Model Cercetare

Rev Quant Finan Acc (2007) 28:55–78

DOI 10.1007/s11156-006-0003-x

A re-evaluation of auditors’ opinions versus statisticalmodels in bankruptcy prediction

Lili Sun

Published online: 15 November 2006C© Springer Science + Business Media, LLC 2006

Abstract Existent empirical evidence on the relative performance of auditors’ goingconcern opinions versus statistical models in predicting bankruptcy is mixed. Thisstudy attempts to add new reliable evidence on this important issue by conductingthe comparison based upon an improved statistical model. The improved statisticalmodel incorporates some new developments advocated by recent bankruptcy predic-tion research (e.g., Shumway, 2001). First, the following non-traditional variables areadded: a composite measure of financial distress, industry failure rate, abnormal stockreturns, and market capitalization. Secondly, a hazard model is employed.

The prediction ability of the hazard model with incorporation of non-financial-ratio variables is superior to that of auditors’ going concern opinions in the holdoutsample. This suggests that a well-developed statistical model could serve as a decisionaid for auditors to better make going-concern judgments. Further analyses revealsome evidence that industry failure rate does not have a significant impact uponauditors’ going concern judgments as it should be; auditors could improve their goingconcern judgments by considering industry-level information in addition to firm-specific information. Finally, we find that auditors’ opinions do have incrementalcontribution beyond stock-market information and industry failure rate in predictingbankruptcy.

Keywords Bankruptcy prediction . Going concern opinions . Financial distress

JEL Classifications M41 . G33

L. Sun (�)Department of Accounting and Information Systems, Rutgers, the State University of New Jersey,Ackerson Hall, Room 317, 180 University Ave, Newark, NJ 07102-1897, USAe-mail: [email protected]

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1 Introduction

In today’s dynamic economic environment, the number and the magnitude ofbankruptcy filings are increasing significantly.1 Given the challenging nature ofbankruptcy prediction task, even auditors, who have a good knowledge of firms’ sit-uations, often fail to make an accurate judgment on firms’ going-concern conditions.It is valuable to explore the relative performance of statistical models and auditors’going-concern opinions in predicting bankruptcy. The result of the comparison sug-gests whether auditors should use statistical models as decision aids when makinggoing-concern judgments. Research has been done to compare the performance ofauditors’ going-concern opinions with statistical models in predicting bankruptcy.The comparison results are mixed. Some studies (e.g. Altman and McGough, 1974;Altman, 1982) show that statistical models outperform auditors’ opinions, while oth-ers (e.g. Hopwood et al., 1994) find that statistical models and auditors’ opinions areindifferent in their prediction ability.

Literature review shows that statistical models used for the comparison with au-ditors’ opinions do not keep pace with the development of bankruptcy predictionmodeling research. It is interesting to build a statistical model with incorporation ofsome improvements suggested by recent bankruptcy prediction work and reevaluatethe relative performance between such an improved statistical model and auditors’going concern opinion. This study serves this purpose. Specifically, this study in-corporates two aspects of improvement suggested by recent bankruptcy predictionwork. First, the following predictors are employed: a composite score of financialdistress, stock-market variables, and industry failure rate. Secondly, a hazard model(Shumway, 2001) is employed.

Our analysis shows that the hazard model with incorporation of both financial andnon-financial variables outperforms auditors’ going concern judgment in the holdoutsample. Further analysis shows that stock market variables are effective in explainingauditors’ going concern opinions, but industry failure rate is not. Our results havethe following contributions and practical implications. First, our study contributes tothe stream of research that compares the relative performance of auditors’ opinionsand statistical models in predicting bankruptcy. Using a recent period of sample, wefind that a hazard model that employs both financial and non-financial variables out-performs auditors’ opinion in predicting bankruptcy. Thus, our findings imply thata well-developed statistical model can serve as a useful decision-aid for auditors tomake judgment in clients’ going concern status. Secondly, the accuracy of auditors’going concern judgment could be improved by focusing on not only firm-level in-formation including traditional financial-accounting information and stock marketinformation, but also industry-level factors, such as industry failure rate. Finally, thisstudy contributes to the stream of research that examines the incremental contributionof auditors’ going concern opinions in predicting bankruptcy. Specifically, we find thatauditors’ opinions do have incremental contribution beyond stock-market informationand industry failure rate in predicting bankruptcy.

1 12 of the 20 largest bankruptcy filings in U.S. history took place in 2001 and 2002. In total, these12 companies, including Worldcom, Enron, UAL Corp, Kmart Corp, brought $381 billion of assets intobankruptcy (Venuti, 2004).

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A re-evaluation of auditors’ opinions versus statistical models in bankruptcy prediction 57

The remainder of this study is organized as follows. Section 2 provides literaturereview. In Section 3, we discuss research questions and specify the research hypothesis.Section 4 describes the research methodology. Section 5 discusses empirical results,while the last section concludes the paper.

2 Prior literature

Research has been done to explore the relative performance of auditors’ going con-cern opinions and statistical models in predicting bankruptcy. Empirical findings onthis topic are divergent. One stream of research (e.g., Altman and McGough, 1974;Altman, 1982; Levitan and Knoblett, 1985; Koh and Killough, 1990) suggests that sta-tistical models outperform auditors’ going-concern opinions in predicting bankruptcyand therefore can be useful aids in the formulation of auditors’ going concern opiniondecisions. On the contrary, the more recent work by Hopwood et al. (1994) suggeststhat auditors’ opinions and statistical models have equivalent performance after mak-ing the comparison considerably more reflective of the auditors’ real-world decisionenvironment.

Now we discuss, respectively, the role of auditors’ going-concern opinions andstatistical models in bankruptcy prediction. SAS 59 (AU341) requires the auditorto evaluate whether there is a substantial doubt about a client’s ability to continueas a going concern for at least one year beyond the balance sheet date. Therefore,“The nature of auditors’ qualified opinions gives rise to the belief that they can signalentity failure.” (Hopwood et al., 1989, p. 28) Research has been done to explorethe usefulness of auditors’ going concern opinions in predicting bankruptcy (e.g.Hopwood et al., 1989, Foster et al., 1998) and to explore why auditors sometimesfail to issue going concern opinions to subsequently bankrupt clients (e.g. McKeownet al., 1991).

The literature on developing statistical models for bankruptcy prediction is exten-sive and continues to grow. Starting from Winakor and Smith (1935), researchershave developed various statistical models using different techniques and predictors.Among earlier models, some well-known ones include Altman’s Z-score (Altman1968), ZETA model (Altman et al., 1977), Ohlson (1980) Logit model, Zmijewski(1984) Probit model, etc.

Later on, more advanced estimation methods are introduced to bankruptcy pre-diction. Artificial Neural Network (ANN) model (e.g., Altman et al., 1994, Tam andKiang, 1992) and Bayesian Network models (e.g., Sarkar and Sriram, 2001; Sunand Shenoy, 2005) are introduced to the field. Data envelopment analysis (DEA) isalso suggested (Cielen et al., 2004). Jones and Hensher (2004) argue that mixed logitmodel outperforms standard binary logit model in predicting financial distress. Hazardmodel are advocated (Shumway, 2001) and employed by later research (e.g. Beaverand McNichols, 2005).

Performance of statistical models can be improved not only through implementingnew prediction tools but also through identifying novel predictors. Earlier studies(e.g., Winakor and Smith, 1935; Altman, 1968) focus on traditional financial ratios.Later on, the usefulness of cash flows in predicting bankruptcy has been explored (e.g.,Gentry et al., 1985; Aziz and Lawson, 1989; Emery and Cogger, 1982). Bond ratings,which are based on both public information and private information conveyed to the

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rating agencies by firms, are employed in predicting bankruptcy (e.g. Barth et al.,1998; Billings, 1999). Shumway (2001) shows that market-based variables, such as,abnormal stock returns, and market capitalization, have incremental prediction powerbeyond traditional financial ratios. Bharath and Shumway (2004) and Hillegeist et al.(2004) suggest the use of Merton option-pricing model that incorporate firms’ assetvolatilities.

3 Research questions and research hypothesis

The purpose of this study is to re-examine the relative performance of auditors’opinions and statistical models in predicting bankruptcy, by developing an improvedstatistical model that incorporates some new features advocated by recent bankruptcyprediction studies. Specifically, the improvement is related to two aspects: adding newpredictors and employing a new statistical tool. Next we turn to detailed discussionon each aspect.

3.1 Bankruptcy predictors

Statistical models used by prior research for the comparison between auditors’ opin-ions and statistical models mainly employ traditional financial ratios as bankruptcypredictors. In this study, we introduce the following additional variables: a compositemeasure of financial distress, stock-market variables, and industry failure rate.

3.2 A composite measure of financial distress

The most typical reason for bankruptcy filing is financial distress. The more financiallydistressed a company is the more likely it will go bankruptcy. Different from individualfinancial ratio which only captures firms’ financial healthiness distress in one orcertain aspects, a composite measure evaluates firms’ financial condition from amultifaceted perspective and therefore is a more informative and reliable measure.Several such composite measures exist as discussed below. Hopwood et al. (1994)introduce a stress indicator which originates from an interview and questionnaireprocess conducted by Mutchler (1984), using sixteen partners, two from each of theBig Eight accounting firms. This stress criterion defines a company into the stressedcategory if the company exhibits at least one of the following financial distress signals:negative working capital, a loss from operations, a retained earnings deficit, and abottom line loss. Secondly, Altman (1968) Z-score is a five-ratio-based score, whichis often used by accounting and finance researchers to measure firms’ financial distress.Thirdly, a three-ratio-based score derived from Zmijewski’s (1984) probit model isalso often used (e.g., Carcello and Neal, 2000; Anandarajan et al., 2001). Finally,some researchers (e.g. Clark and Ofek, 1994) suggest the use of abnormal stockreturns as a composite measure of financial distress, conditioning on the belief thatstock prices in an efficient market are able to reflect firms’ overall healthiness. Notheory or empirical evidence currently exists to favor one measure over the others. Inthis study, we empirically test the effectiveness of the above measures and choose thebetter one(s).

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3.3 Stock-market variables and industry level factors

Shumway (2001) finds that market variables have significant contribution tobankruptcy prediction. Not only firm-level factors but also industry-level factors caninfluence a firm’s survival (Everett and Watson, 1998). Hensler et al. (1997) find anindustry effect on the survival time of initial public offerings, with IPOs in certainindustries (such as the computer and data, wholesale, restaurant, and airline industries)having a shorter survival time and firms in other industries (such as the optical or phar-maceutical industries) enjoying a longer survival time. Honjo (2000) finds that a higherentry rate and higher geographical concentration in an industry lead to a higher hazardrate for firms. In this study, we employ two market variables (abnormal stock returnsand market capitalization) and one industry-level variable (industry failure rate).

3.4 A hazard model

Recent work by Hopwood et al. (1994) that examines the relative performance of au-ditors’ opinions and statistical models employs a static binary logit model. Shumway(2001) elaborates the econometric advantages of a hazard model over a static binarylogit model. First, hazard models control for each firm’s period at risk, while staticmodels do not. Secondly, hazard models exploit each firm’s time-series data by includ-ing annual observations as time-varying covariates. Thirdly, hazard models producemore efficient out-of-sample forecasts by utilizing much more data. The hazard modelcan be thought of as a binary logit model that includes each firm year as a separateobservation. Shumway (2001) further empirically demonstrates that a simple hazardmodel outperforms static models in out-of-sample forecasts. Therefore, this studyemploys a hazard model.

3.5 Research hypothesis

To summarize, this study builds a hazard model with the incorporation of a compositestress measure, two market variables, and one industry-level factor in addition totraditional financial ratios. It is unknown which will perform better in predictingbankruptcy, the auditors’ opinions or the hazard model. Therefore the main hypothesisis formed in a null form:

Hypothesis (Null). The hazard model estimated by this study and the auditors’opinions do not differ in ability to predict bankruptcy.

4 Research method

4.1 Sample and data

The data employed in estimating and testing models span the period from 1991 to2002. This period is chosen to obtain a sizable sample while providing evidencefor a recent period of bankruptcy activity. Firms in this study’s sample are publicfirms traded on major stock exchanges, including NASDAQ, the New York, and

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American Stock exchanges. The following steps are used to identify bankrupt2 firms.First, bankrupt firms are identified through Compustat and Lexis-Nexis BankruptcyReport databases. Next, bankruptcy filing dates are determined using the Lexis-NexisBankruptcy Report library, Lexis-Nexis News, and firms’ Form 8-K reports. Firmswithout available bankruptcy filing dates are eliminated. For each bankrupt firm, themost recent annual report filed prior to its bankruptcy filing date is identified. The lagbetween the fiscal year-end of the most recently filed annual report and bankruptcyfiling date must be less than 2 years.3 Financial-accounting information for bankruptcysample is for the fiscal year-end corresponding to the most recently filed annual reportprior to bankruptcy. Firms in financial or utility industries are excluded. The finalbankruptcy sample consists of 587 firms, which are randomly assigned to the training(344 firms) or the test sample (243 firms). Since the model is trained as a hazard model,for bankrupt firms, firm-years prior to their bankruptcy years are also included into thetraining sample as nonbankruptcy firm-years. 344 training bankrupt firms contribute1,313 nonbankruptcy firm-years. 3,1834 active firms are randomly selected to formthe non-bankruptcy training sample. These active firms contribute 20,918 firm-yearswhich have complete data required by this study. 1,165 active firms are randomlyselected to form the non-bankruptcy test sample. To summarize, the final trainingsample consists of 344 bankruptcy firm-years and 22,231 nonbankruptcy firm-years(the sum of 1,313 nonbankruptcy firm-years of bankrupt firms prior to bankruptcyand 20,198 firm-years of nonbankrupt firms). The final test sample is composed of243 bankrupt firms and 1,165 unique5 active firms.

We obtain financial-accounting information from Compustat and stock informa-tion from CRSP. Auditors’ going concern opinions are obtained by manually read-ing auditors’ reports in annual reports filed in Form 10-K/10-KSB/10-K405/20-F.Table 1 describes the sample selection process.

4.2 Hazard model

A general form of the hazard model (Beaver and McNichols, 2005) used here is asfollows:

ln[h j (t)/(1 − h j (t))] = α(t) + B X j (t). (1)

In Eq. (1), h j (t) is the hazard, or the risk of bankruptcy, at time t for firm j ;h j (t)/(1 − h j (t)) is the hazard ratio, or the likelihood odds; α(t) is the baselinehazard, which is assumed to be a constant; B is a vector of coefficients; and X j (t) is

2 The bankrupt sample in this study consists of firms that file bankruptcy petitions under both Chapter 11and Chapter 7.3 Similar to Begley et al. (1996), we use this requirement to ensure the data used for prediction arereasonably current.4 This was an ex ante-determined stopping point and has no bearing on the randomness of the sample (seeHopwood et al., 1994).5 The study requires auditors’ going concern opinions for the holdout sample. The reason for us to useunique firms instead of all firm-years for these firms in the holdout sample is to reduce the labor-intensivework in manually gathering going-concern opinions. A sample year is randomly assigned to a non-bankruptfirm in the test sample.

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Table 1 Sample selection

Bankruptcy Sample No. of firm-years No. of firmsStep 1: Bankrupt firms identified from Lexis-Nexis Bankruptcy Report

Database974

Minus: bankrupt firms not included in Compustat 134Subtotal 840

Step 2: Bankrupt firms identified from Compustat 413Minus: bankrupt firms that do not havebankruptcy filing dates identified 124Minus: bankruptcy filing dates are not in the period of 1991–2002 19Subtotal 270

Step 3: Total number of bankrupt firms from both sources withbankruptcy filing dates between 1991–2002

1110

Minus: bankrupt firms that do not have such a 10-K filed prior tobankruptcy that the lag between the fiscal year end of the 10-K andthe bankruptcy filing date is within two years

220

Subtotal 890

Step 4: Minus: bankrupt firms that do not have complete information 278Minus: bankrupt firms in financial (SIC 6000–6999) or utility (SIC

4900–4999) industries25

The entire final bankruptcy sample 587

The final bankruptcy training sample [No. of firm-years] [1,657] 344The final bankruptcy test sample 243

Nonbankruptcy sampleNonbankrupt firms with complete information randomly selected in the

periods of 1991–20024,348

The final nonbankruptcy training sample [No. of firm-years] [20,918] 3,183The final nonbankruptcy test sample 1,165

a matrix of observations on bankruptcy predictors, whose values vary with time. Thehazard model is estimated as a multiperiod logit model, as suggested by Shumway(2001), using maximum likelihood method.

The dependent variable in the prediction models is each firm-year’s bankruptcystatus (0, 1) in a given sample year. In a hazard analysis, for a bankrupt firm, thedependent variable equals 1 for the year in which it files bankruptcy, and the dependentvariable equals 0 for all sample years prior to the bankruptcy-filing year. The non-bankrupt firms are coded 0 every year they are in the sample.

Shumway (2001) emphasize that the test statistics produced by a logit program areincorrect for the hazard model because they assume that the number of independentobservations used to estimate the model is the number of firm years in the data.Dividing these test statistics by the average number of firm-years per firm makes thelogit program’s statistics correct for the hazard model. χ2 test statistics reported inthis study have been adjusted accordingly.

To avoid oversampling bias (which occurs when the sample proportion of bankrupt-cies is higher than the population proportion), the hazard model’s intercept, α(t), isadjusted for the difference between the proportion of bankrupt firms in the studysample and that in the real world. Similar to Hopwood et al. (1994), the following

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adjusted model, suggested by Anderson (1972), is employed:

Pr = 1

1 + e−(γ+α+B X )(2)

where: γ = Ln[prop(N B) × prop′(B)] − Ln[prop′(N B) × prop(B)]where: prop(NB) = sample proportion of nonbankrupt firms (NB).

prop(B) = sample proportion of bankrupt firms (B).prop′(NB) = estimated population proportion of nonbankrupt firms.prop′(B) = estimated population proportion of bankrupt firms

In order for the models to predict whether or not a firm will file bankruptcy, a cutoffprobability is needed. Following Hopwood et al. (1994), we use the formula below tocalculate the cutoff:

Cutoff = 1

1 + misclassification cos t ratio= 1

1 + C(N B|B)C(B|N B)

(3)

where C(NB |B) represents the cost for misclassifying a bankrupt firm as nonbankrupt,andC(B|NB) represents the cost for misclassifying a nonbankrupt firm as bankrupt.

The prediction power of the estimated hazard model in the holdout sample ismeasured using Estimated Misclassification Cost (EMC), calculated as follows:

E MC = C(NB|B) × prop′(B) × P(NB|B) + C(B|NB) × prop′(NB)

×P(B|NB) (4)

where P(NB |B) represents the probability that a prediction model misclassifies abankrupt firm as nonbankrupt, calculated as the number of bankrupt firms misclas-sified as nonbankrupt divided by the total number of bankrupt firms in the holdoutsample; P(B |NB) represents the probability that a prediction model misclassifies anonbankrupt firm as bankrupt, calculated as the number of nonbankrupt firms mis-classified as bankrupt divided by the total number of nonbankrupt firms in the holdoutsample; C(NB |B) , C(B |NB) , prop′(NB), and prop′(B)are defined same as above.The advantage of EMC is that it takes into consideration the population proportion ofbankrupt firms and the relative costs of Type I error and Type II error. The analysis ofEMCs are conducted under various misclassification cost ratios ranging from 1:1 to100:1 (C(NB |B) : C(B |NB) ).

4.3 Variables

As of our knowledge, Hopwood et al. (1994) is a more recent study that examinesthe relative performance of auditors’ going concern opinions and statistical models.Therefore, for the traditional financial ratios, we take the seven financial ratios fromHopwood et al. (1994). As discussed earlier, four alternative composite measuresof financial distress are studied. They are: Criterion 1: the Auditor View Criterion;Criterion 2. The Altman Z-score, Criterion 3. Zmijewski’s Probability, and Criterion 4.Stock Return. Two stock-market variables are market capitalization and abnormal

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Table 2 Definitions of financial ratios, stock-market variables, and industry-level variables

Name Definition

NITA Net Income/Total AssetsCASALES Current Assets/SalesCACL Current Assets/Current LiabilitiesCATA Current Assets/Total AssetsCASHTA Cash/Total AssetsLTDTA Long Term Debt/Total AssetsLSALES Natural Logarithm of SalesIFR Industry failure rate, calculated as the average annual industry bankruptcy rate in the past

two years, where annual industry bankruptcy rate = (the number of bankruptcies in atwo-digit SIC industry in a year/the total number of Compustat firms in the sameindustry in the same year) × 100%

CAR Cumulative abnormal return, calculated as a firm’s annual stock return minus thevalue-weighted CRSP NYSE/AMEX/NASDAQ index annual return in the past year

LNMCP Natural log of each firm’s most recent available market capitalization in the last month ofthe past year relative to the total market value in the same day.

stock returns. The industry-level factor is industry failure rate, calculated as the averageannual industry bankruptcy rate in the past two years by two-digit SIC code. To avoidoutliers, all variables are winsorized at first percentile and ninety-ninth percentile.Table 2 provides detailed definitions for financial ratios, stock-market variables, andindustry-level factor; while Table 3 defines alternative composite measures of distress.

5 Empirical results

5.1 Descriptive statistics

Table 4 describes the sample distribution under each stress measure using the testsample. The percentage of bankrupt firms defined as stressed under Criterion 1(Auditor View), Criterion 2 (Altman Z-score), Criterion 3 (Zmijewski Probability),and Criterion 4 (Stock Return) is, respectively, 97%, 90%, 81%, and 91%. The per-centage of nonbankrupt firms defined as stressed under Criterion 1–4 is, respectively,59%, 41%, 25%, and 46%. Since there are more firms (both bankruptcy and non-bankruptcy) being defined as stressed under Criterion 1 (Auditor View), Criterion1 (Auditor View) represents a relatively lower level of stress criterion. Criterion 3(Zmijewski Probability) is a stricter level of stress criterion since fewer firms (bothbankruptcy and nonbankrutcy) are defined as stressed under this criterion. Criterion 2and 4 are in between.

Table 5 provides the mean values of the independent variables in the test sam-ple by the stress status6 (stressed vs. nonstressed) and bankruptcy status (bankruptcyvs. nonbankruptcy). T-tests are used to evaluate differences in mean values between

6 Stress status here is defined under Criterion 4 Stock Returns. If we partition the sample based upon theother 3 alternative composite stress measures, we observe similar patterns in mean values of variablesacross groups.

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Table 3 Definitions of alternative composite measures of distress

Criterion Definition

Criterion 1.Auditor view

A company is classified into the stressed category if it exhibits at least one of thefollowing financial distress signals:

(1) negative working capital in the most recent year,(2) a loss from operations in any of the last three years,(3) a retained earnings deficit in Y-3 (where Y-1 is the last financial statement date

preceding a bankruptcy prediction date),(4) a bottom line loss in any of the last three years.

Criterion 2.Altman Z-score

A company is classified into the stressed category if Altman Z-score derived from themost recent financial statement is smaller than 3. Z-score is defined by Altman(1968) as:

Altman Z-score = 0.012∗(Working Captial/Total Assets) + 0.014∗(RetainedEarnings/Total Assets) + 0.033(Earnings Before Interest and Tax/Total Assets)+ 0.006∗ (Market Value Equity/Book Value of Total Debt) + 0.999 ∗(Sales/TotalAssets)

Criterion 3.Zmijewskiprobability

A company is classified into the stressed category if Zmijewski Probability derivedfrom the most recent financial statement prior to a prediction date is larger than 28%.

Zmijewski’s probability = ∫ y−∞

1√2π

e− z22 d Z , where y is calculated based upon the

following formula from Zmijewski (1984)

y = –4.336–4.513∗(Net Income/Total Assets) + 5.679∗(Total Liabilities/TotalAssets) + 0.004∗(Current Assets/Current Liabilities)

Criterion 4.Stock return

A company is classified into the stressed category if its annual accumulated abnormalstock return in last year is smaller than –15%. A firm’s annual abnormal returns iscalculated by accumulating daily abnormal returns using the following formula:

Annual abnormal return = �ni=1(1 + daily abnormal returni ) − 1

where: n = number of trading days.Daily abnormal return = a firm’s daily return – the CRSP daily value-weighted

NYSE/AMEX/NASDAQ market return index

Table 4 Sample distribution by stress criteria (test sample)

No. of firmsBankruptcy Nonbankruptcy

Stress criterion Stress Nonstress Stress Nonstress

1. Auditor view 236 7 693 4722. Altman Z-score 218 25 483 6823. Zmijewski

Probability197 46 291 874

4. Stock return 222 21 538 627

groups. Some interesting results related to the natural log of sales variable (LSALES)should be noted here. In the nonstressed category, the natural log of sales variable(LSALES) for the bankruptcy group is insignificantly lower than that for the non-bankruptcy group. However, surprisingly, in the stressed group, the bankruptcy grouphas a significantly higher mean value of the natural log of sales variable (LSALES)

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Table 5 Mean variable values (test sample only)

Nonstresseda StressedT-test of T-test of

Nonbankrupt Bankrupt means Nonbankrupt Bankrupt meansVariable (n = 627) (n = 21) difference (n = 538) (n = 222) difference

NITA 0.007 −0.213 5.319∗∗∗ −0.121 −0.385 8.201

∗∗∗

CASALES 0.896 0.541 0.707 1.111 0.881 1.184CACL 2.903 1.498 2.356∗ 3.003 1.403 7.546

∗∗∗

CATA 0.530 0.502 0.542 0.543 0.466 3.933∗∗∗

CASHTA 0.166 0.084 1.897 0.190 0.102 5.281∗∗∗

LTDTA 0.165 0.208 −1.055 0.153 0.260 −6.295∗∗∗

LSALES 5.157 4.979 0.375 4.277 4.769 −3.000∗∗∗

IFR 1.010 1.980 −3.848∗∗∗

0.800 1.400 −7.127∗∗∗

CAR 0.442 0.244 1.307 −0.440 −0.682 14.767∗∗∗

LNMCP −10.467 −12.389 4.268∗∗∗ −11.854 −13.167 8.930

∗∗∗

aThe stress criterion used here is Criterion 4. Stock Return.∗Significant at p < 0.05.∗∗

Significant at p < 0.01.∗∗∗

Significant at p < 0.001.

than the nonbankruptcy group. A possible explanation for the higher sales in thestressed bankruptcy group is that managers sometimes might attempt to boost sales inorder to hit specific sales targets or meet analyst expectations, even at the expense ofprofitability.7 Another possible explanation is that it may be more difficult for largefirms to recover from stress since the recovering requires more resources. Or the largesize of a stressed firm may also indicate that managers in such a firm unwisely expandthe firm’s size, which leads to non-value-generating assets or non-profit-generatingsales. This, in turn, increases its probability of bankruptcy. Further research is desiredto explore why compared to the stressed nonbankruptcy group, the stressed bankruptcygroup has a higher mean value in the natural log of sales.

5.2 The effectiveness of four alternative composite stress measures

To compare the effectiveness of four composite stress measures, we evaluate fitting-levels of models with different measures. The models are estimated using the trainingsample. The model that consists of only seven financial ratios used by Hopwood et al.(1994) is called Model 0 for the following discussion. We add STRESS as an individualvariable to Model 0 to form Models 1.1, 2.1, 3.1, and 4.1, respectively under Criterion1 (Auditor View), Criterion 2 (Altman Z-score), Criterion 3 (Zmijewski Probability),

7 “At one international heavy-equipment manufacturer, managers were so set on hitting their quarterlyrevenue target that they shipped unfinished products from their plant in England all the way to a warehousein the Netherlands, near the customer, for final assembly. By shipping the incomplete products, they wereable to realize the sales before the end of the quarter and thus fulfill their budget goal and make theirbonuses. But the high cost of assembling the goods at a distant location-it required not only the rental ofthe warehouse but also additional labor-ended up reducing the company’s overall profit” (Jensen, 2001,p. 96).

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and Criterion 4 (Stock Return). The variable, STRESS, is set to ‘one’ if a firm isdefined as stressed under a stress criterion, otherwise ‘zero’.

The relative fit between Model 0 and Models 1.1–1.4 are tested using a logit-based version of the Vuong (1989) test for nested models. The relative fit amongnon-nested models 1.1–1.4, are evaluated using Akaike Information Criterion (AIC,Akaike, 1974). Panel A of Table 6 reports the estimations of models. Panel B ofTable 6 presents the comparison of model fit. χ2 test statistics reported in Table 6 areafter-adjustment8 suggested by Shumway (2001).

Panel A shows that the overall fits for all models are significant at a p < 0.001 levelbased upon one-tailed likelihood ratio test. Results from Panel B of Table 6 suggestthat, compared to Model 0, Models 1.1, 2.1, 3.1, and 4.1 have incremental χ2(twice thelikelihood ratio, 2LR) statistics significant at a p < 0.001 level (1 degree of freedom),based upon one-tailed tests. This indicates that a composite stress measure doeshave incremental contribution in predicting bankruptcy beyond individual financialratios. Model fits for non-nested models 1.1–1.4 are compared based upon AkaikeInformation Criterion (AIC, Akaike, 1974 ). AICs are not based upon significancetesting. The established ‘rule of thumb’ is that Model A is considered as definitelybetter than Model B if Model A’s AIC is lower than Model B’s by more than 10(Burnham and Anderson, 1998). According to the results in Panel B of Table 6,among the four models, Model 4.1 and Model 3.1 are the best and their effectivenessis equivalent. Next is Model 1.1, and the worst is Model 2.1. This implies that thereare differences in the effectiveness of four alternative composite stress measures, withthe Zmijewski (1984) Probability and Abnormal Stock Returns as the best, Auditorview (Hopwood et al., 1994) next,9 and Altman Z-score (1964) the worst.

5.3 Analysis of the usefulness of non-financial-accounting factors

We examine the effects of industry failure rate (IFR) and market variables (abnormalstock return (CAR) and market capitalization (LNMCP)) by comparing the fittinglevels of Model 0 with models having these non-financial-accounting variables. Itshould be clarified that effectiveness of these variables, especially market variables, hasbeen documented in previous literature (e.g. Shumway, 2001). Analyses done here aremore conforming rather than discovering. Nevertheless, as of our knowledge, industryfailure rate is a relatively novel predictor variable. Again, models are estimated usingthe training sample. The definitions of IFR, CAR and LNMCP have been providedin Table 2. Table 7 provides detailed information of the average annual industryfailure rate by two-digit SIC during the study period of 1991–2002. The averageannual industry failure rate is 1.35%. Note that some high industry failure rates aredriven by the small number of firms existing in the industry. For instance, the average

8 Adjusted χ2 equals the original χ2 reported by the Logit program divided by 6.4, which is the averagenumber of firms-years per firm in the training sample. 6.4 firm-years per firm = 22,575 firm-years/3,527firms.9 One potential reason to explain the deteriorating performance of the Auditor View Criterion is thatworking capital behavior changed around 1990 to the extent that negative working capital is not a goodstress signal. During that period, a number of firms had credit lines available which allowed them to runworking capital essentially at zero. Sometimes working capital slipped slightly negative for very healthyfirms.

Springer


Tabl

e6

The

effe

cts

ofst

ress

crite

ria

onba

nkru

ptcy

pred

ictio

nm

odel

s

Mod

el0

1.A

udito

rvi

ewM

odel

1.1

2.A

ltman

Z-s

core

Mod

el2.

13.

Zm

ijew

skip

roba

bilit

yM

odel

3.1

4.St

ock

retu

rnM

odel

4.1

Co-

Wal

dC

hi-

Co-

Wal

dC

hi-

Co-

Wal

dC

hi-

Co-

Wal

dC

hi-

Co-

Wal

dC

hi-

Var

iabl

eef

ficie

ntsq

uare

effic

ient

squa

reef

ficie

ntsq

uare

effic

ient

squa

reef

ficie

ntsq

uare

Pane

lA:M

odel

ses

timat

ion

Inte

rcep

t−4

.894

69.7

16∗∗

∗−7

.023

61.9

21∗∗

∗−6

.253

70.3

42∗∗

∗−5

.820

82.3

22∗∗

∗−6

.088

81.2

83∗∗

∗

NIT

A−1

.640

28.5

08∗∗

∗−1

.573

27.4

32∗∗

∗−1

.474

23.3

51∗∗

∗−1

.219

15.0

63∗∗

∗−1

.470

22.1

68∗∗

∗

CA

SAL

ES

0.05

91.

408

0.06

61.

757

0.06

11.

416

0.04

40.

753

0.06

81.

821

CA

CL

−0.2

312.

120

−0.1

461.

035

−0.1

270.

713

−0.0

330.

065

−0.2

262.

132

CA

TA0.

437

0.37

50.

456

0.42

80.

700

0.96

2−0

.017

0.00

10.

365

0.26

1C

ASH

TA−2

.289

3.09

8−2

.618

4.02

6∗−2

.275

3.12

8−2

.424

3.52

7−2

.082

2.55

5LT

DTA

1.57

86.

837∗∗

1.22

94.

151∗

1.02

92.

656

0.41

70.

407

1.45

95.

790∗

LSA

LE

S0.

106

2.26

20.

172

5.82

3∗0.

129

3.37

20.

113

2.68

30.

141

3.85

4∗

STR

ESS

2.08

89.

802∗

∗1.

462

9.51

9∗∗

1.82

518

.470

∗∗∗

1.57

916

.241

∗∗∗

Mod

elFi

tL

ikel

ihoo

dra

tiote

st(C

hi-s

quar

e)59

.829

∗∗∗

(7df

)76

.453

∗∗∗

(8df

)71

.832

∗∗∗

(8df

)81

.329

∗∗∗

(8df

)81

.138

∗∗∗

(8df

)A

kaik

eIn

form

atio

nC

rite

rion

(AIC

)31

94.3

8630

89.9

9531

19.5

7130

58.7

8630

60.0

12

Not

e.D

epen

dent

vari

able

=1

ifa

firm

isba

nkru

ptin

agi

ven

year

,0ot

herw

ise.

∗ Sig

nific

anta

tp<

0.05

.∗∗

Sign

ifica

ntat

p<

0.01

∗∗∗ Si

gnifi

cant

atp

<0.

001.

(Con

tinu

edon

next

page

)

Springer

68 L. Sun

Table 6 (Continued)

Model 0 Model 1.1 Model 2.1 Model 3.1 Model 4.1

Panel B: Comparison of model fit#

Model 0Model 1.1 16.624

∗∗∗

(1 df)− 29.576 31.209 29.983

Model 2.1 12.003∗∗∗

(1 df)60.785 59.559

Model 3.1 21.500∗∗∗

(1 df)−1.226

Model 4.1 21.309∗∗∗

(1 df)

∗Significant at p < 0.05.∗∗

Significant at p < 0.01∗∗∗

Significant at p < 0.001.#The lower diagonal refers to 2LR statistics for the comparisons of nested models, while the upper diagonalrefers to Akaike Information Criterion (AIC) statistics for the comparisons of non-nested models

AICs are not based upon significance testing. Instead, there are established ‘rules of thumb’. The modelwith a lower AIC is better. The established rules of thumb are that two models with AICs apart more than10 are definitely different (Burnham and Anderson, 1998).

2LR statistics conform to the Chi-square distribution, with the degrees of freedom (p – q), given informationmatrix equivalence (Corollary 7.3, Vuong, 1989).

Both AIC statistics and 2LR statistics are calculated as: statistics for models in the first column minusstatistics for models in the first row. For instance, the 2LR statistics for the comparison of Model 1.1 andModel 0 is calculated as: 76.453 (Model 1.1) – 59.829 (Model 0) = 16.624.

annual industry failure rate for ‘Legal services’ is 7.14%; on average, annually thereis only a total of 3 firms in the industry. Industries with relatively high industry failurerates and a sizable number of firms in total ( > 40) include ‘Home furniture andequipment store’ (annual average industry failure rate = 3.76%), ‘Transportation byair’ (3.38%), ‘General merchandise stores’(3.28%), ‘Textile mill products’ (3.26%),‘Apparel and other finished products’(2.91%), ‘Apparel and accessory stores’ (2.57%),‘Miscellaneous retail’ (2.32%), and ‘Motion pictures’ (2.09%).

We test both the individual effect of industry factor and market factor and theircombined incremental contribution together. Table 8 shows that, based upon Vuong’stest for nested models, Model with IFR leads to an incremental χ2of 13.86910 (onedegree of freedom) beyond Model 0, significant at p < 0.001; Model with two marketvariables (CAR and LNMCP) have an incremental χ2of 42.790 (two degrees of free-dom) beyond Model 0, significant at p < 0.001. Model with IFR, CAR and LNMCPtogether have an incremental χ2of 51.437 (three degrees of freedom), significant atp < 0.001.

Next, we add the composite stress measure defined by Zmijewski Probability(1984), two market-variables, and the industry failure rate into the Model 0 to build anew hazard model. Analysis results reported earlier suggest that Zmijewski Probabil-

10 Results reported in the paper are based upon IFR defined by two-digit SIC. We also conduct the analysisusing IFR based upon the industry definition from Barth et al. (1998), which defines industries roughly byone-digit SIC. Similar results are found.

Springer


Table 7 Average annual percentage of bankruptcies by two-digit SIC during the entire study period(y91–02) a

Total number of firms Average annualin an industry percentage of

Two-digit SIC Description of industry annually on average bankruptcies

81 Legal services 3 7.1452 Building materials & garden supplies 19 4.8812 Coal mining 8 4.3941 Transit and passenger transportation 5 3.8157 Home furniture and equipment store 43 3.7645 Transportation by air 46 3.3853 General merchandise stores 50 3.2822 Textile mill products 49 3.2623 Apparel and other finished products 70 2.9156 Apparel and accessory stores 55 2.57

7 Agricultural services 4 2.3859 Miscellaneous retail 134 2.3276 Misc repair services 7 2.2178 Motion pictures 70 2.0955 Automotive dealers & services 23 1.9654 Food stores 45 1.9361 Nondepository credit institutions 94 1.9275 Auto repair, services, parking 15 1.7458 Eating and drinking places 116 1.7480 Health services 141 1.6915 General building contractors 53 1.6117 Special trade contractors 27 1.5939 Misc manufacturing industries 85 1.5742 Motor freight transportation,

warehouse47 1.55

48 Communications 255 1.4825 Furniture and fixtures 41 1.3982 Educational services 22 1.3216 Heavy construction-not building

construction25 1.29

79 Amusement and recreation services 80 1.2833 Primary metal industries 105 1.2750 Durable goods-wholesale 200 1.1637 Transportation equipment 140 1.1399 Nonclassifiable establishment 94 1.1330 Rubber & misc. plastic products 91 1.1214 Nonmetallic minerals, except fuels 20 1.1151 Nondurable goods-wholesale 112 1.0535 Industrial machinery equipment 472 1.0264 Insurance agents,brokers and service 40 0.9432 Stone,clay,glass,concrete products 50 0.9320 Food and kindred products 158 0.8527 Printing,and publishing 99 0.7934 Fabricated metal products 111 0.78

(Continued in next page)

Springer

70 L. Sun

Table 7 (Continued)

Total number of firms Average annualin an industry percentage of

Two-digit SIC Description of industry annually on average bankruptcies

47 Transportation Services 21 0.7449 Electric, gas & sanitary services 278 0.74

1 Agricultural production-crops 20 0.7473 Business services 809 0.7287 Engineering & management services 140 0.7083 Social services 16 0.7029 Petroleum & coal products 41 0.6836 Electronic & other electric equipment 517 0.6813 Oil and gas extraction 272 0.6870 Hotels, other lodging places 38 0.6672 Personal services 19 0.6665 Real estate 90 0.6631 Leather and leather products 21 0.6524 Lumber and wood products, except

furniture38 0.54

62 Security and commodity brokers 88 0.5310 Metal mining 115 0.4844 Water transportation 26 0.4538 Instruments & related products 447 0.4426 Paper and allied products 75 0.3928 Chemicals and allied products 499 0.3063 Insurance carriers 214 0.2767 Holding & other investment offices 725 0.1160 Depository institutions 827 0.08

2 Agricultural production-livestock 4 0.008 Forestry 3 0.009 Fishing, hunting, and trapping 2 0.00

21 Tobacco products 8 0.0040 Railroad transportation 19 0.0046 Pipe lines, except natural gas 4 0.0086 Membership organizations 1 0.0089 Services, NEC 1 0.00

Average 1.35

aFinancial or utility industries are also presented in this table for readers’ reference. However, they areexcluded from this study’s other analyses.

ity and Abnormal Stock Return are equivalently good in measuring stress. The reasonfor us to use the former is because the Abnormal Stock Return stress measure overlapswith the market variable CAR. The most-right column of Table 8 provides the estima-tion of the hazard model with added variables. This hazard model consists of sevenfinancial ratios from Hopwood et al. (1994), three non-financial-accounting variables(IFR, CAR, and LNMCP), and a stress dummy (STRESS) defined under ZmijewskiProbability Criterion. Compared to Model 0, the modified statistical model has anincremental χ2 of 62.620 with four degrees of freedom, significant at p < 0.001 level.

Springer


Tabl

e8

The

effe

ctof

non-

finan

cial

-acc

ount

ing

info

rmat

ion

Mod

el0

Mod

elw

ithIF

R

Mod

elw

ithM

arke

tV

aria

bles

(CA

Ran

dL

NM

CP)

Mod

elw

ithIF

R,C

AR

and

LN

MC

P

Mod

elw

ithZ

mije

wsk

ipr

obab

ility

stre

ssm

easu

re,I

FR,C

AR

&L

NM

CP

Var

iabl

eC

o-ef

ficie

ntW

ald

Chi

-sq

uare

Co-

effic

ient

Wal

dC

hi-

squa

reC

o-ef

ficie

ntW

ald

Chi

-sq

uare

Co-

effic

ient

Wal

dC

hi-

squa

reC

o-ef

ficie

ntW

ald

Chi

-sq

uare

Inte

rcep

t−4

.894

69.7

16∗∗

∗−5

.167

77.1

61∗∗

∗−1

1.20

559

.234

∗∗∗

−10.

736

51.3

40∗∗

∗−1

0.61

149

.639

∗∗∗

NIT

A−1

.640

28.5

08∗∗

∗−1

.606

27.3

02∗∗

∗−1

.330

16.9

74∗∗

∗−1

.311

16.6

00∗∗

∗−0

.993

8.90

0∗∗

CA

SAL

ES

0.05

91.

408

0.06

11.

494

0.11

65.

254∗

0.11

24.

813∗

0.09

23.

286

CA

CL

−0.2

312.

120

−0.2

262.

104

−0.1

250.

814

−0.1

370.

955

−0.0

180.

023

CA

TA0.

437

0.37

50.

337

0.22

1−0

.375

0.26

4−0

.337

0.21

2−0

.554

0.59

4C

ASH

TA−2

.289

3.09

8−2

.046

2.50

6−1

.589

1.42

3−1

.415

1.14

5−1

.488

1.28

3LT

DTA

1.57

86.

837∗∗

1.52

96.

318∗

1.37

75.

169∗

1.35

24.

924∗

0.54

60.

695

LSA

LE

S0.

106

2.26

20.

066

0.82

20.

359

18.2

89∗∗

∗0.

299

11.2

01∗∗

∗0.

268

8.97

1∗∗

IFR

0.40

416

.716

∗∗∗

0.33

29.

903∗∗

0.33

09.

665∗∗

CA

R−1

.200

7.66

9∗∗−1

.247

8.45

9∗∗−1

.090

6.86

3∗∗

LN

MC

P−0

.410

19.1

19∗∗

∗−0

.360

13.6

88∗∗

∗−0

.309

9.81

0∗∗

STR

ESS

(Zm

ijew

ski

Prob

abili

ty)

1.38

210

.012

∗∗

Mod

elFi

tL

ikel

ihoo

dra

tiote

st(C

hi-s

quar

e)59

.829

∗∗∗

(7df

)73

.698

∗∗∗

(8df

)10

2.61

9∗∗∗

(9df

)11

1.26

6∗∗∗

(10

df)

122.

449∗∗

∗

(11

df)

Vuo

ng’s

test

for

nest

edm

odel

s(I

ncre

men

tal

Chi

-squ

are

abov

eM

odel

0)

13.8

69∗∗

∗

(1df

)42

.790

∗∗∗

(2df

)51

.437

∗∗∗

(3df

)62

.620

∗∗∗

(4df

)

Dep

ende

ntva

riab

le=

1if

afir

mis

bank

rupt

ina

give

nye

ar,0

othe

rwis

e.∗ Si

gnifi

cant

atp-

valu

e<

0.05

.∗∗

Sign

ifica

ntat

p-va

lue

<0.

01.

∗∗∗ Si

gnifi

cant

atp-

valu

e<

0.00

1

Springer

72 L. Sun

Table 9 The comparison of prediction ability in test sample between the estimated hazard model andauditors’ going concern opinions

The estimated hazard model Auditors’ opinions

Difference inestimatedmisclassificationcosts (EMCs)

Costratio (Bto NB) % correct % correct

(the hazard model –auditors’ opinions)

NB B EMC NB B EMC

1 to 1 100.0 0.0 0.0105 96.6 44.0 0.0398 − 0.0294∗∗∗

10 to 1 98.4 21.4 0.0983 96.6 44.0 0.0925 0.005820 to 1 96.9 45.7 0.1442 96.6 44.0 0.1510 − 0.006830 to 1 94.4 60.9 0.1778 96.6 44.0 0.2095 − 0.0317∗

40 to 1 91.9 71.6 0.1986 96.6 44.0 0.2680 − 0.0694∗∗∗

50 to 1 90.5 74.5 0.2277 96.6 44.0 0.3265 − 0.0989∗∗∗

60 to 1 88.9 78.6 0.2438 96.6 44.0 0.3851 − 0.1412∗∗∗

70 to 1 87.3 80.7 0.2673 96.6 44.0 0.4436 − 0.1763∗∗∗

80 to 1 85.8 81.9 0.2924 96.6 44.0 0.5021 − 0.2096∗∗∗

90 to 1 84.0 83.1 0.3167 96.6 44.0 0.5606 − 0.2438∗∗∗

100 to 1 82.7 84.0 0.3385 96.6 44.0 0.6191 − 0.2806∗∗∗

∗Significant at p-value < 0.05.∗∗

Significant at p-value < 0.01.∗∗∗

Significant at p-value < 0.001

5.4 Hypothesis testing

Next we compare the performance of the newly-built hazard model with that ofauditors’ going concern opinions in the holdout sample. The holdout sample consistsof 1,165 unique nonbankrupt firms and 243 bankrupt firms. Table 9 presents thecomparison results.

As discussed earlier, statistical models are adjusted for oversampling bias. Theadjustment, γ , is –0.38156.11 Estimated Misclassification Cost (EMC)12 is used tomeasure models’ prediction abilities. There are no theoretical distributions existingfor describing EMC. Bootstrapping is used to estimate the empirical distributions ofEMC and to determine the critical values for hypotheses testing (Hopwood et al., 1994;

11 The sample proportions of bankrupt firms and nonbankrupt firms during the training period are re-spectively 0.015238 (344/22,575), and 0.984762 (22,231/22,575). The study-period population propor-tion of bankrupt firms and nonbankrupt firms are respectively 0.010455 and 0.989545. The populationproportions are the average of annual proportions over the study period. The population number ofbankruptcies is assumed to be equal to the number of bankruptcies in this study’s sample; the popu-lation number of nonbankruptcies is assumed to be equal to the number of active firms in Compustatdatabase. Therefore, as defined in Eq. (2), the adjustment for the modified statistical model is calculatedas: γ = ln(0.984762 × 0.010455) − ln(0.989545 × 0.015238) = − 0.38156.12 The estimated population proportion of nonbankrupt firms, prop′(NB), and the estimated populationproportion of bankrupt firms, prop′(B), are employed in the calculation of EMC. Since EMC is an ex postmeasure, prop′(NB) and prop′(B) are the actual population proportions during the study period. In thisstudy, prop′(NB) = 0.989545, prop′(B) = 0.010455. Again, these population proportions are the averageof annual proportions over the study period.

Springer


Foster et al., 1998). Specifically, to construct the statistical tests for the difference ofEMC between the modified statistical model and auditors’ going concern opinions,the following bootstrapping procedure is performed.

1. Select 22,231 nonbankrupt firm-years randomly with replacement from the 22,231nonbankrupt firm-years in the training sample. Use these with all (344) bankruptfirm-years in the training sample to form a training resample. (There is no need torandomly select bankrupt firms since they are deterministic.) Repeat this process500 times to form 500 training resamples.

2. Select 1,165 nonbankrupt firms randomly with replacement from the 1,165 non-bankrupt firms in the holdout sample. Use these with all (243) bankrupt firms inthe holdout sample to form a holdout resample. Repeat this process 500 times toform 500 holdout resamples.

3. One training resample is randomly paired with one holdout resample. For eachpair of training and holdout resamples, estimate a set of parameters for the hazardmodel, using the training resample. Generate predictions for each holdout firm,using the estimated hazard model with the set of parameters estimated from thetraining sample, and using the auditors’ opinion decision. To operationalize thenull hypothesis (which is, compared models have equivalent prediction power), thepredictions made by the hazard model and auditors’ opinions are then randomlyassigned to each compared model.

4. EMC is computed for each of the 500 holdout resamples using the randomlyassigned predictions for each model. Then for the two compared models, 500 pairsof EMCs are formed and 500 differences in EMC are calculated.

5. Count the percentage of differences in EMC that have a higher value than theobserved difference in EMC for the two compared models. This percentage givesthe alpha level to reject the null hypothesis that the two models compared have thesame EMC.

In Table 9, regardless of cost ratio levels, auditors’ going-concern opinions accu-rately predict 96.6% of nonbankruptcies and 44% of bankruptcies.13 As the cost ratiolevels vary from 1:1 (the cost of misclassifying a bankrupt firm as a nonbankrupt oneversus the cost of misclassifying a nonbankrupt firm as a bankrupt one) to 100:1,the estimated hazard model’s accuracy in predicting nonbankrupt firms vary from100% to 82.7%; its accuracy in predicting bankrupt firms vary from 0.0 to 84%. Thedifferences in EMCs between the hazard model and auditors’ opinions suggest thefollowing. The hazard model significantly outperforms the auditors’ going concernopinions in the holdout sample at all cost ratios levels except for two levels: 10:1,and 20:1. At the cost ratio levels of 10:1 and 20:1, there is no statistical differencebetween the hazard model and the auditors’ opinions. Therefore, the null hypothesisis rejected. The hazard model with incorporation of the Zmijewski Probability stressmeasure, and three non-financial-accounting variables (i.e., abnormal stock returns,market capitalization, and industry failure rate) in addition to traditional financialratios, has significantly better performance than auditors’ going concern opinions in

13 Unlike that of statistical models, the performance of auditors’ opinions is irrelevant to the value of thecutoff calculated based upon the cost ratio (see Eq. (3)).

Springer

74 L. Sun

predicting bankruptcy. This confirms Hopwood et al. (1994, p. 426) that “It could bethat there is a model that would prove to be clearly superior to auditors’ opinions.”

5.5 Additional analyses on auditors’ going concern opinions

Some studies (Hopwood et al., 1989; Foster et al., 1998) have been done to exam-ine the incremental contribution of auditors’ going concern opinions in predictingbankruptcy. It is found that auditors’ going concern opinions have incremental contri-bution in predicting bankruptcy beyond traditional financial ratios, but not beyond loandefault/accommodation and covenant violation variables. Here we examine whetherauditors’ opinions have incremental contribution beyond the composite stress mea-sure, the market-variables, and the industry failure rate. Table 10 presents the resultusing the test sample. Since we only gather going-concern opinions for the test sample,additional analyses reported in this section are based upon the test sample only. Mean-while, the method used is the binary logit model since the number of observationsequals the number of firms in the test sample. Table 10 presents the result. In the leftcolumn is the logit model without auditors’ going concern opinions variable (GC = 1

Table 10 Incremental prediction ability of auditors’ going concern opinions

Model without Going-concern opinion Model with Going-concern opinionVariable Co-efficient Wald Chi-square Co-efficient Wald Chi-square

Intercept −10.995 89.275∗∗∗ −11.330 88.439

∗∗∗

NITA −0.675 5.812∗ −0.361 1.545CASALES 0.166 8.320

∗∗0.138 5.164∗

CACL −0.204 3.951∗ −0.113 1.457CATA 0.126 0.061 0.403 0.567CASHTA −0.935 1.142 −0.862 0.925LTDTA 0.507 0.983 1.014 3.437LSALES 0.411 29.912

∗∗∗0.461 34.330

∗∗∗

STRESS(ZmijewskiProbability)

1.116 18.533∗∗∗

0.818 9.054∗∗

IFR 0.291 12.160∗∗∗

0.270 9.746∗∗

CAR −2.535 59.329∗∗∗ −2.407 51.061

∗∗∗

LNMCP −0.472 41.436∗∗∗ −0.445 34.940

∗∗∗

GC 1.829 36.948∗∗∗

Vuong’s test fornested models(IncrementalChi-square= Model with GC– Model withoutGC)

41.155∗∗∗(1d f )

Dependent variable = 1 if a firm is bankrupt in a given year, 0 otherwise.∗Significant at p-value < 0.05.

∗∗Significant at p-value < 0.01.

∗∗∗Significant at p-value < 0.001.

GC = 1 if a firm receives going concern opinion, 0 otherwise. All other variables are defined in (Table 2)

Springer


Table 11 Explaining auditors’ going concern opinions

Variable Co-efficient Wald Chi-square

Intercept −7.522 30.460∗∗∗

NITA −0.916 9.648∗∗

CASALES 0.189 5.974∗

CACL −0.629 12.980∗∗∗

CATA −0.616 0.924CASHTA 0.204 0.034LTDTA −1.421 6.087∗

LSALES −0.080 0.940STRESS (Zmijewski probability) 2.332 33.835

∗∗∗

IFR 0.164 2.702CAR −0.903 9.852

∗∗

LNMCP −0.386 18.184∗∗∗

Dependent variable: auditors’ going concern opinions (GC). GC = 1 if a firm receives going concernopinion, 0 otherwise.∗Significant at p-value < 0.05.

∗∗Significant at p-value < 0.01.

∗∗∗Significant at p-value < 0.001

if a firm received going-concern opinion, 0 otherwise); in the right column is the logitmodel result with going-concern opinions variable. GC variable is statistically sig-nificant at p < 0.001 level. And the model with GC has an incremental χ2of 41.155,significant at p < 0.001 level. This indicates that auditors’ going concern opinionsdo have incremental contribution in predicting bankruptcy beyond a composite stressmeasure, market variables, and industry failure rate.

The final additional analysis we perform is to examine whether auditors considernon-financial-accounting information (market variables and industry-level factors)when making going-concern judgments. In order to test this issue, we regress auditors’going concern opinions against these variables. Again, we use only the test sampleand employ a binary logit analysis. Table 11 presents the result. We find that marketvariables are significant explanatory variables but industry failure rate is not. Thiscould imply that auditors are not able to pay enough attention to industry-level factorwhen making going-concern judgments. Auditors’ going-concern judgments couldbe improved by taking into account the industry-level information such as industryfailure rate.

6 Conclusions

To compare the relative performance of auditors’ going concern opinions and sta-tistical models in predicting bankruptcy, this paper develops a hazard model withincorporation of a composite stress measure derived from Zmijewski (1984) probitmodel, two market variables (abnormal stock returns and market capitalization), andone industry-level factor (industry failure rate) in addition to traditional financial ratios.Our work is motivated by the fact that statistical models used for comparing the predic-

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76 L. Sun

tion ability of auditors’ going concern opinions with that of statistical models have notincorporated some new features suggested by recent bankruptcy prediction research.

Our results show that the hazard model estimated in this study statistically out-performs the auditors’ going concern opinions in the holdout sample. This suggeststhat a well-developed statistical model as suggested by recent bankruptcy work (e.g.,Shumway, 2001) could serve as a useful decision-aid for auditors’ going concernjudgments.

Further analysis shows that auditors’ going concern opinions have incrementalprediction ability beyond traditional financial ratios, a composite measure of finan-cial distress, and non-financial-accounting information (market variables and industryfailure rate). We also find that market variables have significant power in explainingauditors’ going concern opinions, but industry failure rate does not have such a sig-nificant explanatory power. Auditors’ going concern judgments could be improved byconsidering not only firm-level factors (financial and non-financial) but also industry-level factors (such as, industry failure rate).

The study has its limitations. Similar to other empirical studies in bankruptcyprediction, this study’s results are based upon the particular data set employed. Itshould also be admitted that the significance of predictor variables may becomeunstable across time periods (Begley et al., 1996).

More importantly, the statistical model built in this study incorporates only somenew features suggested by recent bankruptcy studies. Among other development,Merton option-pricing model is of particular interest. Merton model is based uponthe original work of Merton (1974), in which the equity of the firm is a call op-tion on the underlying value of the firm with a strike price equal to the face valueof the firm’s debt. The probability of default depends upon the firm’s underlyingvalue, the firm’s volatility and the face value of the firm’s debt. Different versionsof default measures based upon Merton model have been derived and tested by bothpractitioners and academicians. For instance, researchers in KMV Corporation, sub-sequently acquired by Moody’s, develop the KMV-Merton model, which is availableto its subscribers. Hillegeist et al. (2004) estimate the Black–Scholes–Merton Proba-bility of Bankruptcy (Black and Scholes, 1973; Hillegeist et al., 2004) which is foundto outperform both Ohlson (1980) Model and Altman Z-score (1968). Bharath andShumway (2004) propose a naive alternative to the KMV-Merton model and furtherprove that the former outperformed the latter. The beauty of the naı̈ve alternative isthat while capturing both the functional form and the same basic inputs of the KMV-Merton Model, it does not require solving the simultaneous nonlinear equations asthe KMV-Merton Model does. It would be interesting future research to examine howto better apply the Merton option-pricing model into bankruptcy prediction and howto better utilize the Merton model in facilitating auditors’ going concern decisionmakings.

Acknowledgments This paper is part of my dissertation. I am indebted to my dissertation co-chairsMichael Ettredge and Rajendra P. Srivastava for their guidance and valuable suggestions. I am also grate-ful to suggestions provided by Cheng-few Lee (the editor), an anonymous reviewer, James McKeown,Xiangdong Yang and participants at the University of Kansas AIS workshop. I thank the WhitcombCenter for Research in Financial Services for providing research support through use of the WRDSsystem.

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