Digital Economy, Industry Heterogeneity, and Service Industry Resource Allocation

: Based on the traditional framework of resource mismatch theory analysis and existing literature studies, this paper constructs a model of resource mismatch efﬁciency loss including the digitalization factor of the service industry, measures the resource mismatch of China’s service industry and its sub-sectors, and empirically analyzes the impact of digital economy development on resource mismatch of service industry using panel data of each sub-sector of China’s service industry from 2001 to 2020. The ﬁndings reveal that: (1) Resource mismatch exists in China’s service industry, and the degree of mismatch of capital is more serious than that of labor. (2) Traditional service industries with low digitalization have serious efﬁciency losses, while emerging service industries with high digitalization have almost no efﬁciency losses. (3) The increase in the development of the digital economy can signiﬁcantly improve the resource mismatch in the service industry; appropriate government intervention can improve the capital mismatch but not the labor mismatch; the increase in the proportion of state-owned enterprises is conducive to improving the labor mismatch but not the capital mismatch. Meanwhile, the results of the industry heterogeneity test show that the increase in the digital economy can improve the resource mismatch of both emerging and traditional service industries, but the improvement is more obvious for emerging service industries. Therefore, in the context of the development of the digital economy, we make the following suggestions. The government intervenes appropriately in the capital market, develops emerging service industries, and formulates different digital transformation policies for different industries. Relevant enterprises increase their efforts in technology research and development, and actively explore the direction of digital transformation of service industries. The government and enterprises work together to promote the improvement of China’s economic development level.


Introduction
China's service industry is in a critical period of transformation to modernization, and the transformation and development of traditional service industry has become a key path to promoting the high-quality development of China's economy [1].The "White Paper on the Development of China's Digital Economy (2021)" issued by the China Academy of Information and Communications Technology pointed out that the scale of the country's digital economy will account for 38.6% of GDP in 2020, an increase of 9.7% compared with 2019; the penetration rate of the digital economy in the service industry will reach 40.7%, while industry and agriculture were only 21.0% and 8.9%.The digital economy penetration rates of the service industry, industry, and agriculture increased by 2.9, 1.6, and 0.7 respectively compared with 2019.This shows that the digital transformation of the service industry is far greater than that of industry and agriculture.In other words, compared with industry and agriculture, accelerating the digitalization process can better promote the development of the service industry [2].The high-quality development of the economy cannot be achieved without the reasonable allocation of factors.At the same time, according to resource allocation theory, the high-quality development of the economy also requires that the factor inflow side must have relatively high productivity, otherwise, all forms of factor flow will lead to resource allocation problems [3].The facts in China show that although the total factor productivity of the traditional service industry is lower than that of the emerging service industry [4], a large amount of labor and capital still tends to flow to the lower-productivity traditional service industry, resulting in a serious mismatch of resources across the service industry, which is inconsistent with the traditional factor allocation theory and will certainly seriously hinder the process of high-quality development of the Chinese economy [5].Therefore, China urgently needs to rely on new information technologies such as the Internet of Things and artificial intelligence to break the spatial and temporal restrictions on the flow of capital and labor factors, improve the efficiency of factor allocation, and achieve the goal of service industry transformation as soon as possible [6].
For example, with the application of blockchain, artificial intelligence, big data, etc., emerging service industries such as online education, online medical care, and online banking have broken through the limitations of time and space.People can enjoy the convenience brought by the integration of digital technology and the service industry anytime, anywhere, allowing the unemployed to find suitable jobs in a short period of time, and allowing investors or borrowers to find investment and financing channels faster.This significantly improved the level of resource allocation in the service industry [7].At the same time, according to the long tail theory and scope economy theory in the digital economy, the digital economy enables the development of the "scope economy" and the "long tail effect" in the production and distribution process.Because the emerging service industry has a high degree of digital development, it is more susceptible to the impact of economies of scope and long tail effects, so the resource allocation efficiency of the emerging service industry will be higher than that of the traditional service industry [8,9].So, in the era of the digital economy, since the service industry has become an important industry that promotes the country's economic development, how much misallocation of resources still exists in it?Which sub-sectors of the service sector are these mismatches primarily manifested in?Are there differences in the degree of mismatch between capital and labor factors within the same industry?Are there differences in the degree of resource misallocation across industries?Can it be proved from a mathematical point of view?How much of the resource misallocation can be explained by the digital development of the industry?This paper will mainly answer the above questions through mathematical calculation and empirical testing methods.

Literature Review
In this context, many scholars have investigated the impact of the development of the digital economy on efficiency changes, industrial development, and economic development based on the problem of resource allocation.First, they analyze the impact of the digital economy on efficiency changes.The rapid development of the digital economy has reduced information asymmetry [10] and increased the mobility of information in different industries or sectors, thus reducing the cost of factor reallocation and improving the efficiency of factor allocation [11].Wen et al. [12] show that the transformation of industrial digitalization can effectively reduce the production scale of heavily polluting enterprises and significantly improve the green total factor productivity of manufacturing enterprises through structural and technological effects.Second, they analyze the impact of the digital economy on industrial development.The network effect of the digital economy has gradually emerged [13], while it can rely on powerful platform resources to obtain required factors of production such as labor and capital from multiple channels, reducing the acquisition cost of factors and indirectly improving factor allocation efficiency [14].From the perspective of the digital economy, factor reallocation, and industrial development, factor allocation is the link between the digital economy and industrial structure upgrading [15], and the digital economy can promote the transformation and upgrading of the manufacturing industry by improving the resource allocation ability of enterprises [16].The analysis of Yu [17] and Zhuo et al. [18] showed that the manufacturing industry can promote the development of the manufacturing industry by optimizing resource allocation with empowerment of the digital economy.Ma et al. [19] empirically tested the relationship between the digital economy and manufacturing quality, using factor allocation as a mediator.Li et al. [20] pointed out that the integration of the digital economy and traditional industries transformed traditional industries and promoted the formation and development of new industries, which led to the improvement of labor productivity and the upgrading of industrial structure; Huang et al. [21] examined the positive impact of Internet development on the efficiency of manufacturing industry using microdata from cities, industries, and enterprises.Guo [22] argued that artificial intelligence technology in the digital economy may produce biased substitution for either labor or capital factors, and can achieve industrial transformation and upgrading by accelerating the flow of production factors among industrial sectors.Wen et al. [23] empirically analyzed the relationship between manufacturing digitalization and firms' innovation investment based on data from A-share listed Chinese manufacturing firms and pointed out the impact of digitalization on manufacturing firms' choice of competitive market strategies, i.e., manufacturing firms with higher survivability are better able to cater to digitalization development.Third, is the analysis of the impact of the digital economy on the quality development of the economy.Ma et al. [24] and Tian et al. [25] both empirically tested the positive contribution of the digital economy to economic quality development by improving factor mismatch from the perspective of digital finance.Based on the macro level, Jing et al. [26] theoretically show that the digital economy can promote economic growth by generating new factors, new resource allocation efficiency, and total factor productivity.Shi et al. [27] showed that the platform economy, which represents a new form of the digital economy, can alleviate information asymmetry in transactions, on the one hand, and can solve idle resources in cities and improve resource allocation efficiency through the development of sharing economy to promote high-quality urban development with efficiency changes on the other hand.Xie et al. [28] pointed out that the platform economy, a new business model under the digital economy that connects both users and suppliers and provides information aggregation medium and transaction space for both, can improve resource allocation efficiency and promote high-quality economic development while facilitating the flow of information.Ding [13] explored the possible mechanisms of the digital economy to influence high-quality economic development from three levels: micro, meso, and macro.
Combing the existing literature, most of the studies examined the mechanisms through which the digital economy optimizes resource allocation efficiency and thus promotes efficiency change, industrial upgrading, and economic development at the empirical and theoretical levels.The research on the optimization of resource allocation in the digital economy is more comprehensive and in-depth, but there are also the following shortcomings.First, the existing literature has focused heavily on the impact of the digital economy on economic development, manufacturing upgrading, and industrial structure upgrading, but not from the perspective of industry heterogeneity, especially for the service industry, to study the effect of the digital economy on the improvement of resource mismatch.Secondly, the existing literature has made a lot of theoretical combing on the mechanism of the digital economy affecting resource allocation and lacks the analysis of the impact mechanism at the empirical level.Drawing on the rich theoretical and empirical research of many scholars, this paper constructs a comprehensive evaluation index system for the development of the digital economy.Relying on the loss of resource allocation efficiency model, the resource mismatch of each sub-sector of China's service industry from 2001 to 2020 is measured.The impact of digital economy development on resource allocation in the service industry is empirically studied, and the differential impact of digital economy development on resource allocation in different industries is analyzed from the perspective of industry heterogeneity.In view of this, the possible marginal contributions of this paper include: (1) Separating the capital and labor factors and measuring the relative mismatch degree of both in each service industry separately to provide a reference for the focus of policy improvement.(2) Dividing the service sector into emerging and traditional services according to the degree of impact of the digital economy, calculating their mismatch degrees, analyzing the root causes of the mismatch, and gaining rich policy insights.

Theoretical Mechanism Analysis
The digital economy takes information technology as the core and puts knowledge and data as production factors into the traditional production process, which can gradually informatize traditional factors such as capital and labor, and effectively solve the problem of information asymmetry in the flow of factors.At the same time, the permeability and substitutability of the digital economy also enable the efficient allocation of labor and capital elements through more channels.That is to say, the development of the digital economy can improve the opacity of the capital and labor markets, and improve the allocation efficiency of capital and labor elements with more efficient informatization means.However, different industries have different attributes, and the country's regulation of different industries is also different.In the context of the development of the digital economy, the penetration of information technology in different industries is also different.As the emerging service industry has a high level of information technology, when there is an efficiency loss in its factor allocation, accelerating the development of the digital economy can better and faster adjust the imbalance in factor allocation.For example, in the development of online e-commerce, when the real economy is sluggish, even if stores close down and factories shut down, enterprises can rely on e-commerce platforms such as Alibaba, JD.com, and Pinduoduo to sell the accumulated goods and realize the return of funds.During the severe epidemic period, people can also achieve employment through online teaching and online medical treatment.

Analysis of the Impact of Digital Economy on the Mismatch of Labor and Capital Factors
The digital economy refers to an economic form that achieves optimal allocation of resources and improves the efficiency of resource utilization through information technology.There are three main mechanisms by which the digital economy affects the allocation of capital and labor factors.
(1) In the era of the digital economy, the traditional form of information interaction is changed, and the sharing and circulation of information is more convenient, which improves the allocation efficiency of traditional factors [15].For example, the development of online recruitment platforms such as Boss Direct, WiseLink, and MileagePlus has greatly reduced the waste of labor resources due to frictional unemployment and also solved the employment problem of part of the surplus labor force, improving the allocation efficiency of labor; the application of online lending platforms such as Ant Borrowing and Jingdong White Stripe has broadened the financing channels of enterprises related to emerging service industries, indirectly optimizing the allocation of capital efficiency.(2) The application of digital communication technology breaks the barriers for workers' time and space [29], provides more options for workers' re-employment, shortens the socially necessary labor time [30], improves labor productivity, and thus enhances the efficiency of labor resource allocation.Meanwhile, in the service sector, the digital economy represented by artificial intelligence and cloud computing has given rise to new forms and models such as online education, sharing economy, and platform economy [31], and these new industries and models have reorganized factor allocation patterns within different industries [6], enabling labor and capital factors to be allocated more efficiently to other high-productivity industries and alleviating factor mismatch [32].(3) In product production, information technology can promote the optimization of the enterprise's production factor allocation ability and the level of collaboration between factors, shortening production time while saving production costs [33].Meanwhile, in product sales, the huge logistics network formed based on digitalization and networking broadens the sales channels and scope of enterprises while reducing inventory pressure, making capital turnover more flexible and improving the allocation efficiency of capital factors.
The change in the degree of digitalization of the industry is a direct reflection of the application of the digital economy in the industry.Therefore, this paper proposes the following hypotheses.
Hypothesis 1.The increase in industry digitalization can improve the degree of labor factor mismatch, and the degree of industry digitalization is negatively related to the degree of labor factor mismatch.
Hypothesis 2. The increase in industry digitalization has a certain improvement effect on the degree of capital factor mismatch, and the degree of industry digitalization is negatively correlated with the degree of capital mismatch.

Heterogeneity Analysis of the Digital Economy in Improving Resource Mismatch in Service Industry
The reasonable allocation of factors occupies an extremely important position in the production process, so the degree of industrial development also depends to a large extent on the reasonable degree of factor allocation [34].The emergence of the digital economy has stimulated the active degree of traditional production factor allocation and the improvement of allocation efficiency in a networked manner and has promoted the development of the service industry by integrating data integration, platform empowerment, and other driving factors into traditional and emerging services [35].However, emerging service industries developed by the application of information technology are more influenced by technological innovation and have more significant economies of scope and long-tail effects than traditional service industries that are labor-intensive [14].At the same time, compared with traditional service industries, emerging service industries have many advantages in R&D, production, and circulation, which are as follows: (1) The deeper integration of emerging services with digital technology, higher marginal returns, and lower marginal costs can attract a large inflow of capital, which in turn promotes R&D investment in various products and stimulates innovation momentum, thus promoting the optimal allocation of factors in the service industry.(2) The emerging service industry can better rely on digital platforms to realize ondemand customization and digital production, which reduces ineffective factor flow [36] and improves factor allocation efficiency; (3) The emerging service industry has higher production efficiency compared with the traditional service industry, which can accelerate the allocation of resources and reduce resource waste, boosted by the rapid development of e-commerce platforms.
It can be speculated that the information technology changes brought about by the development of the digital economy have a certain improvement effect on resource mismatch in both traditional and emerging service industries, but the impact on emerging service industries is more significant compared to traditional service industries, which in turn promotes the structural upgrading of service industries.Therefore, this paper proposes the following hypothesis.

Hypothesis 3.
There is a significant difference between the improvement of mismatch between emerging and traditional service industries by the increase in industry digitalization, that is, the improvement of factor mismatch of the service industry by the development of the digital economy is more obvious in industries with a higher degree of digitalization.

Model Construction and Variable Selection 4.1. Service Industry Resource Mismatch Measurement Model
Many scholars have conducted in-depth research on the measurement of efficiency loss in the service industry, and four main measurement methods have been formed: first, the production function method, in which the C-D production function [37], CES production function [38], and beyond logarithm production function [39] are used; second, the profit function method [40]; third, the production frontier method [41]; fourth, the indicator method [42].Among them, the profit function method is the most commonly used method, which firstly requires setting the production function of the enterprise and then solving the resource allocation under the profit maximization condition by introducing an "economic wedge" into the profit function of the enterprise.This paper draws on the general accounting model framework proposed by Aoki [43] to examine the impact of industry resource misallocation on total factor productivity and total output in the service sector by introducing a "distortionary tax" on factors.First, we assume that the final product market is perfectly competitive and satisfies the C-D production function form, and discuss the production problem for the S subsectors of the service industry.
Here, we assume that heterogeneity exists across industries, that the condition of constant returns to scale is satisfied, and that the previously efficient resource allocation state is disrupted by market monopolies, government policies, and other factors.At this time, the capital and labor prices of the industry are (1 + τ Ki ) • r and (1 + τ Li ) • ω, where ω and r are the prices of capital and labor, respectively, in the absence of market mismatches.τ Ki and τ Li represent the "economic wedge", which refers to the factors that cause the mismatch.The profit function of the industry in the resource mismatch scenario can be expressed as: According to the first-order condition of profit maximization and the resource constraints K = ∑ S i=1 K i and L = ∑ S i=1 L i , and . The relative resource mismatch coefficients of capital and labor factors in each sub-sector of the service industry can be deduced: λKi Equations ( 3) and ( 4) are the main measurement formulas in this paper, representing the degree of deviation from the optimal allocation of capital and labor in industry i, respectively.When the relative resource mismatch coefficient is less than 1, it indicates that the actual factor input in industry i is insufficient; when the relative resource mismatch coefficient is greater than 1, it indicates that the actual factor input in industry i is excessive; when the relative resource mismatch coefficient is equal to 1, it indicates that the factor input in industry i is reasonable.
Further, the log difference between the total output of emerging service industry and traditional service industry is used to express the output gap between the two sectors.Where M denotes emerging service industry and N denotes traditional service industry.As follows: Substituting Equations ( 1), (3), and (4) into Equation ( 5), it follows that: From Equation ( 6), it can be concluded that there are three possible reasons for the output difference between emerging and traditional service industries, which are: A. the difference in total factor productivity between the two due to technological differences; B. the difference in factor allocation exists which causes the output gap; C. the two have different production attributes leading to different factor input shares.Therefore, improving the factor allocation status of emerging and traditional service industries can effectively reduce the output gap between them, which also verifies Hsieh and Klenow's [44] view that factor mismatch leads to total factor productivity loss.
The expression for total factor productivity in the emerging services sector is defined by the "Solow residual term" as: where denotes the efficiency loss between the emerging and traditional service sectors due to technological differences; denotes the efficiency loss between the emerging and traditional service sectors due to factor mismatch.It is easy to know that when there is factor mismatch, the value of RAE is negative, which represents the total factor productivity loss due to factor mismatch.
When considering insufficient factor mobility within the industry, the RAE can be decomposed as: When considering inadequate factor mobility between sectors, the RAE can be decomposed as: Among them, RAE L , RAE K ,RAE M , and RAE N denote labor mismatch, capital mismatch, mismatch of emerging service factors, and mismatch of traditional service factors, respectively.

An Empirical Model of the Development of the Digital Economy Affecting Resource Mismatch in the Service Sector 4.2.1. Variable Selection and Handling
Explanatory variables.The explanatory variables are the degree of capital mismatch (lncm) and the degree of labor mismatch (lnwm).In this paper, we apply the values of relative capital mismatch coefficient λKi and relative labor mismatch coefficient λLi derived from Equations ( 3) and ( 4) to indicate the degree of mismatch of capital and the degree of mismatch of labor, respectively.Since there are both positive and negative cases for this value, this paper draws on Wei et al. [45] to use the absolute values of the capital and labor mismatch indices to indicate the degree of mismatch of capital and labor.Meanwhile, the following data are needed to measure the degree of mismatch between capital and labor: the value added of output in each industry Y i , the amount of capital input K i , the amount of labor input L i , the output elasticity of labor α i , and the output elasticity of capital 1 − α i .Calculation of capital input K i by industry: Since the China Statistical Yearbook does not directly give the data of capital input, this paper tries to use "capital stock" to represent "capital input", which is measured by the "perpetual inventory method", and the base period is set to 2001, and the formula for calculating capital stock is shown in Equations ( 10) and (11).
where K i,t , AI i,t , δ, and PI i,2001 are the capital stock, nominal investment, depreciation rate, and fixed asset investment price index of industry i in period t, respectively.The nominal investment is measured by the amount of fixed capital investment in each industry in the society as a whole, following the practice of Yang [46], and the lack of a fixed investment price index in the statistical yearbook is replaced by the "social fixed asset investment price index".The depreciation rate of capital in each industry is set at 4%, following the practice of Wang et al. [47]; the average annual growth rate of capital formation from 2001 to 2020 is calculated as 14.06% by the authors of this paper.Labor input is expressed as the number of employed persons in each industry.Calculation of labor input L i of industries: The labor input is expressed by "the number of employed persons in each industry", and "the number of employed persons in each industry" is equal to "the number of employed persons in the tertiary industry" multiplied by "The ratio of the number of employed persons in urban units in the industry to the number of employed persons in urban units in the industry", the above data are from the China Tertiary Industry Statistical Yearbook.
Calculation of labor output elasticity α i and capital output elasticity (1 The labor output elasticity is borrowed from the method of Tian et al. [23], the values of labor and capital output elasticities α i and (1 − α i ) are obtained by the parametric method on the basis of the C-D production function with constant returns to scale.After taking the logarithm of both the left and right sides of Equation (1), Equation ( 12) can be obtained as follows. ln where Y it denotes the output of industry i in period t, A denotes total factor productivity which is also the level of technology, K it is the capital input of industry i in period t, and L it is the labor input of industry i in period t.By substituting the values of industry output value added Y i , industry capital input K i , and industry labor input L i into Equation ( 12) and using a simple regression with STATA software, we can obtain the labor output elasticity α i and capital output elasticity 1 − α i for each industry.Explanatory variables: The explanatory variable is the degree of digital development of the industry (dod).Referring to the studies of Jiao et al. [48]; Xu et al. [49], the comprehensive evaluation index of the degree of digital development is constructed, and the indexes are standardized by the extreme value method, and the comprehensive value of the degree of digitalization is calculated by substituting dod it = ∑ k X it q k ; (k = 1, 2, . . ., 22) (where X it is the value after dimensionless, and q k is the weight value of the three-level index), and the value is multiplied by the share of each sub-sector of the service industry to represent the degree of digitalization of the industry.The construction of a comprehensive evaluation index system for the degree of digital development is shown in Table 1.
Control variables: Four indicators are selected: the degree of government intervention (ln gi), the degree of industry concentration (ln hhi), the degree of industry monopoly (ln im), and the degree of industry external dependence (ln ed).Among them, the degree of government intervention is measured using the ratio of industry tax revenue to industry value added; industry concentration is measured using the Herfindahl-Hirschman Index; industry monopoly is measured by the number of state-owned enterprises employed in the industry divided by the number of employees in the industry, and industry foreign dependence is measured by the amount of foreign investment in the industry divided by the industry value added.The weights of the corresponding variables are in brackets ().
The results of descriptive statistics of the variables are shown in Table 2.

Data Source
This paper conducts a study based on the panel data of 14 categories of service industry segments in China from 2001 to 2020.Among them, the division of service industry segments is based on the latest national economic industry classification standard (GB/T4754-2017), which divides the service industry into 14 industries.They are wholesale and retail trade; transportation, storage, and postal services; accommodation and catering; information transmission, software, and information technology services; finance; real estate; leasing and business services; scientific research and technical services; water, environment, and public facilities management; residential services, repair, and other services; education; health and social work; culture, sports, and entertainment; public administration, social security, and social organizations.The data are mainly obtained from The China Statistical Yearbook, National Economic and Social Development Statistical Bulletin, The China Taxation Statistical Yearbook, The China Labor Statistical Yearbook, The China Digital Economy Development and Employment White Paper, The China Tertiary Industry Statistical Yearbook, etc.The missing data are estimated by the "interpolation method".
Specifically, the values of capital mismatch and labor mismatch can be calculated by Equations ( 3) and ( 4), which require the value added of output, the amount of capital input, the amount of labor input, and the labor output elasticity for each industry.Among them, the value added of the output of each industry can be found directly through the database of The China Statistical Yearbook; the amount of capital input, labor input, and labor output elasticity cannot be found directly in the database, and need to rely on known data (the amount of fixed capital investment in each industry, the price index of fixed asset investment, the number of people employed in the tertiary industry, the number of people employed in urban units in that industry, and the number of people employed in urban units in that industry) to calculate.These known data are taken from The China Tertiary Industry Statistical Yearbook.The degree of digitalization of the industry needs to rely on the comprehensive evaluation index system of digital development for measurement, which is somewhat complicated, but all the data in Table 1 can be found directly from the database of The China Statistical Yearbook and The White Paper on Digital Economy Development and Employment in China.Data on the degree of government intervention are from The China Tax Statistical Yearbook, data on industry concentration are from The China Labor Statistical Yearbook, and raw values for the degree of industry monopoly and the degree of foreign pre-existence in the industry can also be obtained from The China Statistical Yearbook.

Empirical Model
To further empirically test Hypotheses 1 and 2 presented above, the following benchmark model is constructed in this paper.
In Equation ( 13), i is the service industry, t is the year, dod it is the degree of industry digitalization, µ i is the industry fixed effect, λ t is the time fixed effect, ε it is the random disturbance term, α 0 and β 0 are constant terms, and this paper focuses on the magnitude and direction of α 1 and β 1 .The degree of government intervention (ln gi), industry concentration (ln hhi), industry monopoly (ln im), and industry external dependence (ln ed) are also added as control variables.

Digitalization Degree of Each Industry in the Service Industry
Table 3 reports the degree of digitalization of each industry in different years, and from the results, transportation, storage, and postal services; information transmission, computer services, and software; wholesale and retail trade; finance; real estate; education; and public administration and social organizations have a high degree of digitalization.This is the same result as the ranking derived from The White Paper on the Development of China's Digital Economy and Employment (2019) regarding the share of the digital economy in the service industry in the value added of this industry [50].This fully illustrates the reliability of the comprehensive evaluation index system of industry digitalization constructed in this paper.

Overall Resource Mismatch in the Service Industry
The first column of Table 4 reports the overall resource mismatch of the service industry, while the second, third, fourth, and fifth columns report the mismatch of labor factors, the allocation of capital factors, the mismatch of emerging service industries and the mismatch of traditional service industries, respectively.From the definition of "Solow's residual term", it is clear that when the value of RAE is negative, it means that there is efficiency loss and resource mismatch.The measurement results in Table 4 show that there is a resource mismatch in the service industry as a whole, which is mainly manifested in the mismatch of capital and labor factors.At the same time, the traditional service industry with a low degree of digitalization loses efficiency, while the new service industry with a high degree of digitalization generates efficiency gains.The results of the measurement tentatively indicate that the increased digitalization of the service industry can improve the resource mismatch to a certain extent.

The Degree of Resource Mismatch among Service Industries
In order to examine the resource allocation of the industry segments in different periods.In this paper, the relative resource mismatch coefficients λKi and λLi of service industry segments are measured, and the magnitude of ( λKi − 1) 2 and ( λLi − 1) 2 indicates the degree of mismatch between capital and labor in the industry, respectively; the smaller the value, the lower the degree of resource mismatch.The smaller the value, the lower the degree of resource mismatch.The resource mismatch situation of each service industry is shown in Table 5.
In terms of capital elements, the relative capital mismatch coefficients of several traditional service industries, such as water conservancy, environment, and public facilities management; real estate industry; transportation, storage, and postal services, are all greater than one, indicating that they have excessive capital investment.The relative capital mismatch coefficients of several new service industries, such as information transmission, computer services, and software industry; accommodation and catering industry; financial industry; scientific research, technical services, and geological exploration industry, are all less than 1, indicating that there is a serious lack of capital investment.At the same time, several industries with high capital mismatch are concentrated in the traditional service industry, while the emerging service industry has insufficient capital investment but relatively low mismatch.In terms of the labor force, the relative labor force mismatch coefficients of scientific research, technical services and geological exploration; water conservancy, environment, and public facilities management; education; and culture, sports, and entertainment are all greater than 1, indicating that there is an over-input of the labor force.Several types of industries such as information transmission, computer service, and software industry; accommodation and catering industry; wholesale and retail industry have serious labor input shortages.The industries with a high degree of labor factor mismatch are social security, social welfare, and other residential service industries.According to the measurement results in Tables 3-5, it is found that the factor inputs of the emerging service industries with higher productivity, such as information transmission, computer services, and software, are instead lower than those of the traditional service industries with lower productivity, such as real estate and transportation.This has created a resource mismatch problem in the service industry as a whole.Therefore, increasing the degree of digitalization in the service industry can improve the resource mismatch problem in the service industry to a certain extent.In this paper, we will verify the improvement of resource mismatch by the degree of industry digitalization from an empirical perspective.The results of the empirical analysis of the degree of industry digitalization affecting the degree of resource mismatch in the service industry are shown in Table 6.
The regression results in Table 6 show that increased digitalization of the service sector can significantly improve the mismatch between capital and labor factors in the service sector.Among them, columns (1), ( 2), ( 5), and ( 6) are the results of OLS estimation, and columns (3), ( 4), (7), and ( 8) are the results of FGLS estimation.The regression coefficients of industry digitalization (lndod) are significantly negative for both capital and labor factor mismatches, which shows that the degree of industry digitalization in the service industry is significantly and negatively related to capital and labor mismatches in the service industry.In other words, the increase in industry digitalization can significantly improve the mismatch between labor and capital factors.Meanwhile, the improvement of the mismatch between capital and labor factors is significantly greater than that of the mismatch between labor factors.In terms of the control variables, when the explanatory variable is the capital mismatch (lncm), the coefficient of the degree of government intervention (lngi) is significantly negative at the 1% level, indicating that appropriate government intervention can improve the mismatch of capital in the industry; the coefficient of the degree of industry monopoly (lnim) is significantly positive at the 1% level, indicating that the higher the degree of industry monopoly, the more serious the capital mismatch.When the explanatory variable is labor mismatch (lnwm), the coefficient of the degree of government intervention (lngi) is significantly positive at the 1% level, indicating that excessive government intervention in the labor factor will increase the mismatch; the coefficient of the degree of industry monopoly (lnim) is significantly negative at the 1% level, indicating that a moderate amount of labor flowing into state-owned enterprises can optimize the employment structure and realize the factor.The coefficient of lnim is significantly negative at the 1% level, indicating that an appropriate amount of labor flowing into SOEs can optimize the employment structure and realize the rational allocation of factors.

Robustness Tests
In order to test the robustness of the baseline regression findings, this paper uses the 10%, 50%, 75%, and 90% quantile regressions in turn.
Table 7 shows the regression results for different quartiles.For the capital element, the regression coefficients of the quartiles of the degree of industry digitalization (lndod) roughly show a decreasing trend as the quartiles increase and are all consistent with the baseline regression results.This indicates that the higher the degree of industry digitalization, the lower the negative effect on capital mismatch.In other words, the increase in industry digitalization significantly reduces the degree of capital mismatch in the service industry.For the labor factor, as the quantile increases, the regression coefficients of the quantile of industry digitalization (lndod) tend to decrease and then increase and are consistent with the baseline regression results.This indicates that the increase in industry digitalization can significantly reduce the degree of labor mismatch in the service industry to a certain extent, but when the degree of digitalization exceeds a certain limit, a large amount of labor is replaced by artificial intelligence machines, which is not conducive to the optimal allocation of labor in the service industry.The results obtained using different quantile regressions are basically consistent with the results of the previous benchmark regressions, which fully indicates that the results of this paper are somewhat robust.

Heterogeneity Analysis
In the context of the digital economy, the service industry can rely on a powerful online trading platform to achieve optimal allocation of resources on a larger scale, and the industry realizes the integration of online and offline development.The emerging service industry has a higher degree of digitalization and higher productivity level compared to the traditional service industry, which can better reduce the efficiency loss in the transaction process [51].Therefore, considering that there may be differences in the improvement effect of the traditional service industry with a lower degree of digitalization and the emerging service industry with a higher degree of digitalization on resource mismatch, this paper divides the sample into two groups of emerging service industry and traditional service industry for analysis.Based on The Statistical Classification of Productive Services (2019) and The White Paper on the Development of China's Digital Economy (2021) published by the China Academy of Information and Communications Technology, and combining the calculation results of Table 2 to classify the service industries, the transportation, storage, and postal industries; information transmission, computer services, and software industries; wholesale and retail trade; financial industries; real estate industries; education industries; public administration and social organizations are classified as emerging service industries.The remaining industries, such as accommodation and catering; leasing and business services; scientific research, technical services, and geological exploration; water, environment, and public facilities management, are classified as traditional service industries.
The industry heterogeneity test results are shown in Table 8.When the industry belongs to the traditional service industry, for every 1% increase in the digital development degree of the industry, the capital mismatch degree decreases by 0.811%, and the labor mismatch rate decreases by 0.546%; when the industry belongs to the emerging service industry, for every 1% increase in the industry digital development degree, the degree of capital mismatch decreased by 0.992%, and the degree of labor mismatch decreased by 0.827%.Therefore, it can be concluded that when the degree of digital development of the industry increases, the misallocation of capital and labor elements in the emerging service industry will decrease more significantly.In other words, the increased level of digital development of the industry has a greater effect on the improvement of labor and capital mismatch in emerging services than in traditional services.The authors of this paper argue that there are two main reasons for this phenomenon.One is that emerging service industries have a higher level of digitalization and the marginal cost of production decreases over time, which can improve the marginal return on resources.The second is that the increased digitalization has promoted the development of online platforms, which provide more convenient employment and investment channels for surplus labor as well as surplus capital and improve the efficiency of reallocation of surplus labor and capital.This also verifies Hypothesis 3.

Conclusions and Policy Recommendations
Based on the summary of previous scholars' research results, this paper takes the digital development of the service industry to enhance resource allocation efficiency as the starting point and uses 20 years of China's service industry segment data from 2001 to 2020 to conduct an empirical study on the impact of industry digitalization on resource mismatch in the service industry.First, this paper derives a theoretical model of the efficiency loss arising from resource mismatch by combining the traditional model of resource allocation.Second, using the theoretical model, we calculate the resource mismatch, labor mismatch, capital mismatch, emerging services mismatch, traditional services mismatch, and factor mismatch of each service sector in China from the perspective of efficiency loss.Again, a comprehensive evaluation index for the digitalization development degree is constructed and the digitalization level of each industry is calculated by combining it with existing studies.Finally, the impact of the degree of industry digitalization on the mismatch of labor and capital in the service industry is empirically analyzed.As a result, the following main conclusions are drawn in this paper.
(1) There is an overall resource mismatch in China's service industry.The main manifestation is the mismatch of labor and capital, and there is no more serious efficiency loss for the emerging service industry with a higher degree of industry digitalization.(2) There are different degrees of resource mismatch in each sub-sector of the service industry, and the resource mismatch is more serious for the traditional service industry with a lower degree of industry digitalization.The industries with more serious capital mismatch are water, environment and public facilities management, real estate, transportation, storage, and postal services, capital-intensive production services and residential services, and other services; the industries with more serious labor mismatch are education, health, social security and social welfare, and other laborintensive public services.(3) There is a significant negative relationship between the degree of industry digitalization and the mismatch of labor and capital factors, i.e., the increase in industry digitalization can significantly improve the mismatch of capital and labor, and this improvement effect is heterogeneous between the new service industry and the traditional service industry, i.e., the increase in industry digitalization improves the mismatch of the new service industry to a greater extent than the traditional service industry.
In view of the above conclusions, it can be found that the integration of the digital economy and traditional service industry is indispensable to promoting the high-quality development of China's economy.Because of this, we make the following recommendations.
(1) The government should encourage new technologies to be used in the industry.
(2) The government should encourage the research and development of new technologies, the development of new industries, and the formation of new business models, and accelerate the digital transformation of traditional service industries such as smart logistics, digital commerce, digital finance, and intelligent transportation; promote the digital development of public service industries such as smart elderly care, smart medical care, smart education, and digital government; the government should correctly guide and accelerate the promotion and application of digital culture, digital media, and other digital cultural entertainment industries and application.(3) Accelerate the improvement of talent training mechanisms, improve the digital literacy of workers, and provide a guarantee for the healthy and sustainable development of the digital economy; improve the market supervision mechanism, and strictly punish the improper theft of privacy and malicious competition on the Internet, so as to escort the healthy development of the digital economy.The government appropriately guides the flow of capital to the new service industry with a higher degree of digitalization to improve the overall productivity of the service industry and thus promote the development of China's economy.

Table 1 .
Comprehensive evaluation index system of digital development degree.

Table 2 .
Descriptive statistics of variables.
All of the above data is calculated and exported by the STATA.

Table 3 .
Digitalization by industry in different years.
From S 1 to S 14 , they represent transportation, storage, and postal services; information transmission, computer services, and software; wholesale and retail trade; accommodation and catering; finance; real estate; leasing and business services; scientific research, technical services, and geological survey; water, environment, and public facilities management; residential services and other services; education; health, social security, and social welfare; culture, sports, and entertainment; public administration and social organizations.Data sources are the authors' calculations.

Table 4 .
Overall resource mismatch in the service industry.

Table 5 .
The degree of resource mismatch in different industries.Results of an Empirical Analysis of the Digital Economy to Improve Resource Mismatch in the Service Sector 5.4.1.Baseline Regression Analysis

Table 6 .
The impact of industry digitalization on the degree of resource mismatch.