Can Digital Transformation Definitely Improve Firms’ Markups?

2.1 Theoretical Framework Setting

1. Demand. Drawing on the utility function of Melitz and Ottaviano (2008), this paper assumes that representative consumers obey the following quasi-linear preferences:

   U=q0c+α∫i∈Ωdiqicdi−12γ∫i∈Ωdiqic2di−12η∫i∈Ωdiqicdi2 (1)

   In Eq.(1), q0c  and  qic respectively represent the consumption quantity of representative consumers on traditional goods and digital goods. Parameters a, η measure the elasticity of substitution between traditional and digital goods. γ depicts the degree to which different types of digital products are substituted for each other. Ω represents a collection of heterogeneous product categories. d_i represents the heterogeneity in the degree of digitization of different digital goods. All of the above parameters are positive. Given the budget constraints, considering the utility maximization problem of representative consumers, the aggregate market demand function can be obtained as follows:

   qi=Lqic=Lγdiγα+η∫i∈Ωpididiγ+ηN−pidi (2)

   In Eq.(2), N is the number of categories of digital products, and L is the market size.

2. Supply. It is assumed that the heterogeneity of firms is manifested in both productivity and the degree of digital transformation, and that the two jointly determine the market performance of firms. In particular, as for the relevant settings of productivity, this paper follows the method of Melitz and Ottaviano (2008), where the firm only has labor factor input, and its productivity can be measured by the marginal output of the factor. That is, when labor wages are normalized to 1, the product of the productivity of the firm and its marginal cost of production is also 1. Suppose that each firm entering the industry knows its initial productivity level φ_i from the productivity distribution, after paying a fixed cost of f_e. The initial productivity level determines the enterprise’s innovation efficiency δ_i, which is related to the degree of digital transformation of the firm itself I_i, so that the firm can further know its actual productivity level adjusted for innovation efficiency δ_i φ_i. Drawing on the research of Hallak and Sivadasan (2009) and Gervais (2015), it is assumed that the cost function of the enterprise is f(I_i), and f^′(I_i) > 0, f^″(I_i) > 0, that is, if the enterprise wants to improve its digital transformation level, it needs to pay more fixed cost investment to achieve a higher degree of digital transformation. At this time, the business closure point of the enterprise is:

   cD=Pmax=γα+η∫i∈Ωpididiγ+ηN (3)

3. Equilibrium^[1]. Under the condition of monopolistic competition, according to the condition of maximizing the profit of the firm, the product pricing, the markup rate and the profit function of the firm can be obtained at the equilibrium, respectively:

   p(δ,φ)=12CD+1δφ (4)

   Mu(δ,φ)=12CD−1δφ,Mu(δ,φ)∝δ (5)

   π(δ,φ,I)=L4γCD−1δφ2−f(I) (6)

According to the above analysis, the optimal innovation efficiency of the firm δ^* is determined by Eq. (7):

On this basis, we can get the derivative of δ on the degree of digital transformation I:

Combining Eq. (5) and Eq. (8), we can get Eq. (9):

According to Eq. (9), the relationship between the degree of digital transformation and the markup rate of firms is not a simple linear relationship. There is a threshold value 32φCD for the innovation efficiency of firms in digital transformation. When δ<32φCD, digital transformation can promote the improvement of firm markup rate. When δ>32φCD, digital transformation does not increase the markup rate of firms, but has a negative inhibitory effect on them. Therefore, this paper proposes hypothesis 1 to be tested:

2.2 The Mechanism and Heterogeneity of Digital Transformation Affecting the Markup Rate of Firms

As mentioned before, firm’s markup rate can be expressed as the ratio of the price of the product to the marginal cost of production, which measures the degree to which the price of the product deviates from the marginal cost. Accordingly, the change of the mark-up rate of firms is mainly affected by the combination of product price and marginal production cost. Obviously, if digital transformation can affect either firm’s pricing or marginal production costs, then it will affect the firm markup rate. Combined with Eq. (8) and Eq. (9) in the theoretical framework, it can be seen that the innovation ability of firms is one of the important channels for digital transformation to affect the markup rate of firms. Moreover, the degree of digital transformation of firms also shows the above-mentioned “inverted U-shaped” nonlinear relationship with firm innovation ability.

The economic significance behind the results lies in the fact that digital transformation will promote the improvement of firm innovation efficiency to a certain extent. However, excessive and disorderly digital investment will inhibit the improvement of firms’ innovation capabilities. On the one hand, digital transformation, as an important driving force for the transformation and upgrading of industrial structure, will promote the improvement of firms’ innovation capabilities in many aspects. With the application of digital technologies such as big data and machine learning, the production of firms can be more accurately connected with the needs of consumers. Moreover, it reduces the loss of innovation uncertainty that may be caused by information asymmetry. At the same time, digital technology can also improve the efficiency of the transformation of innovation achievements, enhance the enthusiasm of firms for product iteration and innovation (Abramova and Grishchenko, 2020), and ultimately improve the innovation ability of firms. On the other hand, digital transformation to a certain extent is conducive to optimizing the organizational structure of firms and the circulation of factors within firms, thereby enhancing the competitiveness and innovation capabilities of firms. However, if the degree of digital transformation exceeds a certain threshold, it is not conducive to the improvement of the firm’s innovation ability. From the perspective of micro firms, excessive improvement of the level of digital transformation may lead to internal diseconomies of scale. And digital technology is difficult to effectively match with the production factors within the firm. The result is a loss of productivity. For example, for firms lacking digital transformation capabilities, if they increase digitalization-related investment to promote digital transformation, it will not only squeeze their resources in innovation and R&D, but also increase the risks and uncertainties in the innovation process (Tavassoli, 2018). Therefore, firms need to fully consider the heterogeneity of digital capabilities, as well as the “matching” between their own digital transformation and external macro and meso level construction, such as the construction of new digital infrastructure. Otherwise, blindly expanding the scale and improving the degree of digital transformation will inevitably result in the obstruction of the flow of factors, in particular, the congestion of digital elements and the underutilization of digital equipment and technology. And then, there is a significant decline in the marginal productivity of the R&D and utilization efficiency of firms’ digital investment, which in turn will hinder the improvement of firm innovation efficiency.

In addition, according to Eq. (5), under the condition of endogenous firm innovation efficiency, the degree of digital transformation of firms will also have an impact on firm productivity, and then have an impact on the firm markup rate. Based on the same logic, when the degree of digital transformation does not exceed a certain threshold, firms will inevitably improve their productivity by promoting technological progress and product iteration ability through digital transformation. On the contrary, when the degree of digital transformation exceeds a certain threshold, the impact of digital transformation on productivity will also have a significant marginal productivity diminishing phenomenon or even an inhibiting effect. Based on the above analysis, the following hypothesis 2 is proposed:

In the literature review, it is pointed out that some studies believe that the markup rate of exporting firms tends to be higher than that of non-exporters by virtue of their advantages in factor adjustment and productivity (Cosar et al., 2016). However, some studies using empirical data from China have found that the markup rate of exporters is lower than that of non-exporters To a certain extent, this also explains that the division of research objects and samples leads to the heterogeneity of the impact of digital transformation on the markup rate of firms. For example, there are differences between exporters and non-exporters. In fact, this heterogeneity is not only between exports and non-exports. Similar heterogeneity will exist between industries with different factor intensities, as well as between firms with different ownership properties. Because the factor density of the industry is different, the degree of dependence on digital transformation is also different. Due to the great differences in the institutional mechanisms and management models of firms with different ownership systems, the degree of demand for digital transformation and the degree of utilization of digital transformation will show certain differences. Therefore, it can be expected that the “inverted U-shaped” nonlinear effect of digital transformation on the markup rate of firms will show heterogeneity among firms divided in different ways. Therefore, the following hypothesis 3 is proposed:

3.1 Model Settings

On the basis of the above theoretical analysis, this paper constructs the following econometric model (10), and empirically tests the relationship between digital transformation and firm markup rate by using a two-way fixed effect method:

Among them, i represents the firm, j represents the industry, and t represents the year. Markup_ijt represents the markup rate of firm i in industry j in year t. Digital_it represents the degree of digital transformation at the firm-year level and Digitalit2 is quadratic term. ∑Control_ijt stands for other control variables. v_i represents the fixed effect of the firm. v_j represents the fixed effect of the industry. v_t represents that the fixed effect of the year is controlled, i.e., the factor that changes only with time is controlled. ε_ijt represents the error term. In this paper, the clustering of robust standards is applied at the industry level. The estimation coefficient of the core explanatory variable and its quadratic term, β₁ and β₂, are the focus of this paper. Based on the discussion in the theoretical part, this paper expects β₁ to be significantly positive and β₂ to be significantly negative, that is, an “inverted U-shaped” relationship between digital transformation and firm markup rate. Although the above econometric model can examine the nonlinear relationship between the explanatory variable and the explained variable, it cannot test the threshold value of the effect change of the latter on the former. Therefore, on the basis of the above econometric model, this paper further draws on the method of Wang (2015) to construct the following non-dynamic threshold regression model to estimate the above threshold value ^[1]:

Among them, γ is the threshold value to be estimated. I is an indicative function. The meaning of the remaining variables is the same as in Eq.(10). The advantage of this model is that it can not only use the square of the residuals and the minimization condition to determine the threshold value, but also further use the bootstrap method (hereinafter referred to as BS) to test the significance of the threshold value. The model overcomes the endogenous bias caused by relying on subjective intuition to set the abrupt point of the influence effect.

3.2 Description of the Variable

1. Firm markup rate. In this paper, we draw on the method of De Loecker and Warzynski (2012) to measure the markup rate of firms (DLW method). The basic principle is: Firstly, through the firm cost minimization condition combined with definition of markup rate, the expression of the firm markup rate is μit=θitvαitv−1⋅αitv is the share of variable factor expenditure in total output. Then, the output elasticity θitv of the variable inputs of the firm is estimated by the following transcendental logarithmic production function:

   yit=βllit+βkkit+βmmit+βlllit2+βkkkit2+βmmmit2+βlklitkit+βlmlitmit+βkmkitmit+βlkmlitkitmit+φit+εit (12)

   Among them, y_it, l_it, k_it, m_it respectively represent the total output of the firm, the number of employees, the capital input and the intermediate input, after taking the natural logarithm. β is the relevant parameter to be evaluated, φ is the total factor productivity of the firm, and ε is the error term including unobservable shocks. Finally, considering the endogeneity between variable factor input and productivity in the estimation process using the traditional least squares method, this paper uses the semi-parameter method to estimate the above production functions. It is assumed that productivity obeys a first-order Markov process φ_it = g_t(φ_it–1) + ξ_it. Heterogeneous productivity shocks (residual terms ξ_it) can be obtained by performing a nonparametric regression on the lag term of productivity φ. Then, the output elasticity of variable factor inputs θitv is obtained by generalized moment estimation. Combined with the share of variable factor expenditure αitv , the μ_it of the firm’s markup rate can be calculated.

2. Digital transformation of firms. In the past, the measurement of digital transformation at the firm level mainly focused on a single dimension in the process of digital transformation, which is difficult to reflect the whole picture of firm digital transformation. Although a small number of literatures have begun to try to comprehensively examine the degree of digital transformation of firms through data mining and text analysis (Zhao et al., 2021), there are relatively few core matching keywords, and the analysis of various dimensions of firm digital transformation is not comprehensive. Therefore, on the basis of the existing literature, this paper refers to the research method of Yuan et al. (2021) to construct and measure the degree of firm digital transformation.

   First, a keyword dictionary is constructed by utilizing specific terms in the field of the digital economy. Specifically, a total of 32 important policy documents related to the digital economy published by relevant government agencies during the sample period (2011–2020) are manually screened as text sources for extracting specific terms of digital transformation. After summarizing the above texts, Python is used to analyze the words. After multiple rounds of screening of irrelevant words and inactive words, 536 terms are obtained by manual judgment. On this basis, 536 feature words are matched with the summarized text and the word frequency is counted. After the feature words with a word frequency of less than 5 are eliminated, the duplicate feature words are removed by merging the above feature words with the existing literature keywords.

   Finally, a total of 260 keywords in various dimensions of firm digital transformation are screened to form the final keyword dictionary. Secondly, with reference to the research of Yuan et al. (2021), this paper extracts the “Management Discussion and Analysis” (or “Board Report”) part from the annual financial statements of each listed company from 2011 to 2020 as the text analysis object (Textⁱ) of each listed company. Finally, the text matching analysis between the text matching object (Textⁱ) and the above keyword dictionary is carried out, and the degree of digital transformation of each listed company is scored according to the matching frequency. Specifically, a keyword dictionary is awarded 1 point for each successful match with a text analysis object (Textⁱ). A higher score indicates a higher degree of digital transformation for the firm. In summary, this paper finally selects the ratio of the total score of each firm to the text length to more comprehensively describe the degree of digital transformation of firms.

3. Other control variables. Combined with the relevant conclusions and studies of the existing literature (Yuan et al., 2021), the following variables are selected for control: Asset-liability ratio (Lev), which is expressed as the ratio of total liabilities to total assets of firms. The capital-to-labor ratio (KL), which is expressed as the ratio of fixed assets to the number of employees to reflect the capital intensity of the firm. Firm size (Size), which is expressed in terms of the number of employees. Return on equity (Roe), which is expressed as the ratio of net profit to total assets of firms. The Herfindahl-Hirschman Index (HHI), which is expressed as the square of the ratio of the firm’s sales to the total sales of the industry to reflect the degree of monopoly of the firm in the industry.

3.3 Data Source and Processing Description

The firm-level data used in this paper is mainly derived from the CSMAR database of listed companies. Among them, the text data of the financial statements of listed companies comes from www.cninfo.com.cn. Considering the realistic characteristics of the rapid development of China’s digital economy since 2010, this paper sets the sample interval from 2011 to 2020. On the basis of the above, the data is processed as follows: Exclude the sample of firms with operating income less than 0. Exclude the sample of financial industry firms (industry code J). Exclude the sample of companies with ST, PT and insolvency. All continuous variables were winsorized by 1% at the 1st and 99th percentiles.

4.1 Baseline Regression

Table 1 shows the baseline regression results for the relationship between digital transformation and firm markup rate. The first two columns of Table 1 show the results of the quantitative regression of the linear relationship between digital transformation and firm markup rate in the absence of quadratic terms. The odd number column did not include the control variables, while the even number column included all the control variables, both of which controlled for individual fixed effects, year fixed effects, and industry fixed effects. The regression results show that the estimation coefficients of the core explanatory variables of digital transformation are positive but not significant, which means that the linear effect of digital transformation on the markup rate of firms is not obvious. Therefore, it is necessary to further investigate whether there is a nonlinear relationship between digital transformation and firm markup rate. The last two columns of Table 1 add the quadratic term of digital transformation on the basis of the former, and show the regression results of the econometric model (10) that tests the nonlinear relationship between digital transformation and firm markup rate. It can be seen that whether the control variable is added or not, the estimation coefficient of the digital transformation of the core explanatory variable is positive, and the estimation coefficient of the quadratic term is negative, and both pass the significance test at the level of 1%. This result suggests that there is a significant “inverted U-shaped” relationship between digital transformation and firm markup rate. That is, when the degree of digital transformation is below a certain threshold, the improvement of the degree of digital transformation will promote the improvement of the firm markup rate. However, when the degree of digital transformation is higher than this threshold, continuing to improve the level of digital transformation will have a negative effect on the markup rate of firms. The benchmark regression results are consistent with the theoretical expectations of this paper, and the theoretical hypothesis 1 has been preliminarily verified.

The test results based on the non-dynamic threshold regression model are shown in Table 2. The results show that there is a significant single threshold effect between digital transformation and firm markup rate, and the threshold value of influencing effect transformation is 0.3653. On this basis, the double threshold effect and the three threshold effect of further test are not significant. Once again, the existence of an “inverted U-shaped” relationship between digital transformation and firm markup rate has been confirmed. Thus, the theoretical hypothesis 1 mentioned above has been further tested.

4.2 Robustness Test

1. Change the method of calculation of the explanatory variable. As mentioned above, the production function method (DLW method) is used to measure the markup rate of the firm. Considering that the relevant financial indicators of listed companies are relatively fair and reliable, and the use of financial indicators to measure the markup rate of firms (hereinafter referred to as the accounting method) can avoid the influence of external shocks and cyclical factors to a certain extent. Therefore, this paper uses the accounting method to measure the markup rate of firms, and the specific calculation formula is as follows:

   Priceit−CostitCostit=1−1Markupit=Valueaddit−WageitValueaddit+Netcostmaterialit (13)

   Among them, Markup_it indicates the markup rate of firm i in year t, Price_it indicates the price of the company’s products, and Cost_it represents the marginal cost of firms. Valueadd_it represents the industrial added value of the firm^[1]. Wage_it indicates the total amount of wages payable by the firm for the current year. Netcostmaterial_it represents the cost of net intermediate input factors of the firm. The regression results based on remeasures of the explanatory variables are presented in column (1) of Table 3. Both the core explanatory variables and their quadratic terms pass the significance test at least at the 5% level. This result once again shows that there is a significant “inverted U-shaped” relationship between digital transformation and firm markup rate, which illustrates the stability and reliability of the previous regression estimation results. In addition, within the framework of the DLW method, the firm markup rate (Cobb) is recalculated by changing the transcendental logarithmic production function to the Cobb Douglas production function. The results of the regression are shown in column (2) of Table 3. As shown in the table, the results are basically consistent with the baseline regression results. Therefore, based on the test results of the re-measurement of the explanatory variables, the theoretical hypothesis 1 mentioned above is once again verified.

   Table 3

   Robustness Test Results

   Variable	Replace the explanatory variable		Instrumental variable testing	Exclude the sample of GEM firm	Exclude samples of major deficiencies in internal control	Exclude KV index in the bottom 20% of samples
   	Account	Cobb
   	(1)	(2)	(3)	(4)	(5)	(6)
   Digital	0.0121*	0.1059***	1.9664**	0.1168**	0.1022***	0.1081***
   	(0.0068)	(0.0392)	(0.8938)	(0.0462)	(0.0352)	(0.0364)
   Digital2	–0.0022*	–0.0132**	–0.2135**	–0.0190**	–0.0126**	–0.0133***
   	(0.0013)	(0.0057)	(0.0908)	(0.0085)	(0.0052)	(0.0050)
   LM statistic			26.414***
   Wald F statistic			15.206***
   Control variables	Yes	Yes	Yes	Yes	Yes	Yes
   Fixed effect	Yes	Yes	Yes	Yes	Yes	Yes
   Obs	21,751	19,908	21,487	6,170	21,550	17,464
   R2	0.0417	0.6340	0.0929	0.7534	0.6789	0.6941

2. Endogeneity analysis. In the benchmark regression, this paper includes relevant control variables and uses a two-way fixed effect model to control the unobserved factors at the level of firm and industry, which can alleviate the endogenous interference to a certain extent. However, there may still be potential endogeneity problem between digital transformation and markup rate. First, although this paper controls other variables that affect the markup rate of firms as much as possible, there is still the possibility of missing variables. Second, there may be a reverse causal relationship between digital transformation and the markup rate of firms. The increase in the markup rate of firms may mean that the competitiveness of firms is improved and the factor input structure is optimized, which in turn improves the level of digital transformation of firms. In order to overcome the above-mentioned possible endogeneity problems, this paper uses the instrumental variable method to estimate the model. In the selection of tool variables, the natural logarithm of the interaction terms between the number of fixed telephones per 100 people in each region in 1984 and the number of Internet broadband access ports in each year of the sample period are selected as the instrumental variables. On the one hand, the proliferation of landlines can serve as the beginning of digital transformation. Historically, regions with high landline penetration tend to be regions with a high degree of digital transformation today. The number of Internet broadband access ports is the key combination point to promote the integration of the real economy and the digital economy, and its number intuitively reflects the degree of digital transformation, which also gives the dynamic characteristics of tool variables over time. On the other hand, traditional landlines have less and less impact on today’s economy and society as the frequency of use decreases. And there is also no direct correlation between the number of Internet broadband access ports and the markup rate of firms. Therefore, the exclusivity condition for the selection of tool variables can be satisfied. The results of the robustness test based on the instrumental variables are shown in column (3) of Table 3. The results show that the “inverted U-shaped” relationship between digital transformation and firm markup rate is still robust after considering possible endogenous problems.

3. Firm information disclosure bias. The reason why the firm digital transformation index constructed based on the text analysis method in this paper can more effectively reflect the digital transformation of firms in all dimensions is based on the premise that the information disclosure in the annual reports of listed companies is true and reliable. Zhao et al. (2020) found that the information disclosure of listed companies may be strategic and speculative in some aspects, and then exaggerate their information disclosure. In order to overcome the possible impact of the above-mentioned information disclosure bias on the conclusions of this paper, this paper intends to test the following aspects: ① Considering that most of the companies that choose to be listed on the GEM are high-tech firms, they are more suspected of exaggerating information disclosure related to digital transformation than listed companies in other sectors. Therefore, this paper removes samples of GEM listed companies for re-testing. The results obtained are shown in column (4) of Table 3. ② If there are deficiencies in the internal control of a listed company, an unreasonable organizational structure and distribution of power may lead to distorted information disclosure. To this end, this paper re-examines and exclude the samples of firms with major internal control deficiencies during the sample period based on the results of the external audits of listed companies. The results are shown in column (5) of Table 3. ③ Based on the measurement method of corporate information disclosure quality by Kim and Verrecchia (2001), this paper calculates the information disclosure quality index (hereinafter referred to as the KV index) of listed companies in the sample period by using the dependence of investors on trading volume information, and excludes the bottom 20% of the firms in the index for re-testing. The results are shown in column (6) of Table 3. According to the relevant test results, the “inverted U-shaped” relationship between digital transformation and firm markup rate is still robust and is not affected by the bias of firm information disclosure.

4.3 Heterogeneity Analysis

1. Heterogeneity test based on the export status of firms. According to the previous analysis, there is not only a “counterfactual” low markup rate phenomenom in Chinese export firms, but also a dynamic convergence trend of the markup rate of export firms compared with that of non-export firms. Therefore, it is necessary to examine the possible heterogeneous impact of digital transformation on the firm markup rate of both exporters and non-exporters. In view of this, this paper analyzes the notes to the financial statements of listed companies to determine whether there is an export behavior in the current period, and divides the firms into two groups of samples: export firms and non-export firms. The results of the econometric model (10) are shown in columns (1) and (2) of Table 4. In the two groups of exporters and non-exporters, the quadratic coefficients of digital transformation are negative at the significance levels of 5% and 1%, respectively. The results show that the digital transformation of both exporting and non-exporting firms has an “inverted U-shaped” relationship with their markup rate.

   Table 4

   Results of Heterogeneity Analysis

   Variable	Export firms	Nonexport firms	State-owned firms	Non-state-owned firms	Labor-intensive industries	Capital -intensive industries	Technology-intensive industries
   	(1)	(2)	(3)	(4)	(5)	(6)	(7)
   Digital	0.0885***	0.0871**	0.0856**	0.0947***	0.2481***	0.0703*	0.0151
   	(0.0244)	(0.0359)	(0.0410)	(0.0241)	(0.0683)	(0.0400)	(0.0197)
   Digital2	–0.0074*	–0.0118**	–0.0139**	–0.0116***	–0.0027**	–0.0005	–0.0017
   	(0.0042)	(0.0049)	(0.0063)	(0.0037)	(0.0012)	(0.0079)	(0.0032)
   Control variables	Yes	Yes	Yes	Yes	Yes	Yes	Yes
   Fixed effect	Yes	Yes	Yes	Yes	Yes	Yes	Yes
   Obs	13,317	8,409	7,828	13,802	5,441	5,860	10,425
   R2	0.7100	0.5931	0.6032	0.7149	0.6002	0.6631	0.7426

   The test results based on the threshold regression model (11) are shown in Table 5. The results show that there is a significant difference between the threshold value of export firms and non-export firms. The threshold value of non-export firms is more to the left than that of export firms. In other words, non-export firms will be affected by the negative effects of digital transformation relatively earlier. According to the theoretical analysis of this paper, the improvement of the degree of digital transformation is inseparable from the investment in fixed costs of firms. And according to the new-new trade theory, exporters can overcome high fixed costs by their productivity advantages. Obviously, regardless of whether the firm exports or not, digital transformation has a negative effect on the firm after reaching a certain scale. However, exporters are more likely to promote a higher degree of digital transformation before reaching such a “tipping point”.

   Table 5

   Test Results of the Threshold Model of Export Firms and Non-export Firms

   Sample	Basic assumptions	F-value	P-value	BS times	Thresholds estimates	Confidence interval
   Export firms	HO: Linear relationships	854.44***	0.000	300	0.7144	0.7005, 0.7284
   	H1: Single threshold
   Non-export firms	H0: Linear relationships	107.85**	0.043	300	–0.5144	–0.5283, –0.5004
   	H1: Single threshold

2. Heterogeneity test based on the nature of different property rights. According to theoretical analysis, the heterogeneity of productivity of different firms is an important reason for the differentiation of digital transformation. There are huge differences in the financing constraints faced by firms under different ownership systems, which leads to obvious differences in firm innovation and productivity. To this end, through the screening of the actual controllers of listed companies, this paper divides firms into two samples: state-owned firms and non-state-owned firms, and tests the two sub-samples respectively. Columns (3) and (4) of Table 4 show the empirical results of firms under different forms of ownership. The results show that both state-owned firms and non-state-owned firms show a significant “inverted U-shaped” relationship between digital transformation and firm markup rate. Table 6 shows the empirical results of the further threshold model. Compared with state-owned firms, the threshold for non-state-owned firms is lower. The measurement results also confirm the relevant statements of the above characteristic facts. The possible reason is that non-state-owned firms are facing unfavorable factors such as more severe financing constraints, which restrict the improvement of their digital transformation level. In addition to financing constraints, the administrative monopoly position of state-owned firms has led them to enjoy more policy subsidies and preferential treatment in the process of production and business activities, and they are protected by local governments as an important pillar of employment and tax revenue. The above-mentioned advantages of state-owned firms also lead to their stronger ability to optimize their own factor input structure and improve the level of digital transformation, which is internally consistent with the research of Lu et al. (2014).

   Table 6

   Test Results of Threshold Model between State-owned Firms and Non-state-owned Firms

   Sample	Basic assumptions	F-value	P-value	BS times	Thresholds estimates	Confidence interval
   State-owned firms	HO: Linear relationships	129.07***	0.010	300	0.7144	0.6725, 0.7424
   	H1: Single threshold
   Non-state-owned firms	H0:Linear relationships	945.03***	0.000	300	–0.5004	–0.5144, –0.4864
   	H1:Single threshold

3. Heterogeneity test based on industry factor intensity. Regarding the industry classification of factor intensity of listed companies, this paper uses the industry classification standard issued by the China Securities Regulatory Commission in 2012, and divides the manufacturing industry into three categories: labor-intensive, capital-intensive and technology-intensive. The results of the heterogeneity test based on the three major industry types are shown in the last three columns of Table 4. The results show that the impact of digital transformation on the markup rate of firms is manifested as first promotion and then inhibition. This effect is more obvious in labor-intensive industries, but not yet evident in capital-intensive and technology-intensive industries. The reason may be that the current digital technologies are more widely applied to capital-intensive and technology-intensive industries, but there is still a lot of room for development of various digital technologies in China. For companies in these two types of industries, the current degree of digital transformation is far from negative. At present, firms are still far away from the degree of digital transformation with negative effects. In contrast, the application of digital technologies in labor-intensive industries is relatively low. In other words, the ability of digital transformation to optimize the factor input of firms in labor-intensive industries may not be fully reflected, making it difficult for firms in this industry to improve their digital transformation level simply by relying on the accumulation of digital scale.