The Mechanisms and Prompting Effect of the Development of Digital Economy on Total Factor Productivity

Abstract

The productivity of data factor through digital technology is an important direction to accelerate the formation of new drivers of economic growth. As a big country in the digital economy, China has rich practical experience in this regard. We study the impact of digital economy on the total factor productivity (TFP) and mechanisms through which the impacts get realized. By the empirical analysis on the annual data of 282 prefecture-level cities in China from 2011 to 2022, we find that the development of digital economy can significantly increase TFP, which, however, may take time to be witnessed. On the other hand, the TFP prompting effect, once manifested, will display a nonlinear accelerating tendency. On the mechanisms, our empirical findings support that the development of digital economy improve TFP mainly via reducing the operating costs of the economy, promoting innovations, and enlarging the size of the market. Our findings provide positive evidences for the development of digital economy, which support the industrial policy designed for prompting digital technology and digital industries in China.

Keywords

digital economy productivity effects Solow’s paradox high-quality development

Introduction

Digital technologies represented by the Internet, big data and cloud computing have made data a new factor of production and facilitated the formation and development of the digital economy. Digital technology has become a universal technology to promote global economic transformation (J. Liu et al., 2024). Major economies in the world, including China, have taken the development of digital economy as an important strategy to promote the upgrade of industrial structure and realize high-quality development (Guo et al., 2023). Despite the importance of the digital economy, it has not yet been very clear regarding how and to what degree the development of digital economy can prompt the total factor productivity of the whole society, which calls for a formal analysis.

In literature, there has been a persistent debate and skepticism on whether the digital economy can improve productivity, while it still lacks of cautious evaluation on the efficiency of digital technology inputs among both local governments and enterprises, especially in small and medium-sized cities. Can large-scale inputs in digitalization receive sufficient revenue returns to produce a higher productivity effect? Early studies have largely discussed the existence of this effect. Roach (1987) examined the relationship between computer adoption and productivity from 1977 to 1984 and found little relationship between the two. The renowned “Solow’s Paradox” even stated that, in addition to productivity, the role of computers is everywhere. Afterwards, the debate on Solow’s paradox intensified, and most scholars believe that the paradox does exist, and found that investment in information technology capital can not bring greater returns, and more information technology investment in the industry did not produce higher productivity (Morrison, 1997; Roach, 1991). Of course, some studies have also affirmed the contribution of digital technology to productivity and explored the reasons for the productivity paradox, mainly proposing the time lag effect, measurement bias, mismanagement and other factors (David, 1990; Brynjolfsson, 1993; Ahmad & Schreyer, 2016). It is based on these factors that the productivity paradox of the digital economy is still relatively common. Karacuka et al. (2024) using data from 40 African economies, the study found that the correlation between digitalization and labor productivity is weak, and there is still a productivity paradox in services, which can even have a negative impact. Gao et al. (2025) used data from listed companies in China’s manufacturing industry to study the “digital paradox” in the digital transformation of manufacturing and found that large investments in digital technologies do not necessarily lead to higher returns.

With the increase of information technology investment and the general application of digital technology, the laws of digital technology becomes clarified, most scholars do no longer recognize the existence of the productivity paradox, and believe that information technology has a significant role in promoting economic efficiency (Ahmad & Schreyer, 2016). It was found that the accumulation of information technology capital in the United States at the end of the 90s productivity recovery to play an important role (Stiroh, 2002). Even Solow himself in 2000 that the “productivity paradox” has disappeared. Since then, a large number of scholars have conducted rich research on the productivity effects of IT in different industries and at different spatial scales. Cardona et al. (2013) find that most of the literature supports a positive correlation between IT and total factor productivity. Meng et al. (2023) test the positive impact of the competitiveness of digital cities on TFP by using the data of 15 emerging first-tier cities in China. Pan et al. (2022) finds that there is a positive and nonlinear relationship between the digital economy and TFP across Chinese provinces, and that the digital economy plays an innovation-driven role in the continuous improvement of TFP. S. Liu et al. (2024) revealed that the digital economy has enhanced TFP in the vast majority of industries, but its impact on pharmaceutical manufacturing and the real estate industry was not significant. In addition to research on the existence of Solow’s paradox, some scholars have also discovered an inverted U-shaped relationship between the digital economy and total factor productivity, and that the industry environment may play a moderating role in this relationship (Suo et al., 2024).

While scholars have tended to deny the universality of the productivity paradox, it has been raised again as artificial intelligence has become the main direction of development for the new generation of digital technologies. Acemoglu et al. (2014) point out that the productivity paradox has not disappeared. Van Ark (2016) argues that the new digital economy is still in the “installation phase” and has not yet produced any significant improvements in productivity. Chen and Cai (2022) use China’s provincial panel data to find that AI only has a boosting effect on the scale of economic growth, but not on the rate of growth and efficiency, which is characterized by a new “Solow paradox.” Referring to specific industries, it is found that the productivity paradox of the tourism industry in the digital economy, and both confirmed the existence of Solow’s paradox (Yu & Zuo, 2022). However, in energy industry, it is found that the digital economy can significantly increase the productivity (Che & Wang, 2023).

To these conflicted empirical findings, Brynjolfsson et al. (2019) found that the benefits of AI technology are not reflected in national statistics, and summarized that the modern productivity paradox may be due to over-optimistic expectations, mis-measurement, and the lack of a clear definition of AI. optimistic expectations, measurement bias, concentration of benefits and rent dissipation, and lags in value realization.

Based on the above analysis, it can be seen that the development of digital economy plays an important role in enhancing TFP, and there is a rich literature on the relationship between the two, however, with the continued advancement of digital economy, the research on the relevant mechanisms still needs to be further deepened, empirical research is also urgent to follow up, and the conclusions of the existing research have not been completely agreed upon. From this perspective, this study provide three marginal contributions to the literature: First, this paper theoretically clarifies the mechanism and transmission path of the digital economy affecting TFP through the two dimensions of cost and output. Second, utilizing data from 282 prefecture-level and above cities in China from 2011 to 2022, the specific effects of digital economy on enhancing TFP are empirically examined, including the enhancement effect, the lag effect, and the nonlinear incremental effect. Third, through the mechanism analysis, it is verified that the digital economy can enhance TFP through the three paths of reducing cost, promoting innovation and expanding market scale.

Mechanism Analysis and Research Hypothesis

Cost Reduction and Productivity Effects of Digital Transformation

The process of digital transformation is closely linked to cost reduction and productivity gains. As the digital economy evolves, its operating costs will gradually decrease (Goldfarb & Tucker, 2019).

First, market transaction patterns in the digital economy are characterized by marginal costs approaching zero. This does not mean that there are no costs associated with digital production and services, but rather that the additional costs of new output are significantly lower once the infrastructure and hardware and software systems are in place (Jones & Tonetti, 2020). Initially, governments, businesses and individuals need to invest significant resources in new digital infrastructure, equipment development and acquisition, and learning costs for digital products. Once these conditions are met, the incremental cost of each new unit of output will approach zero. Economist Jeremy Rifkin in suggests that while zero-cost production and supply is difficult to achieve, it has become possible to produce more without significantly increasing total costs.

Second, from the perspective of the law of scale, the digital economy follows a sublinear scaling law of metabolic rate (Y. Li et al., 2023). Digital technology interconnects everything through chips, giving the economic system a networked character (Meka’a et al., 2024). With the expansion of network-based organizations, their operating costs show sub-linear scaling. If the digital economic system is compared to an organism, its internal transaction costs are similar to the metabolic rate of the organism. Max Kleiber’s study of biological evolution and Jeffrey West’s theory of urban science both point out that the metabolic rate or infrastructure needs are proportional to a particular power of scale when scale changes. The digital economy, as an extension of physical space, follows this same pattern of cost changes due to scale expansion. Therefore, the following Hypothesis 1 is proposed.

Hypothesis 1 (H1). The digital economy can significantly increase TFP by reducing operating costs.

Productivity Effects of Increased Output and Digital Transformation

First, the digital economy significantly affects the scale of innovation. In the era of digital economy, the scale of innovation not only shows a super-exponential growth, but also the cost of innovation will drop significantly due to the emergence of free components and new models. The digital economy, as a network economy and a sharing economy, facilitates connections and social interactions between subjects and objects, which in turn generates more innovation and creativity (Cai et al., 2024). It is super-linear scale scaling. Varian’s Law explains the exponential growth of digital technological innovations: the recombination of technological components triggers new trends in technological development. These free digital components and highly valuable digital products incentivize innovators to create a nearly infinite number of combinations, leading to an explosion of innovative products in digital technology (Wang & Ye, 2023).

Second, the digital economy affects market size. While technological innovations can lead to new products and services, it is difficult to increase TFP without an economic impact. Economist Karl Benedikt Frey and historian John Bernard have both pointed out that technology must serve an economic purpose and be applied to production in order to have an economic impact. Digital technological innovations need to generate more profits and a larger market size in order to contribute to social progress and TFP (Y. Liu et al., 2024). Further, there are two ways in which the price of a new product can change: first, digital transformation reduces production costs, thereby lowering product prices, increasing market share and expanding market size; and second, it adds digital intelligence features or creates a disruptive new product that meets higher consumer demand, improves pricing, generates more consumer demand, and creates a larger market size. Therefore, the following Hypothesis 1 is proposed.

Hypothesis 2 (H2). The digital economy can increase TFP by promoting innovation and expanding market size.

Discussion of the Productivity Paradox

The output effects of the digital economy exhibit super-linear growth while costs shrink sub-linearly, foreshadowing a non-linear increase in productivity as digital transformation deepens. However, why is there a productivity paradox in the digital economy?

In the early stages of transformation, digital inputs are mainly used to replace traditional management and production methods, and their empowering and multiplying effects will not be visible until the replacement is complete and a certain level of digital economy connectivity is reached (Huang et al., 2023). At this point, the output effect is not obvious despite the increase in inputs, which may lead to a decrease in the Solow surplus. At the same time, even if the initial output effects are visible, they may not be accurately identified by traditional measures or may be too small to be recognized, showing signs of weakening productivity. These two aspects together contribute to the Solow paradox, but this is only a short-term phenomenon. Rather than being deterred by the negative short-term effects, market venture capital has accelerated into digitalization by high expectations and policy guidance. As digitization advances, the level of networking and intelligence in the economic system increases, the enabling and output effects of the digital economy become more pronounced, and statistical methods are gradually improved, measurement bias is reduced, and the trend of the reduction of the Solow residual gradually eases. In fact, the digital economy exhibits similar lag effects in driving economic growth and environmental protection (Z. Li & Wang, 2022). Therefore, the following Hypothesis 3 is proposed.

Hypothesis 3 (H3). The digital economy can increase TFP, but it has a time lag effect and will be non-linearly increasing.

Methodology and Data

Model Construction

Benchmark Model

Referring to the method of C. Zhao et al. (2023), in order to test the effect of digital economy on TFP, the benchmark model is set as follows:

TF P_{it} = α_{0} + α_{1} Di g_{it} + α_{2} X_{it} + μ_{i} + λ_{t} + ε_{it}

(1)

where subscript $i$ is the city identifier and $t$ is the year identifier. $TF P_{it}$ represents the TFP of region $i$ in year $t$ ; $Di g_{it}$ represents the level of digital economy development of region $i$ in year $t$ ; represents other control variables affecting the TFP; $μ_{i}$ is the individual fixed effect; $λ_{t}$ represents the year fixed effect; and $ε_{it}$ is the random error term obeying an independent homogeneous distribution.

Mechanism Models

In order to test the mechanism of the impact of the digital economy on TFP, the following econometric model is constructed to be tested in combination with the benchmark model, since the theoretical analysis has shown that the impacts generated by each mechanism variable are obvious:

Mechanis m_{it} = β_{0} + β_{1} Di g_{it} + β_{2} X_{it} + μ_{i} + λ_{t} + ε_{it}

(2)

where $Mechanis m_{it}$ represents the mechanism variable to be tested.

Nonlinear Model

In order to test the non-linear impact effect of the digital economy on TFP, two methods are used here: one is to use the threshold effect model; the other is to add the quadratic term of the digital economy index to the baseline model.

The model constructed by method I is:

\begin{array}{l} T F P_{i t} = γ_{0} + γ_{1} D I G_{i t} * I (D I G_{i t} \leq γ) + γ_{2} D I G_{i t} * I (D I G_{i t} γ) \\ + γ_{3} X_{i t} + μ_{i} + λ_{t} + ε_{i t} \end{array}

(3)

The model constructed in method II is:

TF P_{it} = θ_{0} + θ_{1} DI G_{it} + θ_{2} {DIG}_{it}^{2} + θ_{3} X_{it} + μ_{i} + λ_{t} + ε_{it}

(4)

In method I, the digital economy index is the threshold value, I(−) is the indicative function, if the threshold condition in parentheses is satisfied, the value is assigned to 1, otherwise it is 0. If there is a single threshold between the two, and the coefficient of the relationship between the two becomes larger after crossing the threshold value, the nonlinear increasing relationship between the two is verified. In method II, if the coefficient of the quadratic term of the digital economy index in the regression results is positive and significant, and the two run on the right side of the U-curve, the nonlinear relationship can also be verified.

Variable Setting

Explained Variables

This paper focuses on the explanatory variables is the TFP at the city level. At present, the main methods for measuring regional TFP include parametric and non-parametric methods. In the parametric method, it is commonly used to replace the TFP with the estimated Solow residual value given the form of the specific production function. The non-parametric method mainly uses Malmquist productivity index based on DEA model. In this paper, TFP obtained by the Solow residual method is used for the study, and the results obtained by the non-parametric method are used for the robustness test.

For the measurement of the Solow residual, the Solow residual measured by the C–D production function is used instead. The production function is $Y_{it} = A_{it} K_{it}^{α} L_{it}^{β}$ , 0 < α, β < 1, and the Solow residual $A_{it} = Y_{it} / K_{it}^{α} L_{it}^{β}$ . Where $Y_{it}$ is measured by the real GDP converted to 2011; $L_{it}$ is measured by the number of persons employed in urban units at the end of the year; capital input K is the fixed capital stock, estimated by the perpetual inventory method, which is calculated as $K_{t} = I_{t} + (1 - δ) K_{t - 1}$ . The opening fixed capital stock $K_{0}$ is replaced by the fixed capital investment in each municipality in 2011 divided by 10%. $I_{t}$ is the fixed capital investment in year t, which is converted to the constant price level in 2011 using the CPI index; δ is the depreciation rate of fixed capital, which is set at 9.6%. The output elasticities of capital and labor α = .64 and β = .45 are obtained in estimating the Solow residual.

Core Explanatory Variables

At present, the literature on measuring the level of digital economy is relatively rich, but no consensus has been formed, and most of the existing studies are measured by constructing a multidimensional indicator system. From the point of view of research at the prefecture level, the method of constructing an indicator system has been more highly recognized. According T. Zhao et al. (2020), this paper adopts the indicators of four dimensions: Internet penetration, related output situation, cell phone penetration rate and digital finance. The specific index contents are the number of fixed Internet broadband access users, the proportion of telecommunication business income in each region to the whole country, the number of cell phone users at the end of the year, and the China Digital Inclusive Finance Index issued by the Digital Finance Research Center of Peking University. The entropy method is utilized to calculate the digital economy development index of each city.

Control Variables

In order to minimize the estimation bias caused by omitted variables and drawing on existing research (T. Zhao et al., 2020; Zou et al., 2024), this paper controls the following variables that may have an impact on regional TFP: industrial structure (Stru), measured by the ratio of tertiary industry to secondary industry value added; level of economic growth (Rpgdp), measured by the real per capital GDP converted to 2011; population density (Popty), measured by the number of people per unit area; Financial Development Level (Fina), measured by the year-end RMB deposit and loan balances of financial institutions as a percentage of GDP; Government Regulation Intensity (Govoi), measured by the ratio of fiscal expenditures to fiscal revenues; and Educational Dissemination Degree (Edu), measured by the ratio of education expenditures to fiscal expenditures.

Statistical Description of Variables

Considering the existence of negative values in the TFP obtained from the Solow residual, and in order to reduce the estimation bias caused by heteroskedasticity, this paper adopts semi-logarithmic model to estimate equation (1), that is, take the level value of the explanatory variables, and take logarithmic treatment of the core explanatory variables and the control variables, and the results of the statistical descriptions of each variable are shown in Table 1.

Table 1.

Descriptive Statistics.

Variables	Obs.	Mean	Std.	Min.	Max.
$TFP$ ( $Solow' s residual$ )	3,384	0.0000	0.2523	−1.0597	1.2138
$TFP$ ( $Global Malmquist$ )	3,102	1.0176	0.0870	0.4553	2.0941
$Dig$	3,384	−2.5602	0.6586	−5.8098	−0.2324
$Stru$	3,384	−0.0680	0.4687	−2.1750	1.6768
$Rpgdp$	3,384	10.6494	0.5501	8.8416	13.0034
$Pop ty$	3,384	−3.4620	0.9261	−7.5824	−1.1521
$Fina$	3,384	0.8324	0.4123	−0.5312	3.0588
$Govoi$	3,384	0.9210	0.5350	−0.4326	2.8626
$Edu$	3,384	−1.7626	0.2442	−4.5682	−1.0322

Data Sources

The data used in this paper mainly consists of two parts: city level and provincial level. The city-level data come from the China Urban Statistical Yearbook of the relevant year, while individual missing data come from the statistical yearbook of the province or the Statistical Bulletin of National Economic and Social Development of Prefecture-level Municipalities. In the end, if individual data were still missing, they were filled in by linear interpolation.

Results of Empirical Analysis

Benchmark Regression Results

Table 2 shows the results of the benchmark regression. Columns (1) to (3) show the regression results for the current period, lag 1 and lag 2 of the digital economy index without adding control variables. The estimated coefficients of the digital economy index are all significant at the 1% level, and the coefficient of lag 2 is much higher than that of lag 1 and slightly lower than that of the current period. Columns (4) to (6) are the regression results of current period, lag 1 and lag 2 of the digital economy index under the addition of control variables, and the estimated coefficients of the digital economy index are all significant at the 1% level, and the coefficient of lag 2 is still not only much higher than that of lag 1, but also higher than that of current period. This means that the development of digital economy can significantly increase TFP, and there is a lag in this effect, and the first half of hypothesis 3 is verified.

Table 2.

Benchmark Regression Results.

Variables	TFP
Variables	(1)	(2)	(3)	(4)	(5)	(6)
$Dig$	0.0829*** (6.1613)			0.0527***(2.6070)
$L . Dig$		0.0671***(4.9082)			0.0453**(2.4142)
$L 2 . Dig$			0.0826***(6.0785)			0.0717***(3.7122)
$Stru$				−0.0522**(−2.1258)	−0.0578**(−2.2756)	−0.0751***(−2.7536)
$Rpgdp$				0.3364***(9.1006)	0.3429***(9.5773)	0.3316***(9.4723)
$Popty$				0.1080(1.2524)	0.1416(1.4834)	0.1942(1.6327)
$Fina$				−0.1691***(−4.0868)	−0.1613***(−4.2281)	−0.1631***(−4.2493)
$Govin$				0.0625**(2.3402)	0.0624**(2.2925)	0.0491*(1.7549)
$Edu$				0.0488**(2.2003)	0.0577**(2.4846)	0.0489*(1.8662)
City FE	Yes	Yes	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes	Yes	Yes
Observations	3,384	3,384	3,384	3,384	3,384	3,384
R ²	.055	.036	.054	.354	.345	.367

Note. t-Statistics in parentheses.

p < .1. **p < .05. ***p < .01.

The estimation results of the control variables are also basically in line with the expectation, and the coefficients of the variables are consistent in terms of sign and significance, and only the individual coefficients are slightly different at the significance level. Specifically, the industrial structure shows negative significance, which indicates that the structural advancement of blindly pursuing the increase of output value of the tertiary industry by detaching from the secondary industry may not be conducive to the improvement of the TFP of the society, which also confirms the existence of Baumol’s Cost Disease. Economic growth is significantly positive at the 1% level, indicating that quantitative growth is the basis and prerequisite for qualitative growth. The coefficient of population density is positive but not significant, indicating that the agglomeration effect of the population as a whole still needs to be improved. The coefficient of financial development level is significantly negative, again indicating that the direction of economic development from de-realization to de-facto may have a negative impact on the efficiency of growth. The coefficients on government intensity and education penetration are both significantly positive, suggesting the importance of an active government aimed at overcoming market failures and of highly qualified personnel in enhancing economic efficiency.

Robustness and Endogeneity Tests

In order to test the robustness of the regression results, this paper takes three ways of replacing the explained variables, replacing the explanatory variables and endogeneity test.

Replacement of Explanatory Variables

The global Malmquist index obtained from the non-parametric method was used to replace the Solow residual in the regression. The input and output indicators therein are consistent with the Solow residual method. In addition, considering that the global Malmquist is censored data, the range of values is somewhat limited, and in order to exclude possible categorical effects, the panel Tobit model is constructed here at the same time for comparison, and the results are shown in Table 3. Columns (1) and (2) of Table 3 are the estimation results using the fixed panel model, and the coefficient of the digital economy with a lag of 2 periods is higher than the value of the current period; columns (3) and (4) are the estimation results using the panel Columns (3) and (4) are the estimation results of the Tobit model, where the estimated coefficient of the digital economy in the current period is positive but insignificant, while that of the lagged 2-period is significantly positive at the 1% level, which is consistent with the benchmark results.

Table 3.

Robustness Test.

	FE panel		Tobit panel		FE panel
Variables	(1)	(2)	(3)	(4)	(5)	(6)
$Dig$	0.0304*(1.8719)		0.0037(0.8108)		0.0367***(2.6232)
$L 2 . Dig$		0.0552***(3.9623)		0.0146***(3.0994)		0.0842***(5.2495)
$Stru$	−0.0313***(−2.6717)	−0.0431***(−3.2845)	−0.0083(−1.5272)	−0.0105*(−1.7084)	−0.0472*(−1.8316)	−0.0942***(−3.4103)
$Rpgdp$	0.0354*(1.9367)	0.0396*(1.9110)	0.0027(0.4808)	0.0052(0.8225)	0.3365***(9.2590)	0.2910***(7.8232)
$Popty$	−0.0898**(−2.3242)	−0.0756**(−1.9822)	−0.0052**(−2.1838)	−0.0064**(−2.4210)	0.0894(1.0667)	0.1404(1.3972)
$Fina$	−0.0358**(−2.0833)	−0.0206(−1.0368)	0.0055(0.9731)	0.0066(1.0662)	−0.1755***(−3.9670)	−0.2051***(−4.6892)
$Govin$	−0.0048(−0.3945)	−0.0347***(−2.6035)	−0.0051(−0.8785)	0.0003(0.0433)	0.0642**(2.4067)	0.0357(1.3088)
$Edu$	0.0298**(2.2369)	−0.0032(−0.2211)	0.0064(0.7939)	−0.0034(−0.3972)	0.0520**(2.3436)	0.0601**(2.3579)
City FE	Yes	Yes	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes	Yes	Yes
Observations	2,820	2,538	2,820	2,538	3,102	2,538
R ²	.028	.044	—	—	.353	.382

Note. t-Statistics in parentheses.

p < .1. **p < .05. ***p < .01.

Replacing Explanatory Variables

The development of digital economy helps to realize financial inclusion and promote the rapid development of digital inclusive finance, and some studies even use digital economy and digital finance as synonyms without differentiation (Zhang et al., 2020), so this paper switches to the Digital Inclusive Finance Index released by Peking University to measure the level of digital economy development. The results of the robustness test are shown in columns (5) and (6) of Table 3. The results show that the coefficients of the digital economy index are all significantly positive at the 1% level, and the value of lag 2 is higher than the current period, which is also consistent with the benchmark results.

Endogeneity Test

The relationship between digital economy development and TFP may have potential endogeneity problems, both bidirectional causality and omitted variable problems may exist, therefore, the instrumental variable method is used here to re-estimate to test the robustness of the results. The instrumental variables must be highly correlated with the endogenous variables and independent of the residual terms. The number of post offices per 100 people in 1984 in each city and the spherical distance between each city and Hangzhou are utilized here as instrumental variables for the level of digital economy development. To allow the instrumental variables to change over time, they are multiplied with the number of provincial Internet broadband access ports in each city in the previous year, and this cross variable is used as the final instrumental variable chosen. The estimation results are shown in Table 4, columns (1) and (2) are the estimation results of the digital economy index in the current period and lagged 2 periods respectively. From the test results, the K-P LM statistic in columns (1) and (2) are 15.62 and 23.52 respectively, which are both significant at the 1% level, and the C-D Wald F statistic is 25.08 and 53.04 respectively, which are also both greater than the critical value of 19.93 at the 10% significance level of the Stock-Yogo test for weak instrumental variables, which indicates that the set instrumental variables are reliable. In terms of the estimated coefficients, the coefficient of the current period digital economy index in column (1) is 0.4303, which is significant at the 10% level, and the coefficient of the lagged 2-period digital economy index in column (2) is 0.6750, which is significant at the 1% level, which once again verifies the robustness of the benchmark regression.

Table 4.

Endogeneity Test.

	IV		DIF-GMM	SYS-GMM
Variables	(1)	(2)	(3)	(4)
$Dig$	0.4303*(1.8427)		0.0806**(1.9717)	0.1028***(3.9510)
$L 2 . Dig$		0.6750***(4.3023)
$L . TFP$			0.3678***(6.9593)	0.1071**(2.2841)
City FE	Yes	Yes	Yes	Yes
Year FE	Yes	Yes	Yes	Yes
Control	Yes	Yes	Yes	Yes
Kleibergen–Paaprk LM statistic	15.62 [0.001]	23.52 [0.001]
Kleibergen–Paaprk Wald F statistic	25.08 {19.93}	53.04 {19.93}
$AR (1)$			z = −3.60***	z = −2.37**
$AR (2)$			z = −0.10	z = −0.25
Sargan test			$χ^{2} (123) = 3, 400.09$	$χ^{2} (103) = 1, 505.47$

Note. [] values are p-values and {} values are critical values at the 5% level of the Stock-Yogo weak identification test.

p < .1. **p < .05. ***p < .01.

The 2SLS method using instrumental variables assumes that the random error term of the model obeys the spherical disturbance characteristics, and if the assumption is not obeyed, the estimation results are not the most efficient. GMM, on the other hand, does not need to know the exact distributional characteristics of the random error term, and even if the residual term suffers from heteroskedasticity or autocorrelation, the GMM estimation results are more efficient than the 2SLS, therefore, here, lagged 1 period of the explanatory variables are incorporated into the explanatory variables. The results are then re-estimated using difference GMM and system GMM to further test the robustness of the results. Since the GMM uses the lag of the endogenous explanatory variables as instrumental variables, only the estimation results of the GMM are utilized here to test the promotion effect of the digital economy index on productivity, and the lag effect is no longer tested, and the results are shown in columns (3) and (4) of Table 4. The results show that both models reject the existence of first-order autocorrelation but not second-order autocorrelation, and the Sargan value also passes the over-identification test, indicating that the instrumental variables are valid. The coefficient values of the digital economy index in the two models are significantly positive at the 5% and 1% levels, respectively, validating the productivity effect of the digital economy in the benchmark regression.

Mechanism Analysis

The theoretical assumptions point out that economic operation costs, technological innovation, and market size are the three paths through which the digital economy affects TFP.

For the economic operation cost, although China is already a market economy, the transaction cost is still not low, and there is still a lot of work to be done to improve the efficiency of market operation. The Chinese economy also has a very obvious government-led feature, and the local financial expenditures to a certain extent will violate the market principle and have an inhibiting effect on the efficiency of the economy, so the proportion of the government’s budgetary expenditures to the GDP is used to measure the cost, and the higher the proportion, the higher the level of government intervention, and the higher the cost of economic operation. The higher it is indicates that the higher the level of government intervention, the higher the cost of economic operation, and the estimation results are shown in column (1) of Table 5. The results show that the coefficient of the digital economy index is −0.0397, which is significant at the 5% level, indicating that the development of the digital economy can significantly reduce the cost of economic operation.

Table 5.

Mechanism Analysis.

	(1)	(2)	(3)
Variables	Market	Inno.	Con.
$Dig$	−0.0397**(−2.5096)	0.1930**(2.4476)	0.0573**(2.4123)
Control	Yes	Yes	Yes
City FE	Yes	Yes	Yes
Year FE	Yes	Yes	Yes
Observations	3,384	3,384	3,384
R ²	.687	.701	.305

Note. t-Statistics in parentheses. *p < .1. **p < .05. ***p < .01.

For technological innovation, the number of invention patents published by the State Intellectual Property Office (SIPO) in each city is used to measure the number of patents in each region, which is obtained by utilizing the advanced search function on the SIPO website and selecting the region, year, and type of patents, and then counting the number of patents in each region. The higher number of invention patents indicates the higher level of technological innovation, and the estimation results are shown in column (2) of Table 5. The results show that the coefficient of the digital economy index is 0.1930, which is significant at the 5% level, indicating that the development of digital economy can significantly promote regional technological innovation.

For market size, the ratio of total retail sales of consumer goods to GDP is used mainly based on the demand perspective, and the larger the ratio is, the larger the market size is, and the estimation results are shown in column (3) of Table 5. The results show that the coefficient of the digital economy index is 0.0573, which is significant at the 5% level, indicating that the development of digital economy can significantly expand the market size. Hypotheses 1 and 2 are verified.

Analysis of Nonlinear Effects

For the estimation of model (3), the existence of the panel threshold is first tested based on the method of Hansen (1999). After repeated sampling 300 times using the bootstrap method, it is found that the digital economy index threshold variable significantly passes the single-threshold test and fails to pass the double-threshold test, so the single-threshold regression model is set. For the estimation of model (4), if the coefficient of the quadratic term of the digital economy index in the regression results is positive and significant, and the relationship runs on the right side of the U-shaped curve, it can also verify the nonlinear relationship between the two.

Table 6 presents the estimation results based on model (3) and model (4) before and after the inclusion of control variables. Columns (1) and (2) of Table 6 show the estimation results of the threshold model. It can be seen that the coefficients of the digital economy index are characterized by an increase after crossing the threshold, regardless of whether control variables are added or not. Specifically, column (2) shows that when the logarithmic value of the digital economy index is lower than −2.5883, the coefficient of the impact of digital economy development on TFP is 0.0595 and is significant at the 1% level, and when the threshold is crossed, the impact coefficient increases to 0.0759, which is also significant at the 1% level, suggesting that after the accelerated development of the digital economy, the effects of cost, innovation and market effects, etc., begin to fully appear, and the effect of the digital economy on the enhancement of TFP will be significantly increased.

Table 6.

Nonlinear Effect Test.

Variables		(1)	(2)	(3)	(4)
Threshold value	$q$	−2.6382	−2.5883
$Dig \times I (Dig \leq q)$		0.1007***(13.0070)	0.0595***(5.5256)
$Dig \times I (Dig > q)$		0.1136***(11.5822)	0.0759***(6.6703)
$Dig$				0.2825***(4.5371)	0.1697***(2.7019)
$Di g^{2}$				0.0337***(3.2284)	0.0174**(2.1287)
Control		No	Yes	No	Yes
City FE		Yes	Yes	Yes	Yes
Year FE		Yes	Yes	Yes	Yes
Obs.		3,384	3,384	3,384	3,384
$R^{2}$		.061	.362	.068	.357
$F$		91.321	199.706	25.178	43.668

Note. t-Statistics in parentheses. *p < .1. **p < .05. ***p < .01.

Columns (3) and (4) of Table 6 show the regression results with the inclusion of the quadratic term of the digital economy index. It can be found that the quadratic term of the digital economy index shows positive significance regardless of whether control variables are included or not. With the inclusion of control variables, the coefficient value is 0.0174 and is significant at the 5% level. Using the estimated coefficients, we can get the inflection point value of the digital economy productivity effect turning from negative to positive is −4.876, and in the sample data, there are only some individual cities with digital economy indexes lower than this inflection point value in 2011, which indicates that on the whole, China’s digital economy influence effect on the TFP is on the right hand side of the U-curve The digital economy has passed the stage of Solow’s paradox and started to show nonlinear incremental characteristics. The nonlinear effect proposed in hypothesis 3 is verified.

Conclusions and Discussions

This study clarifies the theoretical mechanisms of how the development of digital economy can prompt the TFP from both perspectives of the cost and income. To examine the theory, we conduct empirical studies via the data collected on 282 prefecture-level cities in China during the period from 2011 to 2022. It is found that the development of digital economy is conducive to the enhancement of TFP, and the conclusion still holds after considering the issues of variable selectivity bias and endogeneity. The mediation mechanism test finds that reducing economic operating costs, promoting technological innovation and expanding market size are the three main paths through which the digital economy enhances TFP. There may be a lag in the effect of the digital economy on TFP, but after the lag period, the productivity enhancement effect will be characterized by super-linear growth.

Our empirical findings has strong policy implications. First, it is necessary to continue to promote the balanced construction of digital infrastructure and enhance the digital literacy of various groups of people. Digital transformation is the key work to enhance TFP, the main reason for the lag in its enhancement effect is due to the stage at which it is located, through both hardware and software, continue to narrow the digital divide in all areas of performance, weaving a dense digital network structure, creating the possibility of realizing the zero-cost production and supply of more subjects.

Second, the construction of industrial Internet should be accelerated to realize the transformation of “Internet+” for the whole industry. Industrial Internet is the key to promote the transformation and upgrading of traditional industries, and promote the upgrading of enterprise mode through the integration with consumer Internet. Local governments need to combine the active government and market mechanism, through financial, financial, tax and other policy support, to build a distinctive industrial Internet platform, to promote the integration of digital and real, and to improve the industrial Internet system.

In addition, there should be a precise layout, breakthroughs in core technologies in the digital field, and a strengthening of the independent innovation capacity of the digital economy. Data, algorithms and arithmetic power are the core of the digital economy, and their technological breakthroughs are crucial to boosting productivity and grasping the initiative of development. The state needs to formulate laws and regulations to improve the efficiency of data circulation and guide technological research and development; enterprises and research institutes should take advantage of the new national lifting system and market scale to cultivate core talents and enhance R&D capabilities to ensure synergy in the digital industry chain, supply chain and innovation chain, and provide sufficient protection against digital innovation risks.

Finally, it should be pointed that there are still some limitations in this study. Currently, there is a lack of unified standards for evaluating the level of regional digital economic development. Although this paper has constructed a relatively comprehensive digital economy assessment system based on existing research and data availability, considering the extensiveness of the definition of the digital economy, there is still difficulty in precisely characterizing it, which is a problem that needs further in-depth study in the future. In addition, this study has examined the productivity effects and impact paths of the digital economy. Due to the powerful network and spillover effects of the digital economy, its spatial correlation and the resulting productivity effects must not be ignored. Therefore, subsequent studies can focus on model selection, and may adopt social network analysis or spatial econometric models to study the potential spatial dividends brought by the digital economy.

Footnotes

ORCID iD

Xiaoqi Zhang

Ethical Considerations

This article does not contain any studies with human or animal participants.

Consent to Participate

There are no human participants in this article and informed consent is not required.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is partially supported by the National Natural Science Foundation of China, under the Grant No. 72101268; and the Humanities and Social Sciences Planning Fund Project of the Ministry of Education, under the Grant No. 23YJA790105.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

All data included in this study are available upon request by contact with the corresponding author.

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