Business failure prediction in retail industry: an empirical evaluation of generic bankruptcy prediction models.

He, Yihong ; Kamath, Ravindra

ABSTRACT

This paper investigates whether generic bankruptcy prediction models can maintain their validity when applied to firms from an individual industry, namely, the retail industry. The literature suggests that the classification accuracy of generic models is reduced considerably when they are applied to samples drawn from an individual industry. Our study re-estimates two generic bankruptcy prediction models, one by Ohlson (1980) and one by Shumway (2001), with a mixed industry sample of 354 over-the-counter (OTC) traded small firms during the 1990s. Given the limited sample size for the retail industry, both models are validated with an ex post classification test by reclassifying the sample used to estimate the models, while Lachenbruch's U method (1967) is utilized to overcome the problem of classification bias. Our results indicate that the generic models by Ohlson (1980) and Shumway (2001) are modestly robust in classifying bankruptcy incidence of retail firms one year prior to bankruptcy, but the classification accuracy levels decrease sharply as the lead-time from bankruptcy increases. Overall, the classification accuracies for the retail industry sample are lower than those for the mixed industry sample.

INTRODUCTION

Business failures are anxiety provoking events. Irrespective of one's nature of association with the business, such as whether they are stockholders, creditors, labor unions, governmental bodies, employees, customers or suppliers, they are likely to deem business failures both, costly and stressful. Since the pioneering work by Beaver (1966) and Altman (1968), numerous contributions have been made to the development and refinement of bankruptcy prediction models over the last forty years. Generally the bankruptcy prediction models are initially estimated with cross-sectional data of firms from different industries, and then the validity of resulting models are evaluated by classifying firms into bankrupt or nonbankrupt. The reliance on the data collected from several industries to develop a model, however, is likely to ignore the heterogeneity of the observations, and therefore could introduce bias in the estimation of a model's parameters. Extant literature (e.g., Mensah 1984; Platt and Platt 1990; Platt and Platt 1991; Platt et al. 1994; McGurr and DeVaney 1998) has indicated that numerous factors including many micro as well as macro economic inputs, such as business product cycle, interest rates, and preferences for and uniqueness of capital structure, have different impact on the operations of individual industries, and consequently affect the success of a bankruptcy prediction model when applied to each industry. Accordingly, one relevant inquiry would be to ascertain if a unique bankruptcy prediction model is needed for each individual industry instead of relying on generic models. McGurr and DeVaney (1998) have in fact recommended "... that future failure studies use single industry samples to enhance their predictive accuracy" (p.169).

The primary goal of this paper is to evaluate the effectiveness of two successful generic bankruptcy models by Ohlson (1980) and Shumway (2001) in discriminating between bankrupt and nonbankrupt firms from an individual industry, namely, the retail industry. To further control industry bias, this study avoids large and established conglomerate firms traded on the New York Stock Exchange (NYSE) and/or the American Stock Exchange (AMSE), which are found in the majority of predecessor studies, since these conglomerates often operate across multiple industries. Instead, the sample of firms utilized in this empirical investigation is comprised of 354 over-the-counter (OTC) traded small firms with an average asset size of less than $37 million. Both Ohlson's (1980) and Shumway's (2001) models are first re-estimated with the cross-sectional data of OTC firms. Then, the re-estimated generic models are validated by classifying the retail industry specific sample, while Lachenbruch's U method (1967) is adopted to overcome the problem of classification bias.

Our study extends the previous work, while offering some distinguishing features. First, as discussed above, the sample consists of a group of small OTC firms. Only the firms with assets less than $130 million are included in this study. The average assets of the bankrupt firms and the nonbankrupt firms are $36.4 million and $35.9 million, respectively. Furthermore, by limiting the firm size to this magnitude, we have increased the probability that our sample firms belong to one unique industry (e.g., the retail industry) rather than operating across multiple industries. Second, we contribute to the bankruptcy prediction studies of individual industries by introducing Lachenbruch's U method (1967), which is utilized to examine the possible classification bias, while such bias is not taken into consideration by the existing relevant literature. Furthermore, the validity of models is tested up to three years prior to bankruptcy. Third, this study spans over just the decade of the 1990s, and as a result, reduces the plaguing issue of extracting and pooling the data from several decades. The narrow window of the study coupled with the re-estimation of the two models also helps in reducing the "time bias" (McGurr and DeVaney 1998). Fourth, the sample of 354 mixed industry firms in this examination is considerably larger than those in most previous studies. The process of re-estimating models with the relatively large sample size should enhance the capturing of the temporal nature of the data so as to improve the reliability of the models for validation test. Fifth, the process of matching of bankrupt and nonbankrupt firms is based on three dimensions, namely, the asset size, the industry and the timing of the financial reporting.

The remaining paper is organized in five sections. A brief review of the relevant literature is the subject of the second section. The methodology and the data utilized are described in the third section. The empirical findings are discussed in the fourth section. The last section contains a summary of the paper.

RELEVANT LITERATURE

Some of the earliest studies comparing failed and nonfailed firms can be traced to the 1930s due to the experience of the depression. Beaver (1966, 1968) utilized univariate analysis approach to determine the ability of financial ratios to predict firm failure. Using multivariate discriminant analysis (MDA), Altman's bankruptcy prediction model (1968) relied on a linear combination of five financial ratios from the data of sample firms one year prior to bankruptcy. A composite index called Z-score was used to classify bankrupt and nonbankrupt firms. The MDA method has also been utilized by Deakin (1972), Edmister (1972) and Blum (1974), among others.

Recent bankruptcy prediction studies apply the logistic regression analysis (logit) to overcome the potential deficiencies of the MDA technique (Eisenbeis 1977). While the variable coefficients in a discriminant analysis have a limited use, the coefficients of variables in a logit function are interpretable. Ohlson (1980), Zavgren (1985), Gentry et al. (1985), Platt and Platt (1990, 1994), Shumway (2001), He, et al. (2005), and He and Kamath (2005) are some examples of studies which have utilized the logit methodology. Ohlson's bankruptcy prediction model (1980) relied on eight financial ratios, representing liquidity, profitability, leverage and solvency. The classification results show that Ohlson's model was able to identify about 88 percent of 105 bankrupt firms accurately one year before bankruptcy.

Over time, the wisdom of relying solely on financial statement based ratios to evaluate the financial health of any business was challenged. Zavgren (1985), for example, was skeptical about the capability of financial ratios to capture some of the dynamic firm-specific attributes, given the presence of time lag in receiving the financial information. Such concerns led to investigations of relationship between market behavior and bankruptcy incidence by Aharony et al. (1980), Clark and Weinstein (1983), Katz et al. (1985), and Queen and Roll (1987). Given a semi-strong efficient market, the capital market mechanism might be better suited for broader financial and nonfinancial information, such as solvency deterioration, sales growth decline, or global competition. As a result, the market should be able to assimilate such unfavorable information in a real time, and will alter the prices of securities of any firm to account for the likelihood of impending troubled days ahead, possibly, well before the eventual bankruptcy. The findings in event studies conducted by Aharony et al. (1980) and Clark and Weinstein (1983) revealed that stock returns became significantly negative about three years before the bankruptcy declaration.

Shumway's bankruptcy prediction model (2001) successfully illustrated the benefits of teaming financial statement based ratio variables with the market driven variables for the purposes of predicting bankruptcy. The two market variables in the study exhibited strong segregating ability along with the two financial ratios, while displaying low correlations among variables. Shumway's model reported higher prediction accuracy one year before bankruptcy for a holdout sample, as compared to the benchmark models, which are solely based on financial statement ratios.

By and large, that the bankruptcy prediction models have been developed using cross-sectional data from different industries, the question about their effectiveness in distinguishing bankrupt firms from nonbankrupt firms for industry specific samples has been raised. Platt and Platt (1990) recommended that industry-relative ratios should be used in lieu of the absolute financial ratios for the purposes of model development. The authors contended that such a consideration would produce better classification rates as the industry-relative ratios help stabilize the predictive ability of the model. Altman (1993), however, did not embrace the industry-relative ratio concept for the purpose at hand because of the time lag in obtaining the industry relative data.

McGurr and DeVaney (1998) evaluated the effectiveness of five well-known models developed with the mixed industry data in classifying bankruptcy for a sample of retail firms. The findings confirmed the authors' assertion in that the generic models are likely to be less successful in discriminating between bankrupt and nonbankrupt firms from the retail industry, as compared to the classification results reported for the mixed industry samples in the original studies. They concluded that " ... mixed industry failure prediction models appear to have a limited usefulness in a review of retail firm financial health due to the effect of industry, population, and time biases" (p.175).

He and Kamath (2005) attempted to test the McGurr and DeVaney contention with an improved methodology using re-estimated generic models to predict bankruptcy for a holdout sample of firms belonging to the Equipment and Machinery Manufacturing (EMM) industry. The empirical findings showed that the models performed marginally better for a holdout sample of firms from the EMM industry than for the mixed industry holdout sample, up to three years prior to bankruptcy, and thereby contradicted the commonly held view.

METHODOLOGY AND DATA

Models and Variables

The present study can be viewed as an extension of the McGurr and DeVaney study (1998) because both studies focus on the retail industry. The primary objective here is to examine the effectiveness of two generic bankruptcy prediction models estimated with the mixed industry sample data in discriminating between bankrupt and nonbankrupt firms from an individual industry. Two selected models are by Ohlson (1980) and by Shumway (2001) utilizing the logit methodology. While Ohlson's model utilizes eight financial statement based ratios, Shumway's model uses a combination of two financial ratios and two market driven measures. The variables of these two models are described in Table 2. The size variable, which was used by both models and found to be a significant predictor in both original studies, is not used in our estimations because the size effect is controlled through the pair matching procedure adopted in this study.

Sample and Data

For a failed firm to be considered for inclusion in this study, it has to file bankruptcy during the period of 1990-1999, the firm was traded on OTC market and the total assets of the firm are less than $130 million one year before bankruptcy. The search for the bankrupt OTC firms and their petition dates is conducted with the help of Moody's OTC Industrial Manual, Moody's OTC Unlisted Manual and National Stock Summary. Financial firms (SIC code 6000-6999) are excluded from our sample due to differences in accounting reporting.

The financial data needed to compute the variables for the two chosen models comes from the Compustat Research File, Moody's OTC Industrial Manual and Moody's OTC Unlisted Manual. The market data of Shumway's model is collected from the CRSP, Compustat and OTC Daily Stock Price Record by Standard & Poor. The Industrial Index of OTC Market Indicator collected from OTC Daily Stock Prices Record by Standard & Poor is used as the proxy for the market index until 1993 and the Industrial Index of Nasdaq Market Indicator collected from Nasdaq Daily Stock Prices Record by Standard & Poor is used as the proxy for the post-1993 period.

In an attempt to predict a firm's bankruptcy up to three years prior to bankruptcy, one year pre-bankruptcy financial data is defined as the data within a firm's most recent fiscal year but with no less than six months prior to the date of its bankruptcy filing. Thus, for a firm with a December 31 fiscal year ending, and filing for bankruptcy on March 20, 1999, the financial data of one year before bankruptcy would be the data for the year ending December 31, 1997. If the bankruptcy filing had taken place on August 6, 1999, the financial data of the year ending December 31, 1998 would be adopted as the one year before bankruptcy data. Similarly, the market data would also be lagged at least six months before bankruptcy filing. Even though the 6-month lag could have an undesirable effect on the predictive power of the models, such a convention we believe, substantially increases its practicality and therefore its appeal to practitioners.

Matching Criteria

A nonbankrupt firm is matched with a bankrupt firm by industry, asset size and fiscal year. The industry matching is accomplished by the same first two digits of the SIC codes of the firms. Our restriction of the OTC firm with the asset size less than $130 million itself lends strong support for size matching. Utmost efforts are made to match each nonbankrupt firm as closely as possible to a bankrupt one as per book value of total assets one year before bankruptcy. To assure that the financial statements are reported by the matching firms in the same period, the fiscal year ends of the matching nonbankrupt firms have to be within three months of the same for the bankrupt firms.

Resulting Sample

Our final overall sample consists of 354 OTC firms, i.e., 177 matched pairs of bankrupt and their counterpart nonbankrupt firms. The asset distributions of the two groups are summarized in Panel A of Table 1. The average assets of the bankrupt firms are $36.41 million as compared to $35.93 million of their counterparts. Of the 354 matched firms, about 75 percent of the firms have total assts of less than $50 million, and 92 percent of the firms have assets of less than $100 million, one year before bankruptcy. In comparison, the sample in the McGurr and DeVaney study (1998) consisted of 56 bankrupt retail firms from 1989 to 1993. The asset size of sample companies in their study ranged widely from $3.2 million to $8.3 billion. In some of the retail groups, the mean total assets of the failed and nonfailed firms deviated by more than 75 percent (see Table 2 of McGurr and DeVaney, 1998). Furthermore, due to the small sample size, they were not able to re-estimate the original five models developed with the data utilized from the 1940s to the 1980s. As a result, it is not clear if the loss of classification accuracy of these models in retail industry was a result of the industry bias or time bias of test period or both.

As noted, this paper focuses on prediction of bankruptcy in an individual industry, the retail industry (SIC code 5200-5999). The sub-sample is comprised of 40 retail firms. The asset size distributions are shown in Panel B of Table 1. The average assets of the bankrupt firms in the retail industry are $58.22 million as compared to $52.62 million of the nonbankrupt firms. The t-statistic shows that paired firms are matched closely in size, for the overall sample as well as the retail industry sub-sample.

The He and Kamath study (2005) was able to utilize the re-estimated generic models to predict bankruptcy for a holdout sample of the EMM industry on an ex ante basis, since they had a larger EMM industry sub-sample. However, the sub-sample of 40 retail firms in this study is not large enough to be split in order to accommodate a holdout sample for prediction purpose. Accordingly, the entire sample of 354 firms is used to re-estimate the models. These models are then used to reclassify the 354 mixed industry firms and the 40 retail industry firms, respectively, on an ex post basis. Given the existence of numerous unique aspects of the retail industry as compared to the other industries, our a priori expectation is that these two generic models by Ohslon (1980) and Shumway (2001) will not be able to distinguish bankrupt firms from nonbankrupt firms of the retail industry, as effectively as for the firms from the mixed industries.

EMPIRICAL FINDINGS

Re-estimation of the Models

Since the data setting in this study is different from the ones in the original studies of Ohlson (1980) and Shumway (2001), we first re-estimate these models by using the sample of 354 mixed industry firms in 1990s. The re-estimated Ohlson and Shumway models with the data of one year prior to bankruptcy are presented in Table 2.

The findings of Table 2 indicate that both re-estimated models with 354 mixed industry firms are statistically significant at the 0.01 level one year prior to bankruptcy, and thus, display a strong ability to discriminate bankrupt firms from nonbankrupt firms. Further analysis of the results for Ohlson's model shows that the four variables are statistically insignificant, which are denoted in the table by underlining the p-values. The results of Shumway's model appear to be more favorable. The signs of the coefficients of each of the four variables display the expected relationships with the probability of bankruptcy, and the chi-square statistics indicate that all four variables in this model contribute in a statistically significant fashion toward bankruptcy prediction.

Validation of the Models

Given that there are only 40 firms from the retail industry in our sample, we do not have the luxury of utilizing a holdout sample for the prediction test. Accordingly, the re-estimated models are validated by classification test for the retail industry. Both Ohlson's and Shumway's models, which are re-estimated with one year prior to bankruptcy data of 354 mixed industry firms of the 1990-1999 period in Table 2, are now used to reclassify the 354 mixed industry firms and the 40 retail industry firms for one, two and three years before bankruptcy, respectively. The classification results of each model are reported in Tables 3 and 4.

Panel A of Table 3 reports that Ohlson's re-estimated model is able to classify 151 bankrupt firms and 160 nonbankrupt firms of the 177 pairs mixed industry firms correctly, one year prior to bankruptcy. Thus, Ohlson's model misclassifies 26 bankrupt firms as nonbankrupt (known as Type I error) and 17 nonbankrupt firms as bankrupt (known as Type II error). These figures translate into an overall classification accuracy of 88 percent with 12 percent of Type I error and 7 percent of Type II error, one year prior to bankruptcy. As we attempt to classify bankruptcy two and three years before bankruptcy, the results show a pattern of declining classification accuracy. When Ohlson's re-estimated model is used for classifying 40 retail firms, the comparable figures reported in Panel B of Table 3 are markedly lower at 80, 65 and 70 percent in each of the three years before bankruptcy.

The overall classification results of Shumway's model displayed in Table 4 exhibit a similar pattern between the mixed industry firms and the retail firms. The overall classification accuracy levels for the 354 mixed industry firms are 92, 78 and 72 percent. While the comparable figure for the 40 retail firms indicates modest stability with classification accuracy of 88 percent for one year before bankruptcy, the figures are significantly lower at 60 percent each for two and three years prior to bankruptcy. The disappointing results are largely attributed to an unusually high level of Type I errors as we move further away from the time of bankruptcy filing. Shumway's model reports 20, 75 and 60 percent Type I errors for the retail industry sample for one, two, and three years prior to bankruptcy, while the corresponding Type I error with Ohlson's model are 30, 60, 50 percent.

Since the classification accuracy rates would be upwardly biased under the classification test, Lachenbruch's U method (1967) is adopted to evaluate the robustness of the re-estimated models. In a nutshell, this approach is an iterative process aimed at obtaining a classification accuracy rate which is not adversely affected by the ex post classification bias. As per this method, in each iteration, one pair of matched bankrupt and nonbankrupt firms is held out from the overall 177 pairs of sample firms and the remaining 176 pairs are utilized to derive the bankruptcy model. The model developed is then used to classify the pair of the holdout firms. This scheme is repeated until every pair of observations goes through the process of being held out and classified. The classification results and accuracy rates for each of three years prior to bankruptcy under Lachenbruch's U method for the 354 mixed industry firms and the 40 retail industry firms are reported in the parentheses in Table 3 for Ohlson's model and Table 4 for Shumway's model, respectively. The results obtained are practically identical to those contained in the original classification test. Thus, the re-estimated Ohlson and Shumway models used in the classification test for the retail industry are rather robust and the classification accuracy rates are not found to be upwardly biased.

SUMMARY

This paper is aimed at evaluating the classification effectiveness of two successful generic bankruptcy prediction models in discriminating between bankrupt and nonbankrupt firms belonging to an individual industry. The retail industry is the focus of this inquiry similar to that of McGurr an DeVaney (1998). To fulfill our goal, we utilize financial statement ratio based model by Ohlson (1980) and financial and market information based model by Shumway (2001). The sample in this empirical study is made up of 354 mixed industry firms, including 40 retail firms, traded on OTC market over the recent decade of 1990s. The average assets of 354 firms are less than $37 million, one year prior to bankruptcy. Each of the 177 bankrupt firms is matched with a nonbankrupt firm from the same industry of comparable asset size as well as the timing of its financial reports.

The Ohlson and Shumway models are re-estimated with data of the entire sample of 354 mixed industry firms from the 1990-1999 period. These models are then used to classify the probability of bankruptcy of the 354 mixed industry firms and the 40 retail industry firms, respectively. Our study improves the classification methodology by utilizing Lachenbruch's U method to overcome the potential introduction of an upward bias in the classification process.

Begley et al. (1996) concluded that the re-estimated models by Altman (1968) and Ohlson (1980) with data in a recent period could not classify the bankrupt firms as well as the respective models had in the original studies. Our results are definitely not in agreement with Begley et al. (1996). Instead, we find that with the recent data of small OTC firms, the re-estimated models of both Ohlson (1980) and Shumway (2001) display classification accuracies which are very much comparable to those reported in the original studies.

The classification accuracy levels of both models for the retail industry, however, are significantly lower than those for the mixed industries, particularly, as the lead-time from bankruptcy increases. The finding that the usefulness of generic bankruptcy prediction models is reduced when applied to an individual industry matches with the priori expectation. McGurr and DeVaney (1998) had suggested that the possible causes of such reductions are "industry, population, and time biases". While the population bias can never be fully eliminated, the time bias was well controlled due to the short time span of the data used in the study. Thus, our methodology was predominantly geared toward evaluating the industry bias. Accordingly, we find that the mixed industry based bankruptcy prediction models lose their effectiveness substantially when applied to an individual industry, such as, the retail industry.

Overall, the findings for the retail industry in our study concur with the expectation that the generic bankruptcy prediction models would lose predictive accuracy when applied to an individual industry, but are at odds with the results presented by He and Kamath (2005), where they reported impressive classification and prediction accuracies for the equipment and machinery manufacturing (EMM) industry with help of generic models. One possible explanation of our finding is that the re-estimated models were highly influenced by the large percentage of manufacturing firms in the sample. The breakdown of 354 sample firms shows that only 130 (37 percent) firms are from service industries, including 40 retail firms (11 percent). Given the diametrically opposite findings of our study to what reported by He and Kamath (2005), further research is called for in the area of applying generic bankruptcy prediction models to classify/predict the bankruptcy of firms from individual industries.

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Yihong He, Monmouth University

Ravindra Kamath, Cleveland State University

Table 1. Asset Distribution of OTC Sample Firms, 1990-1999

Panel A--Asset Distribution of the Overall Sample ($000)

 Number Minimum Maximum Mean Standard p-value
 Deviation

Bankrupt
 firms 177 1278 128290 36405 33284
Nonbankrupt
 firms 177 2463 127990 35930 30980
t-test of size difference 0.889

Panel B--Asset Distribution of the Retail Industry Sample ($000)

 Number Minimum Maximum Mean Standard p-value
 Deviation
Bankrupt
 firms 20 5273 126926 58223 39820
Nonbankrupt
 firms 20 4802 127295 52623 38491
t-test of size difference 0.654

Table 2. Re-estimation of the Models with the Data of 354 Mixed
Industries Firms, 1990-1999

 Estimated Standard Chi-square
 Coefficient Error Statistic p-value

Ohlson's Model at 1 Year prior to bankruptcy

Constant -3.757 0.796 22.271 .000
NITA -3.693 1.705 4.690 .030
TLTA 5.798 1.105 27.516 .000
WCTA -1.289 0.998 1.669 .196
CLCA -0.098 0.188 0.273 .602
FUTL 0.004 0.238 0.000 .988
CHIN -0.758 0.331 5.235 .022
OENEG -0.484 1.376 0.124 .725
INTWO 2.143 0.533 16.166 .000
Model 295.935 .000

Shumway's Model at 1 Year prior to bankruptcy

Constant -5.379 0.721 55.636 .000
NITA -6.117 1.666 13.487 .000
TLTA 5.307 0.927 32.740 .000
ERR -2.36 0.477 24.467 .000
SDR 8.371 2.258 13.739 .000
Model 321.065 .000

Where,

NITA = Net income/total assets,

TLTA = Total liabilities/total assets

CLCA = Current liabilities/current assets

FUTL = Fund provided by operations/ total liabilities

CHIN = (NIt - NIt-1)/([absolute value of NIt] + [absolute value
of NIt-1]), where NIt is net income for the most recent period.
The denominator acts as a level indicator. The variable is thus
intended to measure change in net income

OENEG = One if total liabilities exceeds total assets, zero
otherwise

INTWO = One if net income was negative for the last two years,
zero otherwise

ERR = Excess rate of return
(i.e., a firm's rate of return minus the market's rate of return)

SDR = Standard deviation of residual
(Residual = a firm's realized rate of return minus its expected
rate of return)

Note: Firm size, which shows the statistical significance as a
predictive variable in both original models, is not used in this
study because the size effect is controlled by a pair-matching
procedure.

Table 3. Classification Results with Re-estimated Ohlson's Model

Panel A. Classification of 354 mixed industry firms and 40 retail
industry firms

 Total
 Number Classified Status
 Actual of the
 Status Sample B NB

Mixed Industries

Year 1 B 177 151 (151) 26 (26)
 NB 177 17 (19) 160 (158)

Year 2 B 177 124 (124) 53 (53)
 NB 177 22 (24) 155 (153)

Year 3 B 177 113 (112) 64 (65)
 NB 177 29 (31) 148 (146)

Retail Industry

Year 1 B 20 14 (14) 6 (6)
 NB 20 2 (2) 18 (18)

Year 2 B 20 7 (7) 13 (13)
 NB 20 1 (1) 19 (19)

Year 3 B 20 10 (10) 10 (10)
 NB 20 2 (2) 18 (18)

Panel B. Classification Error Rates and Accuracy Levels of 354
mixed industry firms and 40 retail industry firms

 Year 1 Year 2 Year 3

Mixed Industries
Type I error 15% (15%) 30% (30%) 36% (37%)
Type II error 10% (11%) 12% (14%) 16% (18%)
Overall error 12% (13%) 21% (22%) 26% (27%)
Overall accuracy of classification 88% (87%) 79% (78%) 74% (73%)

Retail Industry
Type I error 30% (30%) 65% (65%) 50% (50%)
Type II error 10% (10%) 5% (5%) 10% (10%)
Overall error 20% (20%) 35% (35%) 30% (30%)
Overall accuracy of classification 80% (80%) 65% (65%) 70% (70%)

Note:

1) B--bankrupt firms; NB--nonbankrupt firms

2) Type I error = misclassification of bankrupt firms

3) Type II error = misclassification of nonbankrupt firms

4) Cutoff value = 0.5

5) Year 1 means 1 year before bankruptcy, and so on.

6) The classification results using Lachenbruch's U method are
reported in the parentheses.

Table 4. Classification Results with Re-estimated Shumway's Model

Panel A. Classification of 354 mixed industry firms and 40 retail
industry firms

 Total
 Number Classified Status
 Actual of the
 Status Sample B NB

Mixed Industries

Year 1 B 177 163 (161) 14 (16)
 NB 177 15 (15) 162 (162)

Year 2 B 177 120 (120) 57 (57)
 NB 177 20 (20) 157 (157)

Year 3 B 177 101 (101) 76 (76)
 NB 177 24 (24) 153 (153)

Retail Industry

Year 1 B 20 16 (16) 4 (4)
 NB 20 1 (1) 19 (19)

Year 2 B 20 5 (5) 15 (15)
 NB 20 1 (1) 19 (19)

Year 3 B 20 8 (8) 12 (12)
 NB 20 4 (4) 16 (16)

Panel B. Classification Error Rates and Accuracy Levels of 354
mixed-industry firms and 40 retail industry firms

 Year 1 Year 2 Year 3

Mixed Industries
Type I error 8% (9%) 32% (32%) 43% (43%)
Type II error 8% (8%) 11% (11%) 14% (14%)
Overall error 8% (9%) 22% (22%) 28% (28%)
Overall accuracy of classification 92% (91%) 78% (78%) 72% (72%)

Retail Industry
Type I error 20% (20%) 75% (75%) 60% (60%)
Type II error 5% (5%) 5% (5%) 20% (20%)
Overall error 12% (12%) 40% (40%) 40% (40%)
Overall accuracy of classification 88% (88%) 60% (60%) 60% (60%)

Note:

1) B-bankrupt firms; NB-nonbankrupt firms

2) Type I error = misclassification of bankrupt firms

3) Type II error= misclassification of nonbankrupt firms

4) Cutoff value = 0.5

5) Year 1 means 1 year before bankruptcy, and so on.

6) The classification results using Lachenbruch's U method are
reported in the parentheses.