International Journal of Advanced Research in
Computer Science and Software Engineering
Research Paper
Available online at:
www.ijarcsse.com
Analysing Variable Benchmark DEA: A Comparative Study and
Empirical Evidence
Ayan Mukhopadhyay* Ankit Narsaria Suman Tiwari Bhaskar Roy Karmaker Cognizant Technology Solutions IIM, Shillong IIFT, Kolkata RCCIIT, Kolkata India India India India
Abstract - Bankruptcy prediction from a paradigm of multiplicity of methodologies is very imperative to evaluate the relative performance of a particular method. This paper attempts to investigate the performance of DEA (Data Envelopment Analysis), namely, Variable Benchmark DEA with that of popular methods particularly neural network (namely, multilayer perceptron) and discriminant analysis on Indian data. We note that Indian data has never been explored in this context, to the best of our knowledge. Also, empirical evidence of Variable Benchmark DEA from a comparative perspective as bankruptcy predictor is a rarity. Our result shows, performance of Variable Benchmark DEA is at par with other methods in terms of prediction capability of bankruptcy.
Keywords - Data Envelopment Analysis, Variable Benchmark DEA, Bankruptcy, Multi-Layer Perceptron, Neural Networks, Multiple Discriminant Analysis
I. INTRODUCTION
As pointed out by [1], the study of bankruptcy appeals equally to sociologists, political economists and jurists. Bankruptcy, its history and its study has drawn interest of many and is well studied in literature. As described by [2], Bankruptcy is an integrated legal solution to the problem of overwhelming debt. [3] highlights that the first official law on bankruptcy was passed in the 1542 in England and goes on to describe bankruptcy from the Indian perspective. It also states that the laws of bankruptcy are different in different countries. [1] also states that it is impossible to define bankruptcy in a specific manner that will apply with equal accuracy to different nations, periods and people. Every bankruptcy law, however, no matter when or where devised and enacted, has at least two general objects in view. It aims, first, to secure an equitable division of the insolvent debtor's property among all his creditors, and, in the second place, to prevent on the part of the insolvent debtor conduct detrimental to the interests of his creditors. Assessment of firms‟ financial health is of great importance because the ill performance of a firm incurs direct and indirect cost on the firm‟s stakeholders. The prediction of bankruptcy is therefore widely popular and has also been studied several times. [4] suggests that bankruptcy prediction dates back to 1930s when ratio analysis was used to predict future bankruptcy. Since then, numerous other prediction mechanisms have been suggested.
This paper analyses Variable Benchmark DEA as a predictor for corporate bankruptcy by comparing its performance with other prevalent methods. The choice of the data sample is interesting from an empirical perspective because despite the significant number of reported cases of bankruptcy, there has been little study on the instances of Indian bankruptcy cases. Also, the analysis of Variable Benchmark DEA from a comparative perspective is a rarity. In this paper, we analyse the comparative capability of Variable Benchmark Data Envelopment Analysis by exploring Indian data. As a classifying technique, DEA has several advantages. It is non-parametric in approach. It gives a single measure of performance taking multiple dimensions of corporate aspect of a firm. There is no assumption of a-priori functional form of inputs and outputs correspondence. It also has the capability to solve inverse classification problem. Thus, DEA as a methodology is ideal for use in early detection of financial distress. This paper attempts to apply the DEA technique to Indian cases of bankruptcy with empirical objective and also tries to assess its comparative performance with other methods – MLP (Multi-Layer Perceptron) and MDA (Multiple Discriminant Analysis). MDA is a very common technique for bankruptcy study whereas MLP is an upcoming technique.
The rest of the paper is organized as follows. Section 2 is a review of bankruptcy studies from methodological perspective. It also provides a review of comparative studies made regarding prediction of corporate bankruptcy. Section 3 describes the methodologies that we have adopted in this study. Section 4 describes the sample data and the variables chosen. Results and discussions are done in section 5. Section 6 concludes and highlights some of the future directions for further studies.
II. REVIEW OF LITERATURE
The study of prediction of bankruptcy started in the beginning of the 1930s. Univariate study was the major basis of the research [4]. In 1968, multivariate study regarding bankruptcy was published by [5]. A comprehensive review, provided by [6] categorized the methodologies into statistical models, artificially intelligent expert system models and theoretic models. Statistical models include Univariate Analysis ([7], [8]), Multiple Discriminant Analysis (MDA) ([5], [9]), Linear Probability model ([10], [11], [12]), Logit model ([10], [11]), Probit model ([10], [11 ]), Cumulative Sums (CUSUM) procedure ([13], [14]) and Partial Adjustment Process ([12], [15]). Artificial Intelligent Systems consist of
September - 2013, pp. 910-916 Decision Tree based model, Case Based Reasoning (CBR) model ([19]), Neural Network based model ([17], [18]), Genetic Algorithm based model ([19], [20] and Rough Sets model ([21], [22]. Theoretic category of models includes Balance Sheet Decomposition measure (BSDM) ([23], [24]), Gambler‟s Ruin theory ([8], [25]), Cash Management theory and Credit Risk theory ([26]). As pointed out by [6], Data Envelopment Analysis is not an element of any of the categories mentioned above. DEA as a classifier is studied in [27], [28], [29], [30], [31], [32], [33], [34] and [35]. Among these nine studies, the last five studies are direct applications of DEA as a potential method for prediction of bankruptcy. This paper uses the techniques from [32] and [36] to assess bankruptcy of Indian firms. The study of different models for the prediction of bankruptcy from a comparative perspective has attracted attention of many researchers. Table 1 lists the studies that focussed on comparing different methodologies used for the prediction of bankruptcy.
TABLE 1
REVIEW OF COMPARATIVE STUDIES
Author (Year) Methodologies Compared
Robert A. Collins (1980) Comparison between using data from one period before failure and more periods
James Scott (1981) Comparison of Empirical Predictions and Theoretical Models J. Efrim Boritz, Duane B. Kennedy (1995) Ways of training Neural networks : Back-Propagation and
Optimal Estimation Theory Guoqiang Zhang, Michael Y. Hu, B Eddy Patuwo,
Daniel C. Indro (1997) Neural Networks and Logistic Regression Models
Hongkyu Jo, Ingoo Han (1997) Case-Based Reasoning, Neural Networks, and Discriminant Analysis
Vineet Agarwal, Richard Taffler (2008) Market-based and Accounting-Based Prediction Models
I.M. Premachandra, Gurmeet Singh Bhabra,
Toshiyuki Sueyoshi (2009) DEA and Logistic Regression
Toshiyuki Sueyoshi, Mika Goto (2009) DEA and DEA-DA (Discriminant Analysis) Maryam Khalili Araghi, Sara Makvandi (2012) DEA, Logit and Probit Models
III. METHODOLOGIES
Discriminant analysis (DA), a statistical method of classification, was first used by [5] to differentiate between bankrupt and non-bankrupt firms. It was the first statistical method used for the purpose. Also known as Altman Z-score, the method uses a linear combination of independent variables to assign a “score” to each firm in the training set. Depending on a cut-off point, this score is then used to discriminate between bankrupt and non-bankrupt firms. However, the method‟s performance for out-of sample firms was weak despite its classification power being strong for firms in the sample.
A multi-layer perceptron (MLP) is a feed-forward artificial neural network that can even distinguish between data that is not linearly separable. It maps a set of inputs to a set of outputs using neurons (processing elements). A directed graph is constructed with multiple layers of neurons with each neuron having a non-linear activation function and each layer connected to others through weights (called synaptic weights). At each neuron a simple weighted sum of the inputs is computed and depending on the activation function, it provides inputs to the next layer of neurons. Weights are adjusted on the basis of the error when the expected and actual output are compared. [40] and [41] developed these learning rules. The relationship between DA and MLP has been established in [37] and their classification powers have been compared in [38] and [39].
Data Envelopment Analysis (DEA) is a mathematical programming method that estimates the best practice production frontier by extending Farrell efficiency. DEA was first developed in [42]. DEA is a non-stochastic and nonparametric fractional linear programming approach. When „j‟ units consume „i‟ inputs (x) to produce „r‟ outputs (y), the efficiency of the j0th unit is computed as a solution to the LPP-
Maximize Subject to
September - 2013, pp. 910-916 (1)
For all j, v, u ≥ Ɛ
Since the problem involves maximizing the output, the model is known as output-oriented DEA. The units on the frontier are considered efficient while those enveloped by the frontier can increase their outputs to reach the frontier. The best performers are thus on the best practice frontier. A variable benchmark model of the DEA algorithm is suggested in this paper for the purpose of classification. [44] has suggested that observations belonging to the same group should have the same production possibility set. These are also dominated by the same benchmarks which form a piecewise frontier. Two different frontiers generated in two different groups can be used for the purpose of classification.
The goal, in case of discriminating between non-bankrupt and bankrupt firms, is to identify the bad performers rather than the good firms. The frontier used for classification, is hence, one that identifies the poor performers. The strategy is to identify variables that reflect poor utilization of resources or are unwelcome. The variables used for evaluating the frontier of non-bankrupt firms, for instance, are those that reflect poor financial health and indicate failure. The opposite is true for bankrupt firms as we are interested in finding the “best” firms that failed. Once the benchmarks have been identified, all the firms in the training set are evaluated using the following model –
Minimize δ (2)
Subject to
Here „x‟ represents the inputs and „y‟ the outputs whereas E* is the identified benchmarks and p and r represent the number of inputs and outputs respectively. It has been suggested in [44] that a layering or peeling technique be used where frontiers are evaluated and firms on the frontier are removed. This process is iterated until two distinct hyper planes are identified that dominate disjoint PPS‟s. These hyper planes can now be used for the purpose of classification of the test data set.
IV. POPULATION AND SAMPLE
Our initial sample consists of 105 non-bankrupt and 14 bankrupt firms from database of The Centre for Monitoring Indian Economy (CMIE), which is an independent economic think-tank headquartered in Mumbai, India. The firms considered have filed for bankruptcy either in 1996 or 1997. Our sample does not contain matched pair of instances of bankrupt and non -bankrupt firms, necessarily. It is kind of a mixed sample to prevent loss of information as mentioned by [32]. In real world, the ratio of healthy firms to bankrupt firms is very high, somewhat like 100 to 1 for public companies. Also, we need to mention that our database contains a diverse range of industries. Our intention to use such a sample is to judge the robustness of other methods and the performance of DEA as a tool to assess bankruptcy. We have taken commonly used variables which are used to profile the strength and weakness of financial health of a firm. The variables used in this paper are common with those used by [5]. Table 2 indicates the variables used by different studies regarding bankruptcy.
TABLE 2: REVIEW OF VARIABLES USED
Author (Year) Variables Used
Altman (1993)
• Working Capital / Total Assets • Retained Earnings / Total Assets
• Earnings Before Interest and Tax / Total Assets • Market Value of Equity / Total Liabilities • Sales / Total Assets
Altman (1993)
• Working Capital / Total Assets • Retained Earnings / Total Assets
• Earnings Before Interest and Tax / Total Assets • Market Value of Equity / Total Liabilities • Sales / Total Assets
• Stability of Earnings
• Earnings Before Interest and Tax /Interest Expense
• Current Ratio
• Common Equity / Total Capital
Ward (1995) •Lower operating payment outflows
•Long term investment inflows + Capital assets inflows
•Long-term financing inflows • Short-term financing inflows I.M. Premachandra , Gurmeet Singh Bhabra, Toshiyuki Sueyoshi
(2007)
• Total debt/ Total Assets • Current Liabilities/ Total Assets
September - 2013, pp. 910-916 • Cash flow/ Total assets.
• Net income/ Total assets. • Working capital/ Total assets. • Current assets/ Total assets.
• Earnings before interest and Taxes / Total assets. • Earnings before interest and taxes/ Interest A description of the variables used in this paper is as follows –
• Current Ratio - A liquidity ratio that measures a company‟s ability to pay short-term obligations. The ratio is given by:
• Net Working Capital to Total Assets - Net Working Capital to Total Assets ratio, is defined as the net current assets (net working capital) of a company expressed as a percentage of its total assets. Therefore, the formula is:
• Return on Assets - It is an indicator of how profitable a company is relative to its total assets. ROA gives an idea as to how efficient management is at using its assets to generate earnings. ROA is displayed as a percentage. The formula for the same is -
• Market to Book Ratio - It is a ratio used to calculate a firm‟s market value to its book value. It is given by -
• Interest Coverage Ratio - A ratio used to determine how easily a company can pay interest on outstanding debt. The interest coverage ratio is calculated by dividing a company‟s earnings before interest and taxes (EBIT) of one period by the company‟s interest expenses of the same period. It is given by -
• Total Debt Ratio - A ratio that indicates what proportion of debt a company has relative to its assets. The measure gives an idea to the leverage of the company along with the potential risks the company faces in terms of its debt-load. It is given by -
All the variables used for the analysis are taken related to immediate preceding year of bankruptcy. The descriptive statistics of the variables are given in Table 3, both for the group of bankruptcy and non-bankruptcy. The Wilcoxon‟s rank sum test indicates that the median of all the variables are significantly different. The variable EBDIT (Earnings before Depreciation, Interest and Taxes) was excluded from the analysis, as it did not have significant difference between the two groups. Now, to select the input and the output variable among the set of variables we followed the approach found in [32]. Current ratio, Working Capital to Total Assets, Return on Assets, Market to Book ratio and Interest Coverage ratio are positive in nature and contribute to better financial health of a firm. On the other hand, the Total Debt ratio is opposite in nature. So while evaluating the output oriented negative DEA model for identifying the frontier from the non-bankrupt firms, we took Total Debt ratio as output and Current ratio, Working Capital to Total Assets, Return on Assets, Market to Book ratio and Interest Coverage ratio as inputs. The opposite was done while identifying the frontier from the bankrupt firms. We also mention that for other models of MDA and MLP, no such distinction is needed among the variables. All the variables are considered of the same nature for predicting the financial health of a firm.
The models, once trained were then put to test using another set of data. The test dataset consists of 38 companies - 29 non bankrupt and 9 bankrupt. The test data is acquired from the same source and year as the dataset used to construct the initial sample. A description of the results is summarized in the next section.
TABLE 3:DESCRIPTIVE STATISTICS OF VARIABLES USED Variables --> Current ratio Net Working Capital/Total Assets Return on Assets Market to Book ratio Interest Coverage ratio Total Debt ratio Bankrupt firms Mean 3.134 49.72 12.996 1.162 11.3237 1.67 Median 1.7 45.89 14.21 0.595 11.327 0.98 Standard Deviation 4.816 10.235 6.4236 1.683 0.5651 0.748
September - 2013, pp. 910-916 Non-Bankrupt firms Mean 1.393 15.072 25.0212 1.348 14.7734 11.308 Median 1.27 14.325 24.095 0.42 12.9932 2.585 Standard Deviation 0.397 9.484 8.8872 3.678 8.3668 57.196 Wilcoxon‟s Rank Sum Test
Z score 6.21282 11.312 8.89 5.2161 4.7157 8.793
P value 5.204e-10 1.44e-29 5.97e-19 1.826e-07 2.404e-06 1.45e-18 V. RESULTS
Results show that variable benchmark DEA and MDA outperform MLP in correctly predicting bankruptcy. The first combination of frontiers – identified separately from the bankrupt and the non-bankrupt firms forms a couple of distinct boundaries that successfully differentiates between the bankrupt and non-bankrupt firms included in the training sample. These are subsequently used on the test dataset. The performance of variable benchmark DEA and MDA is observed to be almost identical. They result in no type I error. However, a small percentage of type II error occurs in both the methods. MLP, on the other hand, correctly identifies all the non-bankrupt firms resulting in no type II error. A summary of the errors and the accuracies of the methods are given in Table 4. We find, the performance of variable benchmark DEA is at par with the other two methods chosen as far as the accuracy of prediction is concerned.
TABLE 4
RESULTS
Method Type 1 Error Type 2 Error Accuracy Variable Benchmark DEA - 3.44% 96.55%
MDA - 3.44% 96.55%
MLP 11.11% - 89.89%
However, it is vital to appreciate the aspect of costs of type I and type II errors rather than numerical accuracy in the perspective of prediction. The size of the loan and the recovery rate determine the cost of type I error (loss resulting from a company defaulting on a loan). As suggested by [32], the amount of loan recovered depends upon the nature of the debt and where it ranks among the obligations of the failed company. On the other hand, the cost of a Type II error (the loss represented by the revenue the bank would have received if it had made the successful loan) depends on the spread between the risk free interest rate and the foregone rate of return on the rejected loan. Therefore, the cost of type I error is a lot more than that of type II error. Hence, in terms of the total cost of errors, variable Benchmark DEA and MDA outperform MLP.
The variable bench mark DEA can be successfully applied to predict bankruptcy even when dataset comes from a diverse group of industries. This indirectly indicates about the robustness of the method itself. The following section discusses the conclusions and future scope of study.
VI. FUTURESCOPE AND DISCUSSIONS
The study establishes one more use of potential use of DEA, more specifically variable benchmark DEA as a potential technique for bankruptcy assessment. The classification accuracy in within-sample cases after finding two hyper planes that can be used for classification is 100% for bankrupt firms. It should also be noted that the Asymmetric DEA model, as suggested by [45], uses the same idea as variable benchmark DEA but applies a peeling technique to identify the optimal combination of hyper planes and focuses on minimizing the total misclassification cost and thereby recognizes the importance of avoiding type I errors over type II errors. The misclassification cost of other methods should be compared to that of Asymmetric DEA. The DEA method has the capability to classify and assess the state of financial health of a firm in a very computationally efficient manner without estimation of parameters as done in the other methods. Therefore it can be used as a ready reference for the assessment of firms from investment perspective. The major shortcoming is that it does not have the capability of prediction as found in the other methods. Even the existing dynamic DEA techniques are not suitable for bankruptcy assessment as they cannot handle negative values of variables. So, incorporation of time horizon factor into DEA methods regarding bankruptcy assessment can be a potential future research agenda. The performance of the adopted DEA method can be investigated with other existing econometric methods, DEA methods and hybrid methods. Also, we need to evaluate the capability of the methods in real life scenario of decisional cases and ex ante planning.
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