Download Predictive models of default risk in local governments. A logistic

PREDICTIVE MODELS OF DEFAULT RISK IN LOCAL GOVERNMENTS. A LOGISTIC
REGRESSION
Pina Puntillo
Researcher in Business Economics
University of Calabria
Department of Business Science
Phone +39984492247
Fax +39984492277
E mail [email protected]
PREDICTIVE MODELS OF DEFAULT RISK IN LOCAL GOVERNMENTS. A LOGISTIC
REGRESSION
Key words – Financial risk, local government, logistic regression
Abstract
With the activation of fiscal federalism in Italy it has become an urgent matter to assess the risks of
local authority insolvency and to find the appropriate tools to do this. In other word the fiscal
federalism has led to a growing interest in local government bankruptcy prediction models. In this
context the present research proposes to model the risk of local authorities’ insolvency on the basis
of accounting variables. The purpose of this research is to test the usefulness of financial data for
predicting local government failure in Italy. After a brief literature review on predictive model of
failure the study will then go on to focus on the main drivers of fiscal risk and their effects in
accounting terms. The aim of this phase of the research is to identify the variables to be then used as
explanatory variables in the quantitative models for estimating or predicting insolvency. The
predictive models are an application of regression models that assess the likelihood of the
occurrence of an event. From the various models in the literature identifying financial crises, type of
regression model with a binary dependent variable: it includes the logit and probit regression model.
These are non linear models that use standard or logistic distribution functions. The explanatory
variables of the model are the accounting variables identified in the first phase of the work.
Once constructed on a theoretical basis, the model will then be tested empirically on a sample of
local bodies in Italy..
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PREDICTIVE MODELS OF DEFAULT RISK IN LOCAL GOVERNMENTS. A LOGISTIC
REGRESSION
Summary of contents
Introduction; 1. Financial Distress in Italian Local Governments; 2. Literature Review; 3 Research
Methodology; 3.1 The explanatory variables; 3.2 Dataset;3.3 Hypothesis; 3.4 Logit regression
model; 3.5 Probit regression model; 4 Results; Conclusions.
1. Financial distress in Italian local governments
The reforms In Italy in the 1990s, culminating in the modification of Section V of the Constitution
law, changed the economic and financial structure of local government by affirming the principle of
financial autonomy for all levels of government to guarantee cover for the public functions carried
out by local bodies following the acceptance of the principle of subsidiarity. Thus, the system of
public finance evolved towards a decentralised system characterised by the progressive reduction of
government transfers, by the replacement of the principle of past spending with a criterion based on
expected spending required to cover essential levels of assistance and services (Borgonovi, 2009: p.
15; Paoloni et al., 2007: pp. 577-615). In this new system internal resources and the ability to find
other sources of finance through recourse to capital markets will become increasingly important.
Financial autonomy, in fact, encourages local bodies to act responsibly with regard to the cost of
decision-making and internal competition (Borgonovi, 2005: p. 162).
In view of the foregoing, it is argued, therefore, monitoring of all financial aspects of the institution
produces reflections becomes crucial for the survival of local authorities (Mele et al., 2005: p. 487);
in other words, to avoid situations of financial distress of local authorities, it is necessary to develop
a greater "risk sensitivity" (Speca, 2002; p.772-821), and identify an appropriate methodology for
financial risk assessment. With the introduction of the fiscal federalism the policy makers have
become increasingly concerned with the question of the ‘financial sustainability’ of individual local
councils. According to Deal (2007) the financial health, the fiscal stress and municipal bankruptcy
must be studied in order to avoid future filings of municipal bankruptcy as well as to improve the
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financial health of local governments. Predictive models of risk of failure for local governments
have been tested mainly in the United States and Australia. In Europe there is not currently great
empirical literature, excluding research on rating models adopted by international agencies such as
Moody's, Standard & Poor's, etc.
These rating agencies stress the importance of data from company accounts in the evaluation of the
overall credit worthiness of a business; furthermore, studies carried out on this question have shown
the existence of a significant relationship between ratings and quantitative variables (Cannata, 2001;
p. 37 onwards). the scenario likely to emerge from the full activation of fiscal federalism will
require an ever more careful evaluation of the risk of insolvency and the use of reliable models to
achieve this. Given the current state of public finances, quantitative predictive models for assessing
the risk of insolvency of public bodies have come to play a key role. Only with the ability to
identify quickly and accurately potential crisis situations, will it become possible to adopt effective
corrective measures. Starting from these assumptions, therefore, the work will examine, from a
theoretical perspective, predictive models of financial distress for local governments. In the second
part of the work the model, developed on a theoretical level in the first part, will be tested
empirically in order to demonstrate its validity.
2. Literature Review
Over the years, failure prediction or financial distress models have been much discussed in
accounting and credit management literature. From the late 1960s, when Beaver (1967) and Altman
(1968) published their first failure prediction model, an enormous number of academic researchers
from all over the world have been developing good failure prediction models based on various
modelling techniques. There are numerous examples: Altman et al. (France, 1974), Taffler and
Tisshaw (UK, 1977), Knight (Canada, 1979), Fischer (Germany, 1981), Ooghe and Verbaere
(Belgium, 1982), Ko (Japan, 1982), Fernandez (Spain, 1988), Swanson and Tybout (Argentina,
1988). For a more complete list, see Zavgren (1983), Altman (1984), Taffler (1984), Jones (1987),
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Keasey & Watson (1991), Ooghe et al. (1995), Dimitras et al. (1996), Altman and Narayanan
(1997). Altman & Saunders (1998). Moreover in many papers some attention has been paid to the
comparison of different scoring techniques (for example logit analysis, neural networks and
decision trees) on the same dataset have been published, for example Bell et al. (1990), Altman et
al. (1993), Curram and Mingers (1994), Joos, Ooghe and Sierens (1998), Kankaanpää and Laitinen
(1999)., or to the performance of different types of failure prediction models (Mossman et al.,
1998). However most of researches have focused, from both a theoretical and empirical point of
view with reference to the private sector. This study aims to contribute, from an empirical point of
view, in this field of research with reference to local governments.
Beaver (1967a) was the pioneer in building a corporate failure prediction model with financial
ratios. He was the first researcher to apply a univariate model – a “univariate Discriminant analysis
model” – on a number of financial ratios of a paired sample of failing and non-failing companies in
order to predict company failure. In his studies Beaver demonstrated the predictive ability of
accounting data (Baever HW, 1966; Beaver HW et al., 1968). Univariate analysis is a very simple
technique that classifies a company as healthy if the value assumed by an accounting index is above
the critical value, also called the cut off point; on the contrary, if its value is below the cut off point
the company is considered at risk (Lachenbruch, 1975). Discriminant analysis can also be expressed
graphically:
Fig.1 - Estimate of model through linear discriminant analysis
Bankrupt
healthy
Source: Barontini (2000), The evaluation of credit risk, p. 67.
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The cut off, in other words the critical point that determines the company’s classification,
corresponds, therefore, to the equidistant value between the averages of the two groups. This
methodology provides the same results as those obtained through a multiple linear regression, in
which the dependent variable assumes a dichotomous value (1 in the case of a company crisis and 0
for the healthy company)1.
The Univariate Discriminant analysis is appealing in his simplicity (for each ratio, one simply
compares the ratio value for the firm with a cut-off point and decides on the classification
accordingly), but his main disadvantage lies in his inability to account for the coexisting effects of
many different indicators of default and provides largely arbitrary risk-metrics (Aaro Hazak, Kadri
Männasoo 2007). Moreover the Univariate analysis is based on the stringent assumption that the
functional form of the relationship between a measure or ratio and the failure status is linear. This
assumption is often violated in practice, where many ratios show a non-linear relationship with the
failure status (Keasey & Watson, 1991). Moreover, firm classification can only occur for one ratio
at a time, which may give inconsistent and confusing classifications results for different ratios on
the same firm (Altman, 1968; Zavgren, 1983). This problem is called the ‘inconsistency problem’.
When using financial accounting ratios in a univariate model, it is difficult to assess the importance
of any of the ratios in isolation, because most variables are highly correlated (Cybinski, 1998). In
the same context, the univariate model contradicts with reality in that the financial status of a
company is a complex, multidimensional concept, which can not be analysed by one single ratio.
Finally, the optimal cut-off points for the variables are chosen by ‘trial and error’ and on an ‘ex
post’ basis, which means that the actual failure status of the companies in the sample is known
(Bilderbeek, 1973). Consequently, the cut-off points may be sample specific and it is possible that
the classification accuracy of the univariate model is (much) lower when the model is used in a
predictive context (i.e. ‘ex ante’). In response to Beaver, Tamari (1966) realized a ‘risk index’. It is
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Fisher has demonstrated that there is a close analogy between discriminant analysis and linear regression, given that
the coefficients estimated with the two methodologies are in perfect proportion; only the estimate of the constant
differs.
For more information on this matter see Maddala G. Limited Dependent and Qualitative Variables in Econometrics,
Cambridge University Press, 1983.
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a simple ‘point system’, which includes different ratios, generally accepted as measures of financial
health. Each firm is attributed a certain number of points, between 0 and 100, according to the
values of the ratios for the firm. A higher total of points indicates a better financial situation. This
approach shares the same weaknesses of univariate analysis and provides largely arbitrary riskmetrics. In 1968, Altman (1968) introduced the Multiple Discriminant Analysis (MDA) which is “a
statistical technique used to classify an observation into one of several a priori groups dependent
upon the observation’s individual characteristics… attempts to derive a linear [or quadratic]
combination of these characteristics which ‘best’ discriminates between the groups (Altman, 1968,
p. 592)”. In his study he estimated a model called the ‘Z-score model’ used in an enormous volume
of studies. After the 1980s, the MDA method is frequently used as a ‘baseline’ method for
comparative studies (Altman & Narayanan, 1997).
An MDA model consists of a linear combination of variables, which provides the best distinction
between the group of failing and the group of non-failing firms. For example, Altman’s Z-score
model is a linear combination of the following ratios: working capital / total assets, retained
earnings / total assets, earnings before interest and taxes / total assets, market capitalization / total
debts and sales / total assets (Altman, 1968). The linear discriminant function is the following
(Lachenbruch, 1975):
Di = D0 + D1Xi1 + D2Xi2 + … + DnXin (1)
with Di = discriminant score for firm i (between -∞ and +∞),
Xij = value of the attribute Xj (with j = 1, …, n) for firm i,
Dj = linear discriminant coefficients with j = 0, 1,…, n.
In an MDA model, several (mostly financial) characteristics or ‘attributes’ of a company are
combined into one single multivariate discriminant score Di. This discriminant score is a one
dimensional measure which has a value between -∞ and +∞ and gives an indication of the financial
health of the firm. The score is seen as a risk measure. In most studies, a low discriminant score
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indicates a poor financial health.
In 1980s MDA method has been replaced by conditional
probability models’ (Zavgren, 1983; Zavgren, 1985; Doumpos & Zopoudinis, 1999) as logit
analysis (LA), probit analysis (PA) and linear probability modelling (LPM). Ohlson (1980)
pioneered in using logit analysis on financial ratios in order to predict company failure while
Zmijewski (1984) was the pioneer in applying probit analysis (PA).
On the theoretical the logistic regression is a more appropriate instrument than linear regression,
since it allows to define two distinct classes (good and bad risks) (Hand DJ and Henley WE, 1997,
p. 533). In this study, it allows you to define two distinct classes: local authorities with financial risk
and local authorities with no financial risk. In the author’s opinion, logit and probit models can be
successfully employed in the analysis of the risk of insolvency of local authorities, because they
allow researchers to estimate the probability that a crisis occurs, given the values of the account
variables, that constitute the explanatory variables of the model, i.e. X.
The econometric methodology of the logit analysis was also chosen to avoid some know problems
associated with the Multivariate Discriminant Analysis (MDA). Some of the problems of this
technique are: 1) there are some statistical requirements imposed on the properties of the
distribution of predictors: for example, the variance-covariance matrix of the predictors should be
the same for both groups (failed and no-failed firms); 2) the requirement of normally distributed
predictors certainly reduces the use of binary independent variables (Eisenbeis, 1977; Joy and
Tollefson, 1975). The MDA approach has long been the leading method for predictions of business
failure. The main drawback is certainly the assumption of normally distributed regressors: since
generally the financial ratios are not normally distributed, the maximum likelihood methods and in
particular the logit and probit were the most frequently used (Martin, 1977; Demirgüc-Kunt, 1989;
Lennox, 1999; Trussel J. M.. Patrick P. A, 2009). There are also some problems with the "matching
procedures" that are generally used in the MDA: the failed and no-failed firms are matched based
on criteria such as size and sector, and these tend to be somewhat arbitrary (Ohlson JA, 1980). The
use of logit analysis, instead, avoids essentially all of the problems discussed in relation to MDA.
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The fundamental problem of the estimate may be reduced simply to the following statement: “as the
company belong to a prespecified population, what is the probability that the company failed within
a prespecified period of time?” With logit analysis no assumptions should be made regarding the
prior probability of failure and/or distribution of the predictors. These are the main advantages
compared to discriminant analysis (Ohlson JA, 1980).
Conditional probability models allow to estimate the probability of company failure conditional on
a range of firm characteristics by a non-linear maximum likelihood estimation. The models are
based on a certain assumption concerning the probability distribution. The logit models assume a
logistic distribution (Maddala, 1977; Hosmer & Lemeshow, 1989), while the probit models assume
a cumulative normal distribution (Theil, 1971). In the linear probability models, the relationship
between the variables and the failure probability is assumed to be linear (Altman et al., 1981;
Gloubos & Grammatikos, 1988). Both logit and probit models provide the probability of occurrence
of an outcome described by a dichotomous (or polytomous) dependent variable using coefficients of
the independent variables (Zavgren, 1985; Vranas, 1992). The main difference between logit and
probit analysis is that the former uses the cumulative logistic probability function, while the latter is
based on the cumulative standard normal distribution function. A significant advantage of these
models over discriminant analysis is that they do not require the independent variables to be
multivariate normal (Keasey, K. and Watson, R., 1991). Furthermore, they provide much more
useful information to the financial/credit analysts in bankruptcy prediction, since except for the
classification of the firms into bankrupt and non-bankrupt ones, they also provide the probability of
failure of a firm. Besides the fact that logit analysis has no assumptions concerning the distribution
of the independent variables and the prior probabilities of failure, there are some other important
advantages of LA. First, the output of the LA model, the logit score, is a score between zero and
one, which immediately gives the ‘failure probability’ of the company (Ohlson, 1980; Ooghe et al.,
1993). Second, the estimated coefficients in a LA model can be interpreted separately as the
importance or significance of each of the independent variables in the explanation of the estimated
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failure probability (Ohlson, 1980; Mensah, 1984; Zavgren, 1985), provided that there is no multicollinearity among the variables. Third, LA models allow for qualitative variables with categories
rather than continuous data. In this case, dummies are used (Ohlson, 1980; Keasey & Watson, 1987;
Joos et al, 1998a).
The formula of the linear probability model is that of the multiple linear regression model:
Yi = β0 + β1X1i + β 2X2i +…. + β kXki + ui;
where Yi is binary, so that
Pr(Y = 1|X1;X2;…. ;Xk) = β0 + β1X1i + β 2X2i +…. + β kXki + ui
The linear probability model can also be expressed graphically.
Fig. 2 - Linear probability model
Stock J. H., Watson M. W. (2005) Introduction to econometrics
The linearity that ensures the linear model is easy to use can also be its major drawback, however.
These models run into problems of inference, and the assumptions of normality/homoschedasticity
of the errors are violated (i.e., the remainders are dichotomous and heteroschedastic).
The probit regression model with multiple regressors takes the following form:
Pr(Y = 1|X1,X2, ……Xk) = Ф (β0 + β1X1 + β2X2 +…. + βkXki)
where Ф is the normal distribution function.
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If β is positive then an increase in X increases the probability that Y = 1. If β is negative then an
increase in X reduces the probability that Y = 1. The logit regression model with multiple regressors
takes the following form:
Pr(Y = 1|X1,X2, ……Xk) = F (β0 + β1X1 + β2X2 +…. + β kXki) =
= 1/ 1+e -(β0 + β1X1 + β2X2 +…. + βkXki)
Where F is the standard logistic distribution function.
If β Is positive then an increase in X increases the probability that Y = 1. If βis negative then an
increase in X reduces the probability that Y = 1. Logit and probit simulation often produce similar
results2.
Fig. 3 - Model Probit Logit
Stock J. H., Watson M. W. (2005) Introduction to econometrics
The three models (linear probability, logit and probit) are approximations of the unknown
population regression function
E( Y/X ) = Pr ( Y= 1/X ).
2
For more information on the econometric models used see Stock J.H., Watson M.W., 2005.
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The linear model is probably the easiest to use and read, but fails to capture the nonlinear nature of
the true regression function of the population. The logit and probit regressions model the
nonlinearity in probability. The classic static-econometric methods can be considered the most
commonly used methods for developing business models to forecast failure. In addition to these
traditional statistical methods, academic researchers are beginning to use several alternative
methods to analyze and predict business failure (Balcaen S. and Ooghe H., 2004). These methods
are the result of strong technological progress and the so-called artificial intelligence (AI).
The best-known alternative models that have produced a considerable number of studies on the
prediction of business failure are the survival analysis, decision trees and neural networks (Balcaen
S. and Ooghe H., 2004); in the following table are shortly mentioned the main alternative - even the
lesser known - indicating the academic contributions on the subject of study developed in this
research and summarize the salient characteristics of themselves:
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Table 1 - Alternative methods applied for the prediction of business failure
Methods
Authors
Description of the methods
First-generation
Merton (1974)
This approach stems from the option pricing
models
Black et al. (1976)
model originally developed by Black and Cox in
Geske (1977)
1973, and that finds a first application to the risk
Vasicek (1984)
of insolvency with the work of Merton (1974).The
Crouhy & Galai (1994)
model is based on structural variables of the firm
Jones, Mason & Rosenfeld in which the event of default resulting from the
(1984)
evolution of the assets of the company.
According to the adaptation of Merton and
subsequent authors, insolvency occurs when the
value of the business is less than the value of
liabilities. The corporate debt is modeled as a call
option on assets with a strike price equal to
liabilities, the option will be exercised until the
value of the activity is highest in liabilities.
Default occurs if the option is exercised before it
expires.
Second-generation
Kim,
Ramaswamy
& This evolutionary approach simplifies the first
models
Sundaresan (1993)
class of models both explicitly exogenously cash
Nielsen, Saà-Requejo, Santa flows in the event of default that simplifying the
Clara (1993)
process of default. This happens when the value of
Hull & White (1995)
the assets of the company reaches a certain limit;
Longstaff & Schuwarz (1995)
what changes of the elements considered is the
recovery rate which is exogenous and independent
from the value of the business and therefore from
the event of default.
Despite these efforts in line with the Merton
model, the second-generation models have several
disadvantages which are the cause of the limited
empirical application.
Reduced form models Littermann & Iben (1991) While the structural models observe default as the
Madan & Unal (1995)
result of a gradual process of deterioration of asset
Jarrow & Turnbull (1995) values, the reduced form models (also called
Jarrow, Lando & Turnbull intensity-based models) represent the default as an
(1997)
unexpected event (sudden surprise).
Lando (1998)
These models are highly empirical, and do not
Duffie & Singleton (1999) provide a stochastic process that generates the
Duffie (1999)
default, but they tend to decompose observed
credit spreads on the debt to ensure both the
probability of default, which is an unexpected
event that the LGD (Loss Given Default),
calculated as a complement to the recovery rate.
Expert Systems
Messier & Hansen (1988)
Expert systems are the result of the strong
Hawley et al. (1990)
development of the artificial intelligence. The
method of expert systems has been applied by
Messier and Hansen (1988) for the prediction of
failure. An expert system depends on the
knowledge representation of experts on bankrupt,
and such knowledge is transformed into a set of
rules to be used for the prediction of business
failure.
Decision Trees
Frydman et al. (1985)
A decision tree is a classification tree that can help
(or method of
Joos et al. (1998)
to identify, through an evaluation form, applicants
recursive
requesting a loan with a low or high risk of
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partitioning)
Survival analysis
Lane et al. (1986)
Luoma & Laitinen (1991)
Kauffman & Wang (2001)
Method of linear
programming
Gupta et al. (1990)
Forward Looking
Montesi and Papiro (2003)
Catastrophes theory
(or chaos theory)
Scapens et al. (1981)
Lindsay & Campbell (1996)
insolvency and is built in order to support action
over the granting of credit . Therefore, it can be
used to assess the risk of business failure and the
financial risk of local authorities.
Survival analysis is a statistical methodology that
allows us to study the risk that an individual has to
live or not a certain event in a certain timeframe.
In the case object of study, this method allows us
to study the risk that a firm (or a local authority)
has to fail (declare bankruptcy) in a certain period
of time.
In contrast to classical statistical models, a model
of survival analysis not assume a dichotomous
dependent variable (dummy).
The method of linear programming (LGP) is one
of several techniques derived from mathematical
programming. The model formulates intragroup
and intergroup differences between risky business
and not and, on the basis of these differences, it
calculates a score for each firm and a limit (cutoff) for the discrimination group. This creates a
hyper-plane, which is used to distinguish between
the group of risky business and the group of
healthy companies. The cut-off or limit is
determined (1) maximizing the weighted sum of
the distances between the observations and the
cut-off and (2) minimizing the weighted sum of
violations of the cut-off limit.
The forward looking, proposed by Montesi and
Papiro (2003) is another method used to calculate
the probability of default.
The logic of this method it not proposed to
accurately predict the value that may take some
variable in the future, but to estimate what may be
the true value within a range of possible values
according to a probability distribution. For each
test is generated a scenery of the company, which
includes the development of a complete budget
estimate for each forecast period and for each
period; is determined then the margin of solvency:
it reconstructs the evolution of solvency
requirements in relation to uncertainty assumed. It
is estimated that the financial fragility of the
company against future unforeseen events.
Scapens et al. (1981) were the first researchers
who considered the business failure as a
catastrophic event and who have used
catastrophes theory to explain business failure.
The theory implicitly assumes that firms are
deterministic and predictable, but only in short
periods of time. A second assumption of the
model is that the healthy and no risky firms are
more inclined to fail than unhealthy and risky
firms. It is clear that a model of chaos theory
requires an appropriate measure of chaos. Lindsay
& Campbell (1996) measured the amount of chaos
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Neural networks
Odom & Sharda (1990)
Cadden (1991)
Coats & Fant (1991)
Raghupathi et al. (1991)
Tam e Kiang (1992)
Chilanti M. (1993)
Coats & Fant (1993)
Fletcher & Goss (1993)
Udo (1993)
Weymaere & Martens (1993)
Altman et al. (1994)
Rosenberg e Gleit (1994)
Wilson & Sharda (1994)
Boritz et al. (1995)
Lenard et al. (1995)
Back et al. (1996)
Bardos & Zhu (1997)
Sironi e Marsella (1998)
Yang et al. (1999)
Atiya (2001)
Neophytou et al. (2001)
Daubie & Meskens (2002)
of the companies using the so-called “Lyapunov
exponent”: the larger this exponent, as soon as the
company becomes unpredictable, so it is more
risky.
These models are inspired by research in biology
based on the structure of the human brain, whose
the primary computational units can be considered
the neuron (Rosenblatt 1961; Minsky and Papert,
1969); it was thought that artificial neurons to be
able to solve problems complexes such as the risk
of insolvency (F. D'Annunzio, G. Falavigna,
2004).
Neural networks are created using a set of input
and output nodes that are connected to
intermediate nodes called hidden-layer nodes. The
hidden layers allow the network to generate a
number of mapping functions so that the desired
output can be produced using a given set of inputs.
When applied to the analysis of the business
failure, a neural network allows to assess the risk
of business failure, based on an array of
information input and on an output vector. In
order to build one neural network for predicting
bankruptcy of firms, the researcher must use a
certain algorithm; different algorithms are
proposed, the most common is the backpropagation algorithm (Rumelhart et al.,
1986).The neural network model usually nonlinear interactions in a data set much better than
the statistical procedures of analysis, especially
when the data distribution is unknown (Maher JJ,
Tarun K., Sen TK, 1997).
The alternative methods mentioned above are clearly more sophisticated and computationally more
complex than the classical statistical methods such as discriminant analysis, logit analysis, probit
and lineare (Balcaen S. and Ooghe H., 2004). An interesting question to ask is whether these
alternative methods produce bankruptcy prediction models higher performance than traditional
statistical methods. The question of which forecast method produces the best results has been
relieved in several papers; there are many empirical studies that compare the results and/or
predictive capability of bankruptcy prediction models based on different techniques.
Unfortunately, there is no study that systematically compares all possible methods and that arrives
to identify which method is the best (Balcaen S. and Ooghe H., 2004). Perhaps the reason is to be
found in the fact that no method is the “best” in absolute. What is the best depend on the details of
the problem: the structure and the availability of data, the characteristics used, the objective of the
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research. With reference to selection of predictive model to be used in this study, it is argued that
not only has no generally agreed approach has been achieved, but that the inherent difficulties in
designing a satisfactory method of measuring sustainability make any consensus in future most
unlikely. As a result, this study only considers failure prediction models estimated with classical
statistical techniques, such logistic regression. A second reason why we focus on logistic regression
technique is because it is used in most failure prediction research, both in the earlier versions and in
the most recent ones. Multiple discriminant analysis is by far the dominant classical statistical
method, followed by logit analysis (Altman & Saunders, 1998).
3 Research Methodology
The terms of ‘bankruptcy’, ‘failure’, ‘(cash) insolvency’, ‘liquidation’ and ‘(loan) default’ are
commonly used and sometimes refer to the same failure concept. An overview of the meaning of
these terms can be found in Altman (1993) and in Argenti (1976). It is clear that this study is based
on the ‘legal definition’ of failure. According the Text of the laws on local government, approved
by Legislative Decree 18 August 2000, No. 267 in Articles 244-269 "The financial distress occurs
when the body, municipality or province, is no longer able to perform the essential functions and
services defined, or if there are credits against the organizing third parties to whom are unable to
cope with the ordinary means of restoring fiscal balance or the debt instrument with off balance
sheet" .If it occurs any of these conditions, the Authority has to declare bankruptcy and start a series
of procedures to bring itself to the financial recovery through the previous zero debt3, and then
return to the condition of being "healthy".
The regression models with binary dependent variable allow us to interpret the regression as a
probability model whose dependent variable is equal to one; in other words Y is a variable dummy
or dichotomy in the sense that it can only assume two values 1 or 0. Since in this research we will
study the probability of financial distress of local authorities, in function of some financial ratios, it
3
For debt means the sum of the deficit of the administration to final account last year prior to bankruptcy and debt off
balance sheet which occurred before the reference year of distress, recognized as meeting the institutional purposes of
local government.
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is appropriate to use the regression model with binary dependent variable: y is a dummy that takes
the value 1 if the local authority is ruined, 0 otherwise. As the dependent variable Y is binary, the
regression function of the population corresponds to the probability that the dependent variable is
equal to one, given X. The coefficient β1 associated with a regressor (predictor variable) X is the
variation in the probability that Y=1 associated to a unitary variation in X (Palomba G., 2008, p. 112).
To overcome these problems we use non-linear models specifically designed for binary dependent
variables, in other words probit and logit regression models. Many of the published studies are
characterized by the application of logit analysis (including probit and logit model), which
calculates the conditional probabilities (or logit scores), between 0 and 1, on a sigmoidal curve, that
in the holding an event occurring (Hosmer and Lemeshow, 1989). In this research, the logit analysis
estimates the probability that a crisis occurs, given the values assumed by the variables in the
budget.
A particular feature of this methodology is that it does not require the normality hypothesis as
regards the distribution of the variables considered: even if the independent variables do not satisfy
this condition, as is often the case with budget indexes, the logit analysis still determines consistent
estimates (Maddala, 1983; Maddala, 1992). Estimation of the logit or probit model requires the
identification of parameters β maximising the function; this takes place by solving a system of non
linear equations, obtained by setting at zero the prime derivative of likelihood function with respect
to the single coefficients to be estimated. The logit model assumes a logistic distribution; if, on the
other hand, a normal distribution is assumed the probit model is obtained. In other words the
relation between the probability of the occurrence of an event and the explanatory variables is, in
most cases, non linear. Hence, recourse is made to cumulative distribution functions (in logit
models) or normal (in probit models).
Since the regression with a binary dependent variable Y models the probability that Y=1, it is
reasonable to adopt a non linear formulation that constrains the chosen values to assume values
17
between zero and one. In the logit and probit regressions, therefore, cumulative distribution
functions or CDF are used, because they produce a probability between one and zero, the normal
distribution function for the probit regression, and the logistic CDF for the logit regression, also
referred to as logistic regression.
Thereby apply a logit-probit model, the purpose of this research is to estimate the risk of insolvency
of the Italian local authorities. After identifying the explanatory variables and thus which account
values to insert in the econometric model estimating the risk of insolvency, we go on to the
empirical application of the model on a sample. Once the local authorities that have experienced
problems of insolvency in a given time period have been identified, other local bodies, that can be
considered “healthy” (in the sense that their accounts are in order) are then selected at random. The
budget values of n bodies, that will be used in the model as regressors, are then measured in order to
construct a matrix on which to base the evaluation. The next phase will be the estimation of the
model (probit or logit), that is to say evaluation of the unknown parameters; the model will then be
validated through statistical procedures. The following section will focus, therefore, on factors of
financial risk to be considered as explanatory variables in the econometric models estimating
insolvency risks.
3.1 The explanatory variables
The accounting values representing financial dynamics highlight anomalies or situations that could
lead to financial crisis are as follows:
 financial autonomy;
 recovery time of outstanding payments;
 internal income resources;
 spending on personnel;
 total income;
 outstanding arrears.
18
This study basically maintains that the above-mentioned indexes can be considered as valid proxies
for the financial structure of local authorities. In particular, financial autonomy and recovery time of
payments synthesise tax and rates policies. Spending levels on personnel synthesise the level of
rigidity in the budget, and arrears represent spending commitments that have not be fulfilled for
lack of resources.
We shall now explain why these indexes have been chosen as explanatory variables in the model.
In the evaluation of local authority financial risk tax policy has two aspects. Above all the presence
of considerable sums in taxes or rates indicates that the authority is equipped with a certain financial
flexibility to cope with any future budgetary demands. Since control and collection are two quite
distinct legal parts of the process of guaranteeing income, the means and speed of collecting taxes
are very important. The regulation of collection is, in fact, a determining element in the evaluation
of a local body’s credit worthiness (Mussari, 2002; p. 27-77).
An inefficient system of recovery generates permanent arrears. If these arrears cannot be
transformed into earnings in a reasonable time span, they can have a negative effect on the direction
and value of the administration’s overall turnover.
The reform process aimed at granting autonomy to local bodies hinges on the recognition and
importance of their decision taking authority, especially with reference to budget management. This
implies that local authorities can either deal with debt recovery themselves or delegate the task to
outside agents. In the first case the direct responsibility for recovery can increase the predictability
of incoming cash flows (Carnevale, 2006; p. 39-343), but it also has organisational implications
(staffing, procedural, logistic) and hence related costs.
As regards outstanding debts, the local body can assess the feasibility of adopting coercive
measures or of writing off the debts. Through the Factoring Institute local bodies can subcontract
debt collection to a third party (Piscino 200.).
19
Recourse to a third party implies legal costs for the service, but avoids the costs connected with
coercive measures. It is clear that each authority must make a careful assessment of the costs and
benefits of the two options.
In the econometric model therefore we must include an index of financial autonomy and recovery
time of outstanding debts.
Index of financial autonomy:
Title 1 + (Title 111/Current earnings*100)
This index relates the authority’s earnings (from local taxes/rates and other income) with the total
current income identifying to what extent the authority manages to be financially autonomous with
respect to the total transfers of income from central and regional government. The function of this is
to highlight the level of guaranteed current income from internal sources and to what extent the
resources required come from the State. The higher the value of this index the greater the autonomy
of the authority (i.e. less dependent on transfers from central government) and the consequent
lessening of financial risk.
Recovery time of arrears
Recovery (Title 1 + Title 111) / Controls (Title 1 + Title 111)
In general high percentages indicate structural efficiency and lack of problems regarding debt
collection and low risk of financial difficulties. Low percentages indicate instead lack of or
adequate technical and human resources, likely difficulties in recovering arrears, negative
consequences and, therefore, higher risk of financial difficulties. Spending on personnel is
calculated in the following way:
Spending on Personnel/Current spending (Title 1)
This indicator measures the proportion of overall current spending dedicated to personnel. In the
last five years the Italian parliament has passed various laws regarding spending on personnel in
local government, in an attempt to reduce the overall level of spending and the ratio of spending on
20
human resources vis-à-vis total spending. In the accounts of public bodies this spending is a fixed
item that creates inflexibility and, above all, takes up the greater part of overall income. The Court
of Auditors has, indeed, identified the ability to reduce the proportion of the budget spent on
staffing as a parameter of virtuous behaviour.
The collection of arrears is certainly a crucial factor in the financial management of local
authorities. As regards the monitoring of arrears, it is fundamental to discover the nature of the debt;
in fact, if the repayment of outstanding arrears gives rise to excessive repayment times, this could
have an adverse knock on effect on financial stability of the local authority. In the econometric
model the incidence of outstanding arrears must be treated as an independent variable.
Level of outstanding arrears
Total outstanding arrears/Total commitments)*100
One risk factor of a financial nature linked to the debt position of the authority concerns the
contraction of debts not covered by the budget. When the body does not respect the stipulated
budget procedure, the commitment undertaken is known as a debt “below the line” (Nobile, 2004).
This involves unlicensed budget items that constitute a violation of accounting principles; the
Observer for the financing and accounting of local bodies refers to such payments as monetary
obligations, relating to the provision of a public service, that is valid from a legal point of view, but
is not covered financially. Article 194 of the legislation on Local Authorities (Testo Unico Enti
Locali) attributes to the governing council of the local body the right to recognise the legitimacy of
such “below the line” undertakings and of reintegrating such sums into the budget. The types of
debts “below the line” recognised in Article 194, Section1, derive from executive decisions, cover
for deficits of consortiums, specialised companies or institutions, operating within the limits of their
statute, convention or founding purpose, provided that the obligation to balance the budget is
respected (Article 114), and the deficit incurred by management decisions be covered by the
application of political and financial policies (Articles 31 and 114), by the recapitalisation of the
21
companies set up to undertake local public services, by procedures of compulsory purchase or
occupation concerning works of legally authorised public utility (Dpr. N. 327, 2001), for the
acquisition of goods or services, in violation of the obligations laid down in Sections 1 2 and 3 of
Article 191 (any spending, even if carried out incorrectly, provided that it satisfied the needs of the
body and is covered by the assets of the body is considered a “below the line debt” that can be
reintegrated in the budget). It would be very useful to insert all the possible “below the line” debts
in the econometric model. However, since the relevant information is not easily available, all one
can include in the explanatory variables are those “below the line” debts that have been recognised.
Nevertheless, it would certainly be more fruitful if we could tract down the information on
unrecognised “below the line” payments, especially as it is these payments that, being without
financial cover, often lead to financial deficits. Unrecognised “below the line” debts escape the
attention of official accounting procedures and thus remain an unknown quantity.
Moreover, the model will contain control variables- as regressors- to capture the influence that other
factors of an economic or territorial nature have on the dependent variable. In order to avoid
producing distorted estimates, therefore, it is considered preferable to include in the regression
model, as independent variables, other factors that influence the risk of bankruptcy. These are
supplementary variables that do not interact with the independent variables in the model. If we want
to estimate the causal effect of the variable of interest on the dependent variable correctly it is
necessary, in most cases, to control (i.e. neutralise) the disruptive action exercised by one or more
supplementary variables, defined for this reason as control variables. The following control
variables are included in the model: Total Income, Size of Population, Size of Area, Per capita
Income, Demographic Classification.
Table 2 – Explanatory variables in the model
Explanatory variables
Financial
Autonomy (X1)
Recovery time of arrears
(X2)
Acronym used
afg
vrep
Description
Measures size of own resources (Tit. 1 + Tit. 3) on
current income (Tit. 1 + Tit. 2 + Tit. 3).
Relation between arrears collected and estimates
regarding items 1,2 and 3 of income
22
Proportion of spending on
personnel (X3)
Incidence of arrears
isc
rp
Measures size of spending on personnel in relation
to overall spending
Measures size of spending commitments not paid on
31/12
Total Income (X5)
te
Overall financial resources of the authority. In
accounting terms they are equal to the sum of the
first four items in the budget; part 5 excluded as
contents represent nether income nor expenditure
Average earnings (X6)
redm
Average income
Population (X7)
abitanti
Number of inhabitants in the council considered
Area
Kmq
Total area of authority in kilometres 2KMQ.
Demographic
classification (X9)
cd
Councils grouped in three classes 1A, 2 A,,3 A.
3.2 Dataset
The sample chosen for the research includes local government authorities in Italy- some healthy
from a financial point of view, and others in financial crisis- classified on the basis of different
demographic groupings. The list of authorities whose bad financial state had been declared was
taken from the Ministry of the Interior while, as regards the healthy authorities, the sample was
drawn in a random matter from local authorities throughout the whole country, utilising the web
site: Comuni Italiani. For the construction of the accounting indexes we used the official budgetary
data from the website of the Ministry of the Interior (link Finanza Locale).
The following
classification was then used for the demographic groupings:
a. councils with less than 5000 inhabitants belong to the first grouping;
b. councils with a number of inhabitants between 5,000 and 15,000 belong to the second
group;
c. councils with a population above 15,000 belong to the third group.
The information supplied by the above source enabled us to select in a causal manner, and for each
of these we extracted the following information: population, area in square kilometres, average
income. From the Ministry of the Interior, and specifically from the item “Bilanci Consuntivi” we
collected accounting and other data that allowed us to calculate the explanatory variables, in other
words the determinants of financial crisis: revenues, receipts from current transfers, non-tax revenue
23
(assessed and collected), total revenue and fees for staff, running costs, residual income, total
expenditure. The analysis was carried out for three years 200, 2003 2006. The dataset is reported in
Attachment 1.
3.3 Hypothesis
The hypotheses to be demonstrated are the following:
H1: the increase in financial autonomy, and the rapidity of access to internal sources of
funding decreases the probability of financial crisis;
H2: the increase in arrears increases the probability of financial crisis;
H3: the increase in the proportion of spending on personnel increases the probability of
financial crisis;
H4: membership of the largest demographic group (3) reduces the probability of financial
crisis.
In order to determine which of the explanatory variables considered is statistically significant
regarding the probability of financial crisis, logit and probit models were employed, on the
understanding that their results would not be dissimilar from each other.
3.4 Logit regression model
The logit model assumes the following formulation:
Pr(Y = 1|X1,X2, X3 X4, X5, X6, X7, X8 X9) = F (β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 +β6X6 + β7X7 + β8X8 +
β9X9i)
Where F is the standard logistic distribution function.
The Xs are the explanatory variables illustrated in Table 1.
Y is the dependent variable “crisis/non crisis” that assumes the value of 1 for the authorities in
crisis, and 0 for the healthy authorities.
24
If β is positive, then an increase in X increases the probability that Y=1. If β is negative then an
increase in X decreases the probability that Y=1.
In this study a 5% significance threshold is assumed.
Before the econometric estimation, carried out using STATA software, two variable temporal
dummies were created, one for the year 2003 and the other for the year 2006, while 2000 was
considered the base year. The temporal dummies are generated both to verify whether the
probability of a declaration of financial crisis varies from year to year, and also to evaluate the
existence of a correlation between the years. In Table 2 the statistics are reported, while in 3 and 4
the results of the regressions are found.
Table 3 - Descriptive statistics
Below are reported the results obtained, using non linear models, i.e. logit and probit. With these
models the probability of financial crisis is not estimated directly; instead it is necessary to relate
the derivative of the probability of crisis to the derivative of the regression (though the control
Stata, “Mfx Compute), in this way one can measure the marginal impact of the single regressor on
the probability of financial crisis (Pampel, 2000). In the following table the estimates of the logit
model are reported.
25
Table 4 - Logit model estimates
3.5Probit regression model
The probit model assumes the following formulation:
Pr(Y = 1|X1,X2, X3 X4, X5, X6, X7, X8 X9) = Ф (β0 + β1X1 + β 2X2 + β3X3 + β4X4 + β5X5 +β6X6 +
β7X7 + β8X8 + β9X9i)
Where
Ф is the normal distribution function.
The Xs are the explanatory variables illustrated in Table 1.
Y is the dependent variable: crisis/healthy assumes the value 1 for authorities in crisis and 0 for
healthy authorities.
26
If β is positive, then an increase in X increases the probability that Y=1. If β is negative then an
increase in X decreases the probability that Y=1.
The estimates of the Probit Model are reported in the table below.
Table 5 - Probit model estimates
4 Results
Tables 4 and 5 illustrate the results achieved using a logit and a probit estimator, respectively. In
both cases the estimate was adjusted for heteroschedasticity (Robust) in order to obtain robust
standard errors with respect to the potential heteroschedasticity of the errors. In the Logit Model the
demographic grouping was significant at 10% level, while population was significant at 5%. The
result for demographic grouping (also in the case of Probit) is interesting, in that it indicates that
the increase in demographic grouping reduce the probability of bankruptcy. With reference to the
27
variables of interest, we note that the variable for outstanding debts has, surprisingly, only marginal
significance at 10% level, while there is a 5% significance level for speed of recovery of income
and the incidence of spending on personnel, thereby confirming the expected direction. On the basis
of the results obtained, therefore, it is clear that
-
a unitary increase in the speed of recovery of local sources of income has a negative effect
on the probability of financial crisis, reducing it by around 0.71;
-
a unitary increase in the proportion of spending on personnel determines an increase in the
probability of financial crisis of 0.10.
The estimates carried out with the Probit Model are as follows: the variables Population, Rp, Vrep
and Isc are statistically significant at 5%. In this case as well, the more interesting variables (Vrep
and Isc) confirm the expected direction. In particular:
-
a unitary increase in the speed of recovery of local sources of income (Vrep) has a negative
effect on the probability of financial crisis of approximately 0.09;
-
a unitary increase in the proportion of spending on personnel (Ics) determines an increase in
the probability of financial crisis of 0.14.
In this study has been demonstrated the following hypothesis:
H1: the rapidity of access to internal sources of funding decreases the probability of financial crisis;
H3: the increase in the proportion of spending on personnel increases the probability of financial
crisis;
H4: membership of the largest demographic group (3) reduces the probability of financial crisis.
It is significant that, in both estimations, speed of recovery of local sources of income is found to be
more significant than financial autonomy (i.e., the proportion of local sources of income on overall
current income. It appears, therefore, that the ability to recover money rapidly, rather than the
ability to control one’s sources of income is of greater import as regards the probability of
bankruptcy. In other words, if the authority acquires the right to control a certain amount of their
own resources but does not have the ability to collect them in a short time, then the probability of
28
financial crisis rises. One can state, to sum up, that authorities are more likely to be declared
bankrupt, if they are unable to collect their income in a reasonable time, even if they enjoy greater
control over their resources, than authorities with less financial autonomy, but a better capability to
collect money owed in a short time.
From an accounting perspective the results of the estimates determine the following dynamics:
-
slowness in income collection determines cash flow shortages, that can lead to an increase in
debt, and consequently an increase in spending on servicing the debt; such shortages also
tend to increase the likelihood of “below the line” spending, in that spending cannot be
authorised as there is no financial cover at the time of the operation;
-
an increase in spending on personnel increases the level of rigidity in the budget and hence
reduces the level of financial cover for other expenditure.
It is easy to understand how the results, obtained with non-linear models, are similar. This is an
important aspect as it not only confirms Econometric Theory, but also and above all it confirms the
hypotheses the model rests on.
Conclusions
The results of the econometric analysis are especially interesting in the first place in the light of the
current situation of public finances in Italy.
The implementation of a decentralised system of public finance through the implementation of
fiscal federalism, has handed financial management over to local authorities. Moreover, the
reduction of central government transfers imposes on local authorities greater responsibility in the
running of their own incomes and the management of spending.
Legislation regarding both these aspects provides further confirmation of their importance. As
regards the management of local government sources of income, there have been various pieces of
legislation concerning the activity of local bodies, in particular regulating other means of raising
income, apart from direct taxation. A regulating authority (Albo) has been set up by the Finance
Ministry- DM 11/9/2000 n. 289- to establish the technical, financial and organizational
29
qualifications and competence of members. Moreover, as regards spending on personnel the
government has ruled that public bodies must ensure a reduction of spending in this area, both in
relative and absolute terms.
Within the overall goal of reducing the level of financial risk, it is important to establish a financial
dynamic that ensures a closer correspondence between income and spending in terms of time in
order to obviate shortages of cash flow. Furthermore, it would be advisable to assess sums
earmarked in the budget on the basis of their “sensitivity”, that is to say on the reaction of such
spending to variations in market interest rates over a set time span (Speca, 20002; p. 772-821).
The results of the research are unique in terms of the accounting implications too. The main
consideration in this regard is that accounting data can be evaluated in terms of utility and that
utility can be defined in terms of predictive ability
This study represents the first empirical study in Italy applying an econometric model predictive of
the risk of failure of local authorities. The implications for future research includes the modeling
techniques with the second generation.
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