Focused vs unfocused models for bankruptcy prediction: Empirical evidence for Spain

Laguillo, Gonzalo; Castillo, Agustín del; Fernández, Manuel Ángel; Becerra, Rafael; Laguillo, Gonzalo; Castillo, Agustín del; Fernández, Manuel Ángel; Becerra, Rafael

doi:10.22201/fca.24488410e.2018.1488

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Contaduría y administración

Print version ISSN 0186-1042

Contad. Adm vol.64 n.2 Ciudad de México Apr./Jun. 2019 Epub Dec 10, 2019

https://doi.org/10.22201/fca.24488410e.2018.1488

Focused vs unfocused models for bankruptcy prediction: Empirical evidence for Spain

Gonzalo Laguillo¹

Agustín del Castillo¹

Manuel Ángel Fernández¹^*

Rafael Becerra¹

^¹Universidad de Málaga, España

Abstract

Using financial information from Spanish companies belonging to different economic sectors, this study has developed focused and unfocused models for bankruptcy prediction. The comparison of both types of models has allowed us to determine the superiority of unfocused models, which in most cases show a great predictive capacity and reduce the elaboration cost of numerous focused models. This study also provides insight into the variables that explain bankrupt-cy in different economic sectors and helps decision making on the use of a specific model of bankruptcy prediction.

JEL Codes: C53; G33

Keywords: bankruptcy prediction; financial ratios; logistic regression; economic sectors

Resumen

Usando información financiera de empresas españolas pertenecientes a distintos sectores económicos, este estudio ha desarrollado modelos centrados y descentrados para la predicción de quiebra. La comparación de ambos tipos de modelos nos ha permitido determinar la superioridad de los modelos descentrados, que en la mayor parte de los casos muestran una gran capacidad de predicción y un fuerte ahorro de costes de elaboración frente al desarrollo de numerosos modelos centrados. Este estudio también aporta conocimiento acerca de las variables que explican la quiebra en los diferentes sectores económicos y ayuda a la toma de decisiones sobre la utilización de un determinado modelo de predicción de quiebra.

Códigos JEL: C53; G33

Palabras clave: Predicción de quiebra; ratios financieros; regresión logística; sectores económicos

Introduction

The prediction of corporate bankruptcy has received special attention in financial research over the last five decades, with numerous studies focusing on determining the factors behind it. This monumental research task has generated a wide variety of models, supported in turn by very diverse methodologies. One of the paths initially taken by the literature was the development of models that had been built from a sample of companies belonging to several sectors and which, therefore, could be considered as off-center models (^{Casey and Bartczak, 1985}; ^{Odom and Sharda, 1990}; ^{Altman et al., 1994}; ^{Wilson and Sharda, 1994}). The development of these off-center models has been important throughout time, predominantly those built using samples of medium and large companies from different sectors (^{Charalambous, Chatitou and Kaourou, 2000}; ^{Chen, Härdle and Moros, 2011}; ^{Sangjae and Wu, 2013}). The literature on bankruptcy prediction also highlights the development of models based on samples of companies belonging to specific sectors of activity, which have been called centered models. The most popular of the centered models is the one used for credit institutions (^{Santomero and Vinso, 1977}; ^{Martin-del-Brio and Serrano-Cinca, 1995}; ^{Alam et al., 2000}). Another of the most popular centered models has been used for industrial companies (^{Altman, 1968}; Diamond, 1976; ^{Appetiti, 1984}; ^{Zavgren, 1985}; Grover, 2003). Recently, models have also been developed focusing on companies from other sectors, such as Internet companies (^{Wang, 2004}), hospitality companies (^{Park and Hancer, 2012}; ^{Fernández, Cisneros and Callejón, 2016}), agricultural companies (^{Mateos-Ronco et al., 2011}), construction companies (^{Gill de Albornoz and Giner, 2013}), and commercial and service companies (^{Keener, 2013}).

A detailed analysis of the literature on bankruptcy prediction allows us to observe the existence of a definite pattern regarding the building of off-center models as opposed to centered models, with the former being much more numerous than the latter. However, it is not possible to draw a definite conclusion on the superiority of one type of model over another (^{Bellovary, Giacomino and Akers, 2007}). The absence of a practical conclusion on the superiority of a centered model over an off-center model may be due to the fact that one type of model and another could not be compared homogeneously due to the disparity of methodologies, approaches, available databases, time periods and countries, among other issues. Therefore, the existence of this gap in the literature, which does not make it possible to elucidate the superiority of off-center models over centered models, is an important research issue that this work seeks to solve. To this end, this work has selected different samples of Spanish companies that were and were not in bankruptcy in the 2010-2015 period. Among these samples, some are integrated by companies that belong to different economic sectors and have been used to build off-center models. Other samples contain only companies from a certain sector of activity and have been reserved for the building of centered models. All the models have been built with the same methodology, specifically, Logistic Regression. Having both off-center and centered models developed from homogeneous samples, referring to the same time period and country, and built with the same methodology, has allowed obtaining robust conclusions on the design of bankruptcy prediction models in different economic sectors, and on the efficiency of off-center models, which in most cases imply a great saving of costs compared to the elaboration and development of numerous centered models.

Our work consists of the following parts. Following this introduction, section 2 offers a taxonomy of bankruptcy prediction studies. Section 3 presents the methods of analysis used in this research. Section 4 establishes the process of obtaining and treating the samples, the variables used, and the criteria considered for their selection. Section 5 presents the results of the empirical research. Finally, the main conclusions obtained are detailed.

Review of the literature and research hypotheses

The analysis of corporate bankruptcy has received considerate attention in financial research during the last five decades. Numerous research studies have been carried out focused on determining the factors that cause corporate bankruptcy, with a special focus on how to predict it before it happens. The pioneering authors of empirical studies on bankruptcy prediction were ^{Beaver (1966)} and ^{Altman (1968)}, applying methods of Discrimination Analysis and Multi-discrimination analysis, respectively. From these initial studies, the main concern in the literature on bankruptcy prediction was not only to determine which factors to include in the models, but to assess which method was the most effective in making predictions. According to this criterion, much of the work has been carried out around the so-called pure individual classifiers. These include statistical classifiers, such as the Multi-discriminant analysis and Logistic Regression models, which are based on statistical theory (^{Ohlson, 1980}; ^{Zavgren, 1985}; ^{Tseng and Hu, 2010}; ^{Piñeiro, de Llano and Rodríguez, 2013}). Since the 1990s, other methods such as artificial intelligence, based on Neural Networks (^{Tam, 1991}; ^{Tam and Kiang, 1992}; ^{Wu et al., 2008}; ^{Callejón et al., 2013}), Vector Support Machines (^{Shin et al., 2005}; ^{Min and Lee, 2005}), Genetic Algorithms (^{Rafiei et al., 2011}; Etemandi et al., 2009), Decision Trees (^{Chen, 2011}; Gepp et al., 2010; ^{Li et al., 2010}), and the Combination of Classifiers (^{Ravisankar and Ravi, 2010}; ^{Li et al., 2013}; ^{Sun et al., 2016}) have also been used.

On the other hand, and with reference to the variables considered in the previous literature as bankruptcy predictors, it can be deduced that the most common was the “Profit after Taxes/ Total Assets” ratio, and that the second most frequently used factor was the “Current assets/ Current liabilities” ratio. In addition, the number of variables considered in the construction of the models has fluctuated between 1 and 57 (^{Bellovary, Giacomino and Akers, 2007}).

Another term utilized in the literature is global bankruptcy prediction models, which refers to those that have been developed for companies across a country or region. ^{Korol (2013)} incorporates this approach and makes a comparison between two regions, ^{Platt and Platt (2008)} for three regions of the world, and ^{Alaminos, del Castillo and Altman et al. (2016)} at the global level using a Logistic Regression model. Similarly, ^{Altman et al. (2017)} apply the Z-score for a wide worldwide base of bankrupt companies and ^{Jabeur (2017)} uses Logistic Regression of partial least squares from a diverse base of French companies.

In addition to the abovementioned works, which have largely developed off-center models, the literature also highlights those that have been constructed from samples of companies in specific economic sectors, and which are therefore called centered models. In the Agriculture sector, the work of ^{D’Antoni, Mishra and Chintawar (2009)} and of ^{Mateos-Ronco et al. (2011)} stands out. ^{D’Antoni, Mishra and Chintawar (2009)} used a sample of agricultural companies and concluded that characteristics such as size, type of ownership and age of the entrepreneur were decisive for the probability of bankruptcy. In the Industrial sector, ^{Callejón et al. (2013)} developed a model that achieves an accuracy of 92%, revealing that bankruptcy is negatively related to the ability to repay debt through the funds generated and the profitability of the company. ^{Bartoloni and Baussola (2014)} provided a centered model using methods of Multi-Discrimination Analysis and Enveloping Data Analysis and concluded on the superiority of the latter with regard to predictability. For the Construction and Real Estate sectors, ^{Gill de Albornoz and Giner (2013)} compared the accuracy of the centered models to that of the off-center models, proving the superiority of the former to the latter. Similarly, with companies in the Construction sector, ^{Spicka (2013)} built a centered model that showed that the inadequate relation between debt/profitability and the generation of insufficient reserves are potential causes of bankruptcy. With companies from the Commerce and Services sectors, ^{Keener (2013)} developed a centered model that demonstrated that bankrupt companies had fewer employees, a lower cash to current liabilities ratio and higher debt to equity ratios, and ^{Fallahpour, Lakvan and Zadeh (2017)} tested several Genetic Algorithms, finding that the profitability variables as the most significant. Finally, and with companies in the Hospitality sector, ^{Park and Hancer (2012)} built a centered model with which they detected that the variables Maneuvering Fund/ Total Assets, Total Liabilities/Net Equity, and Total Liability/Total Assets were the best predictors of bankruptcy. For their part, ^{Fernández, Cisneros and Callejón (2016)} showed that by using information close to the time of bankruptcy (one or two years earlier), the most relevant variable to predict bankruptcy in hotels is that which relates EBITDA to current liabilities, but when using information farther away from the time of bankruptcy (three years earlier), the return on assets is the most significant variable.

Although the development of bankruptcy prediction models has been important, it is not possible to find conclusions on the superiority of off-center or centered models in the existing literature. As indicated earlier, this lack of conclusions comparing both types of models may be due to the fact that it has not been possible to homogeneously compare one type of model and another, given the disparity of methodologies, approaches, available databases, time periods and countries with which the existing models have been built. Consequently, this gap in the literature, which does not allow us to elucidate the superiority of off-center models over centered models, has motivated us to formulate the following research hypotheses:

Hypothesis 1 (H1): The introduction of sectoral qualitative variables in an off-center model improves its capacity to predict bankruptcy.

Hypothesis 2 (H2): An off-center model with sectoral qualitative variables predicts bankruptcy correctly in any economic sector.

The case of acceptance of hypothesis H1 would modify the off-center model, indicating that there are sectoral differences to explain the bankruptcy process of companies, but trying to maintain the maximum degree of similarity between the sectors. For its part, not rejecting hypothesis H2 would allow a single explanation of how companies go bankrupt in different sectors.

Methodology

This work uses Logistic Regression techniques and Model Selection Criteria to contrast the research hypotheses proposed. Logistic Regression is a classification technique in which the dependent variable exclusively considers two categories. Moreover, it departs from less restrictive assumptions than other statistical classification techniques and allows the model to incorporate qualitative variables (^{Visauta, 2003}). The logistic function is limited between 0 and 1, providing the probability that an element is in one of the two established groups. This means that, from a dichotomous event, it predicts the probability that the event will or will not take place. If the probability estimate is greater than 0.5, then the prediction is that it does belong to that group, otherwise, the assumption would be that it belongs to the other group considered.

The model is based on the quotient between the probability of an event occurring and the probability that it will not occur. Thus, the probability of an event occurring, P(Yi =1/xi), will be determined by expression (1).

PYi=1/xi=eβ0+β1X1+…+βkXk1+eβ0+β1X1+…+βkXk 1=1+e-β0+β1X1+…+βkXk (1)

Where β ₀ is the constant term and β ₁,…, β _k are the coefficients of the variables.

The Odds ratio indicates the number of times the phenomenon is more likely to occur than not and is formulated according to (2).

Odds=PYi=11-PYi=1=1/1+e-β0+β1X1+…+βkXk1/1+eβ0+β1X1+…+βkXk 1+eβ0+β1X1+…+βkXk=1+e-β0+β1X1+…+βkXk=eβ0+β1X1+…+βkXk (2)

The estimated coefficients (β ₁,…,β _k ) represent measures of changes in the Odds ratio. In this sense, a positive coefficient increases the probability of occurrence, whereas a negative value decreases the probability of occurrence of the same (^{Hair et al., 1999}). Applying logarithms in (2) gives a linear expression of the model, as it appears in (3), in which the coefficients would be estimated by applying the maximum likelihood method.

Yi=ln*PYi=11-PYi=1=ln⁡eβ0+β1X1+…+βkXk=β0+β1X1+…+βkXk (3)

On the other hand, and in reference to the Model Selection Criteria, this work uses both Akaike (AIC), as well as Schwarz (BIC) and Hannan-Quinn (HQC) in order to make the conclusions obtained very robust. These criteria have been successfully employed in previous research on bankruptcy prediction (for example, ^{Alaminos, del Castillo and Fernández, 2016}). AIC is the basic criterion among those based on statistical information (Akaike, 1974). In the general case, it is expressed as it appears in (4).

AIC=2k-2Ln(L) (4)

where k is the number of parameters and L the maximum value of the likelihood function of the estimated model. The basic idea underlying the use of the AIC criterion for model selection is to maximize the logarithm of the expected likelihood function of a given model. ^{Schwarz (1978)} suggested that the AIC criterion might not be asymptotically justifiable and presented an alternative information criterion based on a Bayesian (BIC) approach. This criterion penalizes the number of parameters with Ln (n) instead of with 2. Thus, the expression of the BIC criterion would be as it appears in (5).

BIC=-2Ln L+Lnn×k (5)

with k being the number of parameters, L the maximum value of the likelihood function of the estimated model, and n the number of observations.

On the other hand, HQC can be considered a variant of the BIC criterion, with a penalty for the magnitude of the sample size. ^{Hannan and Quinn (1979)} initially suggested this criterion for selecting the order of self-regression, as it appears in expression (6). As for the AIC and BIC criteria, this criterion selects the model that minimizes the value of HQC.

HQC=-2LnL+2Ln Lnn×k (6)

Data and variables

In order to contrast the research hypotheses established in this work, 12 samples of Spanish companies were used, 6 of them using information corresponding to 1 year before the bankruptcy of the companies (t-1) and another 6 with information from 2 years before bankruptcy (t-2). Samples for both t-1 and t-2 have been considered, including companies belonging to five economic sectors (agriculture, industry, construction, commerce and services, and hospitality), and which are used for the construction of off-center models. Samples from companies in a single sector have also been used for the development of centered models. In all samples, the same number of bankrupt and non-bankrupt companies has been considered, following the criteria applied in most bankruptcy prediction studies (^{Du Jardin, 2015}). Within the scope of this work, a company is considered bankrupt if it has the legal status of bankruptcy, according to the considerations made by the Spanish bankruptcy law 22/2003 of July 9th, as well as the following modifications made to it (Royal Decree Law 3/2009 of March 27th on urgent measures in view of the evolution of the economic situation and Law 38/2011 of October 10th). For its part, the identification of companies belonging to each sector of activity has been done in function of the classification carried out by the CNAE-2009 codes, and the financial information of said companies was obtained from the SABI database (Iberian Balance Sheets Analysis System) belonging to Bureau van Dijk (for the financial years 2010-2015). A breakdown of the number of companies in each sample is shown in Table 1. For the construction of the models estimated in this work, 70% of the data for each sample (validation data) has been reserved for the construction of the models, while the remaining 30% of the data has been used to verify the predictive capability of said models (testing data).

Table 1 Number of companies in the samples

	Estado	t-1	t-2
Off-center models	Not bankrupt	1.500	1.500
Off-center models	Bankrupt	1.500	1.500
Centered models. Agriculture	Not bankrupt	300	300
Centered models. Agriculture	Bankrupt	300	300
Centered models. Industry	Not bankrupt	300	300
Centered models. Industry	Bankrupt	300	300
Centered models. Construction	Not bankrupt	300	300
Centered models. Construction	Bankrupt	300	300
Centered models. Commerce and Services	Not bankrupt	300	300
Centered models. Commerce and Services	Bankrupt	300	300
Centered models. Hospitality	Not bankrupt	300	300
	Bankrupt	300	300

Of all companies in the samples, financial information has been taken to comprise a set of variables as bankruptcy predictors. All the variables have been selected from the previous literature on centered and off-center models. For the off-center models, those that have been considered in 20 or more bankruptcy prediction works have been selected (^{Bellovary, Giacomino and Akers, 2007}). For the Agriculture centered models, the variables proposed by ^{D’Antoni et al. (2009)}, ^{Mateos-Ronco et al. (2011)}, ^{Dietrich et al. (2005)} and ^{Wasilewski and Madra (2008)} were used. For the Industry sector models, those previously used by ^{Callejón et al. (2013)}, ^{Bartoloni and Baussola (2014)}, ^{Zhang et al. (2013)}, ^{Grüenberg and Lukason (2014)} and ^{De Andréz et al. (2012)} were selected. For the Construction sector models, the variables proposed by ^{Spicka (2013)}, ^{Gill de Albornoz and Giner (2013)}, ^{Mínguez-Conde (2006)}, ^{Stroe and Barbuta-Misu (2010)} and Treewichayapong et al. (2011) were used. For the Commerce and Services sector models, those used in the work of Keener (2003) and ^{He and Kamath (2006)} were used. Finally, for the Hospitality sector models, the specific variables were those used in the models by ^{Park and Hancer (2012)}, ^{Fernández, Cisneros and Callejón (2016)}, ^{Cho (1994)}, ^{Gu (2002)}, ^{Youn and Zheng (2010)} and ^{Kim (2011)}. Additionally, and to be used in the off-center models, other qualitative variables have been incorporated (Agriculture Dummy, Industry Dummy, Construction Dummy, Commerce and Services Dummy, Hospitality Dummy) that take a value of 1 if the company belongs to one of the five economic sectors considered, and a value of 0 otherwise. Along with the previous variables, another dichotomous variable was used as a dependent variable, which takes the value of 1 if the company is identified as bankrupt and a value of 0 otherwise. Table 2 shows the definitions of all the variables used as bankruptcy predictors.

Table 2 Definition of the quantitative variables

Code	Definition
	Off-center model variables
VD1	Profit after Taxes/Total Assets
VD2	Current Assets/Current Liabilities
VD3	Operating Funds/Total Assets
VD4	EBIT/Total Assets
VD5	Total Revenue/Total Assets
VD6	Quick Ratio
VD7	Total Debt/Total Assets
VD8	Current Assets/Total Assets
VD9	Profit after Taxes/Net Equity
	Centered model variables, Agriculture
VCA1	Equity/Total Debt
VCA2	EBIT/Financial Expenses
VCA3	EBIT/Total Revenue
	Centered model variables, Industry
VCI1	Operating Income/Total Revenue
VCI2	Sales/Customers
VCI3	(Current Assets-Current Liabilities)/Capital
VCI4	Equity/Non-current Liabilities
VCI5	Financial expenses/Total Revenue
VCI6	Ln (Total Assets)
VCI7	Operating Income/Net Equity
VCI8	Total Revenue/Non-current Assets
	Centered model variables, Construction
VCC1	Financial Expenses/EBIT
VCC2	Operating Income/Total Revenue
VCC3	Equity/Total Debt
	Centered model variables, Commerce and Services
VCCS1	EBITDA/Total Liabilities
VCCS2	EBIT/Financial Expenses
VCCS3	EBIT/Current Liabilities
VCCS4	Sales/Stocks
VCCS5	Sales/Total Assets
	Centered model variables, Hospitality
VCH1	EBITDA/Current Liabilities
VCH2	EBITDA/Total Liabilities
VCH3	Total Financial Debt/EBITDA
VCH4	Total Financial Debt /Capital
VCH5	Credit Sales/Customers
VCH6	Free Cash Flows/Total Debt

Results

Tables 3-8 present the main descriptive statistics of the variables selected for the construction of off-center and centered models for each of the samples. In general, the variables present different average values for companies that are bankrupt compared to those that are not, which makes it possible to confirm that they can be used for the construction of the proposed models.

Table 3 Descriptive statistics. Off-center models

		VD1	VD2	VD3	VD4	VD5	VD6	VD7	VD8	VD9
t-1	Not bankrupt	0.05	3.37	0.24	0.05	2.14	2.34	0.23	0.60	0.04
		(0.21)	(11.68)	(0.30)	(0.41)	(11.34)	(10.25)	(0.28)	(0.29)	(1.95)
	Bankrupt	-0.25	1.81	0.32	-0.20	1.33	0.74	0.42	0.59	0.30
		(1.00)	(4.67)	(0.44)	(0.72)	(1.89)	(1.22)	(0.47)	(0.31)	(2.39)
t-2	Not bankrupt	0.05	3.39	0.24	0.05	2.14	2.36	0.23	0.60	0.03
		(0.21)	(11.80)	(0.30)	(0.41)	(11.43)	(10.37)	(0.28)	(0.29)	(1.95)
	Bankrupt	-0.10	2.74	0.37	-0.07	1.46	1.63	0.38	0.61	0.07
		(0.50)	(20.69)	(0.38)	(0.44)	(2.76)	(20.27)	(0.86)	(0.31)	(2.58)

Standard deviation in parenthese

Table 4 Descriptive statistics. Center models. Agriculture

		VD1	VD2	VD3	VD4	VD5	VD6	VD7	VD8	VD9	VCA1	VCA2	VCA3
t-1	Not bankrupt	0.02	1.55	0.20	0.04	0.93	1.03	0.33	0.45	0.08	2.87	4.99	0.08
		0.03	0.97	0.28	0.04	0.67	0.95	0.21	0.28	0.07	4.56	13.18	0.17
	Bankrupt	-0.03	0.99	0.27	-0.01	0.66	0.46	0.47	0.46	0.16	0.75	-1.14	-0.02
		0.07	0.87	0.28	0.08	0.84	0.42	0.30	0.29	0.57	2.20	17.64	0.29
t-2	Not bankrupt	0.05	3.39	0.24	0.05	2.14	2.36	0.23	0.60	0.03	2.52	2.85	0.08
		(0.21)	(11.80)	(0.30)	(0.41)	(11.43)	(10.37)	(0.28)	(0.29)	(1.95)	(4.31)	(2.24)	(0.17)
	Bankrupt	-0.10	2.74	0.37	-0.07	1.46	1.63	0.38	0.61	0.07	0.96	1.88	0.09
		(0.50)	(20.69)	(0.38)	(0.44)	(2.76)	(20.27)	(0.86)	(0.31)	(2.58)	(1.19)	(2.93)	(0.10)