Mathematical and numerical analysis for Predator-prey system in a polluted environment

1.   Introduction

Jackson (2018) states that "[I]f discretionary accruals are measures of earnings management (EM), then there should be a relation between these and ex-post cases of known manipulation." The present study assesses the ability of the specific accrual methodology based on loan loss provision (LLP) to detect fraudulent earnings in the largest fraud case in the history of the Portuguese banking sector − that of Banco Espírito Santo Group (GBES).

LLP is considered to be the most relevant and discretionary component in the detection of EM in the banking industry (e.g., Cornett et al. 2009; Cohen et al., 2014; Ozili and Outa, 2017; Chaity and Islam, 2022).

Ozili and Outa (2017) argue that LLP research is a fruitful area in banking research for several reasons: (1) it has a direct impact on bank interest margins, and consequently affects banks' overall earnings; (2) it is linked to bank regulators' micro-prudential surveillance and the informativeness of accounting disclosures in financial reports required by accounting standard-setters; and (3) it is a significant accrual, and bank managers have a great deal of discretion in the determination of LLP estimates and such discretion can be exploited to meet opportunistic financial reporting objectives.

A prolific stream of research has covered a wide range of issues relating to LLP. These include topics concerning LLP procyclicality (see Ozili and Outa (2017) for a comprehensive review). The literature on the role of LLP in bank EM is vast. The LLP model has been used to explore bank managers' opportunistic discretion and motivations (e.g., McNichols and Wilson, 1988; Wahlen, 1994; Ahmed et al., 1999; Beatty et al., 1995, 2002; Lobo and Yang, 2001; Anandarajan et al., 2003, 2007; Chang, 2008; Perez et al., 2008; Cornett et al., 2009; Kanagaretnam et al., 2003, 2004, 2005, 2010; Alali and Jaggi, 2011; Leventis et al., 2011; Kilic et al., 2012; Cohen et al., 2014; Bryce et al., 2015; Hamadi et al., 2016; Ozili, 2015, 2017a, b; Andries et al., 2017; Ab-Hamid et al., 2018; Chaity and Islam, 2022), as well as the role of corporate governance mechanisms in constraining the practice of EM (e.g., Wahlen, 1994; Ahmed et al., 1999; Beatty et al., 1995, 2002; Anandarajan et al., 2003, 2007; Chang, 2008; Fonseca and Gonzalez, 2008; Cornett et al., 2009; Kanagaretnam et al., 2003, 2004, 2005, 2010; Dahl, 2013; Bouvatier et al., 2014; Cohen et al., 2014; Curcio and Hasan, 2015; Ozili, 2017a; Ab-Hamid et al., 2018; Chaity and Islam, 2022). The consequences of the financial crisis on United States and European Union bank managers' provisioning policies have also been investigated (e.g., El Sood, 2012; Curcio et al., 2016).

The results of these studies are mixed and, to the best of our knowledge, the ability of the LLP model to detect ex-post cases of banking fraud remains largely unexplored. According to Ozili and Outa (2017), LLP research in this area is scarce. Furthermore, while Ozili and Outa (2017) claim that one major development in the LLP model has been the reduction in construct validity problems, they also observe that the processes, assumptions, methods, and other unobservable factors bank managers consider when making LLP estimates mean that research into the subject is a complex affair. This paper addresses these shortcomings in the literature and makes suggestions for future research.

We apply the LLP model to GBES by using a firm-level time-series regression approach, with data from the period 1992 to 2013. The time-series estimation of EM models, which is in the spirit of Jones's (1991) paper, is scarce in the EM literature. While the most widely used method is the cross-sectional estimation of EM models by year and industry, Owens et al. (2017) point out that firms in a particular industry are not necessarily homogeneous in their accrual-generation process, and this is an important assumption in EM models. Owens et al. (2017) demonstrate that, when models assuming homogeneity and stationarity within industries are employed, firms are inadequately categorised based on the discretion in the accruals. Jackson (2018) argues that "[E]conometrically speaking, discretionary accruals are simply deviations from industry averages".

The main results of this paper reveal that GBES's levels of discretionary LLP (DLLP) in the fraud period (2008 to 2013) are not significantly different from the pre-fraud years (1992 to 2007). Yet, the levels of LLP are significantly higher in the fraud period compared with the pre-fraud years, which is consistent with the procyclical nature of GBES's LLP. Overall, the results of a difference-in-difference approach do not show significant differences in GBES's DLLP compared with non-fraudulent banks in the fraud period. Interestingly, our evidence is consistent with the procyclicality of LLP across the entire sample of banks (including GBES). Additional tests do not support the hypothesis of income smoothing via LLP, either for the entire sample of banks or for GBES.

The proven facts of the fraud reveal a significant undervaluation of loans and financial instruments and an LLP underestimation, something that led us to believe that we would find negative DLLP in the fraud period and significantly different DLLP between the pre-fraud and fraud periods; GBES's DLLP should also have been significantly different from non-fraudulent banks in the fraud period. Nevertheless, the LLP model proved to be ineffective in detecting fraud at GBES and the use of DLLP.

The LLP model proved to be ineffective in detecting an ex-post case of fraud. This is consistent with Jackson (2018) who concludes that in ex-post known cases of material accounting misstatement, discretionary accrual models do not capture EM. This evidence challenges academics and regulators by stressing the importance of considering the complex nature of the LLP estimation process (as it is a function of the accounting system that generates the estimate), as well as the assumptions and the decisions of bank managers and other considerations that remain unknown or unobservable (Ozili and Outa, 2017). This paper explores a fraud case involving a family business group where the assumptions and the decisions of the bank managers and the potentially conflicting goals between family shareholders are highly relevant.

We find evidence that bank provisioning is procyclical with fluctuations in the business cycle. This holds for GBES and for a sample of non-fraudulent Portuguese commercial banks. Overall, our results contribute to the call for better coordination of the actions of accounting setters, regulators, and banking supervisory authorities (Curcio et al., 2016). They also provide support to the debate on the need for dynamic LLP (Ozili, 2017a). A balance must be found between levels of LLP and transparency that are needed by regulators and standard setters alike, and the specific factors that induce LLP procyclicality should be further investigated (Ozili and Outa, 2017).

The remainder of the paper is organised as follows. The following section presents the GBES case. Section 3 explains the research method, and Section 4 describes and discusses the results. Section 5 contains the concluding remarks.

2.   The case of the Banco Espírito Santo Group (GBES)

2.1.   The history of GBES

The history of GBES is intertwined with the history of the Espírito Santo family (Amaral, 2015). GBES started in the second half of the 19th century when the founder, José Maria do Espírito Santo e Silva, established a lottery, currency exchange, and securities business (Amaral, 2015). By the beginning of the 20th century, he was regarded as a major Lisbon banker (Amaral, 2015), and in 1915 he created a company, J. M. Espírito Santo Silva & Cª, in which the partners were mostly members of the family. By the time of his death in 1916, he had accumulated a fortune that made him part of the economic and social Portuguese élite (Amaral, 2015). From 1916 to 1973, his three sons headed the company in succession: José Ribeiro do Espírito Santo e Silva (1916−1932), Ricardo Ribeiro do Espírito Santo e Silva (1932−1955), and Manuel Ribeiro do Espírito Santo e Silva (1955−1972). The Espírito Santo family business adopted the corporate business dynasty costum, whereby the successor had to be a male member of the family.

In 1916, J. M. Espírito Santo Silva & Cª was dissolved, and a new firm (managed by the eldest son), Casa Bancária Espírito Santo Silva & Cª, was created. In 1920, this became a bank − Banco Espírito Santo (BES). In 1932, the founder's second oldest son succeeded his brother as chairman; a new management model was implemented and a new phase of consolidation and expansion of the company began (Amaral, 2015).

The Espírito Santo family business was one of the most important Portuguese business groups, though its growth was strongly driven by the close relationship it had with the Portuguese state between the 1930s and mid-1970s (Amaral, 2015). From 1933 through 1974, Portugal was ruled by a corporatist dictatorship called Estado Novo, a heavily interventionist regime that imposed very strict regulations on practically all aspects of economic activity (Santos, 1984; Silva et al., 2016). During this period, GBES and other Portuguese business groups became huge (Silva et al., 2016). The Estado Novo regime developed a complex system of economic regulations that constrained entrepreneurialism. Banking law was designed to prevent the financial crises caused by the maturity mismatch of commercial banks and imposed quite serious restrictions on the opening of new banks. In addition, through financing and import substitution policies, economic development was based on the construction of infrastructure and the promotion of national industry. As Amaral (2015) describes, BES took advantage of this structural change by creating a chain of branches all over the country, and during World War Ⅱ, it became the Portuguese largest commercial bank after merging with Banco Comercial de Lisboa (BCL) to form Banco Espírito Santo e Comercial de Lisboa (BESCL). The Espírito Santo family also enlarged GBES by establishing the Tranquilidade insurance company and acquiring major sugar, coffee, and palm oil plantations in Mozambique and Angola (Silva et al., 2016). In the 1950s and 1960s, BESCL was actively involved in the internationalisation of the Portuguese economy and followed this expansion by continually opening new branches: the number rose from 47 in 1960 to 82 in 1966. By the middle of 1970, BESCL reinforced its international position with acquisitions, partnerships, and the founding of banks in several countries (e.g., the United States, Angola, and the United Kingdom). Between 1972 and 1973 BESCL co-founded Libra Bank (London) and Banco Inter Unido (Luanda) (Amaral, 2015).

In 1973, GBES's chairman Manuel Ribeiro do Espírito Santo e Silva died, leading to a succession crisis. As was noted above, the three sons of GBES's founder succeeded him in order of birth, but when the last one died, it was not clear who would follow (Lima, 2000). The choice that most respected the principle of succession was José Maria B. C. Espírito Santo Silva, the eldest son of the founder's first-born son, but other branches of the family disagreed because José Maria was the son of divorced parents, which would not present the business in the best light (Amaral, 2015). Eventually, the eldest son of the deceased president took over. Manuel Ricardo P. Espírito Santo e Silva had the skills, the Espírito Santo family name, and a predominant position in terms of assets within GBES (he was married to a cousin, Maria do Carmo Moniz Galvão, great-granddaughter of the founder) (Lima, 2000; Amaral, 2015).

One year after the succession crisis, GBES's new dynastic leadership would be challenged by unexpected and dramatic events. In 1974 and 1975, several revolutions in Portugal and Africa raised questions about the legitimacy of the Espírito Santo family's fortune (Amaral, 2015). On 25 April 1974, a military coup overturned the Estado Novo dictatorship and the new rulers introduced a full-fledged democracy, bringing great changes to the country (Santos, 1984), one of which was the nationalisation of all the economic groups headquartered in Portuguese territories (including firms based in the Portuguese colonies) that had emerged during the Estado Novo. The most significant phase of the nationalisation process took place between March 1975 and July 1976. The banking and insurance companies were the first to be passed into public ownership, and this became part of a new dogma as companies were expropriated (or almost entirely expropriated) without compensation (Amaral, 2015). GBES was no exception, and at the end of September 1975 the Espírito Santo family left the country (Amaral, 2015).

Prevented from developing its activities as a private entity in Portugal, GBES shifted its attention to countries such as Brazil, Switzerland, France, and the United States. A high point was the creation of a holding company, the Luxembourg-based Espírito Santo International (ESI), in 1975 (Amaral, 2015). The business began to re-establish itself in Portugal in 1986, when private banking activity was re-introduced. With the support of Crédit Agricole and a core of Portuguese shareholders, GBES created the International Credit Bank (BIC) and the Espírito Santo Investment Company (ESI). In 1984, a holding company (under the control of ESI), the Espírito Santo Financial Group (ESFG), was founded in Luxembourg. This brought the financial investments of the group under one roof (Amaral, 2015). In 1990, GBES recovered the Tranquilidade insurance company and in 1992 (after a reprivatisation process that had begun the year previously) regained full control of BESCL (renamed Banco Espírito Santo – BES in 1999).

In 1991, Manuel Ricardo Espírito Santo e Silva died. By that time, the branch of the Espírito Santo family that descended from the founder's second-born son had acquired sufficient power to capture the GBES presidency (they were major shareholders of GBES firms and held senior executive positions on the boards of directors) (Lima, 2000). Thus, António Ricciardi (husband of the oldest daughter of the founder's second-born son) succeed as chairman of GBES (Lima, 2000). At the same time, Ricciardi's oldest nephew, Ricardo do Espírito Santo Silva Salgado (grand-grandson of GBES's founder), who had helped rebuild the group from abroad between 1976 to 1982, assumed the position of chief executive officer (CEO) (Lima, 2000). In the following years, he also became CEO of BES and ESFG (Amaral, 2015).

Over time, GBES became extremely complex from an organisational perspective. Between 1991 and 2013 (when Ricardo Salgado was CEO), the group had a presence in 25 countries across four continents through its branches, representative offices, or investees, making it the most international of Portugal's corporate groups (Amaral, 2015). The process of internationalisation was driven by Salgado himself, who betted on the strategic triangle of Africa, Brazil, and Spain. By 2013, this area generated half of GBES's profits − by which time, BES was one of the three largest private Portuguese banks.

Figure 1 shows the basic structure of the Espírito Santo business group in 2013. At its base is the major holding ES Control (ESC), with the partners displayed in the form of a cascade. Five major shareholders were represented at ESC, four of them with family ties: cousins Ricardo Salgado, António Ricciardi, and José Manuel Espírito Santo, and their aunt Maria do Carmo Moniz Galvão Espírito Santo Silva (widow of Manuel Ricardo Espírito Santo). The ESC shareholdings of the four amounted to 17.05%, 17.84%, 18.53%, and 19.37%, respectively. The different family branches occupied positions on the ESC board of directors, where strategic decisions were made and issues (including matters of succession) were decided. The left-hand side of Figure 1 represents the financial areas of the particular business groups, the right side the non-financial areas, and the centre shows the non-operational holding companies. The financial areas include the Luxembourg-based holding ESFG and GBES, which were involved in banking, insurance, and finance. The BES bank had a leading position in the latter: by the end of 2013, it represented about 95% of the value of ESFG assets (in consolidated accounts). At the end of 2013, it released a balance sheet showing a loss of more than €95 billion, and in August 2014, GBES collapsed.

2.2.   The GBES fraud

Over the years, Ricardo Salgado assumed a strong leadership position in GBES, and by the end of 2013, the ESC family branches led by Ricardo Salgado and António Ricciardi began to diverge. This, and the end of an old alliance between GBES and SEMAPA (a Queiroz Pereira family-owned and financial healthy Portuguese business group involved in the production of pulp and paper, cement, and other construction materials) brought GBES's problems to the attention of the general public (Guerreiro, 2018).¹

¹ The alliance ended in 2013 with the Queiroz Pereira family exchanging their 6.67% shareholding in ESC with the 40% Espírito Santo family's shareholding in SEMAPA, and with Pedro Queiroz Pereira (the CEO of SEMAPA) informing the Portuguese Central Bank of the GBES's severe financial problems (Guerreiro, 2018).

Guerreiro (2018) notes that while GBES's consolidated financial statements were public and audited, those of ESC (which represented the Espírito Santo business group as a whole) were "secret" even for its shareholders, and that, every year, Ricardo Salgado gathered the ESC shareholders in Switzerland for a meeting "full of pomp but empty of information, " where the annual accounts were supposedly presented. At the end of 2013, and in the following years, the most significant financial problems of the Espírito Santo business group and the salient details of the GBES fraud became known and proven. The main facts are described below:

● Over the years (and especially from 2008 onwards), BES began to finance many of the Espírito Santo business group's financial and non-financial companies, with the debt being recorded at a much lower value than the real value (so there was a high risk of default) and without recording the appropriated level of LLP. The situation led BES and GBES to be overly financially exposed to the Espírito Santo business group (Ferreira, 2016; Antunes, 2018);

● Overexposure to the bad loans portfolio of BES Angola (BESA) contributed critically to the collapse of BES/GBES. At the end of 2013, the portfolio was valued at approximately €6.1 million (of which BES's total exposure was approximately €3.9 million), with hundreds of thousands of euros going directly to entities controlled by the BESA CEO Álvaro Sobrinho with the consent of Ricardo Salgado (Ferreira, 2016; Antunes, 2018);

● BES was exposed to the non-financial area of the Espírito Santo business group (via ESI) to the tune of an estimated €1.3 billion at the end of 2013 (ESI was a holding firm owned by ESC; it controlled the financial and non-financial branches of the business group) (Ferreira, 2016; Antunes, 2018). A portion of this exposure was related to the ESI's issuance of short-term debt (in the form of commercial paper) that was subscribed to by BES subsidiaries, including two important investment funds (ES Liquidez and ES Rendimento, with 80.95% and 55.8% of its funds invested in ESI's commercial paper, respectively), and sold to BES clients. At the end of 2013, the value of these financial instruments (which exceeded €3 billion) had yet to be reimbursed, and more than half was referred to non-institutional investors (i.e., BES retail customers). The risk of default on the commercial paper by ESI was very high, with BES bearing some of the responsibility and having no recorded LLP in its financial statements (Antunes, 2018).

All these facts are described in detail in the BES Parliamentary Commission Report (2015) and in several audits ordered by the Portuguese Central Bank and conducted by Deloitte, PwC, and KPMG (in 2014, 2015, and 2016). The audit reports also provided evidence of ring-fencing violations, with very significant materiality and a noteworthy impact on the financial and equity situation of GBES. There were also strong indications of fraudulent acts of mismanagement that were to the detriment of depositors, investors, and other creditors. Pages 253−254 of the parliamentary report stated unequivocally that the actions of heads of GBES led to the group's collapse. Ricardo Salgado, who practised an autocratic style of leadership, was singled out for special attention.

In August 2014, the Portuguese Central Bank issued a special resolution that transferred the general activity and the propriety of BES to a new bank (Novo Banco), which was adequately capitalised and purged of problematic assets. The former had concentrated bad debt with no hope of recovery (Ferreira, 2016). Ferreira (2016) argues that the BES, a "bad bank, " was the personification of all the poor decisions that GBES managers had taken over the years. In April 2014, the Portuguese Central Bank dismissed the Espírito Santo family members from the BES executive board, withdrew requests to register the exercise of functions by the family members in the other companies of the group, and compelled the resignation of all members of the Espírito Santo family from the positions they held in BES.² The president of the Portuguese Central Bank declared that the collapse of GBES was due to Ricardo Salgado's mismanagement and fraud (Ferreira, 2016).

² See page 141 of the aforementioned parliamentary report.

In July 2021 and January 2022, Ricardo Salgado and four senior executives were convicted by the Portuguese Securities and Exchange Commission (Comissão do Mercado de Valores Mobiliários) of mismanagement and fined €6.3 million (Cavaleiro and Vicente, 2022). These sentences were later confirmed by the Portuguese Court of Competition, Regulation, and Supervision (Cavaleiro and Vicente, 2022). In Amaral's view (2015), GBES faced a dilemma: how could a position of economic dominance be achieved and sustained while the Espírito Santo family stayed in control? In the end, they tried to resolve the conundrum by engaging in ethically reprehensible managerial practices.

In light of the above, the present paper's central research question was: can EM models (the LLP model in particular) be used to detect extreme cases of EM and thereby help the banking regulators to take action? The following section describes the research method.

3.   Research methods

3.1.   Earnings management detection in GBES – the loan loss provision model

Prior studies have used a variety of proxies to measure EM which can be organized into three broad categories: properties of earnings, investor responsiveness to earnings, and external indicators of earnings misstatements (see Dechowet et al., (2010), for an overview).

As DeFond (2010) notes, the most widely employed models in previous studies were the Jones Model (Jones, 1991); the Jones Modified Model (Dechow et al., 1995); the Performance-Adjusted Discretionary Accruals (Kothari et al., 2005); and the Dechow and Dichev (2002) Model of Accrual Estimation Errors. However, these are all applied to non-financial industries. Financial firms have been excluded largely because the industry operates in a highly regulated business environment (e.g., Cohen et al., 2014; Curcio et al., 2016; Chaity et al., 2022).

Several authors have pointed out that scholars have adopted the specific accrual methodology based on LLP when attempting to detect EM in the banking industry (e.g., Cornett et al., 2009; Cohen et al., 2014; Ozili and Outa, 2017; Ab-Hamid et al., 2018; Chaity and Islam, 2022). LLPs is a specific amount banks set aside as a cushion to absorb expected loss on their loan portfolios; put another way, LLP estimates are a credit risk management tool used to mitigate expected losses on bank loan portfolios (Ozili and Outa, 2017). As Cohen et al. (2014) explain, LLP is an expense item on an income statement. It reflects management's current assessment of the likely level of future losses from defaults on outstanding loans.

According to Cornett et al. (2009) and Cohen et al. (2014), the banking industry is unique in that, in principle at least, a bank manager's basis for judgement regarding LLP is subject to periodic review by regulators. As such, LLP represents a combination of both a nondiscretionary component (the part that raises loan loss allowances to an acceptable level) and a discretionary component (which is seemingly closely regulated) (Cornett et al., 2009). In accordance with the literature (e.g., Cornett et al., 2009; Cohen et al. 2014; Kanagaretnam et al., 2014; Chaity and Islam, 2022), we used the following regression model to estimate DLLP:³

³ This model is very similar to the widely used methods of Beatty et al.(1995, 2002).

Where:

LLP_it = loan loss provisions for bank i in year t;

LNASSET_it = the natural logarithm of total assets for bank i in year t;

NPL_it = non-performing loans (includes loans past due 90 days or more and still accruing interest and loans in nonaccrual status) for bank i in year t;

LLR_it = loan loss reserve for bank i in year t;

LOANR_it = real estate loans for bank i in year t;

LOANIC_it = commercial and industrial loans for bank i in year t;

LOANC_it = consumer loans for bank i in year t;

LOANO_it = other loans for bank i in year t;

LOANB_it = loans to other banks i in year t;

ε = error term.

All variables in (1) were expressed as a percentage of total loans (e.g., Cornett et al., 2009; Cohen et al. 2014; Chaity and Islam, 2022). All βs were estimated using a firm-level time-series approach, and the residual (ε) from (1) was our measure of DLLP.

Model (1) was estimated through the time-series approach. The ordinary least-squares (OLS) method was used to estimate the coefficients of the LLP model (1) for the period 1992−2013.⁴ The fitted coefficients were then used to derive estimated (normal) LLP for each year; DLLP was defined as the residuals from the regression. Higher values of residuals indicated higher DLLP, higher EM, and lower earnings quality.

⁴ The R² from the OLS regression used to estimate the coefficients of the LLP models is 0.78.

We analysed 22 years of GBES consolidated financial statements data (1992−2013) to estimate the firm-level time-series regression model (1). Data were collected from the Bankscope database.

The ability of the LLP model to detect extreme cases of EM was assessed in several ways. First, we categorised the sampled years into a pre-fraud period (1992 to 2007) and a fraud period (2008−2013) and compared the mean, median, and standard deviation of the signed and absolute values of the DLLP. The fraud period was identified using the parliamentary report on the GBES case. The standard deviation of the firm-specific residuals is described by Dechow and Dechev (2002) as a firm-level measure of accrual quality, where a higher standard deviation denotes lower quality. We adapted this procedure to compare the standard deviation value for DLLP in the pre-fraud period with the fraud period. Second, we used a t-test, a Wilcoxon test, and a sdtest to assess whether the differences in the mean, median, and standard values of the DLLP of the pre-fraud and the fraud periods were statistically significant (we considered the signed and the absolute values). Third, we graphically displayed the level (signed values) of reported LLP and the estimated (normal) LLP and DLLP values longitudinally.

3.2.   Earnings management in GBES – a difference-in-difference approach

We built on a related analysis made by Dechow et al. (1995) to test for GBES's EM. Therefore, DLLP of GBES and of a control sample of non-fraudulent banks was regressed on a portioning variable (Fraud = a dummy variable assuming a value of 1 for the fraud period and 0 for the pre-fraud period) and on the interaction of Fraud and GBes (a dummy variable assuming a value of 1 for GBES and 0 for the non-fraudulent banks). According to Dechow et al. (1995), earnings are managed when the estimated coefficient of Fraud is statistically significant. Our main interest lay in the Fraud*GBes coefficient.

The DLLP values of GBES and the control sample were computed using the time-series approach of model (1); the data were drawn from the period 2005 to 2013.⁵ Thus, for the Fraud variable, we considered the fraud period from 2008 to 2013 and the pre-fraud period from 2005 to 2007.

⁵ Bankscope only presents sufficient reliable data on non-fraudulent banks to calculate the LLP model from 2005 onwards.

For the non-fraudulent sample, we selected nine healthy Portuguese banks that could be matched with GBES based on the following characteristics: the type of bank (i.e., commercial); the number of subsidiary companies (i.e., banks with a similar average number of subsidiary firms); and listed firms with consolidated financial statements. We included a bank that was fully owned by the Portuguese state (Caixa Geral de Depósitos). The banks in question were Caixa Geral de Depósitos; Banco Comercial Português; SA-Millennium BCP; Banco Santander Totta SA; Banco BPI SA; Caixa Económica Montepio Geral; Crédito Agrícola Financial Group-CCCAM; Banco Bilbao Vizcaya Argentaria (Portugal) SA; Haitong Bank SA; and Caixa - Banco de Investimento SA.

We also carried out a t-test to assess whether the mean DLLP values were statistically different for GBES and the non-fraudulent banks, taking into account the pre- and fraud periods. We further graphically displayed longitudinally the levels (signed values) of DLLP for the respective groups.

4.   Empirical results and discussion

4.1.   The loan loss provision model evidence

Our main objective was to evaluate the LLP model's ability to detect the GBES fraud. Two distinct periods in the life of GBES were examined: (1) the years preceding the fraud period; and (2) the fraud period itself. As was noted above, we used GBES data from 1992 to 2013 (pre-fraud period: 1992−2007; fraud period: 2008−2013). Descriptive statistics for both periods are presented in Table 1.

The absolute mean and median values of DLLP were similar in both periods, while the standard deviation was slightly higher in the fraud period. Regarding the signed values, the mean and median values showed negative DLLP for the pre-fraud period and positive DLLP for the fraud period; a slightly higher standard deviation in the fraud period is also found.

From Figure 2 we verify that the reported LLP and the estimated LLP (values that were computed through the LLP model) followed a similar pattern, especially from 2002 onwards, except for 2009 and 2010, when the level of reported and estimated LLP differed substantially.

Table 2 displays the mean, median, and standard deviation differences for DLLP (signed and absolute values) in the pre-fraud and the fraud periods. A t-test, a Wilcoxon test, and a sdtest revealed that these values were not significantly different depending on the period.

Overall, the evidence suggests that GBES did not use DLLP in the fraud period differently than during the pre-fraud period. However, Figures 3 (which shows the DLLP from 1992 to 2013) and 4 (which compares LLP and ROA in the same period) reveal a procyclicality in GBES's LLP between 1994 and 1998 and the fraud periods 2009−2010 and 2011−2013. In these periods GBES's LLP and economic performance fluctuated in opposite directions.

Olszak et al. (2017) define the procyclicality of LLP as a negative link between LLP and a bank's business cycle. Ozili (2017a) explains that during economic upturns (or economic booms), banks report fewer problematic loans, and the level of LLP is usually low; by contrast, LLP increases during economic downturns because expected loan defaults are usually high and the extent of LLP is expected to significantly increase if a recession persists.

The t-test results (Table 3) revealed that the level of GBES's LLP was statistically significantly different (higher) between the fraud period (2008 to 2013) and the pre-fraud period (1992 to 2007), confirming its procyclical nature.

Previous studies have provided evidence of the procyclical nature of LLP. El Sood (2012) shows that (in the US context) banks increase LLP to smooth income when they: (1) hit the regulatory minimum target; (2) are in non-recessionary periods; and (3) are more profitable. In crisis periods, they use LLP more extensively to smooth income upwards. Skała (2015) presents evidence that central European banks used LLP to smooth income between 2004 and 2013 and that provisions were procyclical. Ozili (2017b) reports that DLLP by Western European banks was procyclical in the same period. Using data from European commercial banks from 1996 to 2011, Olszak et al. (2017) observed that LLP was procyclical amongst the large and listed institutions. Ozili (2017a) presents similar evidence but in an African context.

Contrary to El Sood (2012), Skała (2015) and Ozili (2017b) who found that LLP procyclicality is linked with income smoothing, while our results reveal the procyclicality nature of GBES's LLP, we do not find significant evidence supporting the view that GBES used LLP in a discretionary way during the fraud period. In essence, the proven facts of the GBES fraud indicate that, in terms of the group's consolidated financial statements, the impact was a significant undervaluation of loans and financial instruments and an income overvaluation (via LLP underestimation).⁶ This should have been reflected in negative DLLP during the fraud period. However, this only applied to the years 2008, 2010, and 2011. Also, DLLP levels should have differed significantly between the pre-fraud and the fraud periods, but we did not find this to be the case. In sum, the LLP model did not prove to be effective in detecting DLLP in the GBES fraud case.

⁶ In terms of the impact on the ESI holding company, the parliamentary report stated that liabilities were significantly undervalued and assets overvalued.

4.2.   Evidence from a difference-in-difference approach

As was described in Section 3.2., the DLLP of GBES and a control sample of non-fraudulent banks was regressed on a portioning variable (Fraud [a dummy variable] = 1 for the fraud period and 0 for the pre-fraud period) and on the interaction of Fraud and GBes (a dummy variable = 1 for GBES and 0 for non-fraudulent banks). We were mostly interested in the Fraud*GBes coefficient. Because data were lacking for non-fraudulent banks, the pre-fraud period was defined as that between 2005 and 2007, while the fraud period was the same as in the previous analysis (2008 to 2013). The baseline model specification was as follows:

Table 4 reports a significantly positive association between Fraud and DLLP and a statistically insignificant association between GBes and DLLP − and, more importantly, between Fraud*GBes and DLLP. The results indicated that, while in general, the banks presented higher DLLP in the fraud period, GBES did not.⁷

⁷ The result holds if we exclude Caixa Geral de Depósitos (a bank fully owned by the Portuguese state).

The results of a t-test (reported in Table 5) revealed that the signed values of DLLP were not statistically significantly different between GBES and the non-fraudulent banks for either period.

Additionally Figure 5 shows the similarity between the DLLP of GBES and the non-fraudulent banks for the period 2005 to 2013 (the exception being the bank Caixa- Banco de Investimento SA).

Overall, the difference-in-difference approach did not reveal significant differences in DLLP levels of GBES and non-fraudulent banks, namely in the fraud period. It is worth noting that the full bank sample (i.e., including GBES) presented higher DLLP in the fraud period (2008 to 2013), which is consistent with the procyclical nature of LLP.

The fraud period included the years of financial crisis (and periods of economic downturn), after which the banking environment in Western Europe became more strictly regulated, especially post-2008 (Ozili, 2017b). The European Union introduced changes to its system of financial oversight by creating a macro-prudential supervision board and three micro-prudential supervisors (Curcio et al., 2016). Furthermore, the procyclical nature of capital requirements and provisioning rules was acknowledged through the introduction of the Basel Ⅱ and Ⅲ Accords (Curcio et al., 2016). Nevertheless, several scholars have documented the procyclicality of LLP amongst European banks in the financial crisis (e.g., Skała, 2015; Olszak et al., 2017; Ozili, 2017b), and the evidence collected in this paper supports their contention.

4.3.   Additional analysis

To ensure that the transition from the Portuguese generally accepted accounting principles (GAAP) to international financial reporting standards (IFRS) did not affect the main results—the latter, which came into force on 1 January 2005, concerned the consolidated accounts of listed companies—we re-estimated the LLP model by including a year indicator to separate the GAAP period from the IFRS period (a dummy = 1 if the year was 2005 or higher and 0 otherwise). Using the argument that the incurred loss model of IAS 39 requires a relatively low level of judgement compared with alternative models that exist under local GAAPs, Marton and Runesson (2017) explored the predictive ability of LLP with respect to actual losses under IFRS and local GAAPs. They discovered that LLP in IFRS bank years predict future credit losses to a lesser extent than in local GAAP bank years. Untabulated results reveal that our baseline results remain qualitatively similar.

In a further analysis, we re-estimated the LLP model by including as a deflator variable total assets rather than total loans. According to Ozili and Outa (2017), one major methodological issue in the literature is the choice of deflator for the LLP (dependent) variable in LLP models. Using this procedure, the untabulated baseline results remain qualitatively similar.

The use of LLP for earnings smoothing

Building on Curcio et al. (2016) and Ozili (2017b), we carried out a test to discover whether GBES and the control sample of non-fraudulent banks used LLP to smooth earnings during the GBES fraud period. The baseline model specification was as follows:

Where:

LLP_it = loan loss provisions for bank i in year t;

NPL_it = non-performing loans (includes loans past due 90 days or more and still accruing interest and loans in nonaccrual status) for bank i in year t;

LNASSET_it = the natural logarithm of total assets for bank i in year t;

LOANC_it = consumer loans for bank i in year t;

EBTP_it = earnings before taxes and loan loss provisions (loan loss provisions added back to profit before tax) for bank i in year t;

Fraud = a dummy variable = 1 for the period of 2008 to 2013, and 0 otherwise (2005 to 2007);

GBes = a dummy variable = 1 for GBES, and 0 otherwise (non-fraudulent banks);

Fraud*EBTP = interaction between Fraud and EBTP

Fraud* EBTP*GBes = interaction between Fraud, EBTP and GBes

All variables in (3) were scaled by total assets (Curcio et al., 2016). Following previous studies (e.g., Curcio and Hasan, 2015; Curcio et al., 2016; Ozili, 2017a, b), the explanatory variables were used principally to test for the discretionary use of LLP. The NPL variable was an ex-post measure of the quality of bank loan portfolios and was expected to be positively related to LLP. LNASSET was used as a proxy for bank size and LOANC (customer loans) was our proxy for the contemporaneous credit risk (Curcio and Hasan, 2015; Ozili, 2017a, b). Following previous studies (e.g., Leventis et al., 2011; Curcio and Hasan, 2015; Curcio et al., 2016; Ozili, 2015, 2017a, b), EBTP was used to test the income smoothing hypothesis. A positive EBTP coefficient would confirm the income smoothing hypothesis, meaning that banks with earnings lower (or higher) than their target values would reduce (or increase) LLP to stabilise them. Finally, we introduced two indicator variables: Fraud (a dummy variable = 1 for the 2008−2013 period and 0 otherwise); and GBes (a dummy variable = 1 for GBES and 0 for the non-fraudulent banks). Thus, we could generate the coefficients of interest: the two interaction terms Fraud*EBTP and Fraud*EBTP*GBes, which were used to investigate whether the non-fraudulent banks and GBES used LLP to smooth income either during the fraud years or the pre-fraud years.

Table 6 displays the estimation of the pooled regression model (3), with year- and bank-fixed effects included to control for the unobservable variables and constant heterogeneity, and robust standard errors to correct heteroskedasticity. In terms of the main results, the EBTP coefficient was negative and statistically significant at 1%, indicating that, over the sample period, banks with higher earnings tended to reduce their LLP. The negative impact of EBTP on LLP suggests that the banks did not apply LLP to smooth their earnings (Olszak et al., 2017). The coefficients of Fraud*EBTP and Fraud*EBTP*GBes were statistically insignificant. The evidence therefore suggests that income smoothing via LLP was not pronounced during the fraud period, neither amongst the full sample of banks nor in GBES.

5.   Conclusions

The present paper aimed to provide empirical evidence regarding the external capacity of the LLP model to detect extreme cases of EM. To achieve this, we examined the largest fraud involving a business group in the Portuguese banking sector − the GBES case. LLP is considered to be the most important and discretionary component when detecting EM in banking institutions (e.g., Ozili and Outa, 2017; Chaity and Islam, 2022). Furthermore, few academics are interested in LLP research (Ozili and Outa, 2017).

Having explored GBES's time-series behaviour from 1992 to 2013 using the LLP model, we conclude that it did not use DLLP in the fraud period differently than in the pre-fraud years. However, we found evidence that the level of LLP was statistically significantly different (i.e., higher) during the fraud period (2008 to 2013) than the pre-fraud period (1992 to 2007). Previous studies have provided evidence of the procyclical nature of LLP and its link with income smoothing (e.g., El Sood, 2012; Skała, 2015; Ozili, 2017b). Our results reveal the procyclicality of GBES's LLP between the fraud and pre-fraud period, but we did not find significant evidence that GBES used DLLP during the fraud period.

The results from the difference-in-difference approach did not reveal significant differences in GBES's DLLP levels compared with non-fraudulent banks in the fraud period. However, the full sample of banks (including GBES) presented higher levels of DLLP in the fraud period (2008 to 2013) compared with the pre-fraud years. This is consistent with the procyclical nature of LLP. Several studies have documented the procyclicality of LLP amongst European banks in the financial crisis (e.g., Skała, 2015; Olszak et al., 2017; Ozili, 2017b), and the evidence we gathered for the present paper points in the same direction. While the procyclical nature of provisioning rules has been emphasised by the Basel Ⅱ and Ⅲ Accords, our evidence reinforces the need for regulators to pay attention to how much discretion banking institutions should be allowed in determining LLP (Ozili and Outa, 2017).

In an additional test, and building on a related analysis from previous studies (e.g., Curcio et al., 2016; Ozili, 2017a, b), we explored whether GBES and the control sample of non-fraudulent banks used LLP to smooth earnings during the GBES fraud period. We found significant evidence that the banks did not use LLP for earnings smoothing between 2005 and 2013 and that it was not pronounced during the fraud period compared with the pre-fraud years (either for the sample as a whole or for GBES).

The GBES fraud revealed a significant undervaluation of loans and financial instruments and an income overvaluation (via LLP underestimation). This should have been reflected in negative DLLP during the fraud period and DLLP levels that differed significantly between the pre-fraud and the fraud periods. In addition, we expected GBES's DLLP levels to be significantly different from those of non-fraudulent banks, particularly during the fraud period. The LLP model did not prove to be effective in detecting DLLP in the present case. This is consistent with Jackson (2018), who found that in known ex-post cases of material accounting misstatements, discretionary accrual models did not capture EM.

While Ozili and Outa (2017) argue that the proxies "(…) used to measure discretionary LLPs and its determinants in most LLP models have low construct validity problems because there have [sic] been some serious commitment among academics and researchers to ensure that each LLP construct and the explanatory variables measure what it intends to measure (…), " they also draw attention to the fact that "[O]ne major methodology issue in the empirical literature is the choice of deflator for LLP (dependent) variable and the explanatory variables"; "LLP research may be complicated by the process, assumptions, methods and other unobservable factors that bank managers take into consideration to determine LLP estimates." The LLP model proved to be ineffective in detecting GBES fraud and, in particular, evaluating the decisions taken by Ricardo Salgado and his management team regarding the use of DLLP. The issues raised by Ozili and Outa (2017) should therefore be explored further.

Acknowledgements

This work is supported by national funds through FCT - Foundation for Science and Technology, I.P., within the scope of multi-annual funding UIDB/04043/2020.

Conflicts of interest

All authors declare no conflicts of interest in this paper.