increase of per capita output.

From the existing literature, whether from the perspective of new classical economics or new structural economics, there are different views on the path choice of economic growth, and the policy propositions do not fully align with each other. This paper seeks to clarify the similarities and differences between the new classical economics and the new structural economics models by comparing the different results of the two equilibrium models under ‘the digital conditions’, which are mainly composed of ‘data elements’. The method of obtaining the time-varying factor output share of the new structural economics is more general.

3 Model

The neoclassical growth model assumes that the production function is exogenous, that is, the relationship between input factors and output is a constant production function, in which the share of factor output is fixed. Obviously, this assumption is more in line with the reality of the developed countries than the developing ones, as in the latter, the shares of factor inputs in final output may change more significantly over time than in the former, so the relationship between inputs and final output may assume a very different form every year in the latter.

Fu (2017) finds that the shares of capital and labor in final output of South Korea and other countries are different from that of developed countries in the neoclassical growth model by one-third and two-thirds respectively. He then established a new structural economics growth model with a time-varying share of capital in final output in response to the doubt about the growth miracle of developing countries. He deduced the important impact of structural change on economic growth, and turned the neoclassical growth model into a special case of the new structural economics growth model. Furthermore, the general equilibrium model of new classical economics not only explains that TFP is the source of economic growth, but also gives the Kaldor model stylized fact that capital share and labor share in final output remain stable for a long time, which is consistent with the developed countries. The general equilibrium model of new structural economics not only explains that the changes of total factor productivity and production structure are the source of economic growth, but also derives the endogenous production function from the given endowment structure and the dynamic process of structural change, which is in line with the developing countries’ choice of comparative advantage based on their own endowment conditions to achieve the circular cumulative development of the upgrading of endowment structure and production structure. Although the introduction of the new structural economics model has made an important contribution to the literature, it has not taken digital development into account. Whether after introducing the data elements will still support the general argument of the new structural economics model still remains to be verified, this is why this study introduces digital development comprising primarily the data elements to redefine the general equilibria of both the new classical economics and the new structural economics.

3.1 Basic model under the general equilibrium framework

Based on the C-D production function, Solow (1957) analyses the source of economic growth. Following Solow’s approach, many economists have expanded their research using a similar general equilibrium model. This study also employs a similar production function model to analyze the similarities and differences between the new classical growth theory and the new structural growth theory.

To establish the basic models for analysis, the following assumptions are required.

• (1) The economy comprises only two sectors, the household sector and the production sector.

• (2) The household sector pursues the maximization of utility, obtains income by selling various elements it owns and uses them for consumption.

• (3) The production sector pursues the maximization of profits, and purchases the elements owned by the household sector as inputs and pays for them.

3.1.1 General equilibrium model of new classical economics

• (1) For the household sector the Utility maximization problem is defined in Eqs. (1) and (2).

  $$\mathop {{\text{max}}}\limits_{{c_{t} }} U_{t} = \int_{0}^{\infty } {e^{(n - \rho )t} } u(c_{t} )dt$$

  (1)

  subject to

  $${\dot{k}}_{t}=\left({r}_{t}-n-{\delta }_{t}\right){k}_{t}+{w}_{t}-{c}_{t}\,\mathrm{and}\,{k}_{t+1}={i}_{t}+\left(1-{\delta }_{t}-n\right){k}_{t}$$

  (2)

  where, c_t represents consumption per person, u(c_t) the instantaneous utility function, In the classic CRRA form,n the population growth rate, and ρ the subjective discount rate, i_t per capita investment, k_t capital per person stock, and δ_t capital depreciation rate. The household sector will maximize its own utility U_t by selecting the consumption level c_t under budget constraints.

• (2) Production sector

  The responding profit maximization problem is defined in Eqs. (3) and (4).

  $${\text{max}}\pi_{t} = pY_{t} - r_{t} K_{t} - w_{t} L_{t}$$

  (3)

  subject to

  $$A_{t} K_{t}^{\alpha } L_{t}^{1 - \alpha } \le Y_{t}$$

  (4)

  The production sector will maximize profit π_t by selecting capital K_t and labor L_t. Y_t represents total output. r_t and w_t denote the prices of capital and labor respectively. A_t signifies neutral technological progress, α and 1-α represent the output elasticities of capital and labor output respectively. Without losing generality, the product price p is standardized to 1. From Formula (3)–(4), the optimal factor demand and dynamic price system can be further obtained.

• (3) For market clearing

  $$\dot{g}_{c} = 0\;{\text{and}}\;\dot{g}_{k} = 0$$

  (5)

  In the general equilibrium state, the market clearing, as shown in formula (5), can be solved to obtain the general expressions of balanced consumption growth rate, capital growth rate and output growth rate.

3.1.2 General equilibrium model of new structural economics

Household sector behavior in the general equilibrium model of new structural economics is similar to that in the general equilibrium model of new classical economics, and its consumption behavior is as defined by Eqs. (1) and (2).

The analysis of the production sector is different from that of the new classical economics. The new structural economics puts forward the hypothesis that the capital production structure is a time-varying variable, that is, the capital output share has different values in different periods, which generates the optimal production function. The production department will minimize the cost by selecting the optimal input level C_t as shown in Eq. (6).

$$\min C_{t} = r_{t} K_{t} + w_{t} L_{t}$$

(6)

subject to

$$A_{t} K_{t}^{{\alpha_{t} }} L_{t}^{{1 - \alpha_{t} }} \ge Y_{t}$$

(7)

where, α_t is the capital production structure, that is, the share of capitaloutput, indicating that there are different values in different periods.

The market clearing condition is defined in Eq. (8).

$$\dot{g}_{c} = 0\;{\text{and}}\;\dot{g}_{k} = 0,\;\dot{\alpha }_{t} = 0$$

(8)

In the general equilibrium state, the market clearing, as shown in Eq. (8), can be solved to obtain the general expressions of balanced consumption growth rate, capital growth rate, output growth rate and optimal capital production structure.

3.2 An extended model under a general equilibrium framework

The factors of production evolve and change overtime. Li and Zhou (2020) summarizes the history of the changes in the factors of production. In the era of agricultural economy, the most important factors of production were land and labor; After the industrial revolution, it became capital; At the beginning of the 20th century, entrepreneurship was emphasized; In the third industrial revolution, it became technology; In the era of digital economy, the key factor of production is data. The data elements defined in this paper are the essential data using information communication technology and modern information network as the carrier. The combination of data and ICT capital can play a role in the production function in two aspects: first, data elements are different from traditional production factors such as labor, capital, etc. It has new features, such as non competitiveness, zero marginal cost, externality, timeliness, etc. These features enable data elements to play an important role in production that traditional factors cannot match, it is mainly reflected in that data elements can not only directly promote economic growth as a production factor. Itcanalso directly improve the micro efficiency of enterprises by reducing information asymmetry in production and enhancing coordination among factors through the information carried by data itself. It can also improve the accumulation efficiency of data elements, that is, improve data analysis and processing capacity, change the production structure, promote the change of endowment structure and indirectly promote macroeconomic growth. Second, it may indirectly promote economic growth by increasing the construction of digital infrastructure.

Data elements are brought into the general equilibrium model to explore the impact of new production factors on economic growth in digitalizationprocess.To do so, another assumption needs to be made as follows.

Assumption 2: There are two ways for developing countries to improve their economic growth in the digitalization developmentprocess. (1) Based on the general equilibrium analysis framework of new classical economics, one can increase the input of data factors and improve total factor productivity to promote economic growth. (2) Based on the general equilibrium analysis framework of new structural economics, in addition to the growth path of new classical economics, there can be some economic growth brought about by changes to the capital production structure and data production structure.

With the continuous development and growth of the digital economy, data elements as a new input factor and data elements driven structural changes have become two important sources of economic growth.

In the following expanded model, this study adopts the assumptions of Xu and Zhao (2020), Liu and Jia (2022a, b), Cai et al. (2022), and assumes that the data elements are owned by the family sector. Cong et al. (2021, 2022) assumed that data elements were owned by intermediate departments or data intermediaries, while Jones and Tonetti (2020) analyses the ownership of data elements by consumers and data intermediary enterprises. In order to simplify the model, only capital, labor and data elements are considered in the new model, and other input elements such as land are not consideredfor simplification purpose. This is consistent with the two benchmark models mentioned above.

The introduction of data elements leads to changes in the market. After the introduction of data elements, the production sector needs to purchase data elements from the household sector to improve its output. Compared with the aforementioned general equilibrium model, only the budget constraints of the household sector change the production function and cost function of the production sector. First, the income level of the household sector changes because of the new data elements added to the factor supply of the household sector. Second, in terms of profit, the production function changes because the production department increases the input of data elements, and the cost function changes because the production department needs to pay data elements to the family department.

3.2.1 Extension of the general equilibrium model of new classical economics

• (1) For the household sector the utility maximization problem can be defined in Eqs. (3) and (9).

  $$\dot{k}_{t} = \left( {r_{t} - n - \delta_{t} } \right)k_{t} + w_{t} + b_{t} d_{t} - c_{t} \;{\text{and}}\;k_{t + 1} = i_{t} + \left( {1 - \delta_{t} - n} \right)k_{t}$$

  (9)

  After the introduction of data elements, the household sector is paid via its own capital, labor and data elements. It is believed that after the introduction of data elements,$r_{t} K_{t} + w_{t} L_{t} \le r_{t} K_{t} + w_{t} L_{t} + b_{t} D_{t}$, that is, the income of the household sector for consumption is higher than when the data elements is not included. At this time, the optimal consumption growth rate of the household sector after the introduction of data elements can be obtained.

• (2) For the Production sector the profit maximization problem can be defined as in Eqs. (10) and (11).

  $$\max \pi_{t} = pY_{t} - r_{t} K_{t} - w_{t} L_{t} - b_{t} D_{t}$$

  (10)

  subject to

  $${A}_{t}{K}_{t}^{\alpha }{L}_{t}^{1-\alpha -\beta }{D}_{t}^{\beta }\le {Y}_{t}$$

  (11)

  The production sector affects the cost and output by adding data elements. Among them, D_t represents the input amount of data elements, b_t represents the price of data. α, β and 1-α-β represent capital output share, labor output share and data output share respectively. The capital per person factor demand function, per capita data factor demand function, factor price system, and capital per person growth rate can be obtained from the optimal production conditions after the introduction of data elements.

3.2.2 Expansion of the general equilibrium model of new structural economics

• (1) Household behavior

  After the introduction of data elements, the family behavior in the general equilibrium model of new structural economics is still the same as that in the general equilibrium of new classical economics, as shown in Eqs. (3) and (9).

• (2) Production sector

  $$\min C_{t} = r_{t} K_{t} + w_{t} L_{t} + b_{t} D_{t}$$

  (12)

  subject to

  $$A_{t} K_{t}^{{\alpha_{t} }} L_{t}^{{1 - \alpha_{t} - \beta_{t} }} D_{t}^{{\beta_{t} }} \ge Y_{t}$$

  (13)

  After introducing data, the optimization of production sectors in the general equilibrium of new structural economics is defined in Eqs. (12) and (13). Among them, (K_t, L_t, D_t) is used to describe the supply of factor endowments for capital, labor and data. Following Fu (2017), it is assumed that (K_t, L_t, D_t) remains unchanged in period t, but will change with the inter-period decision of manufacturers. α_t, β_t refer to the capital production structure and data production structure determined by manufacturers to maximize profits. They represent the optimal production structure that manufacturers can achieve under the factor endowment structure in period t. At this point, we can get the capital factor demand function, data factor demand function, factor price system and capital per person growth rate after the introduction of data.

3.3 General equilibrium calculation results

According to the two different analysis frameworks, different general equilibrium results can be obtained. Under the conditions of general equilibrium, both the production sector and the household sector achieve their own general equilibrium state, and each endogenous variable also has a steady value.

3.3.1 Scenario 1-1 General equilibrium calculation results of new classical economics without data elements

When data elements are not introduced, it can be obtained from Eqs. (1)–(5) that the economic growth rate of a country is related to the relative size of technological progress and capital output share.

• (1) When the consumption per person growth rate is defined in Eq. (14), the household sector maximizes its utility.

  $$g_{c} = \frac{{\dot{c}_{t} }}{{c_{t} }} = \frac{{\alpha A_{t} k_{t}^{\alpha - 1} - \delta_{t} - \rho }}{\sigma }$$

  (14)

• (2) When the demand function of capital element and the demand function of labor factor are ${K}_{t}^{D}=\left({Y}_{t}/{A}_{t}\right){\left\{\left[{r}_{t}\left(1-\alpha \right)\right]/{w}_{t}\alpha \right\}}^{\left(\alpha -1\right)}$ and ${L}_{t}^{D}=\left({Y}_{t}/{A}_{t}\right){\left\{\left[{r}_{t}\left(1-\alpha \right)\right]/{w}_{t}\alpha \right\}}^{\alpha }$, and the dynamic price evolution mechanism is $g_{w} = \dot{w}_{t} /w_{t} = g_{A} + \alpha g_{k}$, $g_{r} = \dot{r}/r = g_{A} - (1 - \alpha )g_{k}$, the capital per person growth rate is defined in Eq. (15), and the production department maximizes profits.

  $${g}_{k}=\frac{{\dot{k}}_{t}}{{k}_{t}}={A}_{t}{k}_{t}^{\alpha -1}-n-{\delta }_{t}-\frac{{c}_{t}}{{k}_{t}}$$

  (15)

• (3) When the change rate of consumption per person growth rate and capital per person growth rate is zero, that is, ġ_c = 0 and ġ_k = 0, the general equilibrium between the two sectors will be achieved.In general equilibrium, the consumption per person growth rate, capital per person growth rate and per capita output growth rate are shown in Eq. (16).

  $${g}_{y}^{*}={g}_{c}^{*}={g}_{k}^{*}=\frac{{g}_{A}}{\text{1} - {\alpha }^{*}}$$

  (16)

Given the values of two kinds of exogenous variables, namely technology level A and capital output share α, we can get the growth rate of consumption per person, capital per person and per capita output in the steady state.

From the above equilibrium results, we get proposition 1.

Proposition 1 When there is no data element, an increase in the technological progress rate or the share of capital output will lead to an increase in the output growth rate. $\partial {g}_{y}^{*}/\partial {g}_{A}=1/(\text{1} - {\alpha }^{*})>0$, $\partial {g}_{y}^{*}/\partial {\alpha }^{*}={g}_{A}/{(\text{1} - {\alpha }^{*})}^{2}>0$.

3.3.2 Scenario 1-2 General equilibrium calculation results of new classical economics when data elements are introduced

When introducing data, it can be seen from Eqs. (3), (5), (9)–(11) that the economic growth rate of a country is related to technological progress, capital input share, data input share and the relative size of data accumulation rate.

• (1) When consumption per person growth rate is defined in Eq. (17), the household sector maximizes its utility.

  $$g_{c} = \frac{{\dot{c}_{t} }}{{c_{t} }} = \frac{{\alpha A_{t} k_{t}^{\alpha - 1} d_{t}^{\beta } - \delta_{t} - \rho }}{\sigma }$$

  (17)

• (2) When the capital element demand function and data elements demand function are $K_{t}^{D} = (Y_{t} /A_{t} )(r_{t} /\alpha )^{\alpha - 1} (b_{t} /\beta )^{\beta } [(1 - \alpha - \beta )/w_{t} ]^{\alpha + \beta - 1}$, $L_{t}^{D} = (Y_{t} /A_{t} )(r_{t} /\alpha )^{\alpha } (b_{t} /\beta )^{\beta } [(1 - \alpha - \beta )/w_{t} ]^{\alpha + \beta }$ and $D_{t}^{D} = (Y_{t} /A_{t} )(r_{t} /\alpha )^{\alpha } (b_{t} /\beta )^{\beta - 1} [(1 - \alpha - \beta )/w_{t} ]^{\alpha + \beta - 1}$ respectively, and the dynamic price evolution mechanism is $g_{w} = \dot{w}_{t} /w_{t} = g_{A} + \alpha g_{k} + \beta g_{d}$,$g_{r} = \dot{r}/r = g_{A} - (1 - \alpha )g_{k} + \beta g_{d}$, and $g_{b} = \dot{b}_{t} /b_{t} = g_{A} + \alpha g_{k} - (1 - \beta )g_{d}$, the capital per person growth rate is Eq. (18), and the production department maximizes profits.

  $$g_{k} = \frac{{\dot{k}_{t} }}{{k_{t} }} = A_{t} k_{t}^{\alpha - 1} d_{t}^{\beta } - n - \delta {}_{t} - \frac{{c_{t} }}{{k_{t} }}$$

  (18)

• (3) When ġ_c = 0 and ġ_k = 0, the general equilibrium between the two departments is achieved. At this time, the consumption per person growth rate, capital per person growth rate and per capita output growth rate are shown in Formula (19).

  $$g_{y}^{ * } = g_{c}^{ * } = g_{k}^{ * } = \frac{{g_{A} + \beta^{ * } g_{d} }}{{{1 - }\alpha^{ * } }}$$

  (19)

Given the values of two types of exogenous variables, namely, technology level A, capital output share α and data elements output share β, we can get the steady growth rate of consumption per person, capital per person growth and per capita output growth.

From the above equilibrium results, we get proposition 2.

Proposition 2 After the introduction of data elements, an increase in the rate of technological progress or the share of capital output, or an increase in the level of data element accumulation or the share of data output will lead to an increase in the growth rate of output. $\partial {g}_{y}^{*}/\partial {g}_{A}=1/(\text{1} - {\alpha }^{*})>0$, $\partial {g}_{y}^{*}/\partial {\alpha }^{*}={g}_{A}/{(\text{1} - {\alpha }^{*})}^{2}>0$, $\partial {g}_{y}^{*}/\partial {g}_{d}={\beta }^{*}/(\text{1} - {\alpha }^{*})>0$, $\partial {g}_{y}^{*}/\partial {\beta }^{*}={g}_{d}/(\text{1} - {\alpha }^{*})>0$.

3.3.3 Scenario 2-1 General equilibrium calculation results of new structural economics without data elements

When data elements are not introduced, it can be obtained from Eqs. (1)–(2) and (6)–(8) that the economic growth rate of a country is related to the relative size of technological progress and production structure.

• (1) When the consumption per person growth rate is Eq. (20), the household sector maximizes its utility.

  $$g_{c} = \frac{{\dot{c}_{t} }}{{c_{t} }} = \frac{{\alpha_{t} A_{t} k_{t}^{{\alpha_{t} - 1}} - \delta_{t} - \rho }}{\sigma }$$

  (20)

• (2) When the capital factor demand function and labor factor demand function $K_{t}^{D} = (Y_{t} /A_{t} )\left\{ {[r_{t} (1 - \alpha_{t} )]/w_{t} \alpha_{t} } \right\}^{{(\alpha_{t} - 1)}}$ and ${L}_{t}^{D}=({Y}_{t}/{A}_{t}){\left\{[{r}_{t}(1-{\alpha }_{t})]/{w}_{t}{\alpha }_{t}\right\}}^{{\alpha }_{t}}$, respectively, and the dynamic price evolution mechanism are$\begin{gathered} g_{w} = \dot{w}_{t} /w_{t} = g_{A} + \alpha_{t} g_{k} + \left[ {1 + \alpha_{t} \ln k_{t} - 1/\left( {1 - \alpha_{t} } \right)} \right]g_{\alpha } ,\; \hfill \\ g_{r} = \dot{r}/r = g_{A} - \left( {1 - \alpha_{t} } \right)g_{k} + \left( {1 + \alpha_{t} \ln k_{t} } \right)g_{\alpha } , \hfill \\ \end{gathered}$

  The capital per person growth rate is shown in Eq. (21), and the production department maximizes profits.

  $$g_{k} = \frac{{\dot{k}_{t} }}{{k_{t} }} = A_{t} k_{t}^{{\alpha_{t} - 1}} - n - \delta_{t} - \frac{{c_{t} }}{{k_{t} }}$$

  (21)

• (3) When ġ_c = 0 and ġ_k = 0, the general equilibrium between the two departments is achieved. Furthermore, the motion equation $\dot{\alpha }_{t} = \left( {g_{k} - g_{A} - g_{k} \alpha_{t} } \right)\;\alpha_{t} /\left( {1 + \alpha_{t} \ln k_{t} } \right)$ of the production function onthe ġ_c = 0 locus is globally convergent at $\dot{\alpha }_{t} = 0$. The growth rate of consumption per person, growth rate of capital per person, growth rate of per capita output and level of production structure in general equilibrium are shown in Eq. (22).

  $${g}_{y}^{*}={g}_{c}^{*}={g}_{k}^{*}=\frac{{g}_{A}}{1-{\alpha }_{t}^{*}}\,\mathrm{and}\,{\alpha }_{t}^{*}=1-\frac{{g}_{A}}{{g}_{k}^{*}}$$

  (22)

Given the value of exogenous variable, namely technical level A, and endogenous variable, namely the value of capital production structureαin different periods, the equilibrium values of consumption per person growth rate, capital per person growth rate and per capita output growth rate can be obtained under the endogenous situation of capital production structure.

From the above equilibrium results, we get proposition 3.

Proposition 3 When there is no data element, the increase of technological progress rate or the change of capital production structure will lead to the increase of the output growth rate. $\partial g_{y}^{ * } /\partial g_{A} = 1/({1 - }\alpha_{t}^{ * } ) > 0$, $\partial g_{y}^{ * } /\partial \alpha_{t}^{ * } = g_{A} /{(1 - }\alpha_{t}^{ * } )^{2} > 0$.

3.3.4 Scenario 2-2 General equilibrium calculation results of new structural economics when data elements are introduced

When introducing data elements, it can be seen from Eqs. (3), (8), (9), (12) and (13) that the level of a country’s economic growth rate is related to technological progress, the level of capital production structure, the level of data production structure and the relative size of data accumulation rate.

• (1) When the consumption per person growth rate is defined in Eq. (23), the household sector maximizes its utility.

  $${g}_{c}=\frac{{\dot{c}}_{t}}{{c}_{t}}=\frac{{\alpha }_{t}{A}_{t}{k}_{t}^{{\alpha }_{t}-1}{d}_{t}^{{\beta }_{t}}-{\delta }_{t}-\rho }{\sigma }$$

  (23)

• (2) When the demand functions of capital, labor and data elements are $K_{t}^{D} = (Y_{t} /A_{t} )(r_{t} /\alpha_{t} )^{{\alpha_{t} - 1}} (b_{t} /\beta_{t} )^{{\beta_{t} }} [(1 - \alpha_{t} - \beta_{t} )/w_{t} ]^{{\alpha_{t} + \beta_{t} - 1}}$, $L_{t}^{D} = (Y_{t} /A_{t} )(r_{t} /\alpha_{t} )^{{\alpha_{t} }} (b_{t} /\beta_{t} )^{{\beta_{t} }} [(1 - \alpha_{t} - \beta_{t} )/w_{t} ]^{{\alpha_{t} + \beta_{t} }}$ and $D_{t}^{D} = (Y_{t} /A_{t} )(r_{t} /\alpha_{t} )^{{\alpha_{t} }} (b_{t} /\beta_{t} )^{{\beta_{t} - 1}} [(1 - \alpha_{t} - \beta_{t} )/w_{t} ]^{{\alpha_{t} + \beta_{t} - 1}}$ respectively.

  And the price evolution mechanism is

  $$\begin{gathered} g_{w} = \dot{w}_{t} /w_{t} = g_{A} + \alpha_{t} g_{k} + \left[ {1 + \alpha_{t} \ln k_{t} - \left( {1 - \beta_{t} } \right)/\left( {1 - \alpha_{t} - \beta_{t} } \right)} \right]g_{\alpha } + \alpha_{t} g_{k} + \left[ {1 + \beta_{t} \ln d_{t} - \left( {1 - \alpha_{t} } \right)/\left( {1 - \alpha_{t} - \beta_{t} } \right)} \right]g_{\beta } ,\; \hfill \\ g_{r} = \dot{r}/r = g_{A} - \left( {1 - \alpha_{t} } \right)g_{k} + \left( {1 + \alpha_{t} \ln k_{t} } \right)g_{\alpha } + \beta_{t} g_{d} + \beta_{t} \ln d_{t} g_{\beta } , \hfill \\ g_{b} = \dot{b}_{t} /b_{t} = g_{A} + \alpha_{t} g_{k} + \alpha_{t} \ln k_{t} g_{\alpha } - \left( {1 - \beta_{t} } \right)g_{d} + \left( {1 + \beta_{t} \ln d_{t} } \right)g_{\beta } , \hfill \\ \end{gathered}$$

  the capital per person growth rate is defined in Eq. (24), and the production department maximizes profits.

  $$g_{k} = \frac{{\dot{k}_{t} }}{{k_{t} }} = A_{t} k_{t}^{{\alpha_{t} - 1}} d_{t}^{{\beta_{t} }} - n - \frac{{c_{t} }}{{k_{t} }}$$

  (24)

• (3) When ġ_c = 0 and ġ_k = 0, the general equilibrium between the two departments is achieved. Furthermore, the motion equation $\dot{\alpha }_{t} = \left\{ {_{{}} [g_{k} - g_{A} - g_{\beta } (\eta_{b\beta } - 1) - \beta_{t} g_{d} ]\alpha_{t} - g_{k} \alpha_{t}^{2} } \right\}/(1 - \alpha_{t} )$ of production function on ġ_c = 0 locus is globally convergent at ${\dot{\alpha }}_{t}=0$. The growth rate of consumption per person, growth rate of capital per person, growth rate of per capita output and level of production structure in general equilibrium are shown in Eq. (25).

  $$g_{y}^{*} = g_{c}^{*} = g_{k}^{*} = \frac{{g_{A} + \beta_{t}^{*} g_{d} }}{{1 - \alpha_{t}^{*} }}\;{\text{and}}\;\alpha_{t}^{*} = \frac{{g_{k} - g_{A} - \beta_{t}^{*} g_{d} }}{{g_{k} }}$$

  (25)

From the above equilibrium results, we get proposition 4.

Proposition 4 After the introduction of data elements, an increase in the technological progress rate or the change of capital production structure, or of the increase of the data element accumulation level, or the change of data production structure, will lead to an increase in the output growth rate. $\partial {g}_{y}^{*}/\partial {g}_{A}=1/(\text{1} - {\alpha }_{t}^{*})>0$, $\partial {g}_{y}^{*}/\partial {\alpha }_{t}^{*}={g}_{A}/{\text{(1-}{\alpha }_{t}^{*})}^{2}>0$, $\partial {g}_{y}^{*}/\partial {g}_{d}={\beta }_{t}^{*}/(\text{1} - {\alpha }_{t}^{*})>0$, $\partial {g}_{y}^{*}/\partial {\beta }_{t}^{*}={g}_{d}/(\text{1} - {\alpha }_{t}^{*})>0$.

4 Theoretical analysis on the choice of economic growth path

This part compares the general equilibrium results of new classical economics and new structural economics under the introduction of data elements to obtain the optimal choice of economic growth path of developing countries.

Before and after data elements are introduced into the general equilibrium model, there may be:

• (1) Following the general equilibrium model of new classical economics: before the introduction of data elements, the corresponding scenario is 1-1. After the data elements are introduced, the corresponding scenario is 1-2.

• (2) Following the general equilibrium model of new structural economics: before the introduction of data elements, the corresponding scenario is 2-1; After the data elements are introduced, the corresponding scenario is 2-2.

In the above two general equilibrium analysis frameworks, the general equilibrium calculation results before and after the introduction of data elements are different. To facilitate comparison, the following are compared separately between scenario 1-1 and scenario 1-2, scenario 2-1 and scenario 2-2.

In the following symbols, NEGE and NSEGE represent the general equilibrium of new classical economics and the general equilibrium of new structural economics respectively. Where, $g_{y}^{{{\text{NEGENO}}}}$, $g_{y}^{{{\text{NEGEYES}}}}$, $g_{y}^{{{\text{NSEGENO}}}}$, $g_{y}^{{{\text{NSEGEYES}}}}$ respectively represent the growth rate of per capita output in general equilibrium before and after the introduction of data elements, corresponding to situations 1-1, 1-2, 2-1 and 2-2 respectively.

Compare the growth rate of per capita output under the two general equilibrium analysis frameworks. The relationship is shown in Fig. 1:

Fig. 1

Change of equilibrium state before and after the introduction of data elements

Figure 1 shows the growth rate of per capita output in general equilibrium under the two analytical frameworks. According to the comparison, the equilibrium state transition path is:(1) Under NEGE, considering that the share of input elements remains stable for a long time, it can be transferred to state $g_{y}^{{{\text{NEGEYES}}}}$ or its special case ${g}_{y}^{\text{NEGENO}}$. If no data elements is introduced, it will be transferred to ${g}_{y}^{\text{NEGENO}}$, and economic growth depends on technological progress. If data elements are introduced, they will be transferred to $g_{y}^{{{\text{NEGEYES}}}}$. Economic growth depends on technological progress and data elements accumulation. Of course, if the economic development is in the early stage of digital economy development, and the input of data elements is negligible, it will be transferred to ${g}_{y}^{\text{NEGENO}}$.

(2) Under NSEGE, consider that the production structure generated from the given endowment structure is a time-varying variable, which can be transferred to any of the states ${g}_{y}^{\text{NEGENO}}$ or $g_{y}^{{{\text{NSEGEYES}}}}$, ${g}_{y}^{\text{NEGENO}}$ or $g_{y}^{{{\text{NEGEYES}}}}$.

• ① If no data elements is introduced, it will be transferred to $g_{y}^{{{\text{NSEGENO}}}}$ or its special case ${g}_{y}^{\text{NEGENO}}$. At ${g}_{y}^{\text{NSEGENO}}$, economic growth depends on the rate of technological progress and upgrading of production structure. If the production structure remains stable for a long time, it is a special case of $g_{y}^{{{\text{NSEGENO}}}}$, which is transferred to ${g}_{y}^{\text{NEGENO}}$.

• ② If data elements are introduced, they will be transferred to $g_{y}^{{{\text{NSEGEYES}}}}$, or some special cases thereof: $g_{y}^{{{\text{NSEGENO}}}}$ or $g_{y}^{{{\text{NEGEYES}}}}$ or $g_{y}^{{{\text{NEGENO}}}}$. In $g_{y}^{{{\text{NSEGEYES}}}}$, economic growth depends on technological progress rate, upgrading of production structure and accumulation of data elements.

  • a. If the influence of data elements is ignored, it will be transferred to $g_{y}^{{{\text{NSEGENO}}}}$, and further, if the production structure remains stable for a long time, it will be transferred to $g_{y}^{{{\text{NEGENO}}}}$.

  • b. If considering the influence of data elements and assuming that the production structure remains stable for a long time, it will be transferred to $g_{y}^{{{\text{NEGEYES}}}}$.

Comparing the economic growth paths of the two analysis frameworks in turn, we posit the following two propositions.

Proposition 5 No matter what kind of general equilibrium analysis framework, technological progress and data elements accumulation can always play a role in driving economic growth after the introduction of data elements.

Proposition 6 Whether or not data elements are introduced, the general equilibrium calculation result of new classical economics is always a special case of the general equilibrium calculation result of new structural economics.

Table 1 shows the trend of economic growth rate under the two analysis frameworks.

Table 1 Comparison of economic growth rates under different analysis frameworks

Compared with the general equilibrium analytical framework of new classical economics, whether the economic growth rate under the general equilibrium framework of new structural economics is improved is related to the rate of technological progress, capital production structure, data production structure and data elements accumulation rate.

Proposition 7 Developing countries need to choose appropriate economic growth paths according to their own endowment structure (See Table 1 for details).

• (1) Under the general equilibrium framework of new classical economics, it is better for developing countries to introduce data elements. At this time, developing countries introduce data elements, and the economic growth rate is $g_{y}^{{{\text{NEGEYES}}}}$, which not only includes the economic growth rate (${g}_{y}^{\text{NEGENO}}$) when data elements are not introduced, but also includes the impact of data elements accumulation rate, capital output share and labor output share on economic growth β^*g_d / (1–α*).

  • ① When β = 0(or g_d = 0), $g_{y}^{{{\text{NEGEYES}}}}$ = ${g}_{y}^{\text{NEGENO}}$. Since the share of data output β (or data elements accumulation rate g_d) is zero, we must have β^*g_d / (1–α*) = 0, the economic growth rate brought about by the introduction of data elements is equal to that when they were not introduced.

  • ② But when β > 0(or g_d > 0), because g_d (or β)and 1–α* are greater than zero, therefore ${g}_{y}^{\text{NEGEYES}}>{g}_{y}^{\text{NEGENO}}$, that is, the economic growth rate brought by the introduction of data elements is higher than the economic growth rate when data elements are not introduced.

• (2) Under the general equilibrium framework of new structural economics, it is better for developing countries to introduce data elements. At this time, developing countries introduce data elements, and the economic growth rate is $g_{y}^{{{\text{NSEGEYES}}}}$, which includes not only the economic growth rate ($g_{y}^{{{\text{NSEGENO}}}}$) when data elements are not introduced, but also the impact of data elements accumulation rate, capital production structure and data elements production structure on economic growth (β^*g_d / (1–α*)). In other words, incorporating the data elements into the production process may be an effective way for developing countries to quickly catch up with their developed counterparts. On the contrary, were developing economies failing to take advantage of digitalization, their income gaps with the developed economies may continue to rise. One important implication of this discussion on the impact of data elements on economic is that digitalization featured with big data can be a great opportunity for the late comer economies to converge with the rich industrialized nations.

  • ① When β_t = 0(or g_d = 0),$g_{y}^{{{\text{NSEGEYES}}}}$ = $g_{y}^{{{\text{NSEGENO}}}}$. Because g_d = 0 (or β_t = 0) is zero, β* tg_d /(1–α* t) = 0, the economic growth rate brought about by the introduction of data elements is equal to that when they were not introduced.

  • ② When β_t > 0 (or g_d > 0), because g_d (or β_t) and 1–α* t are both greater than zero, $g_{y}^{{{\text{NEGEYES}}}} > g_{y}^{{{\text{NEGENO}}}}$, that is, the economic growth rate brought about by the introduction of data elements is higher than the economic growth rate without the introduction.

  • ③ When the capital production structure and data production structure are stable for a long time, the general equilibrium model of new structural economics is transformed into the general equilibrium model of new classical economics.

    • a. When α_t = α,β_t = β,the introduction of data elements and the capital production structure and data production structure are stable for a long time, ${g}_{y}^{\text{NSEGEYES}}$ = ${g}_{y}^{\text{NEGEYES}}$.

    • b. When α_t = α, β_t = 0, that is, no data elements is introduced and the capital production structure is stable for a long time, $g_{y}^{{{\text{NSEGEYES}}}}$ = $g_{y}^{{{\text{NEGENO}}}}$.

Further considering countries with different development levels, we posit another proposition below.

Proposition 8 In the digital economy era, a country has chosen data elements input, and its economic growth rate is related to the share of capital output, the share of data elements output, and the rate of data elements accumulation. Which path is more favorable under the analytical framework depends on the economic development level of the country.

At this time, a developed country may choose the economic growth path under the general equilibrium analysis framework of new classical economics because the share of capital output of developed countries is stable in the long term. However, developing countries should choose the economic growth path under the general equilibrium analysis framework of new structural economics because the share of capital output changes over time.

To sum up, in the digital economy era, both developed and developing countries will promote economic growth by increasing the accumulation of data elements. For developing countries, they should give priority to the economic growth path under the general equilibrium framework of new structural economics in combination with the endogenous production structure of their own endowment structure.

5 Possible extensions

The core basis of this study is the general equilibrium model of new classical economics and new structural economics. It analyzes the impact of the number of input factors and the output share of input factors on economic growth under neutral technological progress conditions. The recent development shows that economic growth is increasingly dependent on biased technological progress and factor allocation. How to measure the impact of the direction of technological progress and the direction of factor allocation on economic growth has become the most cutting-edge research topic. In the context of the digital economy era, there are few studies on the theoretical mechanism of biased technological change and biased factor allocation driving economic growth.

The research of Acemoglu et al. (2012) and Acemoglu and Azar (2020) extends the general equilibrium model of new classical economics from two sectors of production and consumption to three sectors of production, intermediate product and household sectors, discusses the existence and uniqueness of equilibrium, and considers how changes in parameters affect the selection of equilibrium prices and intermediate products. Considering the background of the digital economy era, Cong et al. (2021) introduced data elements into the three sectors general equilibrium model on the basis of Acemoglu et al. (2012) to discuss the impact of data elements on economic growth. Jones and Tonetti (2020), Farboodi and Veldkamp (2021), Xu and Zhao (2020), Cong et al. (2021), Li and Wang (2021), Liu and Jia (2022a, b), Tang et al. (2022) also examines the impact of data elements on economic growth, but the above scholars chose to ignore the impact of the direction of technological progress, assuming that technological progress leads to the constant marginal technological substitution rate of any two elements, that is, neutral technological progress.

If we think that the impact of technological progress on the technical efficiency of different elements (such as capital efficiency, labor efficiency and data elements efficiency) is different, rather than operating under an assumption of homogeneity, that is, technological progress is a biased rather than a neutral process. Then what will happen to the general equilibrium of new classical economics and new structural economics following the introduction of data elements? And whether the conclusions of this paper are still valid? These issues are also worth studying. Based on the idea of Acemoglu (2003), this paper attempts to discuss the change trend in the future regarding economic growth and technical change.

As mentioned above, both general equilibrium analysis frameworks assume neutral technological progress. If this assumption does not uphold, we will further consider biased technological change, and combine the background of rapid development of digital economy: the impact of factor efficiency on economic growth will be underestimated, and the impact of changes in factor efficiency level and factor endowment structure on technological progress and factor allocation will also be underestimated. On the one hand, this phenomenon is caused by the fact that under the assumption of neutral technological progress, the technical efficiency of different factor inputs is not considered. On the other hand, the interaction between the output share of different factor inputs and technical efficiency has not been taken into account. Although these studies are relatively easy to understand for the general equilibrium framework of new classical economics, and new structural economics is more complex to understand because of the endogenous variables of production structure, this logic is also applicable to the general equilibrium framework of new structural economics. Therefore, after considering biased technological change, the technical efficiency in this model may be underestimated.

To be specific, the technological progress rate g_A will be underestimated, which only includes the neutral technological progress rate, while capital technical efficiency, labor technical efficiency and data elements technical efficiency are not included, and the interaction between capital output share α, labor output share 1-α-β, data elements output share β and capital technical efficiency, labor technical efficiency and data elements technical efficiency is not included.

Combined with the above conclusions and the model setting in this paper, we can refer to Fig. 1, Table 1 and Proposition 7. (1) Before introducing data elements: based on the general equilibrium analysis framework of new classical economics, developing countries will choose to increase the rate of technological progress, because the share of capital output is stable for a long time. Based on the general equilibrium analysis framework of new structural economics, developing countries will choose to improve the rate of technological progress and promote the change of capital production structure. (2) After the introduction of data elements: based on the general equilibrium analysis framework of new classical economics, developing countries will choose to improve the rate of technological progress and the rate of data elements accumulation. Based on the general equilibrium analysis framework of new structural economics, developing countries will choose to improve the rate of technological progress and the rate of accumulation of data elements, and promote the change of capital and data production structure. Note that both before and after the introduction of data elements, the general equilibrium calculation results of new classical economics are special cases of the general equilibrium calculation results of new structural economics. Therefore, when considering the introduction of biased technological change, developing countries will be more likely to choose policy propositions based on the new structural economics, and the advantages of the new structural economics analysis framework will also be expanded. In addition, although as mentioned above, the introduction of biased technological progress will underestimate g_A in this model, the impact of neutral technological progress on economic growth rate is correct, and the impact of input factor output share (whether long-term stable or time-varying) on economic growth is also correct, so developing countries will still choose the policy proposition of new structural economics.

The model in this study is placed in a general equilibrium setting considering biased technological change, and the conclusion of this paper, especially proposition 7, is basically unchanged. For the new structural economics with time-varying advantages in capital production structure and data production structure after the introduction of data elements, the general equilibrium policy proposition of the new structural economics with biased technological change is an opportunity to change the economic growth of developing countries.

6 Conclusions

With the development of digital economy, the economic growth path of developing countries is also changing. This paper introduces data elements into the neoclassical general equilibrium model and the new structural general equilibrium model respectively, and studies the choice of economic growth path of developing countries under the two analysis frameworks. First of all, the general expression of economic growth rate under the equilibrium state under two analysis frameworks before and after the introduction of data elements is derived. On this basis, the transfer paths of different economic growth states are compared and analyzed, and the optimal economic growth path of developing countries before and after the introduction of data elements under two different analysis frameworks is obtained, and the applicability of this conclusion in the general equilibrium model with the introduction of biased technological change is discussed.

This study finds that: (1)No matter what kind of general equilibrium corresponding economic growth path the developing countries choose, the economic growth rate after the introduction of data elements will always be higher than before. Under the general equilibrium analysis framework of new classical economics, before the introduction of data elements, the economic growth rate is related to the rate of technological progress and the share of capital output. After the introduction of data elements, in addition to the rate of technological progress and the share of capital output, there are two factors affecting the economic growth rate: the share of data element output and the rate of data elements accumulation. These two factors have a positive impact on the economic growth rate. Therefore, the economic growth rate of developing countries can be improved after the introduction of data elements. Under the general equilibrium analysis framework of new structural economics, before the introduction of data elements, the level of economic growth rate is related to the rate of technological progress and the structure of capital production. After the introduction of data elements, in addition to technological progress rate and capital production structure, there are two factors affecting economic growth rate: data production structure and data elements accumulation rate. The impact of these two factors on the economic growth rate is also positive. Therefore, the economic growth rate of developing countries can be improved after the introduction of data elements. (2) Developing countries find the optimal path of economic growth by comparing the different results of economic growth rates under the two analytical frameworks. This paper believes that when developing countries choose the path of economic growth, they need to combine their own endowment conditions, choose a new structural economics analysis framework for decision-making, increase the accumulation of data elements, promote the change of production structure, form a virtuous circle of production structure change and endowment structure upgrade, and constantly promote economic development by relying on the self strengthening mechanism.

This paper broadens the application scope of the general equilibrium of new classical and new structural economics. However, with the continuous development of the digital economy, there are many factors and related variables that can be considered in this model in the future, not only capital technical efficiency, labor technical efficiency and data elements technical efficiency, but also between countries, data technology, etc. are the direction that this type of study can improve in the future.