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Predicting Firm Financial Distress: A Mixed Logit Model

Stewart Jones David A. Hensher

The University of Sydney ABSTRACT: Over the past three decades the literature on financial distress prediction has largely been confined to simple multiple discriminant analysis, binary logistic or probit analysis, or rudimentary multinomial logit models (MNL). There has been a conspicuous absence of modeling innovation in this literature as well as a failure to keep abreast of important methodological developments emerging in other fields of the social sciences. In particular, there has been no recognition of major advances in discrete choice modeling over the last 15 years which has increasingly relaxed behaviorally questionable assumptions associated with the IID condition and allowed for observed and unobserved heterogeneity. In contrast to standard logit, the mixed logit model fulfils this purpose and provides a superior framework for explanation and prediction. We explain the theoretical and econometric underpinnings of mixed logit and demonstrate its empirical usefulness in the context of a specific but topical area of accounting research, financial distress prediction. Comparisons of model-fits and out-of-sample forecasts indicate that mixed logit outperforms standard logit by significant margins. While mixed logit has valuable applications in financial distress research, its potential usefulness in other areas of accounting research should not be overlooked. Keywords: Financial distress prediction; Mixed logit; Multinomial logit. Data Availability: All data available from public and commercial sources identified in the paper. We appreciate the helpful comments of two anonymous referees, participants at the University of Sydney research seminar series, Bill Greene, Ken Train, Rob Stambaugh, Mike Bradbury, David Johnstone, Paul Bahnson, Raj Srivastava and Marcus O’Connor.

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I. INTRODUCTION The prediction of firm financial distress has been of considerable interest to

accountants and financial economists over the last three decades (Altman 2001). The continual development of conceptually richer and more accurate forecasting models is of importance to regulators, practitioners and academics (Shumway, 2001). Distress forecasts are now widely used for a range of purposes, including monitoring of the solvency of financial and other institutions by regulators, assessment of loan security, going concern evaluations by auditors, the measurement of portfolio risk, and the pricing of defaultable bonds, credit derivatives and other securities exposed to credit risk (Scott, 1981; Shumway, 2001; Altman, 2001; Duffie and Singleton, 2003). Given the broad interest in distress prediction, an improved modeling approach can enhance the state of art in this field as well as providing a new analysis technique having potentially broad application to other areas of accounting research.

While an extensive literature on financial distress prediction has emerged over the past three decades, innovative modeling techniques have been slow to develop. In fact, many commonly used techniques would rate as primitive and dated in other fields of the social sciences. Much of the literature has relied on relatively simplistic multiple discriminant analysis (MDA), binary logistic or probit analysis or rudimentary multinomial logit models (MNL) (see e.g., Altman 1968; Altman, Haldeman, and Narayanan, 1977; Ohlson, 1980; Zmijewski, 1984; Lau, 1987). The relative merits of binary logit, MDA and to a lesser extent probit and tobit models have been discussed in an extensive literature (see e.g., Efron, 1975; McFadden, 1976; Ohlson, 1980; Jones, 1987; Maddala, 1991). Leclere (1999) advanced the literature by providing an interpretative analysis of accounting research which has employed some form of n-chotomous qualitative response variable (such as multinomial logit and ordered probit) (see also Elliot and Kennedy, 1988; and Kennedy, 1992). Methodological discussions are yet to progress beyond this point. The major limitation of the financial distress literature (and other related accounting literatures) is that there has been no recognition of the major developments in discrete choice modeling over the last 15 years which has increasingly relaxed behaviorally questionable assumptions associated with the IID condition (independently and identically distributed errors) and allowed for observed and unobserved heterogeneity.1 The latter in particular has been shown in other fields of the social sciences to have an important role to play in the understanding and prediction of choice outcomes. This literature is reviewed in Louviere, Hensher and Swait (2000), Hensher, Louviere and Swait (1999), Train (2003) and Hensher, Rose and Greene (2005).

This study uses an advanced discrete choice model known as mixed or random parameter ordered logit. The mixed logit design is one of the latest and most advanced techniques now being used in many fields of the social sciences to model discrete choices or outcomes. We seek to explain the conceptual underpinnings of the mixed logit model and how it improves on standard logit.2 We also attempt to demonstrate the empirical usefulness of the model in the specific but topical area of financial distress prediction, a field of inquiry highly amenable to this form of analysis. Using a broad cross section of financial variables employed by researchers over the past thirty years, we compare the predictive performance of mixed logit with standard logit in terms of model-fit and out-of-sample forecasting accuracy.3

The remainder of this paper is organized as follows. Section II discusses the theoretical significance of mixed logit as well as the econometric properties of this model. Section III outlines the research methodology. Section IV provides the results

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and Section V addresses further empirical considerations relating to the estimation and observed performance of the mixed logit model. Concluding remarks and directions for future research are discussed in Section VI.

II. MIXED LOGIT: THEORETICAL AND ECONOMETRIC

CONSIDERATIONS Conceptual Foundations of the Mixed Logit Model

Mixed logit is the latest among a new breed of econometric models being developed out of discrete choice theory (Train, 2003). Discrete choice theory is concerned with understanding the discrete behavioral responses of individuals to the actions of business, markets and government when faced with two or more possible outcomes (or choices) (Louviere, Hensher and Swait, 2000). Its theoretical underpinnings are derived from microeconomic theory of consumer behavior, such as the formal definition of agent preferences as inputs into a choice or outcome setting as determined by the utility maximization of agents. Given that the analyst has incomplete knowledge on the information inputs of the agents being studied, the analyst can only explain a choice outcome up to a probability of it occurring. This is the basis for the theory of random utility (see Louviere, Hensher and Swait, 2000 for a review of literature).4 While random utility theory has developed from economic theories of consumer behavior it can be applied to any unit of analysis (e.g., firm failures) where the dependent variable is discrete.5

The concept of behavioral heterogeneity (individual variations in tastes and preferences), and how this impinges on the validity of various theoretical and empirical models has been the subject of much recent attention in this literature.6 However, econometric techniques to model heterogeneity have taken time to develop, despite a long standing recognition that failure to do so can result in inferior model specification, spurious test results and invalid conclusions (Louviere, Hensher and Swait, 2000; Train, 2003). Starting with the simple binary logit model, research progressed during the 1960s and 1970s to the multinomial logit (MNL) and nested logit models, the latter becoming the most popular of the generalized logit models. Although more advanced choice models such as mixed logit existed in conceptual and analytical form in the early 1970s, parameter estimation was seen as a practical barrier to their empirical usefulness. The breakthrough came with the development of simulation methods (such as simulated maximum likelihood estimation) that enabled the open-form models such as mixed logit to be estimated with relative ease (e.g., Stern, 1997).

Mixed logit and its variants have now supplanted simpler models in many areas of economics, marketing, management, transportation, health, housing, energy research and environmental science (Train, 2003). This can largely be explained in terms of the substantial improvements delivered by mixed logit over binary logistic and MNL models. Considering the case of firm failures, the main improvement is that mixed logit models include a number of additional parameters which capture observed and unobserved heterogeneity both within and between firms.7 For a mixed logit model, the probability of failure of a specific firm in a sample is determined by the mean influence of each explanatory variable with a fixed parameter estimate within the sampled population, plus, for any random parameters, a parameter weight drawn from the distribution of individual firm parameters estimated across the sample. This weight is randomly allocated to each sampled firm unless there are specific rules for mapping individual firms to specific locations within the distribution of firm specific parameters.8 In contrast, the probability of failure for an individual firm using a binary logistic or MNL model is simply a weighted function of its fixed

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parameters (i.e., assumption of homogeneous preferences) with all other behavioral information assigned (incorrectly) to the error term.9 As noted by Hensher and Greene (2003), parameter estimation in the mixed logit model maximizes use of the behavioral information embedded in any dataset appropriate to the analysis. Ultimately, these conceptual advantages afford the analyst with a substantially improved foundation for explanation and prediction.10 The important theoretical advantages of the mixed logit model are further considered in the formal specification and analysis of the model which now follows. An Ordered Mixed (Random Parameters) Logit Model

Like any random utility model of the discrete choice family of models, we assume that a sampled firm (q=1,…,Q) faces a ‘choice’ amongst I alternatives in each of T occasions. Within the context of financial distress, since firms do not choose to fail per se, we prefer to use the phrase outcome domain (or simply outcome) as the descriptor of the observed choice outcome. A firm q is assumed to recognize the full set of alternative outcomes in occasion t and to focus on business strategies designed to result in the delivery of the outcome associated with the highest utility (i.e., nonfailure). The (relative) utility associated with each outcome i as evaluated by each firm q in occasion t is represented in a discrete outcome model by a utility expression of the general form:

Uitq = ßqXitq + eitq (1)

Xitq is a vector of explanatory variables that are observed by the analyst (from any source) and include attributes of the alternative outcomes (where observed), characteristics of the firm and descriptors of the decision context in occasion t, ßq and eitq are not observed by the analyst and are treated as stochastic influences.

To provide an intuitive explanation of how equation (1) operates in an outcome setting, think of the task as being one of representing sources of variance that contribute to explaining a specific outcome. For a specific firm, equation (1) has variance potential associated with the coefficient attached to each observed characteristic (i.e., ß), to each observed characteristic itself (i.e., X) and the unobserved effects term (e). We could expand this equation out to reflect these sources of variance for three characteristics, defining ‘0’ as observed and ‘U’ as unobserved, as (dropping the q and t subscripts):11

Ui = (ß01X01 + ßu1Xu1) + (ß02X02 + ßu2Xu2) + (ß03X03 + ßu3Xu3) + ei (1a)

Each characteristic is now represented by a set of observed and unobserved

influences. In addition each parameter and characteristic can itself be expressed as some function of other influences, giving more depth in the explanation of sources of variance. As we expand the function out we reveal deeper parameters to identify. In the most restrictive (or simplistic) versions of the utility expression, we would gather all the unobserved sources together and replace (1a) with (1b):

Ui = ß01X01 +ß02X02 + ß03X03 + (ßu1Xu1+ ßu2Xu2 + ßu3Xu3 + ei) (1b)

and would collapse the unobserved influences into a single unknown by assuming that all unobserved effects cannot be related in any systematic way with the observed effects:

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Ui = ß01X01 +ß02X02 + ß03X03 + ei (1c)

Furthermore by defining a utility expression of the form in (1c) for each

alternative outcome i and imposing a further assumption that the unobserved influences have the same distribution and are independent across alternatives we can remove the subscript i attached to e. What we have is the functional form for the utility expressions of a multinomial logit (MNL) model. This intuitive discussion has highlighted the way in which an MNL model restricts through assumption the opportunity to reveal the fuller range of potential sources of influence on utility as resident throughout the full dimensionality of equation (1a). Explaining these fuller sources is equivalent to explaining the broader set of sources of observed and unobserved heterogeneity on an outcome domain.

A condition of the MNL model is that eitq is independent and identically distributed (IID) extreme value type 1.12 IID is clearly restrictive in that its does not allow the error components of different alternative outcomes to be correlated. We would want to be able to take this into account in some way. One way to do this is to partition the stochastic component into two additive (i.e., uncorrelated) parts. One part is correlated over alternative outcomes and heteroskedastic, and another part is IID over alternative outcomes and firms as shown in equation (2) (ignoring the t subscript for the present).

Uiq = β′xiq + (ηiq +εiq) (2)

where ηiq is a random term with zero mean whose distribution over firms and alternative outcomes depends in general on underlying parameters and observed data relating to alternative outcome i and firm q; and εiq is a random term with zero mean that is IID over alternative outcomes and does not depend on underlying parameters or data.

The Mixed Logit class of models assumes a general distribution for η and an IID extreme value type 1 distribution for ε.13 That is, η can take on a number of distributional forms such as normal, lognormal, and triangular. Denote the density of η by f(η|Ω) where Ω are the fixed parameters of the distribution. For a given value of η, the conditional probability for outcome i is logit, since the remaining error term is IID extreme value:

Li(η) = exp(β′xi + ηi) / ∑jexp(β′xj + ηj). (3)

Since η is not given, the (unconditional) outcome probability is this logit formula integrated over all values of η weighted by the density of η is as shown in equation (4).

Pi=∫Li(η) f(η|Ω)dη (4) Models of this form are called mixed logit because the outcome probability

Li(η) is a mixture of logits with f as the mixing distribution. The probabilities do not exhibit the well known independence from irrelevant alternatives property (IIA), and different substitution patterns are obtained by appropriate specification of f. This is handled in two ways. The first way, known as random parameter specification,

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involves specifying each ßq associated with an attribute of an alternative outcome as having both a mean and a standard deviation (i.e., it is treated as a random parameter instead of a fixed parameter). The second way, known as the error components approach, treats the unobserved information as a separate error component in the random component. We have chosen to use the former interpretation and hence the reference to a mixed or random parameter model.

The standard deviation of a ß parameter accommodates the presence of preference heterogeneity in the sampled population of firms. While one might handle this heterogeneity in the context of a fixed ß parameter through data segmentation (e.g., a different model for each industry segment) and/or attribute segmentation (e.g., separate ßs for different industry segments), in contrast to treating it all as random, the challenge of these (deterministic) segmentation strategies is in picking the right segmentation criteria and range cut-offs that account for statistically significant sources of preference heterogeneity. A random parameter representation of preference heterogeneity is more general; however such a specification carries a challenge in that these parameters have a distribution that is unknown. Alternative analytical distributions can be evaluated such as the normal, lognormal and triangular.

The identification of the parameter estimates in a mixed logit model is complex. Unlike the simple multinomial logit model which has a closed form solution and guarantees a unique globally optimal set of parameter estimates, the mixed logit model can produce a range of solutions, only one of which is globally optimal.14 In particular we now have an additional set of parameters to identify associated with the unobserved heterogeneity across the sampled firms. This information is captured in the distribution of parameters that are assigned random in contrast to fixed. To take this into account we use Bayes Rule to define the conditional distribution as equation (5) (formally derived in Train (2003)).

Hq(ß|θ) = Lq(ß)g(ß|θ)/Pq(θ) (5)

Lq(ß) is the likelihood of a firm’s outcome domain if they had this specific ß; g(ß|θ) is the distribution in the population of ßs (or the probability of a ß being in the population), and Pq(θ) is the outcome probability function defined in open-form as:

Pq(θ) = ∫ Lq(ß)g(ß|θ) dß (6)

The outcome probability in (4) or (6) cannot be calculated exactly because the integral does not have a closed form in general. The integral is approximated through simulation. For a given value of the parameters, a value of η is drawn from its distribution. Using this draw, the logit formula (3) for Li(η) is calculated. This process is repeated for many draws, and the mean of the resulting Li(η)’s is taken as the approximate outcome probability giving equation (7).

SPi = (1/R)

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R

r=∑ Li(ηir) (7) R is the number of replications (i.e., draws of η), ηir is the rth draw, and SPi is the simulated probability that a firm chooses alternative outcome i.15 There are typically constraints on the η components across alternative outcomes; in particular the values of η are the same for the calculation of the probabilities of each alternative outcome i for a specific outcome occasion.16

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An Application to Financial Distress Prediction

The mixed logit framework presented above is sufficiently general to apply to all forms of discrete outcome models with an extreme value distribution (type 1) for the IID component of the unobserved elements representing the random component of each utility expression. In the current application to financial distress prediction we propose an ordered set of alternatives and hence need to introduce the idea of an ordered logit specification.17

The ordered outcome scale adopted in this study has three levels (described in detail in the next section). Treating this (ranking) scale as if it were both continuous and an interval scale and applying ordinary least squares regression to analyze the relationship between the failure levels and the explanatory variables is not a statistically valid approach. A number of theoretical studies have questioned the validity of the linearity assumption when using a rank ordered response (e.g., Henry 1982; Winship and Mare 1984; Crask and Fox 1987). An appropriate approach which recognizes the nonlinearity of a ranking scale is an ordered response model which defines points on the observed rating scale as thresholds.

Empirical ranking scales are best viewed as discrete realizations of unmeasured continuous variables. The ordered logit model allows one to include ordinal dependent variables into the outcome model in a way that explicitly recognizes their ordinality and avoids arbitrary assumptions about their scale. The essence of the approach is an assumed probability distribution of the continuous variable that underlies the observed ordinal dependent variable. Ordered logit takes into account the ceiling and floor restrictions on models which include ordinal variables, whereas a linear regression does not.

In specifying an appropriate firm failure model, we assume that the three-point ranking scale is a monotonic transformation of an unobserved interval variable. Thus one or more values of an interval-level variable are mapped into the same value of a transformed ordinal variable. An underlying continuous variable is mapped into categories that are ordered but are separated by unknown distances. We cannot, for example, say that the difference between ranks 0 and 1 is identical to the difference between 1 and 2.

Formally, let Y* denote an unobserved (or latent) continuous variable (-∞ < Y* < +∞), and µ0 µ,..., µJ-1, µJ denote the cut-off or threshold points in the distribution of Y*, where µ0= -∞ and µJ = +∞. Define Y to be an ordinal (observed) variable such that Y = j if, and only if, µJ-1 ≤ Y* ≤ µJ; j = 1,2,...,3. Since Y* is not observed but Y is observed, its mean and variance are unknown. Statistical assumptions must be introduced such that Y* has a mean of zero and a variance of one. To operationalize the model, we need to define a relationship between Y* and Y.

The ordered outcome model is based on the following specification: There is a latent regression equation (8).

Yi* = β′xi + εi, εi ~ F(εi |θ), E(εi) = 0, Var(εi) = 1 (8)

The observation mechanism results from a complete censoring of the latent dependent variable as follows:

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Yi = 0 if Yi ≤ μ0, = 1 if μ0 < Yi ≤ μ1, = 2 if μ1 < Yi ≤ μ2, (9) ... = J if Yi > μJ-1. The probabilities which enter the log likelihood function are given by equations (10) and (11). Prob(Yi = j) = Prob(Yi* is in the jth range) (10) Prob(Yi = j) = F((μj - β′xi)) - F((μj-1 - β′xi)), j = 0,1,...,J (11) Let F(.) equal the CDF of the logistic distribution. The log likelihood function is then given by equation (12). log L = Σi log Li = Σi log Prob(Yi = yi) (12) where Yi = the theoretical random variable and yi = the observed value of Yi for firm i The first derivatives are: f((μj-1 - β′xi)) - f((μj - β′xi)) ∂log Li/∂β = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ xi F((μj - β′xi)) - F((μj-1 - β′xi)) (13) where f(.) denotes the appropriate density Λ(1-Λ) for logistic. For convenience, denote fj = f((μj- β′xi)) and Fj = F((μj- β′xi)), and likewise for j-1. By convention, f-1 = F-1 = fJ = 0, and FJ = 1. Then, ∂log Li/∂μj = (fj / (Fj - Fj-1)) and ∂log Li/∂μj-1 = -(fj-1 / (Fj - Fj-1)) . These imply that,

∂log Li/∂μm = 0 if m = -1, 0, or J. Explanatory variables can be readily incorporated into the mixed or random

parameter ordered logit model in the usual manner that they are incorporated into a regression equation. Estimates are obtained for both the parameters associated with each of the firm-specific variables, and the threshold parameters. The threshold parameters indicate the extent to which the categories of the ranking scale are equally spaced in the logit scale.18 All parameters are obtained by iterative maximum likelihood estimation, using the Davidson-Fletcher Powell optimization method with

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the first derivatives used to define the variance matrix. Starting values are obtained by ordinary least squares regression on a binary dependent variable. Sample cell frequencies on the observed rankings are used to initially divide up the real line in order to define the starting threshold values on a normalized scale. The lowest threshold is normalized to zero. The preceding expressions are summed over all outcomes. We use the BHHH estimator19 for the covariance matrix, so the second derivatives are not computed.

III. METHOD

A Three-State Classification Model This study models financial distress in three states:

State 0: non-failed firms; State 1: insolvent firms. For the purposes of this study, insolvent firms are

defined as: (i) failure to pay Australian Stock Exchange (ASX) annual listing fees as required by ASX Listing Rules20; (ii) a capital raising specifically to generate sufficient working capital to finance continuing operations; (iii) loan default, (iv) a debt/total equity restructure due to a diminished capacity to make loan repayments.21, 22

State 2: firms who filed for bankruptcy followed by the appointment of liquidators, insolvency administrators or receivers.23

Sample Selection

We develop two samples for the purposes of model estimation and validation. The estimation sample is based on firm financial distress data collected between 1996 and 2000. Over this period we collect a sample of failed firms (state 2) and a sample of firms with solvency problems (state 1). Firms were observed to fail or have solvency difficulties at different times over this period. We attempted to collect up to five annual reporting periods of data24 on all firms in categories 0,1 and 2, unless certain conditions described below were not met. The sample of nonfailed firms is drawn over the same time period range as the firms in states 1 and 2, and the proportion of failed to nonfailed firms sampled is approximately equal across each of the years the data are collected. To avoid the backcasting problem noted by Ohlson (1980), data are collected only from the financial statements already in the public domain on the date the failure is first made known to the market.25 The same procedure is followed for firms in state 1. To avoid over sampling problems and error rate biases associated with matched pair designs (see e.g., Casey and Bartczak, 1985; Gentry, Newbold and Whitford 1985; Jones 1987) we use a sample of failed and nonfailed firms which better approximates actual fail rates in practice26 (Zmijewski, 1984). This produces a final useable sample of 2,838 firm years in the nonfailed state 0; 78 firms years in state 1; and 116 firm years in state 2.27

Following the approach of Joy and Tollefson (1975), a validation sample is collected for the period 2001-2003 using the same definitions and procedures applied to the estimation sample.28 This produces a final useable sample of 4,980 firm years in the nonfailed state 0; and 119 and 110 firms years in states 1 and 2, respectively. Checks are made to ensure that failed/insolvent firms identified in states 1 and 2 for the estimation sample are not also included in the validation sample. Following a standard practice in the literature, failed/insolvent firms in the validation sample are also excluded from the estimation sample. The larger sample of nonfailed firms in the validation sample reflects a significant increase in the number of new listings on the

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ASX over this period and the fact that the more recent financial distress data was found to be relatively more complete than for the estimation sample.29

Only publicly listed firms on the ASX are included in the estimation and validation samples. Furthermore, only firms who reported cash flow information under requirements of the Approved Australian Accounting Standard AASB 1026 “Statement of Cash Flows” are included in both samples.30 Compliance with AASB standards has been mandatory in Australia under the requirements of the existing Corporations Act (1991) of the day, hence we could find very few instances of noncompliance with AASB 1026. In a very small number of cases, firms are deleted from both samples because no financial statement records could be found. Following the approach of Ohlson (1980) no firm is deleted simply because it is newly or recently listed, and some firms in both our samples only had one or two years of financial reports. Consistent with Ohlson (1980), if a firm produced its annual report after the announcement of failure, then its published financial report of the previous reporting period is used. In the estimation sample, the average lead time between the date of the previous annual report and the announcement of failure was approximately 11.2 months (and 10.4 months for validation sample) which is broadly consistent with the lead time reported in other studies (Altman, 1968; Ohlson, 1980). However, the variance was quite high, with one firm having a lead time of nearly 40 months. The median lead time was 9.1 months for the estimation sample and 8.7 months for the holdout sample.31 Table 1 shows the ‘lead time’ frequency distribution for the sample of failed and insolvent firms used in the estimation sample.

Insert Table 1 With respect to the sample of insolvent firms, we employ the same data

collection procedures used for failed firms. The financial report prior to the indication of the firm’s solvency problem is used for estimation purposes. Whether a firm experienced a solvency problem (as defined in this study) is ascertained from the analysis of the ASX’s Signal G releases.

For the estimation sample, financial statement data is collected on firms in each of the three states from four major sources: (i) Aspect Financial Pty Ltd’s Financial Analysis Database (2003) and DatAnalysis Database (2003) – two leading Australian financial database sources which contains up to 15 years of historical data on all listed companies in Australia (ii) Huntley’s Delisted Company Database (1993-1999), which contains all delisted firms in Australia up until 1999; (iii) ASX Market Comparative Analysis, 2003; and (iv) company financial statements collected from the Australian Securities and Investment Commission (ASIC). For the validation sample, all the financial data and failure statistics are generated from a customised data feed provided commercially to the authors by AspectHuntley Pty Ltd.32 Dependent Variable

For the purposes of this study, states 0-2 are mutually exclusive categories, this being a condition of the ordered mixed logit model. Furthermore, these states represent an increasing severity of financial distress. State 2 is differentiated from states 0-1 insofar as these firms are no longer going concerns. The financial health of these firms deteriorated to the point where filing for bankruptcy was the only option available to the firm. State 1 represents firms which are going concerns, but have experienced financial difficulties serious enough to warrant being described as ‘financially distressed’. State 0 describes firms which are going concerns but have shown no evidence of being financially distressed as defined in this study. Differences in the financial condition of firms in each state is reflected in the

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descriptive analysis of results (see Table 2). Using a number of variables which featured most prominently in the mixed logit and MNL analysis (Tables 3 & 4), Table 2 indicates a noticeable deterioration in the performance of firms across states 0-2 for most variables.

Insert Table 2 Explanatory Variables

We test a number of financial variables used in research over the last three decades (see e.g., Beaver, 1966; Altman, 1968; Altman, Haldeman and Narayan 1977; Ohlson, 1980; Zemjewski, 1984; Casey and Bartczak 1985; Gentry, Newbold and Whitford, 1985; Jones 1987). These financial measures include ratios based on cash position; operating cash flow (CFO); working capital; profitability and earnings performance; turnover; financial structure; and debt servicing capacity. Furthermore, we test reported CFO rather than estimates of CFO. Hribar and Collins (2002) document evidence that earnings management, capital market and other studies using estimates of CFO (as opposed to reported CFO) are prone to significant measurement errors which can potentially contaminate the empirical results of some of these studies. Previous financial distress research testing the predictive performance of CFO has invariably used estimates rather than reported CFO. This is not surprising considering that many of these studies predate the introduction of SFAS 95 (e.g., Casey and Bartczak, 1985). However, in light of Hribar and Collins (2002), this could also potentially explain why so few of these studies have found any supporting evidence for the usefulness of CFO in distress prediction33 (see e.g., Neill, Schaefer, Bahnson and Bradbury, 1991). Ratio measures based on reported CFO are the net operating cash flow number extracted from company cash flow statements prepared under AASB 1026.34

A correlation matrix of key variables found to be significant in the mixed logit and MNL analysis is provided in the Appendix Table 1. An examination of the partial correlations indicates generally weak correlations across most of these covariates, suggesting that predictor variables all provide distinct and unique information.

We now briefly comment on the contextual variables. In contrast to previous research, which has tended to be restricted to industrial or manufacturing firms (Jones, 1987), this study tests the predictive value of financial variables on four major sectors: the old economy sector; the new economy sector; the resources sector and the financial services sector. This classification approach has been adopted for a variety of reasons: (1) it recognizes that industry sectors are structurally different and have different financing, operating and investing characteristics that can undermine inter-sector comparability and generalizability (Ohlson, 1980). We attempt to capture sector-specific affects in our modeling in order to make determinations about the generalizability of our results as well as assess the predictive value of our model to specific sectors; (2) the classification approach gives explicit recognition to the economic characteristics of Australian industry, particularly the emerging importance of the New Economy sector in Australia over the past decade, which now amounts to more than 60% of the market capitalization of the ASX (ASX Market Comparative Analysis, 2003). Firms in the New Economy sector are classified according to the ASX industry classification guidelines, outlined in the ASX Market Comparative Analysis (2003).35 These are: (i) health and biotechnology; (ii) high technology; (iii) internet firms; and (iv) telecommunications. Furthermore, in Australia, the resources sector constitutes the largest and single most important export industry – nearly 30% of all listed firms in Australia are resource companies (see ASX Market Comparative

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Analysis, 2003). The resources sector is classified by the ASX as: (i) gold companies; (ii) other metals and (iii) diversified resources. Financial services are defined by the ASX as banks and finance houses, insurance companies and investment and financial services companies. Old economy firms are defined for the purpose of this study as all firms not being in the new economy, resources and financial services sectors;36 and (3) our classification scheme is sufficiently broad to preserve a statistically sufficient sample size for each major sector, while maintaining meaningful contextual information about the impact of industry sector in our analysis.

IV. EMPIRICAL RESULTS

Several mixed ordered logit models are estimated to identify the statistically significant influences on the probability of a firm failing for various reasons or not failing in specific years. Table 3 summaries the overall model system for both the mixed logit model and MNL. Both models were developed from the full set of variables in the data set, with some common variables occurring in both models as well as some different effects (e.g., sales revenue to total assets for MNL and total debt to total equity for mixed logit). The mixed logit has delivered a very good overall goodness of fit. The log-likelihood has decreased from -2057 (assuming no information other than random shares) to -776. However, for the MNL, the model fit is significantly less impressive. The MNL log-likelihood has only decreased from -2057 to -1972. Using a likelihood ratio test we can calculate the likelihood ratio as -2*(1972-776) = -2392 at 8 degrees of freedom. This is chi-square distributed and at any level of significance the mixed logit is a substantial improvement over MNL. The mixed logit results in Table 3 indicate that some variables have a single fixed parameter whereas other variables (four of them - cash resources to total assets, net operating cash flow to total assets, total debt to total equity and cash flow cover) have up to three parameters representing their role. What is impressive is a recognition that unobserved heterogeneity as represented by the standard deviation parameters is statistically significant for all four financial variables. If the analyst was to estimate a simple multinomial or binary logit model, the opportunity to establish the role of the mean and variance influence of a particular variable (through the structure of its parameter space) would be denied. This is an important finding and recognition of the amount of information loss that is caused by rigid model specifications. The ability to capture important relationships through a random parameter specification has meant that such information has not been assigned (incorrectly) to the IID random component as exists for a standard logit model.

Insert Table 3 In addition we find that for total debt to total equity and cash flow cover, the interaction with the new economy dummy variable has produced a contextual effect suggesting that membership of the new economy has a differential influence on the role of these variables to the failure outcome.

Although the interpretation of the significance of various variables is important and possible in Table 3, the magnitude and direction of impact of each explanatory variable on the probability outcome for each state of financial distress and nonfailure requires us to derive the marginal effects to which we now turn. Results: Marginal Effects

A direct interpretation of the parameter estimates reported in Table 3 is not possible given the logit transformation of the outcome dependent variable required for model estimation. We therefore provide the marginal effects, defined as the

13

derivatives of the probabilities which have substantive behavioral meaning (Louviere, Hensher and Swait, 2000). A marginal effect is the influence a one unit change in an explanatory variable has on the probability of selecting a particular outcome, ceteris paribus. This holds for continuous variables only. For dummy (1,0) variables, the marginal effects are the derivatives of the probabilities given a change in the level of the dummy variable and thus represent the influence of a change in level of the variable upon the probability of choosing a given outcome, ceteris paribus.

The marginal effects need not have the same sign as the utility parameters. Hence the statistical significance of a utility parameter does not imply the same significance for the marginal effect.

∂Prob(yq = j)/∂x = Pj(βj - β ), β = ΣjPjβj. (defined below as δj ) (14)

Neither the sign nor the magnitude of δj need bear any relationship to those of βj. The asymptotic covariance matrix for an estimator of δj would be computed using

Asy.Var.( δ∧

j ) = Gj Asy.Var( β∧

)Gj (15)

where β∧

is the full parameter vector, Gj is a matrix of first derivatives used to establish standard errors of betas,

and Asy.Var.(δ∧

j ) = Σl Σm Vjl Asy.Cov.( β∧

l,β∧

m')Vjm', j = 0,...,J, (16) where Vjl = (1(j=l) - Pl){PjI - δjx′} - Pjδlx′ and 1(j=l) = 1 if j=l, and 0 otherwise.

βj, equal to ∂log(Pj/P0)/∂x, has been suggested as an interpretation of the utility parameters.37 Marginal effects in the mixed logit model are quite involved. Since there is no meaningful conditional mean function to manipulate, we consider, instead, the effects of changes in the covariates on the cell probabilities. These are:

∂Prob(cell j)/∂xi = (f(μj-1 - β′xi) - f(μj - β′xi)) × β (17)

where f(μj-1 - β′xi) is the logistic density, Λ(μj-1 - β′xi)(1-Λ(μj-1 - β′xi).

The marginal effects of each explanatory variable for each of the three outcomes is shown in Table 4 for both mixed logit and MNL. These results suggest that cash resources to total assets, net operating cash flow to total assets, working capital to total assets and cash flow cover have a strong statistical impact on the probability of each of the performance outcomes. Total debt to gross operating cash flow and total debt to total equity are both statistically significant but their t values are smaller than the other variables. It is noteworthy that all random parameters in the mixed logit analysis have a consistent and logical sign across all levels of the response variable. For example, net operating cash flow to total assets has a positive coefficient for Y = 0 (increases in this ratio increase the probability of nonfailure) but negative coefficients across the two financial distress categories. Likewise, total debt to gross operating cash flow has a negative coefficient for Y = 0 (increases in total

14

debt to gross operating cash flow reduce the probability of nonfailure) but positive coefficients across the two financial distress categories, indicating that increases in this value increase the probability of financial distress across each distress state. The marginal effects for the MNL analysis does not produce logical or consistent signs for all parameter estimates, even though nearly all the financial and contextual variables are statistically significant as we found in the mixed logit analysis.

It is noteworthy that measures based on reported CFO produced statistically significant parameters which were relatively stable across each of the three response categories. One potential explanation for why our results differ from previous distress research is suggested by Hribar and Collins (2002), who conclude that estimated CFO is generally a poor proxy for reported CFO. The results could also be attributed, at least in part, to methodological improvements introduced by the mixed logit model.38

In addition the membership of the new economy sector is particularly notable, with the probability of failure increasing when a firm belongs to this sector (primarily IT and technology firms). This result is likely to reflect the pronounced demise of the technology sector in Australia in 2000 (and worldwide), and the subsequent financial collapse of many of these companies. The influence is not uniform across all distress classes with the marginal effects for most financial and contextual variables declining sharply as we move to failure state 2 (outright failure). These results are intuitive, reflecting differences in the financial positions that we would expect of firms in each of the distress states. When a firm reaches more advanced stages of financial distress, such as outright failure, the financial position of these firms would have deteriorated to a more significant extent than firms classified ‘0’ or ‘1’. Likewise, we would expect on average firms in ‘2’ to have deteriorated to a more significant extent than ‘1’ (see Table 2). Hence, significantly larger changes in the magnitude of financial variables, such as operating cash flow, would be required to have any impact on changes to the outcome probability, particularly for firms in the highest distress state (‘2’). Another interpretation of the declining marginal effects across response categories is that once firms enter into structurally ‘irreversible’ decisions, such as liquidation, financial statements, including cash flows, assume less overall marginal significance.

Insert Table 4

V. FURTHER CONSIDERATIONS The analysis in previous sections incorporated the entire data set of 5 annual

reporting periods per firm in the estimation sample. If there was an observed failure it occurred after the last reporting period of data collected in this study. Each observation point on each firm was treated as an independent observation. This suggests two further foci of investigation: (i) a model in which the distress level is the dependent variable but in which the explanatory variables in all 5 reporting periods are linked through a structure such as a geometric distributed lag and (ii) a cross section model estimated on only the last reporting period of financial data before failure.

We estimate a model for each alternative specification and report the findings below. The first modification is to recognize the possibility that performance leading up to failure/insolvency has an accumulating impact on the response outcome. To investigate this we propose a geometric distributed lag of the moving average form:39

β(1-λ)(xt + λXt-1+λ2Xt-2+….)

15

Given a known value for λ, the function is linear in the parameters. We undertook a grid search on λ (over the range 0 to 2), selecting the value which maximizes the log-likelihood of the model. The best fit λ was 0.23. The model in which we allow all financial variables to be the moving average form of geometric distributed lag are summarized in Table 5 below.

Insert Table 5 Comparing Table 5 with Table 3 (the initial model in which we pool all

reporting periods and treated each as an independent cross section) it can be seen that none of the fixed or random parameter variables are significant (other than the constant term). Marginal effects are not reported on the variables reported in Table 5 as none were found to be significant, suggesting that these variables have no affect on the probability of the response outcome.

We also estimated a mixed logit model for the last reporting period in the data set. Again, this specification produced a model statistically and behaviorally inferior to the one reported in Table 3. All but one random parameter variable had a statistically significant standard deviation, and none of the fixed parameters were significant. Once again, the marginal effects are not reported here, as no variables were found to be statistically significant.

These results suggest that the pooled data model reported in Table 3 is preferred to a cross sectional model. Further, the independence of years specification for our model reported in Table of 3 outperforms a geometric lagged model specification which captures time dependencies in the explanatory variables. Model Validation: Probability Outcomes

The overall predictive performance of the mixed logit model and MNL can be investigated by deriving the predicted probabilities for each firm for each outcome on our validation sample. In deriving the probability outcomes for the mixed logit model we have to recognize that some explanatory variables are a composite function of a mean parameter, a distribution around the mean and decomposition of the mean by some contextual effect (in our case it is the new economy effect). Each individual firm is ‘located’ in parameter space on the normal distribution for four financial variables (cash resources to total assets, net operating cash flow to total assets, total debt to total equity and cash flow cover). The precise formulation used to derive the contribution to relative utility of each outcome is:

Preference Distribution for cash resources to total assets

= -.06082089+.08277721*normal density

Preference Distribution for net operating cash flow to total assets = -.01711009+.01229528* normal density

Preference Distribution for total debt to total equity

= .00090835-.00766415*new_econ+.00509659* normal density

Preference Distribution for cash flow cover ratio = -.00519331+.008199972*new_econ+.00519331*normal density where normal densities have mean zero and unit standard deviation. For each individual we randomly draw a location on the distribution given the mean and standard deviation and derive their overall contribution to ‘relative utility’. This is

16

derived a repeated number of times and averaged per firm. We calculate the set of three outcome probabilities using the formula set:

P0 = Phi(-Xb) P1 = Phi(Mu1-Xb) - P0 P2 = 1 - P1-P0

Importantly we focus on a sample enumeration methodology which recognizes

that the estimated model is based on a sample drawn from a population and the application of the model must preserve the full distribution of information obtained from the model system (Horowitz and Louviere 1993). This includes the outcome probabilities. That is, given that the focus is on a sample drawn from a population of firms, the parameterization used to establish the probabilistic outcomes is a representation of the preference profile of a sample. Thus it is necessary to aggregate the probabilities associated with each outcome across the entire sample to obtain the predicted outcome values (i.e. the absolute number of firms predicted to be in each outcome category or outcome category shares). However, while the practice of identifying the outcome probability associated with each outcome for each firm is common and supported practice in accounting research, the use of threshold probabilities to assign firms to specific predicted outcomes is not supported by a correct application of outcome models. The literature on discrete choice analysis (e.g., Hensher, Rose and Greene, 2005) shows that imposing a cut-off allocation rule such as assigning an outcome probability of 1.0 to the alternative whose model derived outcome probability is greater than a specific value (e.g., 0.5 for a binary outcome) is arbitrary and not consistent with the intent of the model (whether binary, MNL or mixed logit).40

Implementing a sample enumeration strategy on our hold out sample, we can compare the predictive performance of mixed logit and MNL. Table 6 compares the forecasting accuracy of both models on pooled data, and on data 1, 3 and 5 reporting periods prior to failure. The overall results indicate that mixed logit has substantially better predictive accuracy than MNL across the pooled results, and in all reporting periods prior to failure. It is noted that the MNL is particularly poor in classifying financial distressed firms. For instance, in predicting state ‘2’ or outright failure, the MNL model’s best performance is only 5% accuracy based on the pooled observations and its best result is 6.4% accuracy three reporting periods prior to failure. The MNL performs better in predicting state 1 (insolvent firms), though the accuracy rate is only 24% on the pooled data with a peak accuracy rate of 29% five reporting periods from the public announcement of insolvency problems. In contrast, mixed logit predicts state ‘2’ with 95% accuracy based on the pooled observations, and is 95% accurate up to three reporting periods prior to failure, with accuracy rates falling to 78% five reporting periods from failure. The model performs very well on predicting nonfailures, and the overall accuracy for predicting state 1 is also impressive, with over 90% accuracy three and five reporting periods prior to the public announcement of insolvency problems. Mixed logit has an overall forecasting accuracy (in terms of predicting accurately across all distress states) of 99.16% on the pooled data, 98.73% from the last reporting period, 99.6% accuracy from the third reporting period, and 98.9% accuracy from the fifth reporting period.

Insert Table 6

VI. CONCLUSIONS

17

In this paper we seek to advance the state of art in financial distress modeling by explicating the theoretical and empirical value of the mixed logit model. With few exceptions, the financial distress literature to date has employed relatively primitive binary logistic models, and in a few cases a rudimentary MNL approach. The literature has not kept abreast of considerable theoretical and empirical developments made in discrete choice modeling in recent years. The focus of recent discussions in the econometric literature has been on improving the behavioral realism of discrete choice models by relaxing the rigid assumptions associated with IID error terms in a manner that is conceptually enriching, computationally tractable and practical. The mixed logit model is one approach that allows the analyst to relax the very rigid assumptions associated with IID, and allows a meaningful interpretation of the role of the mean and variance influence of a particular variable through the structure of its parameter space. Such refinements hold much promise in this field of research. The results of this study confirm the superiority of mixed logit over standard approaches such as MNL. After adjusting for the number of parameters, mixed logit produced a substantially improved model-fit compared with MNL. Furthermore, the out-of-sample forecasting accuracy of the mixed logit design was much superior to multinomial logit.

There are several possibilities for future research arising from this study. First, the benefits of mixed logit are by no means confined to the financial distress literature, but can be usefully applied to many other areas of accounting research. Mixed logit is a highly flexible model and can be applied to a variety of data sources and structures where use of a discrete dependent variable is contemplated, including cross-section, time-series, panel and experimental data. Elliot and Kennedy (1988) and Kennedy, (1992) note several applications in accounting research for use of a discrete dependent variable with multiple alternatives. Further, Leclere (1999) cites at least 21 studies in the leading accounting journals which use an n-chotomous dependent variable such as multinomial logit or ordered probit. Studies cover such diverse fields as predicting management’s choice of accounting method, pension reporting, loan classifications, bond ratings, lobbying positions, disclosure, capital structure analysis and auditing switching (see also Kennedy, 1992).41 As pointed out by Hensher and Greene (2003), estimation of an MNL model is the first step in establishing a more robust mixed logit specification. Such research domains can be readily extended and enriched using a mixed logit framework. Another field where mixed logit could have considerable application is in the broad field of human judgment and decision making, such as cognitive processes and judgment tasks (Libby and Lipe, 1992). As with other areas of accounting research, behavioral accounting research has tended to be narrowly focused on general linear models, such as ANOVA and multiple regression. However, there are now comprehensive illustrations available of the empirical benefits of nonlinear models such as mixed logit in the context of experimental research and behavioral decision making (Louviere, Hensher and Swait, 2000, Hensher, Rose and Greene, 2005).

A second direction for future research could be to evaluate the mixed logit model against other innovative techniques used in credit risk modeling. One other modeling approach becoming more widely used in this literature is structural equation modeling (Duffie and Singleton, 2003). SEM focuses on relationships among latent constructs rather than on the manifest variables used to measure these constructs. It was shown in Section II that mixed logit performs well in capturing latent effects by incorporating observed and unobserved heterogeneity in parameter estimates. Given some conceptual similarities between mixed logit and SEM, a formal comparison of the

18

forecasting performance of these models is needed if either approach is to be relied upon in future research.42

Extending the current model to include other distress categories such as distressed mergers (Clark and Ofek, 1994) would provide a further opportunity to examine the empirical usefulness of mixed logit in forecasting across multiple states of financial distress.

REFERENCES

Altman, E. 1968. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance 23: 589-609.

______________, R. Haldeman, and P. Narayan. 1977. ZETA Analysis: a new model to identify bankruptcy risk of corporations. Journal of Banking and Finance June: 29-54.

______________, 2001. Bankruptcy, Credit Risk and High Yield Junk Bonds. New York, NY: Blackwell Publishers.

Australian Accounting Standards Board. 1992. Approved Australian Accounting Standard AASB 1026: Statement of Cash Flows. Melbourne: Australian Accounting Research Foundation.

Australian Corporations Act 2001. Cwt (http://www.asic.gov.au/asic/ASIC). Australian Stock Exchange. 2003. Listing Rules. Sydney

(http://www.asx.com.au/about/l3/ListingRules). Australian Stock Exchange. 2003. Market Comparative Analysis, Sydney (http://www.asxtra.asx.com.au). Bahnson, P., and J. Bartley. 1992. The sensitivity of failure prediction models.

Advances in Accounting 10: 255-278. Beaver, W. 1966. Financial ratios as predictors of failure. Empirical Research in

Accounting: Selected Studies, supplement to Journal of Accounting Research 4. Boersch-Supan, A., and V. Hajvassiliou. 1990. Smooth unbiased multivariate

probability simulators for maximum likelihood estimation of limited dependent variable models. Journal of Econometrics 58: 347-368.

Brownstone, D., D. Bunch, and K. Train. 2000. Joint mixed logit models of stated and revealed preferences for alternative fuel vehicles. Transportation Research 34: 315-338.

Casey, C., and N. Bartczak. 1985. Using operating cash flow data to predict financial distress: some extensions. Journal of Accounting Research 23: 384-401.

Clark, K., and E. Ofek. 1994. Mergers as a means of restructuring distressed firms: and impirical investigation. Journal of Financial and Quantitative Analysis 29: 541-565.

Cheng, C.S., Liu, C. S., and T. F. Schaefer. 1997. The value-relevance of SFAS No. 95 cash flows from operations as assessed by security market effects. Accounting Horizons 11: 1-15.

Crask, M., and R. Fox. 1987. An exploration of the interval properties of three commonly used marketing research scales: a magnitude estimation approach. Journal of the Market Research Society 29: 317-339.

DeAngelo, H., and L. DeAngelo. 1990. Dividend policy and financial distress: an empirical investigation of troubled NSYE firms. Journal of Finance. 45: 1415-1431.

Delaney, K., 1991. Strategic Bankruptcy: How Corporations and Creditors Use Chapter 11 to their Advantage. Berkeley: University of California Press

19

Duffie, D., and K. Singleton. 2003. Credit Risk: Pricing, Measurement and Management. Princeton: Princeton University Press.

Efron, B. 1975 The efficiency of logistic regression compared to normal discriminant analysis. Journal of the American Statistical Association 70: 892-898.

Elliot, J., and D. Kennedy. Estimation and prediction of categorical models in accounting research. Journal of Accounting Literature 7:202-242.

Financial Accounting Standards Board. 1987. Statement of Financial Accounting Standards 95, Statement of Cash Flows. Stamford, CT: FASB.

Gentry, J., P. Newbold, and D. Whitford. 1985. Classifying bankrupt firms with funds flow components. Journal of Accounting Research 23: 146-160.

Geweke, J., M. Keane, and D. Runkle. 1994. Alternative computational approaches to inference in the multinomial probit model. Review of Economics and Statistics 76: 609-632.

Grandmont, J. 1987. Distribution of preferences and the `Law of Demand'. Econometrica. 55:155-161.

______________. 1992. Transformation of the commodity space, behavioural heterogeneity, and the aggregation problem. Journal of Economic Theory. 75: 1-35.

Greene, W.H. 2003. Econometric Software (2003): Limdep 8 Econometric Modeling Guide Volumes 2, Chapter 19, Econometric Software Inc. New York and Sydney.

Henry, F. 1982. Multivariate analysis and ordinal data. American Sociological Review 47:299-304.

Hensher, D. 1984. Achieving representativeness of the observable component of the indirect utility function in logic choice models: an empirical revelation. Journal of Business 57:265-86.

______________, J. Louviere, and J. Swait, 1999. Combining sources of preference data. Journal of Econometrics 89:197-221.

______________, and W. Greene. 2003. The mixed logit model: the state of practice. Transportation. 30:133-176.

______________, Rose, and W. Greene. 2005. Applied Choice Analysis: A Primer. Cambridge: Cambridge University Press (forthcoming, early 2005).

Hill, N., S. Perry, and S. Andes. 1996. Evaluating firms in financial distress: an event history analysis. Journal of Applied Business Research 12:60-71.

Horowitz, J. and J. Louviere. 1993. Testing predicted choices against observations in probabilistic discrete-choice models. Marketing Science 12(3):270-279.

Hribar, P. and D. Collins. 2002. Errors in estimating accruals: implications for empirical research. Journal of Accounting Research 40:105-134.

Ireland, J..C. 2003. An Empirical Investigation of Determinants of Audit Reports in the UK. Journal of Business Finance & Accounting 30: 975-1016.

Jones, F. 1987. Current techniques in bankruptcy prediction. Journal of Accounting Literature 6:131-164.

Joy, M., and J. Tollefson. 1975. On the financial applications of discriminant analysis. Journal of Financial and Quantiative Analysis December: 723-739.

Kennedy, D. 1992. Classification techniques in accounting research: empirical evidence of comparative performance. Contemporary Accounting Research 8: 419-442.

Kneip, A. 1999. Behavioral heterogeneity of structured properties of aggregate demand. Journal of Mathmatical Economics 31: 49-74.

20

Lancaster, K. 1966. A new approach to consumer theory. Journal of Political Economy 74: 132-157.

______________. 1971. Consumer Demand: A New Approach. New York, NY: Columbia University Press.

Louviere, J., D. Hensher, and J. Swait. 2000. Stated Choice Methods and Analysis Cambridge: Cambridge University Press.

Lau, A.H. 1987. A Five-State Financial Distress Prediction Model. Journal of Accounting Research 25: 127-138.

Leclere, M. 1999. The Interpretation of Coefficients in N-Chotomous Qualitative Response Models. Contemporary Accounting Research 16: 711-747.

______________, 2000. The Occurrence and Timing of Events: Survival Analysis Applied to the Study of Financial Distress. Journal of Accounting Literature 19: 158-189.

Libby, R., and M. Lipe. 1992. Incentives, effort, and the cognitive process involved in accounting related judgements. Journal of Accounting Research 30: 249-273.

Maddala, G.S., 1991. A Perspective on the use of limited-dependent and qualitative variables models in accounting research. The Accounting Review 66: 788-807.

McFadden, D. 1976. A comment on discriminant analysis “versus” logit. Annals of Economic and Social Measurement 5/4: 511-523.

______________, and Ruud, P. 1994. Estimation by simulation. Review of Economics and Statistics 76: 591-608.

______________, and K. Train. 2000. Mixed MNL models for discrete response. Journal of Applied Econometrics 15: 447-470.

Neill, J. D., T.F. Schaefer, P.R. Bahnson and M.E. Bradbury. 1991. The usefulness of cash flow data: a review and synthesis. Journal of Accounting Literature 10: 117-150.

Ohlson, J. 1980. Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research 18: 109-131.

Powell, R. 1997. Modelling takeover likelihood. Journal of Business Finance and Accounting. 24: 1009-1031.

Revelt, D., and K.Train. 2000. Customer specific taste parameters and the mixed logit: households’ choice of electricity supplier. Working Paper, Department of Economics, University of California, Berkely.

Rosen, S. 1974. Hedonic prices and implicit markets: product differentiation in competition. Journal of Political Economy 82: 34-55.

Sándor, Z., and M. Wedel. 2002. Profile construction in experimental choice designs for mixed logit models. Marketing Science 21: 455-475.

Scott, J. 1981. The probability of bankruptcy: a comparison of empirical predictions and theoretical models. Journal of Banking and Finance 5: 317-344.

Shumway, T. 2001. Forecasting bankruptcy more accurately: a simple hazard model. Journal of Business 74: 101-124.

Stern, S. 1997. Simulation-based estimation. Journal of Economic Literature 35: 2006-2039.

Train, K. 2003. Discrete Choice Methods with Simulation. Cambridge: Cambridge University Press

Ward, T. 1994. An empirical study on the incremental predictive ability of Beaver’s naïve operative flow measure using four-state ordinal models of financial distress. Journal of Business Finance & Accounting 21: 547-562.

Winship, C., and R. Mare. 1984. Regression models with ordinal variables. American Sociological Review 49: 512-525.

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Zmijewski, M. 1984. Methodological issues related to the estimation of financial distress prediction models. Journal of Accounting Research 22 (3): Supplement, 59-82.

1 A related problem is that most studies to date have modeled failure as a simplistic binary classification of failure or nonfailure (see Jones, 1987). This has been called into question, one reason being that the strict legal concept of bankruptcy may not always reflect the underlying economic reality of corporate financial distress (Lau, 1987; Delaney, 1991). The two state model can also conflict with underlying theoretical models of financial failure and limits the generalizability of empirical results (Scott, 1981; Bahnson and Bartley, 1992; Hill et al., 1996). Others have argued that the practical risk assessment decisions by lenders and other parties normally cannot be reduced to a simple pay off space of failed and nonfailed (Ward, 1994; Ohlson, 1980). Lau (1987) improved on the methodology of dichotomous prediction models by using a five-state model, but the study has a number of limitations. For instance, the MNL approach selected is not robust to violations of the IID assumption and some of the distress states are hampered by unacceptably small sample sizes. Using a holdout sample, Lau’s model predicted the nonfailure state with reasonable accuracy, but was less impressive in predicting the different states of financial distress. 2 The estimated standard logit model herein is referred to in the literature as multinomial logit (MNL) in contrast to conditional logit. Although there are some interpretative differences between conditional logit and MNL, they have the same functional form. An MNL model can be described by a situation where the main influences on the choice outcome are the characteristics of the observations (i.e., the firms). This is in contrast to conditional logit where the primary influences are the attributes of alternatives (i.e., financial ratios). Our data are described only by the characteristics of firms whose attributes do not vary across outcomes (although such variation exists across the sample). For example, an individual firm’s total debt to total equity ratio (attribute) does not vary across failure outcomes for that individual firm, but it does for the sample as a whole. We have chosen an ordered specification of the outcomes within which it is possible to allow a single characteristic to impact on all outcomes, since the notion of an alternative is not applicable. All model specifications are members of the general family of random utility models (RUM). 3 In advocating the mixed logit model, we acknowledge certain limitations of “static” or single period distress models which draw on multiple-period distress data (Shumway, 2001; Leclere, 2000). Much of the literature is of this genre (see Altman, 2001 for a survey). Shumway (2001) concluded that static models can result in inconsistent and biased estimates. Firm characteristics can change over time, but such problems are not expected to be pronounced in this study given the relatively short time frame in which our estimation sample is drawn. While a hazard analysis is not deemed appropriate to the modeling focus of this study, we did meet some of Shumway’s (2001) concerns by undertaking an assessment of a geometric lag specification to test time dependencies in our estimation sample (see Section V). 4 In the theory of discrete choices, an essential departure from traditional microeconomic theory originated in the now classical works of Lancaster (1966, 1971) and Rosen (1974). This is the postulate that utility is derived from the properties or characteristics of things, rather than the goods per se. Discrete choice theory incorporates the work of the standard Lancaster-Rosen model, but modifies this approach further by assuming that individuals maximize their utility on the basis of their perceptions of characteristics, rather than the characteristics per se (see Louviere, Hensher and Swait, 2000 for an overview). 5 Random utility theory (RUT) is a very general theory of how the analyst represents the preferences of agents where elements of information (known to the agents) are not observed by the analyst. While RUT has gained particular recognition within discrete choice theory in recent years, RUT is not restricted to choice theory and can be implemented in a wide range of possible decision contexts. 6 The modeling of behavioral heterogeneity has been important in many fields of inquiry, including recent economics literature (see Grandmont, 1987, 1992; Kneip, 1999). 7 In addition to fixed parameters, mixed logit models include estimates for the standard deviation of random parameters, the mean of random parameters and the heterogeneity in the means (discussed further below and in Section IV). 8 The moments of an individual firm’s coefficient cannot be observed from a single data point, but rather estimated by assuming a distribution for the coefficients of any particular attribute across all firms in the sample (see Train, 2003, 262-263). 9 A fixed parameter essentially treats the standard deviation as zero such that all the behavioral information is captured by the mean. Standard logit models assume the population of firms is homogeneous across attributes with respect to domain outcomes (i.e., levels of financial distress). For

22

instance, the parameter for a financial ratio such as total debt to total equity is calculated from the sample of all firms (thus it is an average firm effect), and does not represent the parameter of an individual firm. 10 A variety of studies have now demonstrated the superior forecasting accuracy of mixed logit compared to standard logit (see, as examples, Brownstone, Bunch and Train; 2000; Revelt and Train, 2000; Sándor and Wedel, 2002). 11 Based on Hensher, Rose and Greene (2005). 12 Extreme value type 1 (EV1) is a commonly used distribution in discrete choice analysis. The phrase ‘extreme value’ arises relative to the normal distribution. The essential difference between the EV1 and normal distributions is in the tails of the distribution where the extreme values reside. With a small choice set such as two alternatives this may make little difference because the resulting differences in the choice probabilities between the normal and EV1 is usually negligible. When there are more than two alternatives, however, there can be a number of very small choice probabilities. As a result, differences between the distributions can be quite noticeable (see Hensher, Rose and Greene, 2005). 13 The proof in McFadden and Train (2000) that mixed logit can approximate any choice model including any multinomial probit model is an important message. The reverse cannot be said: a multinomial probit model cannot approximate any mixed logit model, since multinomial probit relies critically on normal distributions. If a random term in utility is not normal, then mixed logit can handle it and multinomial probit cannot. 14 The mixed logit model has a likelihood surface that is capable of producing local optima in contrast to a single unique global optimum from MNL. Using the MNL parameter estimates as starting values produces a global solution since it begins the gradient search at a location of the nonlinear surface that tends to be the best starting location for determining the global optimum. 15 By construction, SPi is an unbiased estimate of Pi for any R; its variance decreases as R increases. It is strictly positive for any R, so that ln (SPi) is always defined in a log-likelihood function. It is smooth (i.e., twice differentiable) in parameters and variables, which helps in the numerical search for the maximum of the likelihood function. The simulated probabilities sum to one over alternative outcomes. Train (2003) provides further commentary on this. 16 The simulation method was initially introduced by Geweke (and improved by Keane, McFadden, Börsch-Supan and Hajivassiliou - see Geweke et al 1994, McFadden and Ruud 1994) to compute random variates from a multivariate truncated normal distribution. Although it fails to deliver unbiased multivariate truncated normal variates (as initially suggested by Ruud and detailed by Börsch-Supan and Hajivassiliou (1990), it does produce unbiased estimates of the choice probabilities. The cumulative distribution function in their research is assumed to be multivariate normal and characterized by the covariance matrix M. The approach is quick and generated draws and simulated probabilities depend continuously on the parameters β and M. This latter dependence enables one to use conventional numerical methods such as quadratic hill climbing to solve the first order conditions for maximizing the simulated likelihood function (equation 5) across a sample of q=1,…,Q firms; hence the term maximum simulated likelihood (MSL) (Stern 1997). 17 The most common application of mixed logit involves unordered alternative outcomes. 18 The threshold parameters are essentially constants that redefine the utility scale across the set of outcomes to recognize that the utility scale is nonlinear between outcomes. 19 This is the Berndt, Hall, Hall, Hausman algorithm which uses the sums of squares and cross products of the first derivatives to obtain the asymptotic covariance matrix of the maximum likelihood estimator which contains the parameters of interest. 20 Occasionally we found a financially healthy firm which failed to pays its listing fees. These firms were removed from the sample. 21 Three firms fell into category (iv). These companies were carefully examined to ensure that their financial condition was well differentiated from state 2 (outright failure). For instance, it was found that none of these firms involved creditors granting concessions (such as forgiven principal or reduced interest rates). In two cases creditors converted debt to total equity to alleviate the liquidity problems of the firm. In one case, the firm sought to refinance current debt commitments because of short term liquidity problems. 22 It is noted that other studies (e.g., Lau, 1987; DeAngelo & DeAngelo, 1990) have used reduction in dividends as a measure of financial distress. Lau (1987) for example, examined firms with a greater than 40% dividend per share drop, after a period of three years of stable dividend record. Following Lau’s approach, only a small number of firms (eight in total) satisfied this requirement. More than half of these firms were not associated with any degree of financial distress, and the other half were already absorbed into the other distress categories. As acknowledged by Lau (1987) dividend reductions can be associated with reasons other than financial distress, such as capital investment activities.

23

23 Included in our sample are three principal forms of bankruptcy proceeding available under the legislative provisions of the Australian Corporations Act (2001): (i) voluntary administration (first introduced in Australia in June 1993 under the Corporate Law Reform Act, 1992); (ii) liquidation and (iii) receivership. Voluntary administration has similarities with Chapter 11 provisions in the US, where the company is effectively given a period of time or “breathing space” to reorganize and/or reconstruct. Under Australian voluntary administration laws, once appointed the insolvency administrator has a limited period (28 days) to assess the company and recommend to the creditors whether the company should be wound up or enter into a deed of arrangement (this is a contract that binds the company and creditors and includes such issues as the order by which creditor claims are to be settled from sale of assets). If deed of arrangement stage is not reached, the legislation provides for an automatic transition to liquidation. With respect to (ii) liquidation, there are essentially two types of winding up procedure available: a creditors’ voluntary winding up (decided by special resolution of the company) and a court winding up. In the case of (iii) receiverships, the Corporations Act (2001) provides that a secured creditor, in the event of a firm’s insolvency can appoint a receiver (or a receiver and manager) to recover outstanding claims against the company. We note that the great majority of our failed firm sample fell into categories (i) and (ii). 24 The term ‘reporting periods’ is more accurate than ‘years’. For instance, the last reporting period before failure is not strictly speaking one year before failure. For some firms, the last reporting period may be only 3 or 4 months before failure, and for others it might be longer. Likewise, 5 reporting periods before failure may not necessarily equate to exactly 5 years before failure. 25 The backcasting problem is where a company files for bankruptcy at some point in time after the fiscal year date, but prior to publicly releasing the financial statements. All company financial statements in Australia, including the date of their release to the market, can be checked on the ASX’s Signal G. Signal G disclosures are regulated by the ASX Listing Rule 3.1 which identifies the types of information which Australian companies must disclose to the market on a timely basis. Examples include: the appointment of a receiver or liquidator; information relating to mergers and takeovers; capital reorganizations; loan defaults; share issues; failure to pay listing fees and any other information which could have a material affect on the value of a company’s securities (see also Sections 674 and 675 of the Corporations Act, 2001). Information for release to the market must be lodged by companies with the ASX’s company announcement office (CAO), which is then immediately released to the market under Signal G (see Explanatory Note, ASX Listing Rules, Chapter 3, 97,575; and Chapter 15 of the listing rules). Because all Signal G market releases are electronically dispatched (in ‘real time’), an accurate determination could be made whether a firm’s financial statements were released before or after the announcement of failure. 26 Our own database indicates an average historical failure rate in Australia of between 2-3% over the entire sample period 1996-2003. 27 We screened the nonfailed sample to assess whether there were nonevent (i.e nonfailed) companies that possessed possible characteristics of insolvency or failure that were not captured by the specific indicators defined in states 1 and 2. Distressed firms subject to a merger or takeover is one such example (see Clark and Ofek, 1994). Clark and Ofek (1994) define a distressed merger/takeover according to any or all of the following factors: poor stock price performance; financial distress, such as severe deficiencies in working capital to fund continuing operations; corporate reorganizing in order to rationalize non-performing key assets or the business as a whole; high turnover in directors and senior management. We identified 93 firm years from the estimation sample, and 76 firm years from the validation sample which satisfied the Clark and Ofek definition of a distressed merger. These firm years were removed from the estimation and validation samples accordingly. 28 Joy and Tollefson (1975) note that holdout samples drawn from the same time period as the original sample will not provide an intertemporal validation, and hence cannot provide an adequate test of a model’s predictive ability. 29 The validation sample was generated from a single customized data feed provided commercially to the authors by AspectHuntley Pty Ltd. The data feed had quite complete records on firm failures and delistings, including nonfailed company records between 2001 and 2003. The estimation sample had to be drawn from several databases, resulting in a number of incomplete records which had to be removed from the final sample. 30 AASB 1026 was issued by the AASB in 1991, with a mandatory operative date of June 1992. In most respects, AASB 1026 is very similar to the requirements of SFAS 95. The major difference is that AASB 1026 requires the direct method of reporting operating cash flow (see paragraph 6.2 of AASB 1026).

24

31 A typical example is the telecommunications company One.Tel, which announced failure to the market on May 30, 2001, but its last annual report was released to the market on the September 12, 2000, a lead time of over 8.5 months. 32 AspectHuntley was created in 2003 from a merger of two leading data providers in Australia – Aspect Financial Pty Ltd and Huntley’s Financial Services. 33 The value relevance of reported CFO relative to estimated CFO has been confirmed in other studies – see e.g., Chang, Liu and Schaefer (1997). 34 Except for the total debt to gross operating cash flow ratio (gross operating cash flow is defined under AASB 1026 as gross receipts from customers less payments to suppliers). 35 Further industry statistics below are all based on the ASX Market Comparative Analysis, 2003. 36 Industries include: Alcohol & Tobacco; Building Materials; Chemicals; Developers & Contractors; Diversified Industrials; Energy; Engineering; Food & Households; Infrastructure & Utilities; Media; Miscellaneous Industrials; Paper & Packaging; Property Trusts; Retail; Tourism & Leisure; and Transport. 37 See W.H. Greene, Econometric Software (2003) Limdep 8 Econometric Modeling Guide Volume 2, Chapter 19, Econometric Software Inc., New York and Sydney. 38 A direction for future research is to formally test various CFO estimates and reported CFO in the context of financial distress prediction. 39 Except for finance, resource and new economy. 40 Applying a model estimated on a sample tends to produce less reliable firm-specific predictions than estimating a model based on data for a single firm. In reality, there is usually insufficient data to estimate a unique model for each individual firm. Hence, we draw on samples which provide us the richness to predict at the sample level. Even with the mixed logit model, which provide estimates for firm specific parameters, coefficients for the standard deviation of random parameters are calculated from a distribution of all coefficients in the sample. Hence, inferences can only be validly made at the sample level. By implication, one can still obtain firm-specific predictions, but they are relatively limiting. 41 Some UK studies have used multinomial logit designs in the context of predicting the likelihood of mergers and takeovers (Powell, 1997) and in assessing the determinants of audit reports (Ireland, 2003). 42 Future research can also evaluate the performance of the mixed logit against other widely used advanced discrete outcome models, such as multinomial nested logit. The nested logit retains the advantages of a close ended form but is more flexible than MNL in dealing with the restrictive IID condition because through partitioning (or nesting), potential differences in sources of unobserved heterogeneity can be investigated. However, nested logit only relaxes the IID condition to some extent. We would only totally relax this condition if we allowed all variances and covariances to be different, up to identification, as in the case of the mixed logit model.

25

TABLE 1

Lead Times Between Date of Last Published Annual Report and Date of Failure Announcement Months 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 >20

# of Reports - 2 3 2 2 2 1 4 1 1 3 - 2 - 1 2 - 2 - 6

Mean: 11.2 months; Median 9.1 months, Mode 8 months.

Lead Times Between Date of Last Published Annual Report and Date Solvency Problem First Identified Months 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 >20

# of Reports 1 3 3 2 2 4 2 2 - 2 2 1 2 - - - - - - -

Mean: 6.24 months; Median 6.4 months, Mode 6.5 months.

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TABLE 2 Descriptive Statistics for Significant Covariates in Distress States 0-2

Variables Distress

State N Mean Std. Dev. Min. Max. Net operating cash flow to total assets Nonfailed 2838 -1.26 26.33 -404.76 256.64 Insolvent 78 -5.12 52.17 -168.17 263.77 Failed 116 -17.14 37.53 -193.68 21.87 Cash resources to total assets Nonfailed 2838 19.08 25.10 0.00 177.00 Insolvent 78 7.75 32.40 0.00 99.84 Failed 116 1.49 32.07 0.00 98.65 Cash flow cover Nonfailed 2838 8.24 79.65 -1014.99 1134.00 (net operating cash flow to annual interest payments) Insolvent 78 -1.61 79.39 -475.00 180.23 Failed 116 -25.05 125.48 -988.00 101.35 Sales revenue to total assets Nonfailed 2838 65.96 104.59 0.00 1734.6 Insolvent 78 55.04 78.47 0.00 332.23 Failed 116 54.58 70.49 0.00 327.76 Total debt to total equity Nonfailed 2838 42.69 72.89 0.00 698.87 Insolvent 78 53.64 97.84 0.00 511.90 Failed 116 97.30 134.38 0.00 616.65 Total debt to gross operating cash flow Nonfailed 2838 4.21 13.91 0.00 229.52 Insolvent 78 6.16 16.99 0.00 137.15 Failed 116 13.82 31.08 0.00 185.69 Working capital to total assets (wc = current assets – current liabilities) Nonfailed 2838 6.12 28.13 -850.67 323.00 Insolvent 78 0.77 42.01 -197.40 167.00 Failed 116 -22.21 43.43 -215.26 32.06

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TABLE 3 Fixed and Random Parameter Estimates and Model-Fit Summary for Final Mixed Logit and Multinomial

Logit Models (100 Halton draws)

Variablesa Mixed Logit Parameter

Estimates (t-values) MNL Parameter

Estimatesb (t-values) Fixed parameters: Constant -2.85 (-39.2) -2.6703 (-33.75) Total debt to gross operating cash flow 0.00895 (4.08) -.001654 (-6.7) Working capital to total assets -0.0119 (-10.765) 0.00186 (4.62) Resources sector (1,0) -0.5063 (-3.032) nsc New economy sector (1,0) 0.725 (4.101) 0.40586 (3.12) Finance sector (1,0) ns 0.33873 (2.38) Sales revenue to total assets ns -.00095 (-3.06) Cash resources to total assets - 0.002186 (4.98) Net operating cash flow to total assets - -.00091 9-2.87) Total debt to total equity - ns Cash flow cover - 0.00042 (3.8) Random parameter means: Cash resources to total assets -0.0608 (-7.65) Net operating cash flow to total assets -0.0171 (-9.21) Total debt to total equity 0.0009 (2.68) Cash flow cover -0.0051 (-7.93) Standard deviations of random parameters:

Cash resources to total assets 0.0827(13.173) Net operating cash flow to total assets 0.0122 (6.104) Total debt to total equity 0.00509 (12.66) Cash flow cover 0.0048 (6.836) Heterogeneity in means: Total debt to total equity*New_Econd -0.0076 (-5.75) Cash flow cover*New_Econ 0.00819 (5.287) Threshold Parameters: μ (0 to 1) Mu(0) 0 0 μ (1 to 2) Mu(1) 1.2611 (10.1) 1.0398 (16.6) Log-likelihood at zero -2057.46 -2057.46 Log-likelihood at convergence -776.17 -1971.95 Sample size 2838 2838

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TABLE 3 (Continued)

Descriptive Statistics Variable Mean Std.Dev. Minimum Maximum

New economy sector 0.165 0.371 0.000 1.000 Finance sector 0.138 0.345 0.000 1.000 Resources sector 0.204 0.403 0.000 1.000 Net operating cash flow to total assets -2.159 26.910 -404.760 256.640 Cash flow cover 7.218 81.220 -1014.986 1134.000 Cash resources to total assets 19.050 25.124 0.000 177.000 Total debt to gross operating cash flow 4.375 14.367 0.000 229.520 Total debt to total equity 56.836 152.620 0.000 698.870 Working capital to total assets 3.751 77.675 -850.000 323.000 Sales revenue to total assets 66.050 104.070 0.000 1734.600 a The full list of financial and contextual variables examined in the analysis included: net operating cash flow to total assets; net operating cash flow to sales revenue; cash flow cover (net operating cash flow to annual interest payments); total debt to gross operating cash flow (where gross operating cash flow equals total receipts from customers minus payments to suppliers); two annual periods of negative CFO, coded 1 = yes; 0 = no; three annual periods of negative CFO; coded 1 equal yes; 0 = no; cash resources (cash, deposits and marketable securities) to total assets; cash resources (cash, deposits and marketable securities) to current liabilities; current assets to current liabilities; working capital (current assets – current liabilities) to total assets; total debt to total equity; total liabilities to total equity; total debt to total assets; total liabilities to total assets; market value of equity to book value of debt; interest cover (reported EBIT to annual interest payments); reported EBIT to total assets; return on equity (net profit after tax to total equity); return on assets (net profit after tax to total assets); annual growth in sales revenue; sales revenue to total assets; retained earnings to total assets; natural log of total assets (a control variable for size); new economy sector (if a new economy sector firm coded 1, 0 otherwise); resources sector (if a resources sector firm coded 1, 0 otherwise); old economy sector (if an old economy sector firm coded 1, 0 otherwise); finance sector (if a finance sector firm coded 1, 0 otherwise). b Note that all MNL parameters are fixed. c ns = not significant d Interaction of total debt to total equity and the new economy sector variable (coded 1 if a new economy firm, 0 otherwise).

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TABLE 4 Marginal Effects for Significant Covariates in Final Mixed Logit and Multinomial Logit Models

Panel A: Mixed Logit

Prob (Y=0) Prob (Y=1) Prob (Y=2) Variables (t-values) (t-values) (t-values) Total debt to gross operating cash flow -.00029 (-4.053) .0002 (4.056) .000087(3.800) Working capital to total assets .00039 (9.24) -.00027 (-9.3) -.00011 (-9.54) Resource sector (1,0) .01409 (4.05) -.0099 (-6.74) -.0041 (-5.4) New Economy sector (1,0) -.0315 (-214.15) .021 (9.88) .009 (14.3) Cash resources to total assets .00199 (9.05) -.0014 (-9.5) -.00059 (-11.17) Net operating cash flow to total assets .00056 (8.73) -.00039 (-8.77) -.00016 (-8.31) Total debt to total equity -.0000298 (-2.59) .000021 (2.60) .0000088(2.43) Cash flow cover .00017 (7.66) -.00011 (-7.69) -.00005 (-7.2)

Panel B: MNL

Prob (Y=0) Prob (Y=1) Prob (Y=2) Variable (t-values) (t-values) (t-values) Total debt to gross operating cash flow .0001006 (6.32) -.0000618 (-6.37) -.0000387 (-6.16) Working capital to total assets -.000113 (-4.48) .0000695 (4.50) .0000436 (6.16) Sales revenue to total assets .0000575 (3.02) -.000035 (-3.0) -.000022 (-3.31) Finance sector (1,0) -.0234 (-8.24) .01426 (4.40) .00914 (4.74) New Economy sector (1,0) -.02847 (-11.5) .01733 (5.19) .011146(15.41) Cash resources to total assets -.0001331 (-4.77) .0000818 (4.80) .0000512 (4.95) Net operating cash flow to total assets .00005511 (2.82) -.0000338(-2.83) -.0000212 (-2.82) Cash flow cover -.0000256 (-3.3) .0000157 (3.3) .0000098 (3.8)

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TABLE 5

Fixed and Random Parameter Estimates and Model-Fit Summary for (Distributed Lag) Mixed Logit Model (100 Halton draws)

Variables Mixed Logit Parameter

Estimates (t-values) Fixed parameters: Constant -5.85 (-4.613) Resource sector (1,0) -26.32 (.000) New Economy sector (1,0) -16.732 (-.091) Finance sector (1,0) -39.77 (-.004) Random parameter means: Cash resources to total assets -0.94808 (-.878) Net operating cash flow to total assets -0.0679 (-1.155) Total debt to total equity -.0036 (-.831) Cash flow cover -.099 (-3.305) Working capital to total assets -.0646(1.762) Total debt to gross operating cash flow .0067(.09) Standard deviations of random parameters: Cash resources to total assets 0.056 (.07) Net operating cash flow to total assets 0.004 (.08) Total debt to total equity 0.0004 (.316) Cash flow cover 0.0001 (.005) Working capital to total assets 0.001 (.069) Total debt to gross operating cash flow .0009(.037) Log-likelihood at zero -166.46 Log-likelihood at convergence -14.5 Sample size 1515

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TABLE 6

Forecasting Performance of Final Mixed Logit and Multinomial Logit Models across Distress States 0-2 Pooled Data (Reporting Periods 1-5)

Nonfailure (0) Insolvent (1) Outright Failure (2) Model Actual Predicted Actual Predicted Actual Predicted Mixed 95.60% 95.90% 2.28% 1.84% 2.10% 2.20% MNL 95.50% 99.30% 2.34% 0.58% 2.15% 0.11%

Last reporting period prior to failure

Nonfailure (0) Insolvent (1) Outright Failure (2) Model Actual Predicted Actual Predicted Actual Predicted Mixed 95.70% 96.20% 2.37% 1.71% 1.91% 2.02% MNL 95.70% 99.37% 2.37% 0.59% 1.91% 0.02%

Third reporting period prior to failure

Nonfailure (0) Insolvent (1) Outright Failure (2) Model Actual Predicted Actual Predicted Actual Predicted Mixed 95.70% 95.90% 2.02% 1.97% 2.17% 2.04% MNL 95.60% 99.27% 2.32% 0.59% 2.03% 0.13%

Fifth reporting period prior to failure

Nonfailure (0) Insolvent (1) Outright Failure (2) Model Actual Predicted Actual Predicted Actual Predicted Mixed 96.20% 95.80% 1.93% 1.77% 1.84% 2.37% MNL 96.20% 99.38% 1.93% 0.57% 1.84% 0.04%

version 2.0 32

APPENDIX TABLE 1 Pearson Product-Moment Correlations Between Significant Covariates

Net operating

cash flow to total assets

Cash flow cover

Total debt to gross

operating cash flow

Cash resources to total assets

Working capital to

total assets

Total debt to total equity

Sales revenue to

total assets

New economy

sector Resources

sector

Old economy

sector Finance sector

Net operating cash flow to total assets 1 0.2428 0.0267 -0.1592 0.1523 0.0097 0.1725 -0.1575 -0.0671 0.1383 0.0402

Cash flow cover 1 -0.0174 -0.0199 0.0379 -0.0041 0.1095 -0.0336 -0.0488 0.041 0.021 Total debt to gross operating cash flow 1 -0.0949 -0.0026 0.2328 -0.0052 -0.0324 -0.058 0.0641 0.0174

Cash resources to total assets 1 -0.1047 -0.1529 -0.1595 0.1299 0.0827 -0.2624 0.1523

Working capital to total assets 1 0.0036 0.0637 -0.0007 -0.0407 0.0353 -0.006

Total debt to total equity 1 0.0646 -0.0394 -0.0718 0.0912 -0.001

Sales revenue to total assets 1 -0.0285 -0.2283 0.2525 -0.0794

New economy sector 1 -0.2252 -0.4225 -0.1772 Resources sector 1 -0.4851 -0.2035 Old economy sector 1 -0.3817 Finance sector 1