# Machine Learning and Zombie Firms Classification
## 4 Zombie Indicator Prediction
### CHK Criteria  
It has been argued that the CHK criteria, which use interest rate information, were not suitable when the Bank of Japan implemented the quantitative easing monetary policy and set the policy interest rate at a low level. To confirm such critiques, we built a prediction model for CHK zombie firms. Similarly to the previous model, we set the training period as before 2002 and the test period as after 2003. Because the CHK criteria before the 2000s are less debated, the target data of this setting are qualitatively guaranteed. Table 3 shows the accuracy of this model. During the training period, we correctly predicted the firms' status 91.36% of the time ((7907 + 21,679)/32,384), which was slightly lower than the FN prediction model. Among the predicted zombie firms, the precision was 77.66% (7907/10,181). On the other hand, 97.64% (21,679/22,203) of the firms predicted as healthy firms were genuinely healthy. The recall rates for zombies and healthy firms  
Figure 4: Time series of the firm ratio. This figure shows the time series of the firm ratio based on the predicted status and labeled status. The top figure is during the training period and the bottom figure is during the test period. “Correct” is the sum of “zombie true” and “healthy true”. “Zombie” is the sum of “zombie true” and “zombie false”. were 93.79% (7907/8431) and 90.51% (21,679/23,953). The F1 scores were 0.8497 and 0.9394, respectively. The most interesting point of this model is the accuracy of the test period. Different from the FN prediction model, we observed that only 70.43% ((21,888 + 23,949)/65,083) of the predicted firms' statuses were correct. If a firm was predicted as a zombie firm, this was true 59.74% of the time (21,888/36,636). Among the predicted healthy firms, 84.19% (23,949/28,447) were truly healthy. The accuracy of the predictions of zombie firms was substantially lower than that in the training periods. The recall rates for zombies and healthy firms were 82.95% (21,888/26,389) and 61.89% (23,949/38,697). The F1 scores were 0.6947 and 0.7134, respectively. They were also lower than the values during the training period. What are the reasons for this accuracy deterioration in the test period? One concern is that learning is simply not enough. If the learning was insufficient, then the accuracy of both the training and test periods would be low. Because our prediction model had a high accuracy for the training period, this scenario is not appropriate. In cases where the accuracy during the training period is high, but it is low for a test period, we would consider an overfitting problem. However, we argue that our cross-validation can avoid overfitting issues. After building numerous random forest models, we picked the best model based on the accuracy of the test period. Therefore, we did not select the most fitted model for the training samples. Given that the same procedure was applied to the FN prediction model and successfully predicted the firms' status for the test period, we claim that the overfitting problem does not explain our result. Another explanation is that the used data were qualitatively different between the training and test periods. If the data characteristics are different, it is difficult to make accurate predictions, even if learning is appropriately achieved. Because the input data, which comprised financial accounts in our case, were qualitatively the same for all time, we suggest that the target data, the CHK zombie indicators, are different before 2002 and after 2003. This is consistent with the current critiques of the CHK criteria. The CHK criteria only use prime interest rates and outstanding debts to calculate the theoretical lower bound of interest payments. When interest rates are fixed at a low level, which is remarkable for the Japanese economy after the 2000s, the validity of this criterion is debated. It is not clear why firms pay interests lower than the theoretical lower bound.