Interfaces with Other Disciplines
Bankruptcy theory development and classification via genetic programming

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Abstract

Bankruptcy is a highly significant worldwide problem with high social costs. Traditional bankruptcy risk models have been criticized for falling short with respect to bankruptcy theory building due to either modeling assumptions or model complexity.

Genetic programming minimizes the amount of a priori structure that is associated with traditional functional forms and statistical selection procedures, but still produces easily understandable and implementable models. Genetic programming was used to analyze 28 potential bankruptcy variables found to be significant in multiple prior research studies, including 10 fraud risk factors. Data was taken from a sample of 422 bankrupt and non-bankrupt Norwegian companies for the period 1993–1998. Six variables were determined to be significant.

A genetic programming model was developed for the six variables from an expanded sample of 1136 bankrupt and non-bankrupt Norwegian companies. The model was 81% accurate on a validation sample, slightly better than prior genetic programming research on US public companies, and statistically significantly better than the 77% accuracy of a traditional logit model developed using the same variables and data. The most significant variable in the final model was the prior auditor opinion, thus validating the information value of the auditor’s report. The model provides insight into the complex interaction of bankruptcy related factors, especially the effect of company size. The results suggest that accounting information, including the auditor’s evaluation of it, is more important for larger than smaller firms. It also suggests that for small firms the most important information is liquidity and non-accounting information.

The genetic programming model relationships developed in this study also support prior bankruptcy research, including the finding that company size decreases bankruptcy risk when profits are positive. It also confirms that very high profit levels are associated with increased bankruptcy risk even for large companies an association that may be reflecting the potential for management to be “Cooking the Books”.

Introduction

Corporate bankruptcy affects the economy of every country and is monitored by policy makers seeking to promote economic growth. For example, US business bankruptcy filings declined from 53,931 in 1997, to 44,196 in 1998, and to 37,564 in 1999 (American Bankruptcy Institute, 2001), a period during which growth in the US economy, as measured by gross national product, increased from 3.4% to 4.1% (Bureau of Economic Analysis, 2001).

At the level of the individual firm, the capital markets react to data about going concern prospects for firms. For example, both Beaver (1968) and Altman (1969) showed a negative stock market price reaction as a firm approached failure. Accordingly, the International Accounting Standards (IAS) require, “When preparing financial statements, management should make an assessment of an enterprise’s ability to continue as a going concern.” (International Accounting Standards Board, 2002, IAS No. 1, paragraph 23). If there are significant doubts about a company’s bankruptcy/non-bankruptcy status then the IAS requires information about those uncertainties to be disclosed. Disclosure responsibilities also extend to a company’s auditors. International Standard on Auditing (ISA) section 570 (International Auditing and Assurance Standards Board of International Federation of Accountants, 2003) requires the auditor to modify the auditor’s report by adding an emphasis of matter paragraph if there is significant doubt about the entity’s going concern status and adequate disclosure is made in the financial statements. If adequate disclosure is not made in the financial statements, the auditor should express a qualified or adverse opinion. Thus, auditors are required to signal stakeholders about going concern problems. Although going concern problems can result in outcomes other than bankruptcy, this outcome is probably the one of most concern to stakeholders.

Bankruptcy prediction has been a major topic in accounting and finance for at least a century. Early research focused primarily on univariate models such as individual ratios while later research turned to multivariate models. Recent research has turned to modeling techniques like recursive partitioning, fuzzy logic, and rough sets. Despite a long research history, there is no bankruptcy prediction model based primarily on bankruptcy theory which is generally accepted. Additionally, as noted by Dimitras et al. “A unifying theory of business failure has not been developed …” (1996, p. 487). To improve this situation either greater bankruptcy prediction research convergence or more theory building is needed.

Most prior bankruptcy research utilized techniques producing descriptions for classifying objects into classes based on the objects’ properties. One of the acknowledged difficulties with this type of inductive inference is its’ open-endedness which stems from the fact that there is no natural limit to the level of detail which may be used to describe reality. For example, while bankruptcy models produced by techniques such as neural networks, recursive partitioning, and rough sets theory can produce reasonable classification accuracy, they provide extremely detailed models which are difficult to generalize or develop theory from. Further, multivariate techniques are inadequate according to Michalski because, “The widely used traditional mathematical and statistical data analysis techniques, such as regression analysis, numerical taxonomy, or factor analysis are not sufficiently powerful … for the task of … detecting interesting conceptual patterns or in revealing structure in a collection of observations.” (Michalski, 1983, pp. 112–113). For example, Chen and Shimerda investigated the issue of bankruptcy conceptual patterns by analysis of 26 prior studies involving 65 accounting ratios and other financial items. They found that although seven factors could describe the ratios, “… the question of which ratio should represent a factor has yet to be resolved.” They concluded that since each ratio contains common as well as unique information, … selection of the best representative ratio for a factor is not independent of the ratios selected for other factors.” (Chen and Shimerda, 1981, p. 59). Thus, there is a demand for theory building, including more insight into the pattern and interaction between bankruptcy classification factors. Genetic programming (Koza, 1992) is a recently developed technique that permits a researcher to find a solution to a problem without having to prespecify the type of model. This means the solution can be any model describable by mathematics. The aim is to let the data speak for themselves as far as possible, by minimizing the amount of a priori structure imposed by functional forms and statistical selection procedures. Koza comments that “Genetic programming is fundamentally different from other approaches to artificial intelligence, machine learning, adaptive systems, automated logic, expert systems, and neural networks in terms of (i) its representation (namely programs), (ii) the role of knowledge (none), (iii) the role of logic (none), and (iv) its mechanism (gleaned from nature) for getting to a solution within a space of possible solutions.” (Banzhaf et al., 1998, p. viii). However, it should be noted that there is both logic and knowledge in the programming language which is used to implement the solution mechanism.

Recent research using data from US companies showed that genetic programming is extremely powerful and could be used to generate a simple, yet feature rich model providing new insights on bankruptcy prediction and, therefore, on bankruptcy theory development (McKee and Lensberg, 2002). The current research attempts to improve our understanding of bankruptcy through research convergence and improved insight into the pattern of bankruptcy classification factors. The current study extends this prior research by developing a bankruptcy prediction model using genetic programming for a very broad sample of Norwegian companies and then compares features of the Norwegian and US models.

This research does differ significantly from prior research by (1) the use of non-US data, (2) the analysis of a broad set of variables that were significant in multiple prior studies, (3) the inclusion of fraud prediction factors, (4) the use of primarily private companies, and (5) the use of a longer prediction interval. We believe this research provides important insights for both bankruptcy theory development and bankruptcy prediction.

Section snippets

Literature review

A wide range of international research has been conducted on bankruptcy prediction. In this section, we review key literature in the following areas:

  • The going-concern concept

  • US bankruptcy research directions

  • International bankruptcy research

  • Norwegian bankruptcy research

Research design

Since genetic programming is quite different from classical statistics, the research approach requires some explanation. This section discusses the following main elements of the research approach:

  • General explanation of genetic programming

  • Variable selection process for this study

  • Data selection for this study

  • Variable reduction procedures

  • Final model development

Results

The 500 models generated in the final model development had hit rates of approximately 82% on the training sample and 81% on the validation sample. We then randomly selected one of the models for further analysis. It had a hit rate of 81.7% on the training sample and 80.9% on the validation sample. Table 5 presents the summary statistics for the 500 models.

Further analysis was conducted in order to determine if the model selected was appropriately representative of the 500 models. Our goal was

Summary and conclusions

Bankruptcy is a highly significant worldwide problem that affects the economic well being of all countries. The high social costs incurred by various stakeholders associated with bankrupt firms have spurred searches for better theoretical understanding and prediction capability.

This research used genetic programming to further improve our understanding of both bankruptcy theory and prediction by extending genetic programming to a different national environment. This research differed

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