## 5 Empirical Test and Result Analysis
### Endogenous Treatment
#### 5.3.1 Heckman Two-Step Method  
There may be sample selection bias in this paper. Some enterprises have carried out digital transformation but have not disclosed it in the annual report, which leads to the fact that some samples cannot be observed, so the regression samples cannot represent the whole, resulting in the problem of sample selection. To avoid the impact of this problem on the basic regression results, this paper uses the Heckman two-stage method to test. The results are shown in Table 4. In the first stage, a probit regression model is constructed to \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **(1)** & **(2)** & **(3)** & **(4)** & **(5)** & **(6)** \\ \cline{2-7}  & **Uncontrolled** & **Robust Standard** & **Robust Standard** & **Uncontrolled** & **Robust Standard** & **Robust Standard** \\  & **Heteroscedasticity** & **Errors** & **Level Clustering** & **Heteroscedasticity** & **Errors** & **Level Clustering** \\ \hline \multirow{2}{*}{_Lndigital_} & 0.0125 *** & 0.0125 *** & 0.0125 *** & 0.0109 *** & 0.0109 *** & 0.0109 *** \\ \cline{2-7}  & (0.0025) & (0.0026) & (0.0059) & (0.0022) & (0.0024) & (0.0050) \\ \hline \multirow{2}{*}{_Lusize_} & & & & 0.0734 *** & 0.0734 *** & 0.0734 *** \\ \cline{2-7}  & & & & 0.0030 & (0.0030) & (0.0065) \\ \hline \multirow{2}{*}{_Lev_} & & & & \(-0.0642 *** & \(-0.0642 *** & \(-0.0642\) \\ \cline{2-7}  & & & & 0.0183) & (0.0187) & (0.0390) \\ \hline \multirow{2}{*}{_Growth_} & & & & \(-0.0034\) & \(-0.0034\) & \(-0.0034\) \\ \cline{2-7}  & & & & (0.0027) & (0.0027) & (0.0040) \\ \hline \multirow{2}{*}{_Raa_} & & & \(-0.0718\) & \(-0.0718\) & \(-0.0718\) \\ \cline{2-7}  & & & & (0.0519) & (0.0494) & (0.0703) \\ \hline \multirow{2}{*}{_Cashflow_} & & & 0.1140 *** & 0.1140 *** & 0.1140 * \\ \cline{2-7}  & & & & (0.0429) & (0.0435) & (0.0606) \\ \hline \multirow{2}{*}{_Mb_} & & & & 0.0055 & 0.0055 & 0.0055 \\ \cline{2-7}  & & & (0.0075) & (0.0079) & (0.0138) \\ \hline \multirow{2}{*}{_Fhl1_} & & & & 0.0757 *** & 0.0757 *** & 0.0757 * \\ \cline{2-7}  & & & (0.0178) & (0.0188) & (0.0437) \\ \hline \multirow{2}{*}{_Dlab_} & & & & 0.0412 & 0.0412 & 0.0412 \\ \cline{2-7}  & & & (0.0469) & (0.0465) & (0.0936) \\ \hline \multirow{2}{*}{_Bg4_} & & & & 0.1420 *** & 0.1420 *** & 0.1420 *** \\ \cline{2-7}  & & & & (0.0090) & (0.0096) & (0.0218) \\ \hline \multirow{2}{*}{_Langer_} & & & & 0.0933 *** & 0.0933 *** & 0.0933 *** \\ \cline{2-7}  & & & & (0.0082) & (0.0088) & (0.0200) \\ \hline \multirow{2}{*}{_cons} & 2.8000 *** & 2.8000 *** & 2.8000 *** & 0.9390 *** & 0.9390 *** \\ \cline{2-7}  & (0.0248) & (0.0245) & (0.0549) & (0.0722) & (0.0735) & (0.1620) \\ \hline Industry & control & control & control & control & control & control \\ \hline Year & control & control & control & control & control & control \\ \hline \(N\) & 9767 & 9767 & 9767 & 9767 & 9767 \\ \hline \(R^{2}\) & 0.150 & 0.150 & 0.150 & 0.302 & 0.302 & 0.302 \\ \hline adj. \(R^{2}\) & 0.146 & 0.146 & 0.146 & 0.298 & 0.298 & 0.298 \\ \hline \end{tabular} Note: In parentheses is the standard error of regression coefficient, * \(p<0.1\), ** \(p<0.05\), *** \(p<0.01\).  
\end{table} 
Table 3: Basic regression results. calculate the inverse Mills ratio (_Imr_) to test whether the common characteristic variables of listed companies will affect the digital transformation dummy variable (Treat). The 2014 informatization policy dummy variable (_Inform_) is selected as the exclusive constraint variable because the policy affects the digital transformation of enterprises ([PERSON] et al., 2021 [58]); in the second stage, _Imr_ is added to the model (1) as a control variable to test the influence of possible selective errors on the research conclusions. The regression results show that the _Imr_ coefficient is \(-0.480\), significant at the 1% level, and the sample has a selection bias. The variance inflation factor (VIF) of _Ludigital_ is \(1.34\), indicating that the _Ludigital_ coefficient is not sensitive to the exclusive constraint and the collinearity problem is small.