# Machine Learning and Zombie Firms Classification
## 6 Robustness Test  
In this section, we conducted logistic regression to predict the FN zombies as a robustness test. The dependent variable for logistic regression was the FN zombie indicator, which was the same as the random forest model in Section 4.1. The candidates for the explanatory variables were the 20 financial accounts shown in Figure 5. However, some financial accounts were highly correlated; for example, the \"EBIT\" and the \"net income\" were the two most important variables for the FN prediction model, but their correlation coefficient was 0.982. This is natural, because the \"net income\" is calculated by subtracting the income taxes from the \"EBIT.\" To exclude multicollinearity, we excluded the financial accounts whose correlation coefficient was over 0.7. There were 13 remaining financial accounts (the explanatory variables for the logistic model were \"EBIT\", \"EBIT/sales\", \"income taxes\", \"retained earnings brought forward\", \"ordinary income\", \"short-term loans and bonds\", \"ordinary income/sales\", \"long-term loans payable\", \"equity capital\", \"interest expenses/sales\", \"current portion of long-term loans\", \"interest and dividends income\", and \"interest expenses\"). Table 7 shows the prediction results. We observed that the overall accuracy for the training period was 85.47% ((3737 + 23,943)/32,384). Among the predicted zombie firms, only 46.41% (3737/8052) of the firms were correctly predicted as zombies. A total of 98.4% (23,943/24,332) of the predicted healthy firms were correct. When we looked at the test period, the accuracy was 82.68% ((4876 + 48,932)/65,083). The precision for the zombie firm and healthy firm predictions was 32.06% (4876/15,209) and 98.11% (48,932/49,874). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Financial Accounts** & **Rank (CHK)** & **Rank (FN)** & **Profitability** & **Subsities** \\ \hline EBIT & & 1 & X \\ Net income & & 2 & X \\ EBIT/sales & & 3 & X \\ Income taxes & & 4 & X \\ Net income/sales & & 5 & X \\ Retained earnings brought & & 6 & X \\ forward & & 7 & X \\ Income taxes/sales & & 8 & X \\ Ordinary income & & 9 & X \\ Short-term loans and bonds & 2 & 9 & X \\ Ordinary income/sales & & 10 & X \\ Current portion of long-term & 1 & 17 & X \\ loans & 1 & 17 & X \\ Interest expenses & 3 & 20 & X \\ long-term loans payable & 4 & 13 & X \\ Interest expenses/sales & 5 & 16 & X \\ Interest and dividends income & 6 & 19 & \\ Non-operating expenses & 7 & & \\ Interest and dividends & & 8 & \\ income/sales & & & \\ Long-term loans and bonds & 9 & 18 & X \\ Non-operating expenses/sales & 10 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Important financial accounts for CHK and FN criteria. This table shows the characteristics of financial accounts for classification under CHK and FN criteria. Rank (CHK [FN]) shows the rank of contributions of financial accounts for CHK [FN] criterion. The column of profitability has a mark “X” if financial accounts are related to firms’ profitability, and the column of subsidies has a mark “X” if they are related to creditors’ supports such as zombie lending. “EBIT” refers to the earnings before income taxes & others in Figure 4.  
The logistic model resulted in smaller F1 scores than our random forest model. The F1 scores for the zombie firms and healthy firms in the training period were 0.6137 and 0.9105, respectively, and 0.4638 and 0.8967 in the test period. All the values representing the model performance, such as the accuracy, precision, recall, and F1 score, were better for our random forest model than the logistic model. Notice that the explanatory variables used in the logistic model were selected based on the variable importance levels of the random forest model. Traditional statistical approaches must involve variable selection. In such a case, it is not clear which financial accounts should be used. This procedure may create unintended selection biases.