The Dependent Variable and Discrete Response Models

This study compares firm failures across different European countries and also across different countries and regions of the United Kingdom. The most common approach that quantitative studies in this research area adopt for the definition of their dependent variable, is the binary classification (see for example Altman 1968; Altman et al, 2010). This means that, at the cross-section, firms can be either failed or not failed.

However, this study uses more classifications for the failed firms. All eventually failed firms in the sample have been classified into three categories depending on the point in time of the observation. There are three possible outcomes for each firm-year observation in the sample and these outcomes can be denoted with a number that can be linked with their status.

i. The first category includes firms that have not failed at the given year when the observation takes place. This means that these firms are not in financial distress and have not been under insolvency procedures for liquidation at that time. Such firm-year observations have an event_failure status of zero.

ii. The second category includes firms that are in financial distress in a given year. These are firms that are not under liquidation but they have negative equity which means that their total liabilities exceed their total assets. For

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the year when these firms are in financial distress their firm-year observation has the event_failure status of one.

iii. Finally, the third category relates to firms that are insolvent and are liquidated (in some countries the equivalent term is bankrupt) or are in the process of liquidation in the year observed. Such firm-year observations have the event_failure status of two.

The chosen states of the dependent variable in the present study have been established with a clear rationale. Non-failed firms are financially healthy firms that have no particular adverse financial or legal information against them at the time of observation. Financially distressed firms, are weak financially (being in negative equity) but their performance is not at a stage where their creditors or their owners have not entered the legal process of insolvency that will lead to the liquidation of the firm (at the time of observation). With little hope for the firm to perform well again, it is expected that liquidation is the last resort for creditors and owners. This classification is similar to the classification that Tsai (2013) adopted when researching corporate financial distress and bankruptcy, and to Johnsen and Melicher (1994). There is, however, a difference in that their “financially distressed” category contained firms that had defaulted on their loan obligations or that were reducing dividend payments, whereas this study uses negative equity as the measure of financial distress. A further difference is that their studies were focused on listed companies whereas this analyses SMEs. Given the three possible states of the dependent variable, the traditional binary classification of the dependent variable would not be sufficient to accommodate effectively three potential states for each firm. Instead, multinomial responses are preferable because they are able to accommodate multiple outcomes. Multinomial dependent variables can use similar econometric techniques as are available for binary dependent variables although with certain modifications, which are explained in the following sections.

One significant characteristic of multivariate discrete-responses is that the dependent variable may be either ordered or unordered in nature. In situations where there is no natural ordering of the alternative stages of the dependent variable, unordered models should be preferred. The key characteristic of

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unordered responses is that neither their chosen values, nor their particular order signals a specific status for the dependent variable whereas they have no effect on the estimation inference or interpretation (Wooldridge, 2010).

The second category of multinomial responses is the ordered response. This type of ordered response dependent variable is effectively used in ordered response (also known as discrete-choice) models which are effectively generalizations on the simple binary models (Brooks, 2008) and dependent variables specifications. The ordered response (also known as ordinal response) can take values {0,1,2,3…n} for some known value of n (Wooldridge, 2010). In this case, the numbers that are selected as states of the dependent variable cannot be arbitrary and while they do not have to have a specific meaning themselves, they need to have an ordered and specified hierarchy between them. The dependent variable should therefore behave in an ordinal fashion with respect to each predictor (Harrell, 2015).

When the stages of the dependent variable have a logical or natural order, ordered response models should be preferred. For example, when there is a monotonic increase or decrease in the credit quality of a firm, this order should be reflected in the dependent variable (Brooks, 2008). If the credit quality for a company is ranked in a scale from zero to six where zero is the lowest ranking and six is the highest ranking, the fact that six is better than five or zero contains important information for the credit quality of the company even if the chosen numbers of the dependent variable have only ordinal meaning (Wooldridge, 2010). However, with an ordered response dependent variable, one cannot make inferences with regards to the difference between the ordinal scales. For example one cannot conclude that the difference between credit quality rankings four and two is somehow twice the difference between one and zero (Wooldridge, 2010). That means that in substantive terms the difference between zero and two on the coded response may be different from the difference between four and six (Jackman, 2000).

In statistical terms, one can check the consistency of the order if there is an independent variable X that is related to the log odds of an event Y (that is, the

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dependent variable). One can then plot the mean of X stratified by the alternative levels of Y which should be in a consistent order (Harrell, 2015).

Given the nature of the research, the ordered response fits better the definition of this study’s dependent variable. Selecting an unordered response would result in loss of efficiency with the use of unordered response dependent variable (Johnsen and Melichen, 1994) models. In the context of this study’s data, one would expect that a non-failed firm (event_failure=0) is “better” than a firm into financial distress (event_failure=1) which is “better” than a firm into liquidation (event_failure=2). Conceptually, ordered response models have the ability to classify different states in a firm’s financial situation. This is a useful characteristic because not all firms that are financially distressed end up bankrupt and not all bankrupt firms have been in financial distress. In the context of ordered response dependent variables, it is important that the discrete responses should not be close substitutes as this will increase the errors in the model (Johnsen and Melicher, 1994). This is a requirement that complies with the nature of the data used in this study. Therefore, there is some usefulness to treat financial distress and liquidation differently as two distinct statuses of firms’ failure.

In the quantitative literature on firm failure there have been examples of ordered response dependent variables although mostly from the corporate failure literature (Johnsen and Melichen, 1994; Tsai, 2013) as opposed to the SMEs literature. Nevertheless, the validity of the ordered response dependent variable model remains the same, from a statistical perspective. Johnsen and Melichen (1994) used an ordered-response approach, provided evidence that a further category of financially weak companies that sits between the non-bankrupt and the bankrupt firms is a valid option, and it may result in better model accuracy. In their research, the particular classification of the dependent variable reduced classification errors from the econometric model. In addition, the authors noted that in the large companies of their sample, the three states of financial health of the companies appeared to be statistically independent.

In summary, there is evidence from the literature that considers a binary status for the dependent variable. However, given the comparative nature of this study and the inclusion of alternative states for the failed firms, a multinomial dependent

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variable will be used. Given the directional nature of the failure event (where a liquidated firm is in a worse state than a firm which is under financial distress), the ordered response specification is chosen for the dependent variable. This specification will be used for the modelling approaches that are discussed in the following sections.