Determinants and predictive powers of bankruptcy models for firms in Korea and the U.S.

Kim, Jounghyeon Article Determinants and predictive powers of bankruptcy models for firms in Korea and the U.S. Global Business & Finance Review (GBFR) Provided in Cooperation with: People & Global Business Association (P&GBA), Seoul Suggested Citation: Kim, Jounghyeon (2016) : Determinants and predictive powers of bankruptcy models for firms in Korea and the U.S., Global Business & Finance Review (GBFR), ISSN 2384-1648, People & Global Business Association (P&GBA), Seoul, Vol. 21, Iss. 2, pp. 65-85, https://doi.org/10.17549/gbfr.2016.21.2.65 This Version is available at: https://hdl.handle.net/10419/224353 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ GLOBAL BUSINESS & FINANCE REVIEW, Volume. 21 Issue. 2 (FALL 2016), 65-85 pISSN 1088-6931 / eISSN 2384-1648∣Http://dx.doi.org/10.17549/gbfr.2016.21.2.65 ⓒ 2016 People and Global Business Association GLOBAL BUSINESS & FINANCE REVIEW www.gbfrjournal.org1) Determinants and Predictive Powers of Bankruptcy Models for Firm s in Korea and the U.S. J ounghyeon Kim A ssistant Professor, Department of Economics, Chosun University, Gwangju, Republic of Korea A B S T R A C T Using a cross-section data set of manufacturing firms in Korea and the U.S., this paper explores the most significant factors that determine firm default during the periods of 1991-2001 and 1991-2003, respectively. Based on the findings, a probit default model is constructed to perform better than two default prediction models such as Altman’s z-score model and the new Altman z-score model. To improve the predictive power, z-score is incorporated into the model as one of the explanatory variables with other significant default factors, which can provide additional information in predicting bankruptcy. It is found that z-score, leverage, and short-term debt ratios are the most important determinants of default for firms in both Korea and the U.S. However, soft budget constraint (SBC), defined as the ability of a firm with a low z-score to obtain short-term bank loans, and ownership concentration (ownership by the largest shareholders) are identified as strong indicators of the likelihood of bankruptcy only for Korean firms. Moreover, based on these and other significant default factors of age of a firm, export ratio, and inventory ratio, the probit default model for both Korean firms and US firms is found to perform better than the two Altman models. This suggests that the additional information gained from the z-score and the non-financial default factors in the default regression model can help improve the predictive power of a default prediction model. Keywords: Z-Score; Default Factor; Soft Budget Constraint; Ownership Concentration; Model Power Ⅰ. Introduction Bankruptcy generally results from financial distress, i.e., insolvency, when the market value of a firm’s assets is insufficient to pay its total debt. Prolonged unprofitability exacerbates a firm’s insolvency, which eventually causes bankruptcy (Pompe and Bilderbeek, 2005). Many studies have focused on finding the determinants of a firm’s † Jounghyeon Kim Assistant Professor, Department of Economics, Chosun University, Gwangju, Republic of Korea E-mail: jhye[email protected]c.kr bankruptcy. For example, financial ratio analysis has been widely used to predict a firm’s bankruptcy based on univariate (Beaver, 1966) and multivariate (Altman, 1968; Altman et al., 1977) approaches. They find that the ratios in the categories of profitability, liquidity, and leverage are important indicators of predicting bankruptcy. 1) 1) Beaver (1966) identifies the following financial ratios as most significant in predicting bankruptcy: X1 = cash flow / total debt, X2 = net income / total assets, X3 = total debt / total assets, X4 = working capital / total assets, X5 = current assets / current liabilities, and X6 = no-credit interval (defensive assets - current liability to fund expenditures for operations). Altman (1968) develops the z-score model, based on 66 US manufacturing firms from 1946 through 1965 and 5 financial variables. The model is GLOBAL BUSINESS & FINANCE REVIEW, Volume. 21 Issue. 2(FALL 2016), 65-85 66 In another aspect, Daily and Dalton (1994) find that governance structures, such as the composition of the board leadership structure and the board of the directors, are related to a firm’s bankruptcy. 2) Based on bankrupt firms in Canada, Thornhill and Amit (2003) find that environment, management, age, and size of a firm are important determinants of bankruptcy and that younger firms are more exposed to bankruptcy because they have less resources and financial management skills. However, Pompe and Bilderbeek (2005) find that it is more difficult to predict bankruptcy of young firms than old firms, i.e., established firms. They argue that young firms are small, less experienced, and financially weak, so when faced with financial distress, bankruptcy is more likely to occur unexpectedly compared to older and larger firms. In addition, many bankruptcy models have been developed to better predict the likelihood of a firm’s bankruptcy. Altman (1968) estimates the Altman z-score model based on the financial ratios proven to possess explanatory power in the univariate. Later, Altman et al. (1977) constructs the ZETA model that better predicts bankruptcy than Altman’s z-score model. Johnson and Melicher (1994) expands a firm’s financial state to three states - bankrupt, financially weak, and non-bankrupt - and find that the additional information provided by the multinomial model helps reduce misclassification error compared to the binomial model (two-state model of bankrupt and non-bankrupt firms). 3) More recently, using parametric defined as Z=1.2X1+1.4X2+3.3X3+0.6X4+0.999X5 from “Return on Investment Manual: Tools and Applications for Managing Financial Results” by Robert Rachlin (1997) where X1 =          , X2 =          , X3 =       , X4 =                  , amd X5 =        . Altman et al. (1977) define X1 = EBIT/total assets, X2 = standard error of estimate of EBIT/total assets, X3 = EBIT/total interest payments, X4 = retained earnings/total assets, X5 = current assets/current liabilities, X6 = common equity/total capital, and X7 = total assets. 2) Through logistic regression by controlling for financial variables and firm size, they find that the interaction between a dual leadership structure (CEO/board chairperson) and a few independent directors has a significant effect on bankruptcy. 3) Using the financial variables of Beaver (1966) and Altman et al. (1977), they show that the multinomial model performs and non-parametric approaches, Moody’s (Sobehart and Stein, 2000; Kocagil and Reyngold, 2003) develops its own default prediction model and shows that it performs better than Altman’s z-score model and other risk default models such as the hazard model or the univariate ROA (return on assets) model. 4) Denis and Mihov (2003) use Altman’s z-score as one of the characteristics in identifying the debt source. They find that the credit quality of a firm is related to the choice of the type of debt. That is, a firm in good financial shape borrows from public sources, whereas a firm in financial distress borrows from non-bank private sources. A firm of average soundness borrows from banks. 5) Using the revised Altman z-score model (Altman, 2000), Allayannis et al. (2003) analyzes the relationship of z-score (financial performance) to different types of debt, such as local currency debt and hedged and unhedged foreign currency debt. They find that both foreign currency debt and local currency debt hurt financial performance in the Asian financial crisis. 6) Based on firm-level panel data, Alexeev and Kim (2008) identify soft budget constraint (SBC) firms in Korea that increase their bank loans while having a low z-score. Recently, Kim (2016) finds that the z-score bankruptcy threshold is higher in countries with better quality of institutions. That is, the z-score bankruptcy threshold has been found to be higher in the U.S., which has a higher institutional quality than Korea. Similar to previous studies, this paper also uses the z-score model in regression analysis and estimates a probit default model. In addition to other potential better in terms of the total number of misclassification errors than the binomial model. 4) Sobehart and Stein (2000) incorporate the financial statement and ratio data into the pure structure model (Merton model) and show a gain in accuracy. 5) Based on 1,560 new debt issues of 1,480 US public firms in 1995 and 1996, they observe that firms under financial distress (high chance of default), i.e., z-score less than 1.81 (bankruptcy threshold), take a higher proportion of borrowing from non-bank private sources (20.8%) than from banks (12.1%) or public sources (13.4%). 6) The revised z-score model excludes the sales/total assets ratio from Altman’s z-score model in order to reduce the potential industry effect. The model can be used for evaluating the financial state of non-manufacturing US and non-US firms. Jounghyeon Kim 67 default factors, the z-score is incorporated into the model to improve the predictive power. To construct the probit default model, the paper examines the determinants of bankruptcy for manufacturing firms in Korea and the US, two countries with different institutional environments. This paper contributes to the existing literature by shedding light on how propensity to corporate default differs in the two countries. In addition, the probit default model is estimated by taking into account the z-score, which reflects the overall financial situation of a firm, as well as its non-financial aspects, such as concentration of ownership and SBC, which may help improve the ability to predict the likelihood of bankruptcy. It is found that z-score, leverage, and short-term debt are the most important determinants of default for firms in both Korea and the U.S. 7) For Korean firms, soft budget constraint (SBC) and ownership concentration are also identified as strong indicators of likelihood of bankruptcy, whereas they do not appear to be significant default factors for US firms. 8) This might be due to fact that the present study uses a relatively weak proxy for the SBC for US firms and the less likelihood of expropriation by an entrepreneur in the U.S., thanks to its more diversified ownership structure (Judge et al., 2008). Next, based on the significant default factors identified by probit default regressions, this study also constructs a default model for Korean firms and US firms and then compares their models’ predictive power via Moody’s power curve and accuracy ratio with the existing bankruptcy models such as Altman (1968)’s z-score model, which is a widely used benchmark model in literature and the new Altman z-score model, which is estimated by Kim (2016). It is found that the default model outperforms other models with the greatest model 7) For Korean firms, leverage, shortand long-term debts, shortterm bank loans, and soft budget constraint (SBC) emerge as factors that increase the likelihood of default, whereas z-score, a firm’s age, export ratio, and ownership concentration appear to reduce the likelihood of default. Details about SBC are discussed in Section Ⅱ. 8) The result for ownership concentration is consistent with the finding of Alexeev and Kim (2012). power, i.e., the highest accuracy for predicting bankruptcy. That is, the model performs better than a benchmark model of Altman’s z-score model, which is solely based on financial variables. This suggests that using additional information obtained from the z-score and the non-financial default factors in the default regression model can improve the predictive power of a model. This paper is organized as follows. In Section Ⅱ , methodology for the empirical analysis is briefly discussed. In Section Ⅲ , variables, data, and sample selection for Korean and US firms are presented, default factors are identified, and default models are constructed. In Section Ⅳ , default model powers are explored via Moody’s power curve and accuracy ratio, and compared with those of the two Altman models. Finally, Section Ⅴ presents the conclusion. Ⅱ. Methodology The Altman z-score model presents the overall index score for a firm’s financial state and predicts the likelihood of its bankruptcy, which is indicated by its z-score falling below the z-score threshold for bankruptcy. 9) This implies that the overall financial state of a firm is an important indicator of bankruptcy. Hence, the z-score is included as one of the predictors in the default probit regression model along with other potential default factors. They may help to improve the model power by providing additional information in predicting bankruptcy. To generate z-scores for Korean firms, a new Altman z-score model, which is developed by Kim (2016) based on the Altman (1968) method (discriminant function analysis), is used instead of 9) He initially finds a midpoint threshold (2.675) to test how well the model classifies firms, and suggests two bound thresholds (1.81 and 2.99). A firm with a z-score above 2.99 and below 1.81 is taken into account as unlikely and likely to go into bankruptcy, respectively. The likelihood of bankruptcy for a firm is uncertain between the two bounds, which is called the “gray area” or “ignorance zone”. GLOBAL BUSINESS & FINANCE REVIEW, Volume. 21 Issue. 2(FALL 2016), 65-85 68 Altman’s z-score model. This is because the original Altman z-score model appears to less effective for predicting bankruptcy of Korean firms compared to US firms. 10) When Altman’s z-score model is used to estimate the z-scores of Korean firms and to predict their likelihood of bankruptcy, the rate of correct classification (53.5%) is lower than that of US firms (83.3%) by about 30% points. 11) Moreover, the financial profiles of Korean firms may be different from those of the US firms that were used in estimating the original Altman z-score model. Another default factor that is included in the model is soft budget constraint (SBC). First introduced by Kornai (1979), SBC has been discussed in many studies. 12) Dewatripont and Maskin (1995) state that the existence of sunk cost leads to SBC, i.e., an unprofitable project can be persistently financed due to the sunk cost. Berglöf and Roland (1997) argue that SBC is attributed to the sunk cost on existing loans and that, as a result, a credit crunch occurs on new loans. Huang and Xu (1998 and 1999) contend that SBC results from the interaction between banks and large firms, so that bad loans for bad projects keep accumulating and lead to firms’ default. Alexeev and Kim (2008) find that SBC plays a role in preventing financially distressed firms from being removed from the market, especially before the financial crisis of 1998, that SBC significantly affects the default of Korean firms during the crisis, and that the phenomenon of SBC substantially drops after the crisis. Above studies imply that SBC distorts information about a firm’s financial state and that a firm under SBC is at a high risk of bankruptcy. For this reason, 10) For similar reasons, Altman et al. (1977) constructed the ZETA model. 11) The samples of 86 Korean firms (43 default firms and 43 non-default firms) and 60 US firms (30 default firms and 30 non-default firms) used by Kim (2016) are classified by a midpoint threshold (2.675). 12) Kornai (1979) defines soft budget constraint (SBC) under a socialized regime, describing it as allowing firms to grow regardless of their current and future financial state, while sustaining financial distress via bailouts for a longer period of time despite their unprofitability. SBC is also characterized as appearing not only in a transition economy, but also in a market-based economy (Kornai et al., 2003). SBC is also incorporated into default probit regression models as one of potential default factors. Alexeev and Kim (2008) define SBC as a condition under which a firm can borrow from banks even if it has a low Altman z-score. Similarly, this paper defines SBC as pertaining only to short-term bank loans, and a firm is classified as an SBC firm if it experiences SBC for at least one year in the sample period. 13) Also included are a firm’s age, which is known to have a negative relationship to the likelihood of bankruptcy (Altman, 1993; Thornhill and Amit, 2003), ownership variable, which is identified as an important determinant of the likelihood of bankruptcy (Alexeev and Kim, 2012), and other potential default factors such as shortand long-term debts. Finally, based on the significant default factors found from regression analysis, a final default model is estimated, which improves the model performance. After that, how well the model performs is evaluated using Moody’s two power metrics - the power curve and the accuracy ratio, and comparison is made with other default models such as the original Altman (1968)’s z-score model and the Kim (2016)’s new Altman z-score model. Ⅲ. Empirical Analysis A. Variables, Data, and Sample Selection for Korean Firms Variables used in probit regression include z-score [ZS], soft budget constraint [SBC], leverage [LEVR], several other financial debt ratios, and 6 non-financial control variables: the age of firm [FAGE], investment ratio to total assets (t-1) [INVS], export ratio to revenue (sales) [EXPO], and ownerships by majority 13) Alexeev and Kim (2008)’s definition of SBC encompasses total bank loans, adjusted bank loans, and short-term bank loans. In order to determine SBC firms, they initially set the cutoff value of a low z-score (i.e., 10th-percentile) at 0.3, whereas it is found the cutoff value to be -0.73 for the entire sample (4,325 Obs.). The difference in the cutoff value is due to the new Altman z-score model. Jounghyeon Kim 69 shareholders, banks, and foreigners [OWNS, OWNB, and OWNF, respectively]. Five different debt ratios are introduced in order to search for the factors that are closely related to default. First, two different shortand long-term debt ratios are defined: the ratio of debt to total debt [S(L)DTD] and the ratio of debt to total assets [S(L)DTA]. Similarly, three different shortand long-term foreign loan ratios and bank loan ratios are defined: the ratios of foreign loans and bank loans to total debt [S(L)FLTD and S(L)BLTD], to total assets [S(L)FLTA and S(L)BLTA], and to shortand long-term debt [SF(B)LSD and LF(B)LLD, respectively]. The unbalanced panel data at the firm level for the empirical analysis are collected from Korea Investors Service-Financial Analysis System (KIS-FAS) and Maekyung Annual Corporation Reports (MKACR) on firms listed in the Korea Stock Exchange (KSE). The initial data set for Korean firms contain 5,557 observations (Obs.) covering 669 firms from 1991 to 2001. 14) Firms are divided into two groups: default firms and non-default firms. 15) Some irrelevant firms are removed, such as firms that belong to nonmanufacturing industries, as well as those identified as Chaebol firms in some years and non-Chaebol firms in others. 16) The final panel data set contains 108 default firms (703 Obs.) and 381 non-default firms (3,522 Obs.). From this panel data, a cross-section sample (489 firms) is taken for use in estimating a default model. The sample for regression analysis is selected by matching defaulting firms to non-defaulting firms in terms of asset size. The data are thereby converted into cross-section data (489 Obs.), which consist of 108 default firms and 381 non-default firms. 17) Based on the sample, 14) See also Alexeev and Kim (2012) and Kim (2016) about these data. 15) “Default” means that a firm has filed for bankruptcy, is bankrupt, or has anything similar in its corporate history. 16) Eleven firms are identified as Chaebol firms in some years and as non-Chaebol firms in other years of the sample period. However, they are included in generating z-scores from the entire sample (4,325 Obs.) in order to identify SBC firms. The sample data are gathered only from manufacturing firms because Altman’s z-score model was developed based on the manufacturing sector. 17) Sample selection is performed by matching non-default firms each firm’s z-score and a SBC dummy variable in relations to the low z-score are generated by the new Altman z-score model of Kim (2016) and used in regression analysis with other variables. 18) My initial conjecture is that ZS, SBC, and LEVR are the most likely potential default factors. A higher z-score would presumably reduce the likelihood of bankruptcy because it means that a firm is in a better financial shape. Likewise, higher SBC and leverage increase the likelihood of bankruptcy because they indicate financial distress (low z-score) and financial burden, respectively. 19) These three variables are referred to as “basic” factors, and they are commonly included in default probit regression. In addition to the three basic factors, other potential default factors are examined that are likely to be important in determining bankruptcy, and then based on them, a default model is found that best captures the likelihood of bankruptcy during the sample period. One of the distinct features of the model is that it uses not only bankruptcy information i.e., z-score that the Altman z-score model generates, but also new information gained from other variables, including non-financial variables in relation to bankruptcy, such as ownership structure, a firm’s age, investment ratio, and export ratio. These new variables may provide additional information for to default firms as follows: First, 108 observations from 108 default firms (703 Obs.) are chosen for one year before the default year and then, given the observations, 108 observations from 381 non-default firms (3,522 Obs.) are paired with them based on asset size in the given year. Second, as in the first step, the remaining 273 non-default firms (2,391 Obs.) are matched as closely as possible to 108 default firms, weighted according to the distribution in each sample year. By repeatedly doing so, all 381 observations (non-default firms) are matched and finally selected. 18) Based on the cross-section sample of 108 default firms and 381 non-default firms, 86 firms (consisting of 43 firms in each group) are selected, and a new Altman z-score model is estimated via multiple discriminant analysis (MDA). The new estimated model is 54321 1.5070.4674.8834.6692.2570.768= XXXXXZ +++++− . It is statistically significant based on Wilks’ lambda criterion, and the overall predictive power is 87.2%. Refer to Kim (2016) for more details on this model. 19) Increase in borrowing may help a firm to improve its financial state unless it is in extreme financial distress or exposed to excessive leverage. GLOBAL BUSINESS & FINANCE REVIEW, Volume. 21 Issue. 2(FALL 2016), 65-85 70 Variables Total Firms Default Firms Non-Default Firms t-statistics Obs. Mean S.D. Min. Max. Obs. Mean S.D. Min. Max. Obs. Mean S.D. Min. Max. ZS 489 0.444 1.443 -5.678 6.280 108 -0.825 1.332 -5.561 1.322 381 0.804 1.259 -5.678 6.280 -11.722*** SBC 489 0.129 0.335 0.000 1.000 108 0.398 0.492 0.000 1.000 381 0.052 0.223 0.000 1.000 10.450*** FAGE 489 29.27 11.69 6.000 97.00 108 28.16 9.189 10.00 54.00 381 29.58 12.30 6.000 97.00 -1.118 INVS 489 0.076 0.098 0.000 1.171 108 0.063 0.086 0.000 0.530 381 0.079 0.102 0.000 1.171 -1.529 EXPO 489 0.306 0.282 0.000 1.000 108 0.273 0.263 0.000 0.979 381 0.316 0.286 0.000 1.000 -1.414 OWNS 489 28.11 16.30 0.000 100.0 108 21.33 15.22 0.000 67.30 381 30.03 16.10 0.000 100.0 -5.017*** OWNB 489 6.679 10.02 0.000 89.70 108 8.169 14.73 0.000 89.70 381 6.256 8.191 0.000 56.50 1.754* OWNF 489 5.580 11.62 0.000 91.60 108 4.204 13.54 0.000 91.60 381 5.971 11.00 0.000 86.00 -1.396 LEVR 489 0.654 0.269 0.125 2.046 108 0.898 0.346 0.338 2.046 381 0.585 0.194 0.125 1.942 12.179*** SDTD 489 0.645 0.172 0.055 0.990 108 0.628 0.197 0.055 0.990 381 0.650 0.163 0.224 0.976 -1.175 LDTD 489 0.355 0.172 0.010 0.945 108 0.372 0.197 0.00 0.945 381 0.350 0.163 0.024 0.776 1.175 SDTA 489 0.412 0.196 0.069 1.786 108 0.549 0.281 0.076 1.786 381 0.374 0.142 0.069 0.828 8.835*** LDTA 489 0.242 0.195 0.007 1.652 108 0.349 0.308 0.007 1.652 381 0.211 0.134 0.007 1.403 6.791*** SFLTD 489 0.043 0.082 0.000 0.672 108 0.032 0.056 0.000 0.327 381 0.046 0.088 0.000 0.672 -1.509 LFLTD 489 0.042 0.066 0.000 0.584 108 0.023 0.033 0.000 0.173 381 0.047 0.072 0.000 0.584 -3.315*** SBLTD 489 0.270 0.173 0.000 0.864 108 0.304 0.177 0.000 0.740 381 0.260 0.170 0.000 0.864 2.340** LBLTD 489 0.121 0.125 0.000 0.663 108 0.129 0.154 0.000 0.663 381 0.119 0.115 0.000 0.657 0.734 SFLTA 489 0.028 0.058 0.000 0.612 108 0.027 0.046 0.000 0.252 381 0.028 0.061 0.000 0.612 -0.239 LFLTA 489 0.025 0.040 0.000 0.414 108 0.020 0.028 0.000 0.143 381 0.027 0.043 0.000 0.414 -1.608 SBLTA 489 0.183 0.143 0.000 0.927 108 0.263 0.183 0.000 0.927 381 0.160 0.120 0.000 0.696 6.961*** LBLTA 489 0.088 0.142 0.000 1.357 108 0.139 0.237 0.000 1.357 381 0.073 0.096 0.000 1.274 4.316*** SFLSD 489 0.068 0.113 0.000 0.805 108 0.058 0.097 0.000 0.418 381 0.070 0.117 0.000 0.805 -0.948 LFLLD 489 0.230 1.238 0.000 25.41 108 0.131 0.311 0.000 1.916 381 0.258 1.392 0.000 25.41 -0.937 SBLSD 489 0.412 0.219 0.000 0.916 108 0.462 0.208 0.000 0.855 381 0.398 0.221 0.000 0.916 2.693*** LBLLD 489 0.327 0.253 0.000 0.991 108 0.316 0.270 0.000 0.991 381 0.330 0.248 0.000 0.971 -0.512 Notes: *, **, and *** denote that sample means are statistically different at the level of 10%, 5%, and 1%, respectively. ZS: Z-score, SBC: soft budget constraint, FAGE: age of a firm, INVS: the ratio of investment to total asset (t-1), EXPO: the ratio of export to revenue (sales), OWNS, OWNB, and OWNF: ownerships by majority shareholders, banks, and foreigners, respectively, LEVR: leverage, S(L)DTD: the ratio of short (long)-term debt to total debt, S(L)DTA: the ratio of short (long)-term debt to total assets, S(L)FLTD: the ratios of short (long)-term foreign loans to total debt, S(L)BLTD: the ratios of short (long)-term bank loans to total debt, S(L)FLTA: the ratios of short (long)-term foreign loans to total assets, S(L)BLTA: the ratios of short (long)-term bank loans to total assets, SF(B)LSD: the ratios of short-term foreign (bank) loans to short-term debt, LF(B)LLD: the ratios of long-term foreign (bank) loans to long-term debt. Table 1: Descriptive statistics for Korean firms in the sample predicting bankruptcy and help improve the predictive power of the model. Prior to running regressions, the different characteristics of the firms in each group are examined from the variables to be used in the regression analysis. Table 1 summarizes their descriptive statistics and contrasts default and non-default firms for Korean firms. The last column shows the statistical differences between default and non-default firms in terms of ZS, SBC, OWNS, OWNB, LEVR, shortand long-term debt ratios [S(L)DTA], shortand long-term bank loan ratios [S(L)BLTA], the ratios of short-term bank loan to short-term debt and total debt [SBLSD and SBLTD, respectively], and long-term foreign loan ratio [LFLTD]. As conjectured earlier, default firms possess much lower ZS and OWNS, whereas they are higher in SBC and LEVR. In the default group, the z-score is negative and far below the cutoff of -0.73 for a low z-score, which implies that default firms are quite financially distressed and burdened than non-default firms. Jounghyeon Kim 71 B. Default Factors and Default Model Regression is performed using the variables explained in the earlier section to scrutinize the default factors and the default model. First, a “basic” default model is established by performing probit regression only on ZS, SBC dummy variable, and LEVR, which I believe are the most likely significant determinants of default. This is to observe whether the model correctly captures the sign and significance of the estimated coefficients. Second, by incorporating into the model the different types of financial debt ratios defined earlier, it is determined which debt ratios are significant factors of default to form a “partial” default model. Third, by adding 6 non-financial control variables to the partial default model, it is observed how the inclusion changes the significant factors and which control variables have significant effects on default. This is the “full” default model. Finally, a default model is estimated by running regression only on significant factors found in the full default model. In all regressions, it is checked for multi-collinearity in explanatory variables with three commonly used indicators: variance inflation factor (VIF), condition number, and determinant of the correlation matrix. 20) The basic default model estimates the significant coefficients for ZS, SBC, and LEVR, and correctly captures the negative effect of ZS and the positive effect of SBC and LEVR on default. 21) Moreover, it is found from the partial default model that the ratios of various types of debt to total assets are significant default factors, whereas the ratios of debt to total, shortand long-term debt are not significan t. 22) Accordingly, full default regression is performed 20) There is no consensus on detecting multi-collinearity. A rule proposed by Allison (1998) is followed that it is present if the variance inflation factor (VIF) is greater than 2. Moreover, a rule of thumb states that there is a concern of multi-collinearity if the condition number (the ratio of the largest eigenvalue to the smallest eigenvalue) is greater than 15 and the determinant of the correlation matrix is close to zero. Thus, if the condition number is one, there is no collinearity. These indicators are computed using the “collin” command in STATA. 21) The regression result from the basic default model is available upon request. on basic factors, financial ratios of debt to total assets, and control variables. The full default regression model describes the relationship between default and all potential default factors as follows: ttttt NFNFVLEVRSBCZSD εββββββ + ′ + ′ ++++ 543210 = where D, FV, and NFV represent default dummy variable, financial variables, and non-financial variables (control variables), respectively. Table 2 presents the regression results from the model. Equation 1 (Eq. 1) in the first column is included only to examine whether the financial ratios of shortand long-term bank loan or foreign loans to total debt are statistically significant in the full default regression. It shows that the debt ratios S(L)FLTD and S(L)BLTD are still not as significant as in the partial default regression. 23) Thus, it can be concluded that no types of debt to total debt are significant default factors in any of the regression models. Equations 2 through 2-2 represent full default regressions. 24) They show that ZS, SBC, and LEVR 22) The partial default model is separately run on various ratios of debt to total debt and to total assets. In the regressions with the financial ratios to total debt, only LFLLD and LBLLD appear to be marginally significant at the level of 10%. Therefore, they are not taken into account as strong indicators of default at significance levels of 1% and 5%. In the regressions with the financial ratios to total assets, S(L)DTA and SBLTA appear to be statistically significant at levels of 1% and 5%, respectively, which implies that the ratios of debt to total assets are more likely to be important factors of default than are the ratios of debt to total debt. The regression results from the partial default models are available upon request. 23) This result may be spurious because the condition number is greater than 15. Thus, in order to completely remove the possibility of multi-collinearity, insignificant variables are excluded, such as ownership by banks, ownership by foreigners, and investment ratio, as well as one significant variable, FAGE, from control variables, and then the regression is run again. This reduces the condition number to 14.39, and the regression still generates insignificant debt ratios, leaving other variables significant. 24) Condition numbers in Equations 2 and 2-1 are slightly above 15, which implies some, but still acceptable, multi-collinearity. Regression is performed without putting S(L)DTA, S(L)BLTA, and S(L)FLTA together, due to the high correlation between SDTA and SBLTA (0.743) and between LDTA and LBLTA (0.794). When they are combined in regression, the condition number is 18.72, which may have led to spurious regression results. GLOBAL BUSINESS & FINANCE REVIEW, Volume. 21 Issue. 2(FALL 2016), 65-85 72 Variables Dependent Variable: D Eq. 1 Eq. 2 Eq. 2-1 Eq. 2-2 Eq. 3-1 Eq. 3-2 Eq. 4-1 Eq. 4-2 ZS -0.265** (0.131) -0.273** (0.132) -0.276** (0.131) -0.469*** (0.122) SBC 0.478* (0.257) 0.524** (0.255) 0.501** (0.252) 0.342 (0.252) 0.874*** (0.214) 1.008*** (0.218) 0.871*** (0.214) 1.080*** (0.211) LEVR 1.921*** (0.511) 1.721*** (0.553) LEVR(t-1) 0.697 (0.457) 1.998*** (0.495) SFLTD -1.120 (1.034) SBLTD 0.309 (0.550) SDTA 1.911*** (0.496) 2.157*** (0.625) 2.661*** (0.473) SFLTA -1.554 (1.288) -2.244 (1.467) -2.666** (1.293) SBLTA 1.476** (0.633) 1.419** (0.673) 2.684*** (0.566) LFLTD -2.567 (1.961) LBLTD -0.975 (0.913) LDTA 1.581** (0.695) 2.002** (0.898) 2.413*** (0.772) LFLTA -3.804 (2.468) -3.773 (2.454) -4.192* (2.364) LBLTA 0.525 (0.695) 0.550 (0.716) 1.825*** (0.691) FAGE -0.026*** (0.007) -0.026*** (0.007) -0.026*** (0.007) -0.027*** (0.008) -0.024*** (0.007) -0.024*** (0.007) -0.023*** (0.007) -0.022*** (0.007) OWNS -0.019*** (0.005) -0.019*** (0.005) -0.019*** (0.005) -0.019*** (0.005) -0.021*** (0.005) -0.022*** (0.005) -0.020*** (0.005) -0.021*** (0.005) OWNB 0.004 (0.008) 0.003 (0.008) 0.003 (0.008) 0.011 (0.007) -0.003 (0.008) 0.001 (0.007) -0.001 (0.008) 0.007 (0.006) OWNF 0.000 (0.007) 0.002 (0.007) 0.002 (0.007) -0.001 (0.007) 0.001 (0.007) -0.002 (0.007) 0.001 (0.007) -0.004 (0.007) INVS 0.847 (0.827) 0.196 (0.782) 0.220 (0.789) 0.962 (0.825) -0.027 (0.834) 0.641 (0.874) -0.092 (0.839) 0.570 (0.882) EXPO -0.582** (0.293) -0.693** (0.282) -0.681** (0.281) -0.548* (0.290) -0.694** (0.278) -0.548* (0.287) -0.724*** (0.276) -0.608** (0.271) Constant -0.703 (0.479) -0.649 (0.486) -0.709 (0.449) 0.270 (0.349) -1.435*** (0.362) -1.125*** (0.359) -1.296*** (0.381) -0.203 (0.284) Observations 489 489 489 489 489 489 489 489 Pseudo R20.345 0.330 0.331 0.317 0.323 0.306 0.319 0.267 Collinearity Indicators Avg. VIF 1.53 1.48 1.46 1.36 1.45 1.30 1.13 1.20 Condition No. 18.52⍏15.19⍏15.76⍏12.51 14.50 14.65 13.13 11.84 Det. (corr. mtx.) 0.07 0.21 0.19 0.17 0.22 0.22 0.57 0.38 Cutoff Value Correct Classification Rate for Default and Non-Default Firms 0.5 84.66% 85.28% 84.87% 84.66% 85.89% 84.05% 85.48% 84.25% 0.22 78.73% 79.35% 79.55% 79.14% 77.91% 77.51% 78.53% 77.71% Notes: *, **, and *** represent the significance at the level of 10%, 5%, and 1%, respectively, and robust standard errors are in p arentheses. The cutoff value of 0.5 is the expectation by chance, and 0.22 (108/489) is the random chance of default in the sample. ⍏represents the concern of collinearity. D: default dummy, ZS: Z-score, SBC: soft budget constraint, FAGE: age of a firm, INVS: the ratio of investment to total asset (t-1), EXPO: the ratio of export to revenue (sales), OWNS, OWNB, and OWNF: ownerships by majority shareholders, banks, and foreigners, respectively, LEVR: leverage, S(L)DTA: the ratio of short (long)-term debt to total assets, S(L)FLTD: the ratios of short (long)-term foreign loans to total debt, S(L)BLTD: the ratios of short (long)-term bank loans to total debt, S(L)FLTA: the ratios of short (long)-term foreign loans to total assets, S(L)BLTA: the ratios of short (long)-term bank loans to total assets. Table 2. Full default regression models for Korean firms: probit regression Jounghyeon Kim 79 Model Variable Methodology Data Model Altman DF MDA Probit for model for score 1. Probit Default Korea ○○Korea (489) Korea (489) 2. New Altman Korea ○○Korea (86) Korea (489) 3. Altman ○○US (66) Korea (489) Notes: Altman, DF, MDA, and Probit represent factors from Altman’s model, factors from probit regression, multiple discriminant function analysis, and probit regression, respectively. The number of observations is in parentheses. Table 7. Model composition for variables, methodology, and data for Korean firms Ⅳ. Comparison of Model Power A model that correctly classifies default and non-default firms with a higher accuracy rate is regarded as having a higher level of predictive power. Among many bankruptcy prediction models, Altman’s z-score model is one of the most widely used benchmark models for predicting the likelihood of a firm’s bankruptcy. Another popularly used model in relation to predicting bankruptcy is the hazard function model. Yang and Temple (2009) examine a firm’s exit rate via a non-parametric estimation with a hazard function, and find that a firm’s size is an important determinant. Moody’s constructs default prediction models using both parametric and non-parametric approaches for public and private firms to estimate the probability of a firm’s bankruptcy, and shows that its models perform better than Altman’s z-score model, the hazard function model, and other existing credit risk models (Sobehart and Stein, 2000; Kocagil and Reyngold, 2003). Similarly, using two Moody’s power metrics - power curve and accuracy ratio - to compare the model powers of the final default model estimated in Section Ⅲ with those of the original Altman model and the new Altman model, this paper determines the model that provides the best performance. Table 7 summarizes the set of variables, methodologies, and composition of data for these models. As shown in the table, the first two models are estimated using different variables and methods, but with the same data, whereas the last two models are estimated using the same Altman variables and methods, but with different data. In order to make the model powers comparable, the same data set is applied to all three models in generating outputs (scores). The first model is the “Probit Default Korea” model, which was estimated as a final default model from the probit regression in subsection B of Section Ⅲ . The second model is the “New Altman Korea” model, which was re-estimated using the discriminant analysis by Kim (2016). The third model is the “Altman” model, which is the original Altman z-score model. Next, based on the model scores generated by these models, a power curve is constructed, the accuracy ratio is computed in order to compare model powers, and the most powerful model is determined. A. Power Curve A power curve is a measure that evaluates model power via the relationship between the cumulative percentage of sample firms excluded from the data set and the cumulative percentage of default firms excluded from the data set. Given a percentage of firms excluded from the same data set, if a model excludes a higher percentage of default firms than other models, the model is regarded as more powerful than others. Accordingly, a “perfect” model is the one that gives all default firms worst scores than non-default firms. In contrast, a “random” model is the one that eliminates default firms at the same rate as non-default firms. That is, a random model is the 45-degree line on the graph that shows the relationship between the percentage of default firms excluded ( y axis) and the percentage of sample firms excluded ( x axis). The power curve is constructed as follows. First, GLOBAL BUSINESS & FINANCE REVIEW, Volume. 21 Issue. 2(FALL 2016), 65-85 80 A B Accuracy Ratio = B/(A+B) 020 40 60 80 100 Percent of Default Firms Excluded(%) 020 40 60 80 100 Percent of Sample Excluded(%) Probit Default Korea Model New Altman Korea Model Altman Model Random Model A Power Curve and Accuracy Ratio for Korea Figure 1. Power curves based on 489 observations of Korean firms scores from an estimated model are sorted from worst to best. Second, a certain percentage of the sorted scores are repeatedly excluded from the worst until all scores are removed. 42) At the same time, the percentages of sample firms and default firms excluded are cumulatively computed. Third, the power curve is drawn using the result of computation. Following these procedures, the scores are computed from the three models - the final default model (Probit Default Korea model), the new Altman z-score model (New Altman Korea model), and the original Altman z-score model (Altman model) - with a single data set (108 default and 381 non-default firms), and a power curve for each model is constructed, as shown in Figure 1. In the graph, the power curve of the Probit Default Korea model is furthest away from the 45-degree line, which indicates that the model performs better than the other two. With less than 20% of the sample excluded, there is almost no difference between the new Altman Korea model and the Altman model. In most parts above 20%, the curve suggests that the former has a little higher model power than the 42) Each time, lowest 20 scores (firms) from 489 (about 4%) in the sample are excluded, except for the final removal (9 firms). latter. This is consistent with the argument made in Section Ⅱ that the original Altman z-score model is less powerful than the new Altman z-score model in classifying Korean firms. 43) Therefore, it can be concluded that the Probit Default Korea model is most powerful, followed by the new Altman Korea model and the Altman model. Next, scores are computed from the three models with the same data set (420 Obs.) used in the estimation of the final default model for US firms. The first model is the Probit Default US model, which was estimated as the final default model from the default probit regression in Table 6. The second model is the New Altman Korea model, which was estimated using the discriminant function analysis for Korean firms by Kim (2016). 44) The third model is the Altman model, which is the original Altman z-score model. The second and third models are the same ones used for comparing model powers for Korean firms. Table 8 summarizes 43) Model power is generally expected to decline when a model is applied to a different sample or an “out-of sample”. Thus, the higher power of the new Altman z-score model may be ascribed to using “in-sample” data (489 firms). 44) As the Altman’s z-score model is previously applied to Korean firms in the comparison of model, the new Altman z-score model is applied to US firms. Jounghyeon Kim 81 A B Accuracy Ratio = (B/A+B) 020 40 60 80 100 Percent of Default Firms Excluded(%) 020 40 60 80 100 Percent of Sample Excluded(%) Probit Default US Model New Altman Korea Model Altman Model Random Model A Power Curve and Accuracy Ratio for the U.S. Figure 2. Power curves based on 420 observations of US firms Model Variable Methodology Data Model Altman DF MDA Probit for model for score 1. Probit Default US ○○US (420) US (420) 2. New Altman Korea ○○Korea (86) US (420) 3. Altman ○○US (66) US (420) Notes: Altman, DF, MDA, and Probit represent factors from Altman’s model, factors from probit regression, multiple discriminant function analysis, and probit regression, respectively. The number of observations is in parentheses. Table 8. Model composition for v ariables, methodology, and data for US firms the composition of variables, methodology, and data for these models. Based on the scores generated by the three models with a single data set (84 default and 336 non-default firms), power curves are drawn, as shown in Figure 2. The new Altman Korea model is located closest to the 45-degree line, which implies that it has the lowest level of model power. This is not surprising since the application of the new Altman Korea model to another sample set (US firms) likely reduces its predictive power. The difference in model power between the Altman model and the Probit Default US model is not apparent due to the similarity in their power curves, which implies that the final default model, which is found to be the best representative for US firms, is as powerful as the original Altman z-score model. 45) B. Accuracy Ratio As shown in Figures 1 and 2, the power curve provides visual and qualitative assessments of model performance. However, it is difficult to compare overall model powers, especially when power curves have similar shapes. Therefore, the curve is converted into a numerical metric (accuracy ratio) to measures comparative performance. In other words, the accuracy ratio converts the power curve into a single numerical measure that represents the overall 45) The power curves overlap for the most part. However, with less than 20% of the sample excluded, the power curve of the Probit Default US model is located a little bit further away from the 45-degree line than that of the Altman model. With around 40% of the sample excluded, the power curve of the latter is located slightly further away from the 45-degree line than that of the former. GLOBAL BUSINESS & FINANCE REVIEW, Volume. 21 Issue. 2(FALL 2016), 65-85 82 Model Sample No. of Obs. Probit Default Korea New Altman Korea Altman “In-sample” 489 [108:381] 60.08% (60.24%) 51.82% 51.14% Subsample 1 163 [36:127] 60.87% (59.91%) 54.43% 53.95% Subsample 2 163 [36:127] 59.91% (59.91%) 51.32% 50.61% Subsample 3 163 [36:127] 52.99% (53.95%) 50.61% 51.09% “3-fold overall” AR 489 [108:381] 57.88% (58.03%) 51.82% 51.14% Note: The ratios of default and non-default firms are in brackets. The percentage in parentheses is the accuracy ratio of another “Probit Default” model (Model B) in Table 3. There is no significant difference in model power between Model A and Model B. Table 9. Comparison of accuracy ratios for Korean firms predictive accuracy. The accuracy ratio is defined as a ratio of the area (B) below the power curve and the area above the random model (A + B). Hence, the higher the accuracy ratio, the more powerful the model. 46) The area under the power curve is approximated using the Riemann sum method because the power curve is drawn by discrete coordinates, i.e., it is not a continuous function. First, the right Riemann sum and the left Riemann sum are separately computed at each coordinate point, and then averaged. 47) The accuracy ratios from the power curves for Korean firms are summarized in Table 9. As shown in the first row, the model power ranks are consistent with the order graphically found in Figure 1. The Probit Default Korea model is identified as the most powerful with 60.08% model power, followed by the New Altman Korea model (51.82%) and the Altman model (51.14%). This finding supports the claim that using z-score as one of the predictors and incorporating additional default information from other significant default factors (non-financial variables) into the default prediction model can help improve the model performance. Next, in order to evaluate the robustness of the model performance, accuracy ratios are computed on k subsamples and a k -fold “out-of sample”, following the procedures of Moody’s “ k -fold test”. 46) The accuracy ratio of the perfect model would be 100%, whereas the accuracy ratio of the random model would be 0%. 47) Since the power curve is monotonically increasing, the right Riemann sum is overestimated, whereas the left Riemann sum is underestimated. This is the reason for taking the average of the two Riemann sums. First, 108 default and 381 non-default Korean firms are equally divided into 3 subsamples, each subsample consisting of 36 default firms and 127 non-default firms. 48) This produces 3 different subsamples with an identical default rate (about 0.22). Second, by estimating the new default model with two of the three subsamples and computing the scores for the remaining subsample, an accuracy ratio on the latter is obtained. These procedures are performed three times for all combinations. Lastly, the scores for each remaining subsample are combined, and an accuracy ratio on the 3-fold “out-of-sample” is computed, which is the “3-fold overall” accuracy ratio. Table 9 summarizes the accuracy ratio on each subsample and the 3-fold out-of-sample computed from the three models. 49) Overall, the accuracy ratios on the subsamples are relatively stable and close to those on the initial in-sample in each model, which implies that no subsample affects the model power. Moreover, the model power ranks for the 3-fold out-of-sample do not digress from those for the initial in-sample. The Probit Default Korea model with an accuracy ratio of 57.88% is still the most powerful, 48) In selecting subsamples, the first observation in each group from the sample is assigned to subsample 1, the second observation to subsample 2, the third observation to subsample 3, the fourth observation to subsample 1 again, the fifth observation to subsample 2, the sixth observation to subsample 3, and so on. 49) Instead of re-estimating the new Altman z-score model and the original Altman z-score model from two subsamples, the initial models are used in scoring each subsample because the data set for the original Altman z-score model is unavailable. As a result, the accuracy ratios of these models on both the initial in-sample and the 3-fold out-of-sample are identical. Jounghyeon Kim 83 Model Sample No. of Obs. Probit Default US New Altman Korea Altman “In-sample” 420 [84:336] 60.01% (60.29%) 55.28% 60.20% Subsample 1 140 [28:112] 58.98% (57.76%) 57.45% 63.27% Subsample 2 140 [28:112] 62.96% (62.96%) 55.92% 59.29% Subsample 3 140 [28:112] 60.20% (60.20%) 53.47% 57.45% “3-fold overall” 420 [84:336] 60.01% (60.58%) 55.28% 60.20% Notes: The ratios of default and non-default firms are in brackets. The percentage in parentheses is the accuracy ratio via another “Probit Default” model (Model A) in Table 6. There is no significant difference in model power between Model A and Model B. Table 10. Comparison of accuracy ratios for US firms followed by the New Altman Korea model (51.82%) and the Altman US model (51.14%), suggesting that model performance is quite robust across the data set. In sum, among the three default models, the Probit Default Korea model provides the highest model power, followed by the New Altman Korea model and the Altman model. This suggests that the non-financial factors such as SBC, age of a firm, ownership structure, and export ratio that are found to be significant in the default model can help improve the model power. Next, based on the power curves for US firms, an accuracy ratio for each model that measures comprehensive model power with a single numerical unit is computed and presented in Table 10. The results in the first row indicate that the model power ranks are consistent with the results obtained from power curves. That is, for the initial “in-sample” consisting of 420 observations, the New Altman Korea model is the least powerful with 55.28% model power, and the power of the Probit Default US model is almost equivalent to that of the Altman’s z-score model. It is found that the former provides slightly worse performance than the latter. However, the accuracy ratio (60.29%) of another Probit Default US model (Model A) in Table 6 in subsection D of Section Ⅲ shows slightly better performance than that (60.20%) of the Altman model, which implies that the additional information from the significant factors such as SBC and inventory ratio found in the full default regression may also help improve the model power for US firms. Finally, the robustness of model performance is evaluated using Moody’s “ k -fold test”. The initial sample is divided into three equal subsamples with an identical default ratio (20%) and the accuracy ratio of each subsample is computed by applying to each the new estimated models from the other two subsamples. Table 10 summarizes the accuracy ratios of each model when applied to the subsamples and the 3-fold “out-of-sample”. It shows that the accuracy ratio of each subsample does not vary significantly compared to the accuracy ratio of the initial “in-sample”, which implies that none of the subsamples influence the model performance. Moreover, the accuracy ratio for the combined 3-fold out-of-sample is very similar to that for the in-sample, and the model power ranks do not change among the three models. 50) This suggests that the model performance is quite robust across the data set. Ⅴ. Conclusion Many studies in the existing literature examine the significant determinants and the predictive models of bankruptcy. Similarly, this paper also explores the most important default factors by estimating probit 50) When applied to both the 3-fold out-of-sample and the initial in-sample, the accuracy ratios of the two Altman models appear to be identical for the same reason as noted for Korean firms in footnote 49. GLOBAL BUSINESS & FINANCE REVIEW, Volume. 21 Issue. 2(FALL 2016), 65-85 84 default models for manufacturing firms in Korea and the U.S. in the sample periods of 1991-2001 and 1991-2003, respectively. In addition to other potential default factors, this study incorporates the z-score as one of the factors into the probit model. This is because the z-score, which reflects the overall financial situation of a firm as well as its non-financial aspects, such as ownership and soft budget constraint (SBC), may help improve the ability to predict the likelihood of bankruptcy. A probit default model is constructed based on significant factors and its predictive power is compared with those of other bankruptcy models, such as the new Altman z-score model and the Altman’s z-score model. For Korean firms, probit regression indicates that z-score, SBC, leverage, including shortand long-term debts, and short-term bank loans are the most significant default factors. Debts, especially bank loans have emerged as important factors in Korea as the financial market liberalized domestically and internationally in the 1990s. Unobserved bad or short-term loans from banks put highly leveraged firms, particularly SBC firms, in financial trouble and at a high risk of bankruptcy. In addition, age of a firm, export ratio, and concentration of ownership are also identified as significant determinants of default. For US firms, z-score, leverage, short-term debt, and inventory are found to be the most significant default factors. Although SBC is identified as a significant factor in some cases, SBC and ownership concentration do not appear to be significant overall. This may be due to the fact that a relatively poor proxy for SBC is used for US firms and that US lenders, given a better quality of institutions, have more information concerning the ability of financially troubled firms to pay back their loans. Moreover, because US institutions have more diversified ownership structures, they may be less prone to tunneling by insiders. These results for Korean and US firms help shed light on how propensity to corporate default differs in the two countries. Based on the significant default factors found from probit regression analyses, a default model is constructed to outperform existing default prediction models such as the new Altman z-score model and the Altman’s z-score model. To this end, in addition to other significant default factors, z-score is incorporated into the model as one of the explanatory variables, which may provide additional information for predicting bankruptcy. The power of the probit default model is compared with those of the two Altman z-score models using Moody’s two power metrics: the power curve and the accuracy ratio. It is found that the probit default model possesses the highest level of predictive power for both Korean firms and US firms. 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