# Machine Learning and Zombie Firms Classification
## 1 Introduction
Using the profitability measure to classify zombies raises the issue of selection bias because only low-profitability firms are selected as zombies, whereas the concept of zombie firms includes direct and indirect support from creditors and/or the government. Zombie firms are firms that are insolvent, but still exist in the market because of creditors' support. Profitability is intentionally ignored by CHK and is repeatedly described in the notes of [PERSON] et al. (2022) [3]. Zombie firms may be less profitable, but not all low-profitability firms are zombie firms. In addition, [PERSON] et al. (2020) [8] showed that the selection bias is severe if the profitability measure is used to identify zombies. In this study, we adopted the CHK and FN criteria as zombie indicators. The former was intended to capture support from creditors and the latter is from one of the first studies to adopt the profitability measures for zombie criteria. We employed machine learning  
Figure 1: Policy interest rates of Bank of Japan and zombie firm ratio. Blue solid line is a policy interest rate set by Bank of Japan. Yellow dotted line is a zombie firm ratio under the CHK criteria and green dashed line is a zombie firm ratio under the FN criteria. We observe that when policy interest rate drops below the 1%, there is a large gap between two zombie firm ratios. techniques to show the differences between the two zombie indicators, and we argue that they are more likely to reflect the different aspects of a firm's status. In the first part of this research, we ran a simple random forest model whose input data were from publicly available firm-level financial information to predict zombie firms. When analyzing the differences between zombie indicators by using machine learning techniques, it is a prerequisite that the machine learning model has a high prediction accuracy. We built each forecast model for the FN and CHK criteria. We showed that our machine learning model could predict FN zombie firms without using interest rate information. Our FN prediction model correctly predicted 74% of the zombie firms and almost 100% of the non-zombie firms in the training samples. A similar accuracy was observed for the test samples. In contrast, we observed that the CHK zombie predictions made by the machine learning model had as high of an accuracy for the training period as that of the FN zombie prediction model, but a lower accuracy for the out-of-sample periods than the FN prediction; 60% of the predicted zombie firms were correct and 84% of the predicted healthy firms were correct. Since our procedure to build the prediction model was the same for both models, an inappropriate learning process or overfitting were less likely to be the case. Rather, this suggests that the characteristics of zombie firms according to the CHK criteria were different between the training and test period, which is consistent with the critique that the CHK criteria do not work when the interest rate is low. In the second part of this research, we applied a machine learning model to examine the differences between the CHK and FN criteria. Firstly, we used the prediction model of FN zombies to predict CHK zombie firms. We used the model built in the first part, but changed the correct data from an FN zombie indicator to a CHK zombie indicator. If the CHK and FN criteria are qualitatively similar, the prediction of CHK zombies should have as high of a predictability as the prediction of FN zombies. We observed a substantial reduction in the accuracy of the CHK zombie prediction. Among the predicted zombie firms, only 34% of them were categorized as CHK zombie firms. This suggests that the CHK and FN criteria are heterogeneous and reflect different aspects of firm status. Secondly, we compared the contributions of financial accounts to classify the zombie firms in each prediction model. We observed that the most essential features differed for the CHK and FN criteria, and we support the heterogeneity discovered in the primary  
Figure 2: Share of all listed firms in Japan.