On corporate financial distress prediction: What can we learn from private firms in a developing economy? Evidence from Greece
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Abstract
Using a large dataset that includes nearly 31,000 Greek private firms we examine the determinants of the probability of corporate financial distress. Using a multi-period logit model, we find that profitability, leverage, the ratio of retained earnings-to-total assets, size, the liquidity ratio, an export dummy variable, the tendency to pay out dividends and the growth rate in real GDP are strong predictors of the probability of financial distress for Greek private firms. A model including these variables exhibits the highest in-sample and out-of-sample performance in terms of correctly classifying firms that went bankrupt as more likely to go bankrupt. The predictive ability of the model remains when we increase the forecast horizon, suggesting that the model works well over short and longer time horizons.
Keywords
Corporate financial distress Bankruptcy prediction Private firms Discrete hazard (multi-period logit) model Financial statements Greek debt crisisJEL Classification
G13 G17 G33 C411 Introduction
The failure of a firm is an event of major concern in economic life. Consequently, the prediction of corporate financial distress has received considerable attention in the field of corporate finance. Academic researchers and practitioners have developed various models to forecast financial distress using either accounting or stock market information. Following the seminal work of Beaver (1966) and Altman (1968), there have been a substantial number of studies that make use of accounting ratios to predict corporate bankruptcy.^{1} More recent studies have focused on Merton’s (1974) structural market-based model for pricing corporate debt to derive the probability of corporate default.^{2} Shumway (2001) and Campbell et al. (2008) use a discrete hazard model that incorporates both accounting and stock-market-based variables to forecast bankruptcy.
Despite the fact that predicting the probability of corporate financial distress has received a significant amount of attention, our understanding of the prediction of corporate financial distress is far from complete. There are two gaps in the literature that this paper goes some way towards filling. Much of the literature to-date has focused on publicly-traded firms in developed economies, for which data is more widely available. Much less attention has been devoted to the determinants of the probability of corporate financial distress for private firms and less still to the determinants of the probability of financial distress of private firms in developing economies. Indeed, to our knowledge there is no empirical research that addresses the question of what drives the likelihood of private firms entering financial distress in a developing economy.^{3} We attribute this to the difficulty of obtaining private firms’ financial data and information on when a private firm goes bankrupt.
This paper contributes to the literature by examining the determinants of the probability of financial distress for private firms in a developing economy, that of Greece. There are several reasons why examining the determinants of the probability of financial distress for private firms is important. First, private firms, especially small- and medium-sized enterprises (SMEs) are of key importance for economic activity, employment and innovation in many countries. With respect to Greece, for example, 99.9% of Greek firms are defined as SMEs, they account for 84.9% of the total workforce and 69% of the value added in the economy (OECD 2015). Similarly, SMEs are the backbone of the economy in the Eurozone. According to Wymenga et al. (2012), across the Eurozone SMEs account for around 98% of all Euro area firms, around 75% of total employment and generate around 60% of gross value added while over 99% of US and UK firms are privately owned and are responsible for more than half of the GDP of the US and the UK, respectively. Second, the evidence shows that private firms are different from public ones. Private firms are smaller, more leveraged, more dependent on trade credit and bank loans, invest more, and face higher borrowing costs.^{4} These differences between private and public firms raise the issue of whether the (non-stock-market) factors that predict the probability of bankruptcy for public firms are (a) the same for private firms and (b) have the same sign as those for public firms and perhaps similar orders of magnitude as well. Third, providing information on the probability of bankruptcy for private firms is quite challenging as these firms do not have their shares traded on a stock exchange and hence there is a lack of market data. As a result, the information we can use to predict bankruptcy is mainly derived from financial statements. Therefore, examining whether it is possible to successfully predict the probability of financial distress for private firms is essential, not least because it will help in formulating policy relating to the supply of credit by banks and the cost of credit for this type of firm. Evidence on the performance of bankruptcy forecast models for private firms will also provide insights into the usefulness of information contained in financial statements for private firms.
Using a large dataset of Greek private companies, we estimate the probability of corporate financial distress for Greek private firms over the period 2003–2011. In addition to being a developing economy where private firms predominate, Greece provides a challenging test for models predicting the probability of bankruptcy given the debt crisis that enveloped the country from 2009 to 2011 following the global financial crisis. Further, examining bankruptcy around the Greek debt crisis allows us to see the degree to which business failures in the crisis period could be predicted by pre-crisis-data.
We develop multi-period logit (discrete hazard) models to evaluate the variables that are significantly associated with the prediction of financial distress for Greek private firms.^{5} In the literature to date, discrete hazard models have tended to be used to predict the probability of financial distress for publicly-traded firms in developed economies and tend to use both accounting information, usually in the form of accounting ratios, and stock market information; see, for example, Shumway (2001), Campbell et al. (2008) and Charalambakis and Garrett (2016). Studies making use of accounting information only have tended to use discriminant analysis or, more predominantly, traditional logit or probit models; see, for example, Altman (1968), Ohlson (1980), Taffler (1983) and Zmijewski (1984). These latter models are single-period (static) classification models in which the probability of bankruptcy does not change over time as the models ignore the fact that firms change through time. Shumway (2001) shows that estimating the probability of financial distress using static models leads to biased and inconsistent estimates of the probability of bankruptcy and incorrect inferences concerning the statistical significance of the predictor variables. Shumway (2001) proposes estimating the probability of bankruptcy using a discrete hazard model which is a dynamic model that captures the fact that firms change over time, enabling the probability of bankruptcy to change over time as a function of a vector of explanatory variables that also vary with time. Shumway (2001) finds that using a discrete hazard model to estimate the probability of bankruptcy, up to half of the accounting ratios that had previously been used to forecast bankruptcy for US firms are not statistically significant, that is, they are not statistically related to failure. Given this and given that there seems no reason why the probability of financial distress does not change over time for private firms, the discrete hazard model or, equivalently, the multi-period logit model, seems an appropriate choice of model to estimate the probability of financial distress, notwithstanding the presence of a financial crisis in our case, which one might expect to cause a firm’s probability of financial distress to change.
We find strong evidence that a model that contains seven firm-specific variables, along with the growth rate of real GDP and a dummy variable that captures the Greek debt crisis best explains the likelihood that a Greek private firm will experience financial distress. In particular, we find that profitability, retained earnings-to-total assets, size and liquidity are negatively associated with the probability of financial distress for Greek private firms while leverage is positively related to the probability of financial distress. We also find strong evidence that the probability of a private firm going bankrupt decreases when it exports and pays out dividends. Interestingly, we find that the dummy variable for the Greek debt crisis is negatively associated with the probability of financial distress, meaning that bankruptcies were less common during the crisis than might be expected. This finding is borne out by the average number of bankrupt firms within the crisis period decreasing to more than half those in the pre-crisis period. In particular, the average number of bankrupt firms was 271 for the period 2006–2008 while the average number of bankrupt firms was 134 for the crisis period of 2009–2011. In terms of macroeconomic influences on the probability of financial distress we find that the growth rate in real GDP is negatively related to the probability of financial distress. Forecast accuracy tests show that in-sample, this model correctly classifies 87% of those firms that subsequently went bankrupt as likely to go bankrupt. In addition, the results do not change when we extend the forecast horizon from one year to two and three years, suggesting that the model is quite robust with respect to the horizon over which the probability of financial distress is predicted, at least in the short- to medium-term.
To examine the out-of-sample forecasting performance of our preferred model, and to examine the extent to which our findings may be driven by the debt crisis that enveloped Greece following the global financial crisis, we re-estimate our preferred model excluding the Greek debt crisis to investigate whether the nature of the relationship between the predictor variables and the probability of bankruptcy changes and to examine whether, out-of-sample, our preferred model is still able to correctly classify those firms that subsequently went bankrupt as likely to go bankrupt. With the exception of size, which becomes insignificant, the estimated parameters have the same sign and are of similar magnitude to the full-sample estimates. More importantly, the model correctly classifies 88% of firms that went bankrupt during the Greek crisis as likely to go bankrupt.
We also investigate whether the results differ when we split the sample into small and medium-sized private firms based on the number of employees.^{6} We find that the signs and the magnitude of the estimated coefficients of the seven firm-specific variables vary across small and medium firms.
The rest of the paper is organized as follows. Section 2 provides a review of the literature and some methodological background to modelling the probability of financial distress using the discrete hazard/multi-period logit approach. Section 3 describes the dataset. Section 4 presents the results for the various models we estimate, the results from forecast accuracy tests and robustness checks. Section 5 concludes.
2 Literature review and empirical design
Several econometric techniques have been used to predict financial distress for publicly traded firms. Beaver (1966) uses univariate analysis to investigate the ability of accounting data to predict bankruptcy. Based on this method a financial ratio for the firm of interest is compared to a benchmark ratio to discriminate a failed firm from a non-failed firm. Altman (1968) employs multiple discriminant analysis to determine the Z-score, a widely used measure for predicting bankruptcy. The objective of discriminant analysis is to generate a linear combination of variables that best separate the bankrupt firms from the non-bankrupt ones. Although popular, this method is subject to some limitations. First, it fails to provide a test of the significance of the individual variables. Second, it assumes that the predictors are distributed as multivariate normal. Third, it prevents the use of dummy variables that can enhance the predictive ability of the bankruptcy forecast models.
Altman et al. (1977) use quadratic discriminant analysis to forecast bankruptcy. Ohlson (1980) estimates a conditional logit model to generate the probability that a firm will enter bankruptcy (known as the “O-score”) while Zmijewski (1984) estimates a probit model. Lau (1987) uses a multinomial logit model that allows for more than two states of financial distress. Another strand of the literature draws on the Merton (1974) option pricing framework to derive the probability of default. In these models, equity is viewed as a call option on the firm’s assets and the probability of going bankrupt is simply the probability that the call option is worthless at maturity, i.e., the market value of total assets is less than the face value of total liabilities. Vassalou and Xing (2004) employ the Merton model to investigate whether default risk is priced in equity returns. Duffie et al. (2007) show that the default probabilities derived from Merton’s model can have significant predictive power and consequently can generate a term structure of default probabilities.
Etheridge and Sriram (1997) examine the performance of neural networks with respect to corporate financial distress prediction. They find that the neural network outperforms multivariate discriminant analysis and logistic models. Nittayagasetwat (1996) applies a neural network to forecast bankruptcy for US firms. He finds that his neural network model exhibits higher predictive ability than a logit model. While neural network techniques can provide higher classification rates, they cannot provide any information on the significance of the predictor variables. It is therefore more difficult to assess the contribution of the predictor variables to the prediction of financial distress.
Shumway (2001) argues and shows that the models used by Altman (1968), Ohlson (1980) and Zmijewski (1984) are misspecified as they do not properly address the length of time that a healthy firm has survived, thereby inducing bias. He overcomes this problem by employing a discrete hazard model which is econometrically equivalent to a multi-period logit model. This model has two main advantages. First, it allows researchers to take advantage of all the available firm-year observations. Second, it is a dynamic model in the sense that it enables the probability of bankruptcy to change over time as a function of a vector of explanatory variables that also vary with time. In his empirical work, Shumway (2001) finds that a discrete hazard model delivers the best performance in terms of out-of-sample predictive ability. Since the seminal work of Shumway (2001), Hillegeist et al. (2004) and Agarwal and Taffler (2008) have used discrete hazard models to compare the performance of accounting-information-based and stock-market-information-based bankruptcy prediction models for US and UK firms, respectively. Chava and Jarrow (2004) extend the model of Shumway (2001), highlighting the importance of including industry effects in the discrete hazard model. They also provide evidence that the predictive power of accounting variables weakens when stock-market-based variables are included in the model. Bharath and Shumway (2008) use a discrete hazard model to examine the contribution of the probability of default derived from the Merton (1974) model to predicting financial distress. They find that the probability of default based on the Merton model is not a sufficient statistic for default. Using US data, Campbell et al. (2008), building on the work of Shumway (2001), find that the default probability based on the Merton model has relatively little forecasting power in a discrete hazard model when conditioning on accounting and stock-market-based variables. Tinoco and Wilson (2013) compare hazard models with neural networks and Z-score models using UK data. They find that a panel logistic model with time-varying covariates, which is equivalent to a hazard model, that combines accounting, stock market and macroeconomic variables outperforms the neural network approach and Z-score approach. Similarly, Bauer and Agarwal (2014) show that for the UK, the hazard model developed by Shumway (2001) outperforms the Z-score model developed by Taffler (1983) and the contingent claims model of Bharath and Shumway (2008).
While there is a wealth of evidence on the prediction of financial distress for publicly-listed firms in developed markets, evidence is a little harder to come by for developing markets and for private firms. Kwak et al. (2012) predict bankruptcy for Korean firms after the 1997 financial crisis. Using the accounting variables that Altman (1968) and Ohlson (1980) use, Kwak et al. (2012) estimate their bankruptcy prediction model using multiple criteria linear programming (MLCP). They find that their model works as well as traditional multiple discriminant analysis and traditional logit analysis. However, other than noting where there is a significant difference in the means of the variables for bankrupt and non-bankrupt firms, Kwak et al. (2012) do not focus on the sign and significance of the variables in the prediction of bankruptcy as they are concerned with a comparison of MLCP with traditional multiple discriminant analysis and traditional logit analysis. In examining the predictors of financial distress in the trading and services sectors in Malaysia, Alifiah (2014) finds that the likelihood of distress is negatively related to the debt ratio, the working capital ratio and net income to total assets while it is positively related to the total asset turnover ratio and the base lending rate. Charalambakis and Garrett (2016) evaluate the contribution of accounting and stock-market-based information to the prediction of bankruptcy across developed and emerging markets using discrete hazard models. While they find that book leverage combined with three stock-market-based variables best predict the probability of financial distress for UK firms, they find that stock market information has no significant role to play in predicting the probability of distress for Indian firms. Rather, they find the probability of financial distress in India is negatively related to an accounting-based measure of profitability and positively related to the ratio of current liabilities to total assets.
In terms of evidence regarding the determinants of the probability of financial distress for private firms, again it is quite sparse and almost exclusively focused on developed economies. Of those studies that investigate the probability of financial distress for private firms, Falkenstein et al. (2000) evaluate the credit risk of US private firms using Moody’s RiskCalc™^{7} and find that the relationship between financial variables and credit risk differs quite substantially across public and private firms. Cangemi et al. (2003) use Standard and Poor’s Credit Risk Tracker to examine the default risk of French private firms using the maximum expected utility (MEU) approach. Altman and Sabato (2007) find that the probability of not defaulting for 2000 SMEs in the US is positively related to EBITDA-to-total assets, retained earnings-to-total assets, cash-to-total assets and EBITDA-to-interest expense while it is negatively related to short-term debt-book equity. Altman et al. (2010) combine both qualitative and financial information in a default prediction model for UK SMEs. In addition to finding that the accounting ratios used by Altman and Sabato (2007) significantly predict the probability of default for UK SMEs, they find that data relating to legal action by creditors to recover unpaid debts, company filings and audit reports/opinions significantly increase the performance of their model. However, such information is not always available in advance or may not be updated frequently enough to facilitate accurate predictions. Diekes et al. (2013) use a probit model and find that business credit information improves the accuracy of default predictions for private firms in Germany.
With regard to inference in relation to (2), Shumway (2001) shows that it is necessary to adjust the Wald statistics that test the significance of the coefficients. The reason for this stems from the fact that the discrete hazard model can be thought of as a multi-period logit model. The multi-period logit model in turn is a logit model in which each firm-year observation is treated as if it were an independent, separate firm. However, in the discrete hazard/multi-period logit model firm-year observations are not independent of each other: a firm that went bankrupt last year, for example, cannot go bankrupt this year and therefore the test statistics need to be adjusted to reflect this. Shumway (2001) shows that this is easily done through the Wald statistic: for the multi-period logit model, the test statistics need to be scaled by the average number of firm years per firm.
3 Sample and data
The sample consists of Greek private firms that operated in Greece over the period 2003–2011. The source of our data is the ICAP database, which contains annual publicly available data mainly derived from financial statements for nearly 60,000 Greek private firms.^{8} We exclude financial firms and state-owned enterprises from the sample.^{9} We also exclude firm-year observations for which we do not have available data. Our final sample includes 30,886 firms and 188,065 yearly observations. To forecast corporate financial distress we need to define which firms enter financial distress and when this occurs. The ICAP database identifies the year of the private firm’s death and the type of death (bankruptcy, liquidation, inactivity due to insolvency state, mergers and acquisitions and resolution). We consider a private firm to be financially distressed if it has either (a) been declared bankrupt, liquidated or dissolved or (b) been inactive due to being in a state of insolvency. Firms that have managed to resolve the insolvency state or have been the subject of a merger or acquisition are regarded as non-bankrupt firms. Using these criteria for classifying bankruptcy there are 1770 bankrupt firms in our sample with 5957 firm-year observations and 29,116 non-bankrupt firms with 182,108 firm-year observations.
Definition of firm-specific variables
Variable | Definition |
---|---|
EBITDA_TA | \({\displaystyle{\frac{\text{Earnings before interest, tax and depreciation}}{\text{Total assets}}}}\) |
BLEV | \({\displaystyle{\frac{\text{Book value of total debt}}{\text{Total assets}}}}\) |
RET_TA | \({\displaystyle{\frac{\text{Retained earnings}}{\text{Total assets}}}}\) |
SIZE | Natural logarithm of total assets |
LIQUID | \({\displaystyle{\frac{({\text{Current assets}} - {\text{current liabilities}})}{\text{Total assets}}}}\) |
EXPORT | Dummy variable equal to one if a firm exports, zero otherwise |
DIVPAY | Dummy variable equal to one if a firm pays out dividends, zero otherwise |
To account for any industry effects that may have an impact on the prediction of financial distress we include industry dummies in all of our models. To define the industry dummies, we classify firms into industries according to the NACE industry classification code (following NACE Revision 2). The NACE industry classification code is the European standard industry classification system. Based on the two-digit NACE code classification, we place firms into 16 industry groups, constructing 16 corresponding industry dummies. The industries are: Agriculture, forestry and fishing; Mining and quarrying; Manufacturing; Construction; Electricity, gas, steam and air conditioning supply; Water supply, sewerage, waste management and remediation activities; Wholesale and retail trade; Transportation and storage; Accommodation and food service activities; Information and communication; Real estate activities; Professional, scientific and technical activities; Administrative and support service activities; Education; Human health and social work activities; and Arts, entertainment and recreation.
Descriptive statistics, full sample
Variable | Mean | Median | Standard Deviation | Min. | Max. |
---|---|---|---|---|---|
EBITDA_TA | 0.06 | 0.05 | 0.14 | − 0.52 | 0.56 |
BLEV | 0.30 | 0.18 | 0.33 | 0.00 | 1.22 |
RET_TA | − 0.14 | 0.00 | 0.47 | − 3.38 | 0.38 |
SIZE | 14.12 | 14.09 | 1.49 | 5.03 | 18.41 |
LIQUID | − 0.00 | 0.00 | 0.36 | − 1.19 | 0.97 |
EXPORT | 0.23 | 0.00 | 0.42 | 0.00 | 1.00 |
DIVPAY | 0.27 | 0.00 | 0.45 | 0.00 | 1.00 |
Descriptive statistics for non-bankrupt and bankrupt firms
Variable | Mean | Median | Standard Deviation |
---|---|---|---|
Panel A: Non-bankrupt firms | |||
EBITDA_TA | 0.06 | 0.05 | 0.13 |
BLEV | 0.29 | 0.18 | 0.32 |
RET_TA | −0.12 | 0.00 | 0.42 |
SIZE | 14.14 | 14.10 | 1.47 |
LIQUID | 0.01 | 0.01 | 0.35 |
EXPORT | 0.23 | 0.00 | 0.42 |
DIVPAY | 0.28 | 0.00 | 0.45 |
Panel B: Bankrupt firms | |||
EBITDA_TA | − 0.04 | − 0.00 | 0.20 |
BLEV | 0.31 | 0.00 | 0.40 |
RET_TA | − 0.76 | − 0.28 | 1.06 |
SIZE | 13.59 | 13.60 | 1.92 |
LIQUID | − 0.19 | − 0.16 | 0.52 |
EXPORT | 0.15 | 0.00 | 0.35 |
DIVPAY | 0.09 | 0.00 | 0.28 |
EBITDA_TA | BLEV | RET_TA | SIZE | LIQUID | EXPORT | DIVPAY | |
---|---|---|---|---|---|---|---|
Panel C: t statistics testing for differences between means | |||||||
Non-bankrupt versus bankrupt sample | 60.76*** | − 4.06*** | 107.48*** | 28.01*** | 41.54*** | 15.65*** | 32.64*** |
To deal with extreme observations, we winsorize the independent variables at the 1st and 99th percentiles of the distribution. Descriptive statistics for the firm-specific variables for the full sample are reported in Table 2. Looking at Table 2, we observe that the profitability and debt ratios are positively skewed since the respective means are greater than the respective medians, whereas the ratio of retained earnings-to-total assets and the liquidity ratio are negatively skewed. Further, on average, private firms have negative retained earnings. Focusing on the export and dividend dummy variables, less than 25% of the firms in the sample are involved in export activity while 27% of them pay out dividends. Table 3 reports the descriptive statistics for the sample of bankrupt and non-bankrupt firms. As we would expect, bankrupt firms are on average less profitable, more levered, smaller and accumulate more losses relative to non-bankrupt firms. Bankrupt firms are also less liquid, less likely to export and less likely to pay out dividends relative to non-bankrupt firms. Panel C of Table 3 documents the difference in the means of the variables between non-bankrupt and bankrupt firms. In all cases, the null hypothesis that there is no difference between the means for bankrupt and non-bankrupt firms is rejected. The significant differences in the means of the variables suggest that bankrupt and non-bankrupt firms differ markedly and that these differences may have some ability in predicting the probability of financial distress. We turn our attention to this in the next section.
4 Results
4.1 The predictive ability of multi-period logit models
Results for multi-period logit models predicting the probability of financial distress
BPM1 | BPM2 | BPM3 | BPM4 | BPM5 | |
---|---|---|---|---|---|
Panel A: Bankruptcy prediction models for Greek private firms | |||||
Constant | − 3.8563*** (43.72) | − 3.7067*** (39.38) | − 3.9559*** (43.69) | − 3.8191*** (40.82) | − 3.2700*** (27.58) |
EBITDA_TA | − 1.8623*** (25.42) | − 1.7627*** (22.86) | − 1.7480*** (22.70) | − 1.4407*** (18.20) | − 1.4071*** (14.64) |
BLEV | 0.6682*** (15.39) | 0.5752*** (11.10) | 0.5936*** (11.98) | 0.5686*** (11.14) | 0.5610*** (10.82) |
RET_TA | − 0.8182*** (132.73) | − 0.7496*** (95.98) | − 0.7504*** (97.06) | − 0.7203*** (91.99) | − 0.7398*** (97.25) |
SIZE | − 0.0949*** (5.02) | − 0.1039** (5.90) | − 0.0808** (4.11) | − 0.0796** (4.01) | − 0.0638** (4.25) |
LIQUID | − 0.3563*** (6.99) | − 0.3559*** (7.01) | − 0.3589*** (7.29) | − 0.3409*** (7.18) | |
EXPORT | − 0.4364** (6.53) | − 0.3644** (4.54) | − 0.3658** (4.56) | ||
DIVPAY | − 1.1838*** (20.66) | − 1.2220*** (21.91) | |||
GRCRISIS | − 1.5655*** (22.75) | ||||
GDP GROWTH | − 0.1466*** (12.77) | ||||
Industry dummies | Yes | Yes | Yes | Yes | Yes |
Log likelihood | − 8881.94 | − 8860.47 | − 8842.69 | − 8758.43 | − 8675.31 |
Pseudo R^{2} (%) | 11.36 | 11.57 | 11.75 | 12.59 | 13.42 |
Wald statistic | 2276.36*** | 2311.77*** | 2354.87*** | 2523.39*** | 2689.62*** |
Number of observations | 188,065 | 188,065 | 188,065 | 188,065 | 188,065 |
Model i versus Model j | LR statistic |
---|---|
Panel B: Likelihood ratio tests | |
BPM5 versus BPM4 | \(\chi ^{2}(2) = 27.27^{***}\) |
BPM5 versus BPM3 | \(\chi ^{2}(3) = 54.91^{***}\) |
BPM5 versus BPM2 | \(\chi ^{2}(4) = 61.98^{***}\) |
BPM5 versus BPM1 | \(\chi ^{2}(5) = 67.78^{***}\) |
Area under the receiver operating characteristics (ROC) curve (AUC) and accuracy ratios
Models | AUC | SE | z | AR |
---|---|---|---|---|
BPM1 | 0.7984 | 0.0062 | 48.13 | 0.5968 |
BPM2 | 0.8061 | 0.0059 | 51.88 | 0.6122 |
BPM3 | 0.8042 | 0.0059 | 51.56 | 0.6084 |
BPM4 | 0.8115 | 0.0059 | 52.80 | 0.6230 |
BPM5 | 0.8191 | 0.0054 | 59.09 | 0.6382 |
In-sample forecast accuracy tests
Decile | BPM1 | BPM2 | BPM3 | BPM4 | BPM5 |
---|---|---|---|---|---|
1 | 52.88 | 53.56 | 53.22 | 53.38 | 54.52 |
2 | 15.14 | 14.92 | 15.03 | 15.37 | 15.14 |
3 | 7.74 | 8.47 | 7.74 | 7.63 | 7.80 |
4 | 5.54 | 5.31 | 5.48 | 6.27 | 5.48 |
5 | 3.84 | 4.12 | 4.01 | 3.96 | 4.12 |
6–10 | 14.86 | 13.62 | 14.52 | 13.39 | 12.94 |
No. of bankrupt firms | 1770 | 1770 | 1770 | 1770 | 1770 |
Out-of-sample forecast accuracy tests
Decile | BPM1 | BPM2 | BPM3 | BPM4 | BPM5 |
---|---|---|---|---|---|
1 | 55.09 | 56.08 | 57.57 | 57.83 | 58.07 |
2 | 15.38 | 15.38 | 11.66 | 11.41 | 10.92 |
3 | 7.94 | 6.20 | 7.69 | 7.94 | 8.19 |
4 | 4.22 | 5.46 | 5.21 | 6.20 | 6.20 |
5 | 5.21 | 4.72 | 4.96 | 4.96 | 4.96 |
6–10 | 12.16 | 12.16 | 12.91 | 11.66 | 11.66 |
No. of bankrupt firms | 403 | 403 | 403 | 403 | 403 |
Extending the forecast horizon
2-year forecast horizon | 3-year forecast horizon | |
---|---|---|
Constant | − 4.9595*** (49.86) | − 4.5039*** (27.67) |
EBITDA_TA | − 1.3925*** (9.97) | − 1.0796** (5.01) |
BLEV | 0.5397** (7.74) | 0.5138** (5.64) |
RET_TA | − 0.7138*** (64.65) | − 0.7475*** (48.57) |
SIZE | − 0.0249 (1.51) | − 0.0281 (1.30) |
LIQUID | − 0.3207** (4.94) | − 0.2991** (4.76) |
EXPORT | − 0.3382** (4.75) | − 0.2775** (4.35) |
DIVPAY | − 0.9961*** (16.80) | − 0.9110*** (10.99) |
GRCRISIS | − 0.5667*** (6.78) | − 0.9862*** (27.06) |
GDP GROWTH | 0.0144 (0.92) | − 0.2117*** (19.31) |
Industry dummies | Yes | Yes |
Log likelihood | − 7256.25 | − 5180.47 |
Wald statistic | 1632.15*** | 1185.83*** |
Pseudo R^{2} | 0.1011 | 0.1027 |
Number of observations | 157,556 | 128,378 |
Out-of-sample and in-sample forecast accuracy tests when extending the forecast horizon
Decile | 2-year horizon | 3-year horizon |
---|---|---|
Panel A: Out-of-sample forecast tests | ||
1 | 53.87 | 48.65 |
2 | 11.46 | 11.49 |
3 | 7.16 | 9.12 |
4 | 6.88 | 8.11 |
5 | 6.88 | 6.08 |
6–10 | 13.75 | 16.55 |
No. of bankrupt firms | 349 | 296 |
Panel B: In-sample forecast tests | ||
1 | 46.74 | 43.60 |
2 | 14.43 | 14.84 |
3 | 10.18 | 8.94 |
4 | 6.51 | 7.93 |
5 | 5.66 | 5.59 |
6–10 | 16.48 | 19.10 |
No. of bankrupt firms | 1414 | 984 |
While the parameters are statistically significant in all of the models considered in Table 4, a natural question that arises is whether each model contains additional incremental predictive information. To investigate this, we compare the five bankruptcy prediction models to evaluate which model incorporates the most relevant information about the probability of financial distress. A comparison of each model’s pseudo-\(R^{2}\) shows that while BPM5 has the highest pseudo-\(R^{2}\) of 14%, the lowest pseudo-\(R^{2}\), that for BPM1, is only a little lower at 11%. This raises the possibility that while the parameters in BPM5 are all statistically significant, one of the other more parsimonious models may perform just as well. Panel B of Table 4 reports likelihood ratio tests of the null hypothesis that model BPM5 contains no incremental predictive information over BPM1 through BPM4. Despite the fact that the pseudo-\(R^{2}\) experiences only a reasonably modest increase from BPM1 to BPM5, the likelihood ratio tests strongly show that the additional variables in BPM5 relative to the other models have significant incremental predictive ability: in all cases, models 1 through 4 are rejected in favour of model 5.
Bankruptcy prediction models including and excluding the Greek crisis period
BPM5, Full sample | BPM5 Excluding the Greek crisis | |
---|---|---|
Constant | − 3.2700*** (27.58) | − 3.7856*** (41.87) |
EBITDA_TA | − 1.4071*** (14.64) | − 1.5552*** (20.32) |
BLEV | 0.5610*** (10.82) | 0.6509*** (17.00) |
RET_TA | − 0.7398*** (97.25) | − 0.7429*** (111.59) |
SIZE | − 0.0638** (4.25) | − 0.0372 (0.82) |
LIQUID | − 0.3409*** (7.18) | − 0.2690** (4.68) |
EXPORT | − 0.3658** (4.56) | − 0.3360* (3.82) |
DIVPAY | − 1.2220*** (21.91) | − 1.2235*** (28.65) |
GRCRISIS | − 1.5655*** (22.75) | |
GDP GROWTH | − 0.1466*** (12.77) | − 0.1142*** (7.48) |
Industry dummies | Yes | Yes |
Log likelihood | − 8675.31 | − 66618.15 |
Pseudo R^{2} (%) | 13.42 | 12.55 |
Wald statistic | 2689.62*** | 1899.84*** |
Number of observations | 188,065 | 126,282 |
As a final check on the performance of the models reported in Table 4 we follow Sobehart and Keenan (2001), Vassalou and Xing (2004) and Agarwal and Taffler (2008) among others and use the Area Under the Curve (AUC) criterion and the accuracy ratio (AR) to evaluate the models’ fit in terms of predictive ability. The AUC is based on the area under the Receiver Operating Characteristics (ROC) curve and is an indicator of the quality of the model: the larger is the AUC, the better is the model at predicting the probability of financial distress. To arrive at an estimate of the AUC for each model, we first calculate the ROC curve. The ROC curve for each model BPM1 through BPM5 ranks firms from the highest estimated probability of default to the lowest and splits them into integers between 0 and 100 (these can be thought of as percentages). For each integer of the firms with the highest estimated probability of financial distress, we calculate the percentage of those firms that actually failed. These figures are then cumulated and the ROC curve plots them against the integer. If a model is incapable of distinguishing between bankrupt and non-bankrupt firms then the ROC curve will be a 45 degree line. The greater the predictive power of the model, the more bowed the curve will be and this is why the AUC forms the basis of a measure of the model’s predictive ability and hence the quality of the model. If the bankruptcy prediction model is incapable of distinguishing between bankrupt and non-bankrupt firms (the ROC curve is a 45 degree line), the AUC is equal to 0.5; if the bankruptcy prediction model is perfectly capable of distinguishing between bankrupt and non-bankrupt firms the AUC is equal to 1. Engelmann et al. (2003) use the AUC to develop the accuracy ratio (AR) of the model which in turn forms the basis of a statistical test to evaluate whether the model performs better than one that, in this case, randomly allocates firms as being bankrupt or not. The accuracy ratio is defined as \({\text {AR}} = 2\times ({\text {AUC}} - 0.50\)). An AR of zero shows that the model is incapable of performing better than a model which randomly allocates firms as being bankrupt or not. The higher the AR the better is the model at predicting the probability of bankruptcy. Results from the estimated AUC and the corresponding ARs are presented in Table 5. We also report a z-statistic, defined as \(z =\frac{\widehat{AUC}-0.5}{{\text {std.error}}(\widehat{AUC})}\), testing the null hypothesis that there is no difference in the performance of the bankruptcy prediction model and a random classification model with AUC equal to 0.5. The z statistics reported in Table 5 are all large and statistically significant, showing that all five models outperform the random classification model. This is also confirmed by the AR as in all cases the AR is greater than zero. However, the model with the largest AUC and the highest accuracy ratio is BPM5, a finding that is consistent with the results in Table 4.
4.2 In-sample and out-of-sample forecast accuracy
Bankruptcy prediction when small- and medium-sized firms are separated
Small firms | Medium firms | |
---|---|---|
Constant | − 6.6248*** (47.13) | − 10.9983*** (6.92) |
EBITDA_TA | − 1.0507** (4.29) | − 1.9586 (2.56) |
BLEV | 0.5479*** (5.85) | 1.4435** (4.00) |
RET_TA | − 0.7358*** (46.17) | − 0.8853** (5.67) |
SIZE | − 0.0118 (0.19) | 0.2218 (1.16) |
LIQUID | − 0.5344*** (7.83) | − 0.4010 (1.34) |
EXPORT | 0.0496 (0.30) | − 0.6689** (4.45) |
DIVPAY | − 1.3641*** (15.26) | − 0.9109* (2.84) |
GRCRISIS | − 2.3919*** (25.79) | − 2.9695** (3.90) |
GDP GROWTH | − 0.1909*** (11.18) | − 0.2781** (3.88) |
Industry Dummies | Yes | Yes |
Log Likelihood | − 5228.96 | − 443.54 |
Wald statistic | 1352.81*** | 143.29*** |
Pseudo R^{2} | 0.1145 | 0.1391 |
Number of observations | 163,613 | 17,276 |
To investigate whether this is the case, we examine the ability of the models in Table 4 to predict the probability of financial distress out-of-sample as this should be the ultimate criterion when evaluating bankruptcy prediction models. We re-estimate the multi-period logit models described both above and in Table 4 using data from 2003 to 2008, a period prior to the Greek debt crisis. Since the estimation sample stops prior to the Greek debt crisis and we are forecasting out-of-sample, we do not include the dummy variable for the Greek debt crisis in BPM5.^{12} We then use the estimated coefficients from each model to predict corporate bankruptcies throughout the Greek debt crisis period of 2009–2011. The results are shown in Table 7. We observe that our preferred model, BPM5, exhibits the best out-of-sample performance. It classifies 88.34% of firms that went bankrupt during the period of the financial crisis into deciles 1 through 5 and although it has the same misclassification rate as BPM4, BPM5 correctly classifies a slightly higher percentage of bankrupt firms into the first decile. These results suggest that our best model in terms of in-sample predictive performance, BPM5, works well in forecasting bankruptcy not only out-of-sample but also during the crisis period. However, the possibility remains that while the model works well over the whole crisis period, it may not work so well for each year of the crisis. To investigate whether the out-of-sample predictive ability of BPM5 sustains for each year of the crisis,^{13} we estimate BPM5 with data from 2003 to 2008 and use the estimated coefficients to predict bankruptcy in 2009. We then re-estimate the model extending the sample until 2009 and use the model to predict the probability of financial distress in 2010. Finally, we re-estimate the model using data until 2010 and use the estimated parameters to predict the probability of financial distress in 2011. For each model, we report the percentage of firms that went bankrupt that are classified by the model as firms that have a higher probability of financial distress, that is, we report the percentage of those firms that went bankrupt that the model places in deciles 1 through 5, for each corresponding year of the crisis. We find that the model correctly classifies 87.5% of bankrupt firms in 2009, 89.66% of bankrupt firms in 2010 and 87.94% of bankrupt firms in 2011. Overall, the out-of-sample predictive ability of our model is high for both the crisis period as a whole and each year within the crisis period.
4.3 Extending the forecast horizon
In this subsection we explore the ability of our best model, BPM5, to predict the probability of financial distress when we extend the forecast horizon from one year to two and three years. In order to do this, we use (with the exception of the dummy variables) \({\mathbf {x}}_{it-2}\) and \({\mathbf {x}}_{it-3}\) rather than \({\mathbf {x}}_{it-1}\) in (2). The results are presented in Table 8. As can be seen, the signs and the magnitudes of the estimated coefficients on the variables are similar to those documented in Table 4. Profitability, retained earnings-to-total assets, the export dummy variable, the dividend payout dummy variable, the crisis dummy variable and the GDP growth rate are negatively related to the probability of financial distress while leverage is positively related to the probability of financial distress. The only notable difference is that when we extend the forecast horizon, size is no longer significant, suggesting that size is important for predicting the probability of financial distress over the short term (one year) but it’s importance subsides over longer forecasting horizons. Therefore, with this one exception, the variables that were found to predict the probability of financial distress in Table 4 remain strongly associated with the probability of financial distress over longer forecast horizons.
Table 9 reports results from repeating the in-sample and out-of-sample analysis of Tables 6 and 7 for the 2 and 3-year forecast horizons. The interesting finding here is that the forecast accuracy of the model remains strong. As expected, the forecast accuracy of the model decreases when we increase the forecast horizon. However, BPM5 still performs well. Looking at Panel A of Table 9, we observe that the misclassification rate of the model when forecasting out-of-sample increases from 11.66% when forecasting 1-year-ahead to 13.75 and 16.55% for a 2 and a 3-year forecast horizon respectively. This means that the model correctly classifies 86.25% of bankrupt firms for a 2-year horizon and 83.45% of bankrupt firms into deciles 1 through 5. For completeness the in-sample results are presented in Panel B of Table 9. The in-sample test documents that the model allocates more than 80% of bankrupt firms to deciles 1 through 5 at both the 2 and 3-year horizons (83.52 and 80.9% respectively).
4.4 Additional robustness checks
The first robustness check we perform is related to the in-sample and out-of-sample forecasting ability of our preferred model discussed in Sect. 4.2. In terms of ability to classify bankrupt firms as having higher probabilities of going bankrupt, BPM5 works well both in-sample and out-of-sample and seems to do a decent job of predicting the probability of financial distress over the Greek debt crisis period. However, while our earlier results show that BPM5 forecasts well, a question we did not directly address is whether the nature of the relationship between the predictor variables and the probability of financial distress is substantively different once we allow for the effects of the Greek debt crisis. In other words, to what extent are the results in Table 4 driven by the Greek debt crisis? Table 10 reports results from estimating the model using the full sample and from estimating the model using a sample running from 2003 to 2008. With respect to the pre-Greek-crisis period, the estimated parameters have the same sign and are of similar magnitudes to those from estimating the model using the entire sample period with one exception: that of size. In the pre-Greek-debt-crisis sample period, the coefficient on size becomes much smaller and statistically insignificant. This suggests that outside of a crisis, size is relatively unimportant in predicting the probability of financial distress relative to the other variables.
A second robustness check we perform is to determine how the model performs when we split firms into small-sized firms and medium-sized firms. Although our earlier models contain the log of total assets as a proxy for size, this is not how the European Union defines size. Therefore, following the recommendation of the Commission (2003), we define the size of a firm based on the number of employees. A small firm is considered to be a firm with less than fifty employees while a medium-sized firm is a firm with fifty to 249 employees. This leads to samples containing 26,534 small firms with 163,851 firm-year observations and 2460 medium-sized firms with 17,315 firm-year observations. Table 11 reports the results from estimating BPM5 using these two samples. A notable difference in the results for small firms compared to the results for the whole sample is the insignificance of the export dummy variable for small firms: there is no statistically significant association between export activity and the probability of financial distress for small firms. For medium-sized firms, leverage, retained earnings-to-total assets, the export dummy variable and the dividend payout dummy variable are significant and have the expected signs. However, profitability and liquidity are not significant predictors of financial distress for medium-sized firms. The results also reveal that the predictive power of leverage and the GDP growth rate increases for medium-sized firms compared to small firms while the predictive power of the liquidity ratio and dividend payout is stronger for small firms than medium firms.
A final robustness test we consider is whether the inclusion of macroeconomic variables beyond the growth rate in real GDP affects the probability of financial distress for private firms. We augment BPM5 with three macroeconomic variables: the term spread, defined as the difference between the 10-year Greek government bond yield and the 10-year German government bond yield, domestic credit to the private sector scaled by GDP, and Greek public debt scaled by GDP. None of these additional macroeconomic variables are statistically significant.
5 Concluding remarks
In spite of their economic importance, little is known about what determines the probability of financial distress for private firms, particularly in a developing economy. This paper examines the probability of financial distress for private firms in a developing economy using the discrete hazard/multi-period logit approach (Shumway 2001). Using a large dataset of Greek private firms covering the period from 2003 to 2011 we find that seven firm-specific factors, many of which have been found to successfully predict the probability of financial distress for public firms in both developed and developing economies, as well as for SMEs in the US and UK, are strongly associated with the probability of financial distress for private firms in Greece. Profitability, retained earnings-to-total assets, size, liquidity, a dummy variable for export activity and a dividend payout dummy variable are negatively associated with the probability of bankruptcy whereas leverage is positively related to the probability of bankruptcy. We further find that after controlling for the Greek debt crisis, the real GDP growth rate has a significantly negative impact on the probability of financial distress and therefore matters when forecasting financial distress for Greek private firms. A model that controls for the Greek debt crisis and incorporates these variables exhibits the highest predictive ability based on both in-sample and out-of-sample forecast accuracy tests. The model also retains its predictive power when we increase the forecast horizon from one to two and three years. To examine the extent to which our findings are driven by the Greek debt crisis, we re-estimated our preferred model excluding the Greek debt crisis. With the exception of size, which becomes insignificant, the estimated parameters have the same sign and are of similar magnitude to the full-sample estimates. The model also correctly classifies 88% of firms that went bankrupt during the Greek debt crisis as likely to go bankrupt. We also find that when we split firms in to size according to the number of employees, the impact of the variables on the probability of financial distress can vary across small and medium-sized firms.
Footnotes
- 1.
- 2.
- 3.
There have been some papers in the more recent literature that focus on the probability of financial distress for publicly traded firms in developing economies. Kwak et al. (2012) examine the probability of financial distress for Korean firms while Charalambakis and Garrett (2016) use discrete hazard analysis to investigate the determinants of financial distress for Indian firms.
- 4.
- 5.
Shumway (2001) shows that a discrete hazard model is equivalent to a multi-period logit model where the multi-period logit model is defined as, “...a logit model that is estimated with data on each firm in each year of its existence as if each firm year were an independent observation.” (Shumway 2001, p. 105). We use the terms discrete hazard and multi-period logit interchangeably.
- 6.
One of the ways The European Union defines firm size is based on the number of employees (Commission 2003).
- 7.
The ten ratios that are used as inputs in Moody’s RiskCalc™ are: assets-to-consumer price index; inventories-to-cost of goods sold; liabilities-to-assets; net income growth; net income-to-assets; the quick ratio; retained earnings-to-assets; sales growth; cash-to-assets and the debt service coverage ratio.
- 8.
The ICAP database is the largest business database in Southeastern Europe. It is provided by the ICAP group (http://www.icap.gr), who are an Information Partner with Bureau van Dijk, the providers of the Amadeus database, and who have a partnership with Dun and Bradstreet. The ICAP Group is the only company in Greece recognized by the Bank of Greece as an External Credit Assessment Institution and in July 2011, ICAP was accepted by the European Securities and Markets Authority as a Credit Rating Agency.
- 9.
The financial firms we exclude from the sample are those that have NACE codes 64-66; the NACE code industry classification is the European standard industry classification system. The NACE codes follow the NACE Revision 2 classification. The list of Greek state owned enterprises includes public utilities (water, electricity and gas) and public enterprises from other sectors such as transportation, telecommunications and the defense industry. The list of Greek state owned companies is available from the ICAP database.
- 10.
Omitting the Greek crisis dummy from the model leads to a flip in sign for the real growth rate of GDP variable, which is counterintuitive.
- 11.
For Greek listed firms, profitability is marginally significant at the 10% level. In addition, Charalambakis (2015) finds that sales-to-total assets is strongly associated with the probability of financial distress for Greek listed firms but unreported results show that the ratio of sales-to-total assets is insignificant as a predictor of bankruptcy for Greek private firms.
- 12.
Recall from earlier that the Greek debt crisis dummy variable takes on the value 1 from 2009 to 2011, zero otherwise.
- 13.
We would like to thank an anonymous referee for suggesting this.
Notes
Acknowledgements
We would like to thank the anonymous referees for helpful and thoughtful comments that have improved the paper. We would also like to thank Heather Gibson and seminar participants at the Economic Research Department of the Bank of Greece for their valuable comments.
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