The explained variable in this study is a firm's innovation investment (Y). A firm's innovation investment is measured based on research and development (R&D) investment. Considering the significant differences in the total amount of R&D investment among firms of different sizes, the R&D intensity index, rather than the scale of R&D investment, better reflects the level of R&D investment appropriate for a firm relative to its size (Jeon & Jung, 2024). Following Jeon and Jung's (2024) approach, this study adopts the ratio of R&D investment to operating revenue multiplied by 100 as a measure.

The explanatory variable in this study is a firm's digital transformation (X). A firm's digital transformation (X) is measured using Wu et al. (2021)) approach. In terms of methodology, annual report textual data of Chinese A-share listed companies were collected, and the frequency of relevant keywords related to “firm digital transformation” was counted to obtain the frequency of firm digital transformation (FX). The specific keywords included artificial-intelligence technology, big-data technology, cloud-computing technology, blockchain technology, and the application of digital technology, totaling five dimensions and 76 specific terms. Furthermore, to mitigate the impact of outliers and heteroscedasticity on the empirical results, the final measure of firm digital transformation (X) was subjected to a logarithmic transformation based on the frequency of firm digital transformation (FX), as shown in Eq. (1).

Additionally, a robustness test was conducted by replacing the explanatory variable following the approach of Zhao et al. (2021). Specifically, based on four dimensions, namely digital technology application, Internet business models, intelligent manufacturing, and modern information systems, 99 relevant terms were selected. A new measure of a firm's digital transformation (referred to as digital transformation 2 and denoted as X2 in this study) was constructed based on the frequency of these terms.

The mediating variable in this study is firm TFP (Z). The estimation of the sample firms’ TFP (LP TFP or LPTFP) is based on the LP method proposed by Levinsohn and Petrin (2003). Similar to the construction of the firms’ digital transformation (X) measure, the estimated LPTFP measure obtained using the LP method underwent a logarithmic transformation to mitigate the impact of outliers and heteroscedasticity on the empirical results, as shown in Eq. (2).

To ensure the robustness and reliability of the empirical findings, this study included a set of control variables at both the micro and regional levels, as shown in Table 1.

Instrumental variable methods were employed to control for potential endogeneity issues in the model specified in Eq. (1), and the empirical results are presented in Table 4.

Two variables were selected as instrumental variables for digital transformation (X): the New Products Sales Income of Industrial firms above the Designated Scale in the region (IV1) and the Length of Optical Cable Lines in the region (IV2). As both instrumental variables are regional-level variables, their values are unlikely to be influenced by micro-level corporate factors, thus ensuring their degree of exogeneity. Digital transformation fundamentally involves the application of new digital technologies (Chen et al., 2022; Gilch & Sieweke, 2021). IV1, which represents the sales income of new products, effectively reflects the extent to which a company's environment accepts new technology. IV2 indicates the basic conditions required for a company to introduce digital technology. Intuitively, IV1 and IV2 are likely to positively influence a company's digital transformation level, thus ensuring the validity of the instrumental variables. Furthermore, statistical measures obtained through regression were used to test the exogeneity and validity of the instrumental variables from a statistical standpoint. In column (1), the p-value of the Hansen J statistic (p-HJ) is greater than 0.1, suggesting that the hypothesis that instrumental variables are exogenous cannot be rejected at the 10 % significance level. The CD-F statistic was greater than 19.93, indicating that the hypothesis of weak instrumental variables could be rejected, even at the strictest critical value. Therefore, the selection of instrumental variables was considered reasonable.

Table 4 reports the empirical results of the instrumental variable-fixed effects (IV-FE) regression and instrumental variable-random effects (IV-RE) regression using the instrumental variables. In columns (1) and (2), the estimated coefficients of the lagged explanatory variable (digital transformation, L.X) remain significantly positive at the 5 % and 1 % levels. Therefore, even after controlling for endogeneity issues using instrumental variable methods, the conclusion that digital transformation significantly promotes firm innovation investment remains robust. This finding provides further evidence that supports Hypothesis 1.

To further examine the robustness of Hypothesis 1, we employed an alternative specification by replacing the core explanatory variable. Specifically, lagged one-period digital transformation 2 (L.X2) and lagged two-period digital transformation (L2.X) were used as the core explanatory variables in the regression specified in Eq. (3). The results are reported in Table 5. Both fixed effects (FE) and random effects (RE) regressions were employed, and the heteroscedasticity issues were confirmed using firm-level cluster-robust standard errors.

From the results reported in columns (1)–(4) of Table 5, it can be observed that even with the replacement of the core explanatory variable, the coefficient estimates of L.X2 and L2.X remain significantly positive at the 1 % level. This confirms the robustness of Hypothesis 1.

When firms face high financial constraints, their limited ability to obtain external financing may intensify resource competition between the production and innovation departments. This strengthens the negative mediating mechanism of TFP, leading to variations in the impact of digital transformation on innovation investments. This study first measured the level of financial constraint using the SA index and divided firms into high and low financial constraint groups. The impact of digital transformation on a firm's innovation investment and the mediating mechanism of TFP are then examined for heterogeneity between the two groups. Regarding the heterogeneity analysis of the impact of digital transformation on firms’ innovation investment, regressions were conducted separately on the high- and low-financing constraint groups using Eq. (3). The results are reported in columns (1) and (4) of Table 7. Regarding the heterogeneity analysis of the mediating mechanism of TFP, regressions were performed separately on the high- and low-financial constraint groups using Eqs. (4) and (5). The results are reported in columns (2), (3), (5), and (6) of Table 7. Fixed effects (FE) regression was employed and robust standard errors clustered at the firm level were utilized.

Columns (1) and (4) of Table 7 show that the coefficient estimate of the explanatory variable L.X is significantly positive at the 1 % level in the low financial constraint group, while it is not significant in the high financial constraint group. This indicates that the promotion effect of digital transformation on a firm's innovation investment mainly exists in the low financial constraint group, but is not significant in the high financial constraint group. Further analysis suggests two reasons for this heterogeneity.

First, the degree of the mediating effect differs, and the negative mediating effect of TFP is higher in the high financial constraint group than in the low financial constraint group. Based on the coefficient estimates of the main variables in columns (2), (3), (5), and (6), it can be seen that the negative mediating mechanism of TFP is significant in both the low and high financial constraint groups. Even after controlling for the influence of TFP, the promotional effect of digital transformation on a firm's innovation investment remained significant in the high financial constraint group. This indicates that in the high financial constraint group the contradiction between TFP and innovation investment in terms of fund allocation is more intense because of weaker financing capacity, which leads to a more pronounced negative mediating effect of TFP. Specifically, for each unit increase in digital transformation, the negative impact on innovation investment through the TFP channel is approximately 0.061 (i.e., 0.004 × 15.288) units in the low financial constraint group and approximately 0.087 (i.e., 0.005 × 17.370) units in the high financial constraint group.

Second, the degree of the direct promotion effect differs; after controlling for the influence of TFP, the direct promotion effect of digital transformation on a firm's innovation investment is lower in the high financial constraint group than in the low financial constraint group. From the empirical results in Columns (3) and (6), the coefficient estimate of the explanatory variable L.X is 0.186 in the low financial constraint group and 0.136 in the high financial constraint group. This indicates that after controlling for the influence of TFP, the direct promotion effect of digital transformation on firms’ innovation investment in the low financial constraint group is approximately 1.37 times higher than that in the high financial constraint group, which also contributes to the insignificant impact of digital transformation on firms’ innovation investments in the high financial constraint group.

The empirical findings indicate that from the perspective of financial constraints, there is competition for capital between the production and innovation departments. When the level of financial constraints is high, this competition intensifies, strengthening the negative mediating mechanism of TFP, and rendering the overall impact of digital transformation on firms’ innovation investment insignificant. By contrast, when the level of financing constraints is low, firms have sufficient ability to obtain financial support, which can alleviate this competition. Therefore, in the low financial constraint group, the overall impact of digital transformation on firms’ innovation investments is significantly positive.

There is competition for labor between the production and innovation departments within firms. The dependence of firm innovation activities on labor mainly involves highly educated personnel, specifically those with higher levels of human capital, such as employees with a bachelor's degree or higher (Carlo et al., 2016). Therefore, this study measures the level of a company's human capital using the proportion of employees with a bachelor's degree or higher. Companies are divided into two groups: those with high and those with low human capital. This division allows us to examine the impact of digital transformation on firms’ innovation investment and the heterogeneous performance of the mediating mechanism of TFP between the two groups of samples. To analyze the heterogeneity of the effect of digital transformation on firm innovation investment, samples from the high and low human capital groups were subjected to regression analysis based on Eq. (3). The results are reported in columns (1)–(6) of Table 8.

Columns (1) and (4) of Table 8 reveal that in the high human capital group, the estimated coefficient of the explanatory variable L.X is significantly positive at the 5 % level. By contrast, in the low human capital group, the estimated coefficient of the explanatory variable L.X. was not significant. This indicates that the promotional effect of digital transformation on firms’ innovation investments is primarily present in the high-human-capital group. This difference can be explained in two ways, similar to financial constraints.

First, there was a difference in the degree of the mediating effects. The negative mediating effect of TFP is greater in the low human capital group than in the high human capital group. Based on the coefficient estimation results for the main variables in columns (2), (3), (5), and (6), it is evident that the negative mediating mechanism of TFP is significantly valid in both the high and low human capital groups. In the low-human capital group, even after controlling for the impact of TFP, the promotional effect of digital transformation on firms’ innovation investments remains significant. Second, there was a difference in the degree of direct promotional effects. After controlling for the impact of TFP, the direct promotional effect of digital transformation on firms’ innovation investment in the low-human capital group was lower than that in the high-human capital group.

Therefore, the empirical findings suggest that from the perspective of human capital, there is competition for resources between the production and innovation departments. When the level of human capital is low, owing to the relative scarcity of higher-level human capital, this competition intensifies, reinforcing the negative mediating mechanism of TFP, which in turn makes the overall impact of digital transformation on firm innovation investment insignificant. When human capital is high, competition is effectively alleviated.