# Machine Learning and Zombie Firms Classification
## 1 Introduction  
In this study, we propose a machine learning approach to predict zombie firms without using data on interest rates. There are several criteria that can be used to detect zombie firms. In this research, by using machine learning techniques with only publicly available firm-level financial accounts, we examined the differences between two major zombie criteria, and we argue that that they are more likely to reflect the different aspects of a firm's status. The concept of zombie firms (zombies), as defined by [PERSON] [1] and [PERSON] et al. [2] (CHK), is widely known. [PERSON] (2006) [1] defines zombie firms as insolvent firms that should exit the market, but are being kept alive due to help from creditors. Banks can avoid recording losses and being exposed to stricter capital requirements by funding these unprofitable zombies to prevent them from bankruptcy. CHK showed that such zombie lending distorts market competition, reduces the profitability of non-zombies, and creates a strong barrier for the entry of new firms, which lead to substantial costs for society. Zombie firms were originally analyzed during the 1990s in Japan, but they have attracted more attention since the COVID-19 pandemic. Many governments were forced to enact emergency responses for business firms, such as subsidies, public guarantees on their loans, and tax breaks. [PERSON] et al. (2022) [3] found that these non-negligible supports ended up helping firms that were already distressed before the COVID-19 outbreak and suggested that emergency supports may create new zombies. Zombie firms are not issues of the past; they are an important challenge, even today. Because the concept of zombie firms is widely known and accepted, but there are no consensus measures to detect zombie firms, several criteria have been proposed. [PERSON] (2006) [1] and CHK used prime interest rates (The prime interest rate is an interest rate at which banks lend to their most creditworthy customers. If the lender is trustworthy, bank lending is less risky from the bank's viewpoint and their interest rates would be low) to calculate the theoretical minimum required interest payments for firm bonds, considering a firm to be a zombie if its interest payments were lower than this theoretical value. We refer to these zombie firms as CHK zombie firms and these criteria as CHK criteria. Followingthe CHK criteria, [PERSON] and [PERSON] (2011) (FN) [4] introduced a profitability measure to identify zombie firms. This was motivated by their findings that the interest rates for some healthy firms are lower than the prime lending rate because of competition among banks. The FN criteria successfully tracked the trend in the nonperforming loan ratio of Japanese banks. The FN criteria were widely accepted, especially in studies of Japanese cases after the 2000s (e.g., [5; 6; 7]). Although several zombie criteria have been proposed, there is an ongoing debate about the validity of these criteria. Interest payment criteria such as the CHK criteria are questioned when the policy interest rate is low. As FN (2011) [4] pointed out, healthy firms may pay substantially low interest rates and be classified as zombies, even if they have a high profitability and no insolvency concerns. Figure 1 shows the policy interest rates of the Bank of Japan and the zombie firm ratio according to the CHK and FN criteria. After the late 1990s, the policy rate dropped below 1% and the CHK zombie firm ratio increased, leading to an increase in the gap between the CHK zombie firm ratio and the FN zombie ratio. Figure 2 shows the distribution of firms categorized as zombie firms and healthy firms according to both criteria. The firms categorized as zombies by the CHK and FN criteria comprised less than 10% for all years. On the contrary, the share of firms categorized as zombies by only the CHK criteria increased over time and reached over 40%.