Abdelkader Derbali
email: derbaliabdelkader@outlook.fr

Dr Lamia Jamel
email: lajamel@yahoo.fr

Dependence of default probability and recovery rate in structural credit risk models: Case of Greek banks

Keywords: probability of default, recovery rate, number of default, expected value of losses, bootstrapped quantile regression, simultaneous quantile regression JEL Classification: C14, C15, G12, G21, G32 microstructure, Islamic Finance, energy economics,

The main idea of this paper is to examine the dependence between the probability of default (PD) and the recovery rate (RR). For the empirically methodology, we use the bootstrapped quantile regression and the simultaneous quantile regression for a sample of 17 Greece banks listed in Athens Exchange over the period of study from January 02, 2006 to December 31, 2012. The measurement of this dependence is determinate by using 7 indicators such as; the probability of default, the recovery rate, the number of defaults, the expected value of losses, the growth rate of GDP in Greece and three dummy variables (the exit of another firm of the Athens Exchange, the new firm is listed in the Athens exchange and the date of the failure of Greece). The main empirical results show that the probability of default and the recovery rate are inversely related. Based on this result, the banks are obliged to maximize their recovery rate to reduce their probability of default.

Introduction

This literature review briefly recapitulates the way credit risk models, which have studied during the last thirty years, treat Recovery Rate and, more specifically, their relationship with the Probability of Default of firm. These models can be divided into two main categories (Atman et al., 2002) such as, Credit pricing models and Portfolio credit value-at-risk (VaR) models.

Thus, credit pricing models can in turn be divided into three main approaches as, "First generation" structural-form models, "Second generation" structural-form models, and Reduced-form models.

These three different approaches, together with their basic assumptions advantages, drawbacks and empirical performance as, First generation structural-form models: the Merton approach, Second generation structural-form models, Reduced-form models, Credit value-atrisk models, and some latest contributions on the PD-RR relationship 1 .

It has been noted that default probabilities and default rates and average recovery rates are negatively correlated [START_REF] Altman | The link between default and recovery rates: effects on the procyclicality of regulation capital ratios: Theory, Empirical evidence, and implications[END_REF]. Then, both variables also seem to be driven by the same common factor that is persistent over time and clearly related to be the business cycle: in recessions or industry downturns, default rates are high and recovery rates are low. Thus, the main idea for this study is to answer the question follows: As the Probability of Default is depended to the Recovery Rate and conversely. Then, we use the bootstrapped quantile regression and the simultaneous quantile regression for a sample composed of 17 Greece banks listed in Athens Exchange during the period through January 02, 2006 to December 31, 2012. To estimate this dependence, we utilize 7 indicators such as; the probability of default, the recovery rate, the number of defaults, the expected value of losses, the growth rate of GDP in Greece and three dummy variables (the exit of another firm of the Athens Exchange, the new firm is listed in the Athens exchange and the date of the failure of Greece). The main empirical findings demonstrate that the probability of default and the recovery rate are inversely correlated. Based on these findings, the banks are obliged to maximize their recovery rate to decrease their probability of default.

Then, the rest of this paper is structured as follows: The literature review is developed on section 2. The dependence between the probability of default and the recovery rate is presented in section 3. In section 4, we describe the data, the econometric methodologies and 1 PD : the Probability of default, RR: The Recovery Rate.

the model used in this paper. Section 5 discusses and analysis of the econometric findings.

Finally, the sixth section is considered to conclude.

Literature review

The main idea of this study is to describe and to determinate the relationship of dependence between probability of default and the recovery rate. In the literature, this dependence is treated by many authors. The table 1 shows the main works that developed and studied the dependence between the PD and the RR.

Credit Pricing models

First generation structural-form models Merton (1974), Black andCox (1976), Geske (1977), Vasicek (1984), Crouhy andGalai (1994), Jones et al. (1984).

PD and RR are a function of the structural characteristics of the firm. RR is therefore an endogenous variable.

PD and RR are inversely related. et al. (1993et al. ( ), Nielsen et al. (1993)), Hull and White (1995), Longstaff and Schwartz (1995).

Second generation structural-form models

Kim

RR is exogenous and independent from the firm's asset value.

RR is generally defined as a fixed ratio of the outstanding debt value and is therefore independent from PD.

Reduced-form models

Litterman and Iben (1991), Madan and Unal (1995), [START_REF] Jarrow | Pricing derivatives on financial securities subject to credit risk[END_REF], Jarrow et al. (1997), Lando (1998), [START_REF] Singleton | Modeling the term structures of defaultable bonds[END_REF], Duffie (1998) and Duffee (1999).

Reduced-form models assume an exogenous RR that is either a constant or a stochastic variable independent from PD.

Reduced-form models introduce separate assumptions on the dynamic of PD and RR, which are modeled independently from the structural features of the firm.

Latest contributions on the PD-RR relationship

Frye (2000), [START_REF] Jarrow | Default risk and diversification: theory and applications[END_REF], Carey and Gordy (2001), Altman and Brady (2002).

Both PD and RR are stochastic variables which depend on a common systematic risk factor (the state of the economy).

PD and RR are negatively correlated.

In the "macroeconomic approach" this derives from the common dependence on one single systematic factor. In the "microeconomic approach" it derives from the supply and demand of defaulted securities.

Credit value at risk models

CreditMetrics®

Gupton, Finger and Bhatia (1997) Stochastic variable (beta distr.) RR independent from PD CreditPortfolioView® Wilson (1997a and[START_REF] Wilson | Portfolio credit risk (II)[END_REF].

Stochastic variable RR independent from PD

CreditRisk+®

Credit Suisse Financial Products (1997). [START_REF] Wilson | Portfolio credit risk (I)[END_REF]( ), Crosbie (1999)).

Constant RR independent from PD

KMV CreditManager®

McQuown

Stochastic variable RR independent from PD

Dependence between the probability of default and the recovery rate: analytical analysis

By analyzing the previous literature, we can conclude that the default probability was estimated according to several approaches. So, the default probability can be estimated by basing itself on historical series of default by measuring the risk by the rating or the score (Altman, 1968). Empirically, the measures of score call on to alternatives as the analysis in main component, the logistic regression and the Probit analysis.

Jonkhart (1979) deducts the default probability from the spreads of rates available on markets.

The works of Jonkhart are carried out by Iben and Litterman (1989), Wu and Yu (1996), Altman (1988[START_REF] Altman | Measuring corporate bond mortality and performance[END_REF], Asquith et al. (1989), Rosenberg and Gleit (1994), Hand and Henely (1997) and Thomas (2000), who deducted the default probability from historical data on the bonds having been lacking by type of rating and by type of term. Merton (1979), Black and Scholes, Black and Cox (1976), Geske (1977) and Lee (1981) deducted the default probability from the volatility of assets. This method is intended for the highly-rated credits.

In our paper, we are going to base ourselves on the analysis developed by Merton (1974). So, Merton's model is based on the hypothesis which the company k has a certain quantity of debt with zero-coupon. The nominal value of this debt is F k and it becomes due in the maturity date T. The Firm is declared default if, in the date T, the value of its assets is lower than its nominal value, is, if kk V (T) < F . The recovery rate spells then under the following shape:

𝑅 𝑘 = 𝐹 𝑘 𝑉 𝑘 𝑇 (1)
And the loss in the case of default is:

𝐿 𝑘 * = 1 -𝑅 𝑘 = 𝐹 𝑘 -𝑉 𝑘 𝑇 𝐹 𝑘 (2)
By using the function of Heaviside (𝚯), we can determinate the loss individual can be expressed by the following form:

𝐿 𝑘 = 1 - 𝑉 𝑘 𝑇 𝐹 𝑘 Θ 1 - 𝑉 𝑘 𝑇 𝐹 𝑘 (3)
So, in the Merton's model, the losses value and the recovery rate are directly determined by the value of assets to the date of maturity.

Thus, the stochastic modeling of the market value of a company V k (T) allows to evaluate his credit risk. The probability density function (pdf) of markets values in the date of maturity k Vk P (V (T)) . So, the default probability is given by: 𝑃 𝐷,𝑘 = 𝑃 𝑉 𝑘 𝑉 𝑘 𝑇 𝑑𝑉 𝑘 𝑇 𝐹 𝑘 0 (4)

And the recovery rate will be calculated as follows: The evolution in the time of the market value of a single firm k is modeled by a stochastic differential equation of the following form:

𝑅 𝑘 = 1 𝑃 𝐷,
𝑑𝑉 𝑘 𝑉 𝑘 = 𝜇𝑑𝑡 + 𝑐𝜎𝑑𝑊 𝑚 + 1 -𝑐 𝜎𝑑𝑊 𝑘 (6)
This equation describes a process of correlated diffusion to a determinist term dt  and a correlated linearly diffusion. The parameters of this process are; the constant  , the volatility So, the evaluation of the prices of the options on the financial market is based on two parameters important to know the volatility and the fluctuations of assets (Gatfaoui, 2006;Giovanni et al., 2012). In this aligned, the fluctuations in the prices of assets are understandable by two different and independent risk factors which are the systematic factor and the idiosyncratic factor.

Therefore, the pricing of assets is improved there because the distortions of the price of the underlying are decomposed into two parts:

 A component
𝑋 𝑚 = 1 𝐾 𝑉 𝑘 𝑇 𝑉 0 -1 = 1 𝐾 1 + 𝜇Δ𝑡 + 𝑐𝜎𝜂 𝑚 ,𝑡 Δ𝑡 + 1 -𝑐𝜎𝜀 𝑘,𝑡 Δ𝑡 -1 𝑁 𝑡=1 𝐾 𝑘=1 𝐾 𝑘=1 (8)
For K  , we can express the average on k as the value of the hope , kt  . For the independence of , kt  for different k and t, we can write then:

𝑋 𝑚 + 1 = 1 + 𝜇Δ𝑡 + 𝑐𝜎𝜂 𝑚 ,𝑡 Δ𝑡 + 1 -𝑐𝜎 𝜀 𝑘,𝑡 Δ𝑡 𝑁 𝑡=1 (9)
With :

𝜀 𝑘,𝑡 = 0 (10)

Then, the expression of 𝑿 𝒎 + 𝟏 will be simplified as follows:

𝑋 𝑚 + 1 = 1 + 𝜇Δ𝑡 + 𝑐𝜎𝜂 𝑚 ,𝑡 Δ𝑡 𝑁 𝑡=1 = 𝑒𝑥𝑝 𝑙𝑛 1 + 𝜇Δ𝑡 + 𝑐𝜎𝜂 𝑚 ,𝑡 Δ𝑡 𝑁 𝑡=1 ≈ 𝑒𝑥𝑝 𝜇 - 𝑐𝜎 2 2 𝑇 + 𝜎 𝑐∆𝑡 𝜂 𝑚 ,𝑡 𝑁 𝑡=1 ( 10
)
In this stage, we apply the logarithm to the function above. The random variable , mt  follows a standard normal distribution. Then, we obtain:

𝑙𝑛 𝑋 𝑚 + 1 = 𝜇 - 𝑐𝜎 2 2 𝑇 + 𝜎 𝑐𝑇 1 𝑁 𝜂 𝑚 ,𝑡 𝑁 𝑡=1 (11) Thus, the variable m ln(X 1)  is normally distributed with average 2 () 2 cT T   
and variance 2 cT  . So, by basing itself on the normal logarithmic distribution, we can write the probability density function as follows:

𝑝 𝑋 𝑚 𝑋 𝑚 = 1 𝑋 𝑚 + 1 2𝜋𝑐𝜎 2 𝑇 𝑒𝑥𝑝 𝑙𝑛 𝑋 𝑚 + 1 -𝜇𝑇 + 1 2 𝑐𝜎 2 𝑇 2 2𝑐𝜎 2 𝑇 (12)
For a single firm k we can write:

𝑙𝑛 𝑉 𝑘 𝑇 𝑉 0 = 𝑙𝑛 1 + 𝜇Δ𝑡 + 𝑐𝜎𝜂 𝑚 ,𝑡 Δ𝑡 + 1 -𝑐𝜎𝜀 𝑘,𝑡 Δ𝑡 𝑁 𝑡=1 ≈ 𝑙𝑛 𝑋 𝑚 + 1 𝜇 - 𝑐𝜎 2 2 𝑇 + 𝜎 𝑐𝑇 1 𝑁 𝜂 𝑚 ,𝑡 𝑁 𝑡=1 (13)
Thus, the market return Since, we considered a homogeneous portfolio; we omit the index k in follows. This allows a better rating and effective results. The probability density function for the market value of a firm is given by the following form:

𝑃 𝑣 𝑉 𝑇 = 1 𝑋 𝑚 + 1 2𝜋(1 -𝑐)𝜎 2 𝑇 𝑒𝑥𝑝 𝑙𝑛 𝑉 𝑇 𝑉 0 -𝑙𝑛 𝑋 𝑚 + 1 + 1 2 (1 -𝑐)𝜎 2 𝑇 2 2(1 -𝑐)𝜎 2 𝑇 (14)
So, the individual probability of default is given by the following function:

𝑃 𝐷 𝑋 𝑚 = 𝑝 𝑣 𝑉 𝑇 𝑑𝑉 𝑇 = Φ 𝑙𝑛 𝑉 𝑇 𝑉 0 -𝑙𝑛 𝑋 𝑚 + 1 + 1 2 (1 -𝑐)𝜎 2 𝑇 2 2(1 -𝑐)𝜎 2 𝑇 𝐹 0 (15)
Where, Φ denotes the cumulative standard normal distribution. The expected value of the loss

of individual default * () 1 VT L F 
can be calculated as follows:

𝐿 * 𝑋 𝑚 = 1 𝑃 𝐷 𝑋 𝑚 1 - 𝑉 𝑇 𝐹 𝑝 𝑣 𝑉 𝑇 𝑑𝑉 𝑇 𝐹 0 = 1 𝑃 𝐷 𝑋 𝑚 Φ 𝑙𝑛 𝑉 𝑇 𝑉 0 -𝑙𝑛 𝑋 𝑚 + 1 + 1 2 (1 -𝑐)𝜎 2 (1 -𝑐)𝜎 2 𝑇 -exp 𝑙𝑛 𝑋 𝑚 + 1 -𝑙𝑛 𝐹 𝑉 0 Φ 𝑙𝑛 𝑉 𝑇 𝑉 0 -𝑙𝑛 𝑋 𝑚 + 1 + 1 2 (1 -𝑐)𝜎 2 (1 -𝑐)𝜎 2 𝑇 (16)
The expected recovery rate is:

𝑅 𝑋 𝑚 = 1 -𝐿 * 𝑋 𝑚 (17)
In the case of a homogeneous portfolio, the loss of a portfolio (average loss) is obtained by the following form:

𝐿 𝑋 𝑚 = 𝑃 𝐷 𝑋 𝑚 𝐿 * 𝑋 𝑚 (18)
For clarity, we introduce the function:

𝐴 𝑋 𝑚 = 𝑙𝑛 𝐹 𝑉 0 -𝑙𝑛 𝑋 𝑚 + 1 (19)
Where B is the composite parameter which is written as follows:

𝐵 = 1 -𝑐 𝜎 2 𝑇 (20)
However, the expressions of ()

Dm PX and   m RX
are simplified as follows:

𝑃 𝐷 𝑋 𝑚 = Φ 𝐴 𝑋 𝑚 + 1 2 𝐵 2 𝐵 (21)
And,

𝑅 𝑋 𝑚 = ℮ -𝐴(𝑋 𝑚 )Φ 𝐴 𝑋 𝑚 + 1 2 𝐵 2 𝐵 Φ 𝐴 𝑋 𝑚 + 1 2 𝐵 2 𝐵 (22)
The relationship between the probability of default and the recovery rate does not depend on B only, but it is set by () m AX . Thus, the parameter B can be measured by the probability of default and the recovery rate. In addition, reversing the expression of ()

Dm PX , we can express A in terms of

D P : 𝐴 = 𝐵Φ -1 𝑃 𝐷 - 1 2 𝐵 2 (23)
To clarify the effect of the idiosyncratic fluctuations and the market fluctuations on the volatility, Schäfer and Koivusalo (2011) proposed a relationship of functional dependence for the probability of default and the recovery rate. The recovery rate is expressed by the following form:

𝐿 𝑃 𝐷 = 1 𝑃 𝐷 𝑒𝑥𝑝 -𝐵Φ -1 𝑃 𝐷 - 1 2 𝐵 2 Φ Φ -1 𝑃 𝐷 -𝐵 (24)
If should be noted that this functional relationship depends on a single parameter B. We can see that for higher values of B lead to an overall decrease in the recovery rate. From the equation above

 

D RP , we can obtain the functional relationship of the portfolio loss and default probabilities:

𝐿 𝑃 𝐷 = 𝑃 𝐷 -𝑒𝑥𝑝 -𝐵Φ -1 𝑃 𝐷 - 1 2 𝐵 2 Φ Φ -1 𝑃 𝐷 -𝐵 (25)
For a high value of K   K  , the idiosyncratic is zero and the market return  is feasible. We can estimate the value of the probability of default as follows:

𝑃 𝐷 𝑋 𝑚 ≈ 𝑁 𝐷 𝑋 𝑚 𝐾 ( 26
)
The loss of the portfolio is then obtained as the average of the individual losses:

𝐿 𝑋 𝑚 = 1 𝐾 𝐿 𝑘 𝐾 𝑘=1 (27)
We can deduce the following relationship:

𝐿 𝑋 𝑚 = 𝑃 𝐷 𝑋 𝑚 1 -𝑅 𝑋 𝑚 (28)
The recovery rate is expressed as follows:

𝑅 𝑋 𝑚 = 1 - 𝐿 𝑋 𝑚 𝑃 𝐷 𝑋 𝑚 ≈ 1 - 𝐾 𝐿 𝑋 𝑚 𝑁 𝐷 𝑋 𝑚 ( 29
)
Several studies have shown that the number of default ()

Dm

NXis strictly non-zero. This is justified based on a large portfolio is measured by K. If we based on the evolution of a portfolio, we can obtain different values for the market return () m X , the number of defaults

Data and empirical model

In this section, we identify the sources of our data. We present the data itself and describe the regression model. Finally, we use to investigate the relation of dependence between the probability of default and the recovery rate.

Data

In this paper, we employ the indicator of 17 banks quoted in the Athens Exchange of through the period from January 02, 2006 to December 31, 2012. The list of banks included in this study is presented in the Table 2. The balance sheet data is collected from Statistical Bulletin of The Athens Exchange. In this study, we use the regression analysis to identify the dependence between PD and RR. The descriptive statistics applies to find the mean, the maximum, the minimum and standard deviation, Skweenes and Kurtosis of those variables.

The Pearson correlation tests applied to deal with the problems.

Econometric methodology

In this study, we utilize two econometric techniques to quantify the dependence between the probability of default and recovery rate. Those techniques are the Bootstrapped Quantile Regression and the Simultaneous Quantile Regression.

Then, we employ these two techniques because the parameter quantile regression provides an estimate of the change in a specific quantile of the response variable produced by a unit change in the predictor.

Empirical model

In our study, we use two models who describe the dependence between the probability of default and the recovery rate. We estimate the probability of default in function of seven variables. All these variables are explained in follows (Frye, 2000;Altman, 2001;Gordy, 2001;Altman et al., 2002;[START_REF] Altman | The link between default and recovery rates: effects on the procyclicality of regulation capital ratios: Theory, Empirical evidence, and implications[END_REF]Bruche and Gonzalez-Aguado, 2008;Becker, 2013). The probability of default is estimated by the model presented as follow:

(Equation 1)

𝑃𝐷 𝑡 = 𝑓 𝑅𝑅 𝑡 ,

Results and Discussion

Within the framework of this paper, we present a descriptive statistics analysis of the various variables used in all estimations. These variables are utilized to estimate the dependence between probability of default and recovery rate.

First of all, the number of the observations is limited to 1748 observations concerning the two models. Table 3 shows all the descriptive statistics (mean, max, min, the standard deviation, the Skewness and the Kurtosis) relative to variables used in the different estimation of the variable PD.

According to this Table , we can remark that the maximum of probability of default is equal to 0.7606353 through the period of study. However, the maximum of recovery rate is equal to 1.

This finding implies that the probability of default can be absorbed by the recovery rate.

For the two statistics of skewness (asymmetry) and kurtosis (leptokurtic), we can observe that the two variables used in our study are characterized by non-normal distribution. The positive sign of the skewness coefficients indicate that the variable is skewed to the right and it is far from being symmetric for all variables in except of the recovery rate and the expected value of losses. Also, the Kurtosis coefficients confirm that the leptokurtic for all variables used in this study show the existence of a high peak or a fat-tailed in their volatilities. Then, we employ two types of estimations, such as, the Bootstrapped Quantile Regression and the Simultaneous Quantile Regression. The choice of the two methodologies is justified by the objective of this paper. Then, the purpose of this study is to examine the correlation among the Probability of Default and the Recovery Rate. Those econometric techniques allow describing the dependence between tow variables based on their volatilities.

Figure 1 shows the evolution of the probability of default and the recovery rate for each year (2006)(2007)(2008)(2009)(2010)(2011)(2012). In Figure 2, we present the volatility of the PD and the RR through the period from January 02, 2006 to December 31, 2012. In this study, we made a test of the correlation between the various utilized variables. Table 4 reports the empirical results relative to the correlation. So, the empirical findings present that all the coefficient of correlation of Pearson does not exceed the limit of tolerance of 0.7, so it does not cause problems during the estimation of the model which measures the PD. Also, we conduct an unit root test for time series. Thus, we employ the Augmented-Dickey-Fuller and Phillips-Perron test. According to the results shown in Table 5 andTable 6, we find that all the calculated values of the t-student or t-statistical values are inferior to the critical thresholds of 1%, 5% and 10%. In this case, all the variables employed in this paper are stationary. minimization of the probability of default of the existing banks in the financial market of Greece.

In the table 8, we utilize the Simultaneous Quantile Regression. Then, we find that all the values of the statistical Pseudo-R² are equal to 0.80 in all estimates. Then, we can remark that the estimated model is characterized by a good linear adjustment.

In the model (PD), the probability of default is estimated based on other explicative variables.

The results of estimation are presented in Table 7.

After employing the second econometric techniques (Simultaneous Quantile Regression), we conclude that all the results have almost the same significance thresholds then the first econometric methodology. Then, for the two econometric techniques the impact of different variables remains the same.

Empirically, we can find that the probability of default is inversely related to the recovery rate. The recovery rate is not constant; it decreases with increasing of the probability of default. This empirical finding is confirmed by these figures follows. On these figures we presented the volatility of probability of default and recovery rate of all Greek banks and by year. The dependence between PD and RR is justified by the correlation coefficients of Pearson who presented in Table 4.

Conclusion

The dependence between the probability of default and the recovery rate has a crucial influence on large credit portfolio losses. Thus, the probability of default and the recovery rate are often modeled independently in current credit risk models: KMV model, CreditMetrics model, CreditRisk+ and Credit Portfolio View.

In this paper, we utilize the bootstrapped quantile regression and the simultaneous quantile regression for a sample composed of 17 Greek banks listed in Athens Exchange over the period from January 02, 2006 to December 31, 2012. To estimate this dependence, we utilize 7 indicators such as; the probability of default, the recovery rate, the number of defaults, the expected value of losses, the growth rate of GDP in Greece and three dummy variables (the exit of another firm of the Athens Exchange, the new firm is listed in the Athens exchange and the date of the failure of Greece)..

Finally, we conclude that the probability of default and the recovery rate are inversely related.

This result is confirmed by those table and figure presented in the fourth section.

Based on the results found in this study, the banks are obliged to maximize their recovery rate to reduce their probability of default.

  By supposing the existence of a process of underlying distribution of the value of the company, we can easily deduct all the results relative to the measure of the probability of default and the recovery rate.So, we consider a homogeneous portfolio of size K. The nominal value of this portfolio is k FF  and the first market values are 0

σ

  and the correlation c between the firm return and the market return. The process of Wiener indicated by k dW and m dW , describes the idiosyncratic fluctuations and the market fluctuations respectively.



  of market volatility stemming from systematic fluctuations in the price time is divided on N stages, we arrive at the discreet formulation of the stochastic differential equation above. The market value of k firms in the maturity can be written in the following form:𝑉 𝑘 𝑇 = 𝑉 0 1 + 𝜇Δ𝑡 + 𝑐𝜎𝜂 𝑚 ,𝑡 Δ𝑡 + 1 -𝑐𝜎𝜀 𝑘,are independent random variables and they follow a normal distribution law. We will try in what follows to determine market return m X , the number of default all k firms over a period of time to maturity.

Figure 1 :Figure 2 :

 12 Figure 1: The volatility of the PD and the RR (by year)

  The dependence between the Probability of Default and the Recovery rate of all banks is shows in figure3, figure 4, figure 5, figure 6, figure 7, figure 8 and figure 9. All these Figure shows the dependence between the Probability of Default and the Recovery rate of all banks by years (see, figure 3, figure 4, figure 5, figure 6, figure 7, figure 8 and figure 9)

Figure 3 :Figure 4 :

 34 Figure 3: The volatility of the PD and the RR in 2006 (by Banks)

Table 1 : The treatment of the dependence between PD and RR Main models and related empirical results Treatment of PD Relationship between PD and RR

 1

Table 2 : List of Banks Name of Bank The study period

 2

	ALPHA ΒΑΝΚ (ΚΟ)	02/01/2006 -31/12/2012
	ASPIS BANK (ΚΟ)	02/01/2006 -30/06/2010
	ATTICA BANK (ΚΟ)	02/01/2006 -31/12/2012
	BANK OF CYPRUS (CR)	02/01/2006 -31/12/2012
	BANK OF GREECE (CR)	02/01/2006 -31/12/2012
	ΕΓΝΑΤΙΑ BANK (ΚΟ)	02/01/2006 -20/09/2007
	ΕΓΝΑΤΙΑ BANK (ΠΟ)	02/01/2006 -20/08/2007
	EMPORIKI BANK (CR)	02/01/2006 -29/04/2011
	EUROBANK EFG (ΚΟ)	02/01/2006 -31/12/2012
	GΕΝΙΚΙ ΒΑΝΚ (CR)	02/01/2006 -31/12/2012
	MARFIN EGNATIA BANK (CR)	02/01/2008 -31/03/2011
	MARFIN FINANCIAL GROUP (ΚΟ)	02/01/2006 -30/03/2007
	MARFIN POPULAR BANK (ΚΟ)	02/01/2008 -11/04/2012
	NATIONAL BANK (CR)	02/01/2006 -31/12/2012
	PIRAEUS BANK (CR)	02/01/2006 -31/12/2012
	PROTON BANK S,A, (CR)	02/01/2006 -31/12/2012
	TT HELLENIC POSTBANK (CR)	02/01/2008 -30/12/2011

  𝑁𝐷 𝑡 , 𝐿 𝑡 , 𝐷𝑢𝑚𝑚𝑦1 𝑡 , 𝐷𝑢𝑚𝑚𝑦2 𝑡 , 𝐷𝑢𝑚𝑚𝑦3 𝑡 When, 𝑷𝑫 𝒕 denotes the probability of default at the moment t, 𝑹𝑹 𝒕 denotes the recovery rate at the moment t, 𝑵𝑫 𝒕 denotes the number of default at the moment t and 𝑳 𝒕 denotes the expected value of losses at the moment t. 𝑫𝒖𝒎𝒎𝒚𝟏 𝒕 indicates that a new firm is listed in

the Athens Exchange at the moment t. This variable that takes the value 1 when a new firm is listed in the Athens Exchange and takes 0 in the opposite occur. 𝑫𝒖𝒎𝒎𝒚𝟐 𝒕 indicates that a new firm is going out of the Athens Exchange at the moment t. This variable that takes the value 1 when a new firm is going out of the Athens Exchange and takes 0 in the opposite occur. 𝑫𝒖𝒎𝒎𝒚𝟑 𝒕 indicates that Greece declare his failure at the moment t. This variable takes the value 1 after the date of failure and 0 before the date of failure. The employed data are daily and which are collected from the publication of the Athens Exchange.

Table 3 : Descriptive Statistics

 3

	Variable	Obs	Mean	Std Div	Min	Max	Skewness Kurtosis
	PD	1748	0.5007853	0.0845174	0.1545267	0.7606353	0.2988851	2.873225
	RR	1748	0.7433242	0.0993225	0.0076826	1	-0.0383176	2.363317
	ND	1748	6.653638	1.326654	-0.0109848	10.00634	0.1338035	2.517658
	L	1748	-0.109574	0.6235335	0.4428743	0.4199632	-6.181387	104.6915
	Dummy1	1748	0.0005721	0.0239182	0	1	41.7732	1746.001
	Dummy2	1748	0.0040046	0.063173	0	1	15.70727	247.7183
	Dummy3	1748	0.4302059	0.4952465	0	1	0.2819365	1.079488

Table 4 : The matrix of correlation

 4

		PD	RR	ND	L	Dummy1	Dummy2 Dummy3
	PD	1.0000
	RR	-0.1116	1.0000
		(0.0000)*
	ND	0.8495	0.1209	1.0000
		(0.0000)*	(0.0000)*
	L	0.1059	0.1264	0.5142	1.0000
		(0.0000)*	(0.0000)*	(0.0000)*
	Dummy1	0.0057	0.0115	0.0115	0.0072	1.0000
		(0.8132)	(0.6306)	(0.6311)	(0.7621)
	Dummy2	0.0272	-0.0330	0.0343	0.0269	-0.0015	1.0000
		(0.2564)	(0.1680)	(0.1520)	(0.2611)	(0.9495)
	Dummy3	00016	-0.7990	-0.3087	-0.3878	-0.0208	0.0181	1.0000
		(0.9469)	(0.0000)*	(0.0000)*	(0.0000)*	(0.3850)	(0.4498)
	Value significant in a threshold of: (*) 1%; (**) 5% et (***) 10%.

Table 5 : The unit root test of Augmented-Dickey-Fuller

 5

	Variables t-statistic	Critical	Critical value	Critical value	The hypothesis rejected
			value at 1%	at 5%	at 10%
	DP	-12.106	-3.430	-2.860	-2.570	H0: presence of unit root. So the variable is stationary
	RR	-4.256	-3.430	-2.860	-2.570	H0: presence of unit root. So the variable is stationary
	ND	-10.285	-3.430	-2.860	-2.570	H0: presence of unit root. So the variable is stationary
	L	-13.770	-3.430	-2.860	-2.570	H0: presence of unit root. So the variable is stationary
	Dummy1	-41.797	-3.430	-2.860	-2.570	H0: presence of unit root. So the variable is stationary
	Dummy2	-41.942	-3.430	-2.860	-2.570	H0: presence of unit root. So the variable is stationary
	Dummy3	-12.868	-3.430	-2.860	-2.570	H0: presence of unit root. So the variable is stationary

Table 6 : The unit root test of Phillips-Perron

 6

	Variables	t-statistic	Critical	Critical	Critical	The hypothesis rejected
			value at 1%	value at 5%	value at 10%
	DP	-233.223	-20.700	-14.100	-11.300	H0: presence of unit root. So the variable is stationary
	RR	-297.631	-20.700	-14.100	-11.300	H0: presence of unit root.

Table 7 : Estimation by Bootstrapped Quantile Regression Dependent variable: PD Period of estimation : 2006 -2012 Explicative variables

 7

		Estimation 1	Estimation 2	Estimation 3	Estimation 4	Estimation 5	Estimation 6	Estimation 7	Estimation 8
	RR	-0.075498	-0.0753065	-0.0754981	-0.0364969	-0.075498	-0.0364969	-0.0364969	-0.0364969
		(-4.35)*	(-4.44)*	(-4.38)*	(-1.85)***	(-4.42)*	(-1.75)**	(-1.81)***	(-1.82)***
	ND	0.071905	0.0719024	0.0719049	0.0727096	0.071905	0.0727096	0.0727096	0.0727096
		(85.20)*	(86.20)*	(85.13)*	(98.80)*	(81.03)*	(98.13)*	(97.62)*	(97.55)*
	L	-0.0747226	-0.0747128	-0.0747225	-0.073463	-0.0747226	-0.073463	-0.073463	-0.073463
		(-11.79)*	(-11.69)*	(-11.70)*	(-9.98)*	(-11.48)*	(-9.90)*	(-9.99)*	(-9.84)*
	Dummy1		-0.0085701			-0.0085487	-0.0035373		-0.0035373
			(-2.18)**			(-2.18)**	(-1.28)		(-1.29)
	Dummy2			0.0006389		0.0006387		0.0042401	0.0042401
				(0.06)		(0.06)		(0.31)	(0.31)
	Dummy3				0.0121234		0.0121234	0.0121234	0.0121234
					(1.45)		(1.35)	(1.42)	(1.41)
	CONSTANT	0.070721 (4.70)*	0.0706089 (4.82)*	0.0707216 (4.79)*	0.0288906 (1.70)***	0.070721 (4.76)*	0.0288906 (1.59)	0.0288906 (1.66)***	0.0288906 (1.67)***
	Number of obs	1748	1748	1748	1748	1748	1748	1748	1748
	Pseudo R²	0.7997	0.7997	0.7997	0.8007	0.7997	0.8007	0.8007	0.8007
	Value significant in a threshold of: (*) 1%; (**) 5% et (***) 10%.

Table 8 : Estimation by Simultaneous Quantile Regression Dependent variable: PD Period of estimation : 2006 -2012 Explicative variables

 8

		Estimation 1	Estimation 2	Estimation 3	Estimation 4	Estimation 5	Estimation 6	Estimation 7	Estimation 8
	RR	-0.075498	-0.0753065	-0.0754981	-0.0365789	-0.075498	-0.0365789	-0.0365868	-0.0365789
		(-4.41)*	(-4.23)*	(-4.20)*	(-1.84)***	(-4.37)*	(-1.57)	(-1.91)***	(-1.83)***
	ND	0.071905	0.0719024	0.0719049	0.0727134	0.071905	0.0727134	0.0727117	0.0727134
		(83.62)*	(82.21)*	(84.06)*	(100.93)*	(82.91)*	(46.53)*	(99.74)*	(96.00)*
	L	-0.0747226	-0.0747128	-0.0747225	-0.0734714	-0.0747226	-0.0734714	-0.07347	-0.0734714
		(-11.71)*	(-11.56)*	(-11.89)*	(-10.03)*	(-11.66)*	(-10.01)*	(-10.25)*	(-9.98)*
	Dummy1		-0.0085701			-0.0085487	-0.0035433		-0.0035433
			(-2.20)**			(-2.21)**	(-0.80)		(-1.27)
	Dummy2			0.0006389		0.0006387		0.0042446	0.0042409
				(0.05)		(0.05)		(0.30)	(0.31)
	Dummy3				0.0121102		0.0121102	0.0121108	0.0121102
					(1.37)		(1.42)	(1.42)	(1.41)
	CONSTANT	0.070721 (4.75)*	0.0706089 (4.61)*	0.0707216 (4.79)*	0.0289338 (1.66)***	0.070721 (4.72)*	0.0289338 (1.61)	0.0289489 (1.73)***	0.0289338 (1.64)***
	Number of obs	1748	1748	1748	1748	1748	1748	1748	1748
	Pseudo R²	0.8021	0.8022	0.8031	0.8022	0.8022	0.8032	0.8032	0.8032
	Value significant in a threshold of: (*) 1%; (**) 5% et (***) 10%.

To pursue our empirical analysis, we estimate the variables PD in Table 7 and the Table 8. So, we estimate the variable PD by using 8 estimations for each of both variables and by using two econometric techniques.

In the table 7, we employ the Bootstrapped Quantile Regression. Then, we notice that all the values of the statistical Pseudo-R² are almost equal to 0.80 in all estimates. So, we can conclude that the estimated model is characterized by a good linear adjustment.

In our model, the probability of default is estimated based on other explicative variables. The results of estimation are presented in Table 7.

This table summarizes all estimations relative to the model (PD), we show that there are four significant variables with different thresholds. The first one, it is the variable RR, is statistically significant and negative in a 1% threshold in four estimations (1, 2, 3 and 5), in a 5% threshold in the sixth estimation and in a 10% threshold in the last estimations. In this context, the variable RR has a negative impact on the probability of default of the Greek banks. Then, when the recovery rate increases, the banks have profit to supply an important exposure to failure. We can conclude that a high recovery rate allow to absorb losses incurred by banks in Greece.

The variable ND is statistically significant and positive in a 1% threshold in all estimations.

The number of default of banks affects their probability of default. Thus, the high numbers of default reflect that the probability of default is high.

The variable L (the expected losses) is statistically significant and negative in a 5% threshold only in all estimation. This confirms the literature, because the high value of the expected losses allows the bank to minimize their probability of default in future.

For the three dummy variables used in our study, we conclude that only the dummy1 variable is significant in 5% threshold in the estimation 2 and 5. This variable affects negatively the probability of default. Then, the entry of a new bank in the Athens Exchange leads to the We, also, use a Kruskal-Wallis equality-of-populations rank test. The Kruskal-Wallis oneway analysis of variance by ranks is a non-parametric method for testing whether samples originate from the same distribution. It is employ for comparing more than two samples that are independent, or not related. The parametric equivalent of the Kruskal-Wallis test is the one-way analysis of variance (ANOVA). The results of this test can accept the hypothesis H0.

ie the average of the different types of sample studied are not significantly different (Mean Rank = 6 < Index Kruskal-Wallis = 6,713).

We calculate also the Value-at-Risk on four confidence level chosen (see, Table 9).


Dr Aida Sy

Dr Lamia Jamel
email: lajamel@yahoo.fr

Dr Abdelkader Derbali
email: derbaliabdelkader@outlook.fr

Do ownership structure and quality of financial information affect the cost of debt of Tunisian listing firms?

Keywords: Corporate governance, Board of Directors, ownership structure, cost of debt JEL Classification: G32, G34

Do ownership structure and quality of financial information affect the cost of debt of Tunisian listing firms?

Aida Sy, Lamia Jamel, Abdelkader Derbali

Introduction

Studies on corporate governance were a great number of recent works, mainly following the financial crisis of 2007. The financial information is an important part of corporate governance has attracted the interest of the standard setters.

There exists a vast literature on the subject of factors influencing the average cost of debt to firms. Thus, we show the existence of frequent reference to variables such as size, profitability, asset tangibility, growth options, or level of leverage (see, among others, [START_REF] Rajan | What do we know about capital structure? Some evidence from international data[END_REF]. More recently, however, growing attention is being paid to variables with a direct impact on the severity of information asymmetries between debtors and creditors, which can have a significant influence on the cost of debt. Specifically, analysis including ownership and corporate governance issues (see [START_REF] Anderson | Board characteristics, accounting report integrity, and the cost of debt[END_REF]Elyansiani et al., 2010;[START_REF] Boubakri | Control/ownership structure, creditor rights protection, and the cost of debt financing: international evidence[END_REF], the accounting information quality (see [START_REF] Anderson | Board characteristics, accounting report integrity, and the cost of debt[END_REF][START_REF] Armstrong | When does information asymmetry affect the cost of capital?[END_REF] and analyst activity (see [START_REF] Mansi | Analyst forecasts characteristics and the cost of debt[END_REF].

Thus, the evolution of corporate finance means reflects the strategic nature of the financial structure. The latter extends to all financial strategic compartments which allow the company to carry on business, i.e. to acquire its assets. Whatever the diversity of its components, aggregation distinguishes debt capital. A debate between researchers often on the issue of debt-equity mix for better enterprise value [START_REF] Caby | La création de valeur de l'entreprise[END_REF]. [START_REF] Leland | Informational Asymetries, Financial Structure, and Financial Intermediation[END_REF] show that the value of a firm is more correlated with the share of capital held by the shareholder leader and therefore it is in connection with the financial structure.

In addition and as an external mechanism of government, institutional investors may force leaders to improve their financial publication. Many articles recently published in the financial press have continued to raise the activism of institutional investors and their willingness to constrain managers to improve their transparency.

Moreover, the ownership structure and the quality of information can play both a leading role in the evolution of the cost of debt in firms.

The aim of our paper is to examine the effect of the ownership structure and the quality of financial information on the cost of debt of Tunisian listing companies. We use in this study three factors such as; the ownership structure, the quality of financial information's and the cost of corporate debt. We employ a sample of 28 Tunisian listing companies during the period from 2007-2015. The empirical results find that the ownership structure and the quality of financial information have an important role in determining the characteristics of the cost of debt of each Tunisian listing firm. The results also indicate that the cost of debt is related positively to factors from the boards, to the size of the company and the stock exchange listing and negatively to the institutional participation on the capital of firm.

The rest of this paper is structured as follow. Section 2 shows a literature review concerning the impact of the ownership structure and the quality of financial information on the cost of debt. In section 3, we present the econometric methodology employed in this paper. Section 4, indicates data characteristics. In section 5, we report the empirical finding. Finally, section 6 concludes and remarks.

Literature review

A review of major studies on the boards allows us to identify several criteria associated with the effectiveness of the control exercised by this mechanism. This is mainly on the size of the boards of director independence, financial motivations of outside directors and combines the functions of CEO (Chief Executive Officer) and chairman.

Several authors argue that a large board strengthens its ability to control and improve its information sources. Thanks to its diversified structure, a boards composed of a large number of directors provides better environmental links and demonstrated greater expertise. In this sense, [START_REF] Pearce | Board composition from a strategic contingency perspective[END_REF] and [START_REF] Dalton | Number of directors and financial performance: A meta-analysis[END_REF] found that companies with a large board perform better. Lipton and Lorsh (1992) found that the large boards make the process of communication and decision-heavier and more difficult decision. Moreover, they are often faced with problems of coordination and a risk of collusion between the members of the board. [START_REF] Jensen | The modern industrial revolution, exit and the failure of internal control systems[END_REF] believes that a larger board is less effective and more subject to the influence of the CEO. Some empirical studies support this presumption.

In particular, [START_REF] Yermack | Higher market valuation of companies with a small board of directors[END_REF] and [START_REF] Eisenberg | Larger board size and decreasing value in small firms[END_REF] found that the size of the board is negatively correlated with company performance. Furthermore, [START_REF] Core | Corporate governance, CEO compensation and firm performance[END_REF] show that an executive compensation is higher in companies with lots of agency and having weak governance structure problems manifested, among others, a large board.

The percentage of capital held by outside directors highlights the incentives of these directors, as shareholders, to perform their duties effectively controllers (Alexander and Paquerot, 2000). This conclusion is also shared by [START_REF] Minow | The Ideal Board. Corporate Governance[END_REF] who said that the best way for a director is similar in behavior to a shareholder is to be himself a shareholder. This can be explained by the fact that a director with a significant shareholding is likely to be stronger advocates its interests and therefore to challenge about the direction because decisions will impact its own wealth [START_REF] Patton | Why do not directors rock the boat?[END_REF].

Similarly, [START_REF] Jensen | The modern industrial revolution, exit and the failure of internal control systems[END_REF] argues that the detention of a percentage of the company's capital as a means to align the interests of directors with those of shareholders and thus exercise effective management control of the company. Over the financial commitment of external directors, the greater the flexibility of the leader will be low. Supporters of the duality feel it is important that the organization is headed by one person.

They argue that both roles allows for clear leadership with a view to formulating and implementing the strategy and should therefore lead to superior performance [START_REF] Godard | Les déterminants du choix entre un conseil d'administration et un conseil de surveillance[END_REF].

Moreover, they argue that the separation of functions dilutes the authority of the leader and increases the likelihood that the actions and expectations of the manager and the board of directors are in contradiction, which can create some rivalry between them. Few studies support this theoretical current and show that combines the functions improves firm performance [START_REF] Boyd | CEO duality and firm performance: a contingency model[END_REF][START_REF] Godard | Faut-il limiter le cumul des fonctions dans les conseils d'administration ?[END_REF]. [START_REF] Demsetz | The structure of ownership and the theory of the firm[END_REF], [START_REF] Shleifer | Large shareholders and corporate control[END_REF] and [START_REF] Agrawal | Large shareholders and the monitoring of managers, the case of antitakeover charter amendments[END_REF] suggest that the concentration of capital is essential to effectively control management executives by shareholders. Indeed, in a company whose capital is much dispersed, none of the owners has an incentive to invest in the control of leaders as it will only bear the cost while all shareholders benefit from this action. It is therefore possible to observe the behavior of "free rider" in a widely held and therefore leaders can unleash their opportunism in the management of the firm.

Institutional investors are thought to play an active role in corporate governance. These individuals represent shareholders indeed influential partners for the company as their financial resources are important and allow them to become 'active investors' in the management control of the firm [START_REF] Agrawal | Shark repellents and the role of institutional investors in corporate governance[END_REF]. They can influence the decisions of leaders in order to maximize the return on their investment and consequently improve the performance of the company.

These agents also have privileged access to information because of their activity and many investments they make, which means a better understanding of the performance of the sector, a wealth of information on the environment and therefore a better assessment of the performance of the leader (Alexander and Paquerot, 2000). In addition, these shareholders have demonstrated a greater capacity for processing financial and economic information.

They have in fact special skills enabling them to analyze in the company's accounts, growth prospects and quality of management. These advantages allow them to effectively control the management of executives at a lower cost compared to isolated individual shareholders.

The presence of institutional investors can thus influence the disciplinary power of the boards.

Indeed, these shareholders tend to assume supervision of leaders, which reduces the potential contribution of the Boards in this regard. The study of [START_REF] Agrawal | Firm performance and mechanisms to control agency problems between managers and shareholders[END_REF] supported this hypothesis.

According to [START_REF] Jensen | Theory of the firm: managerial behavior, agency costs and ownership structure[END_REF], more the share of capital held by the leaders, the greater the divergence between their interests and those of shareholders is low. In fact, the leader holding a high proportion of equities has little interest in maximizing personal wealth by opportunistic behavior detrimental to the assets of the company, since it is impacted. Therefore, it is expected that the disciplinary role of the boards is less important in companies where the managerial ownership is high [START_REF] Bathala | The determinants of Board composition: an agency perspective[END_REF][START_REF] Rediker | Boards of directors and substitution effects of alternative governance mechanisms[END_REF][START_REF] Denis | Ownership and board structures in publicly traded corporations[END_REF][START_REF] Fernandez | Alternative internal controls as substitute of the board of directors[END_REF].

In the financial models of agency theory, debt appears as an effective way to resolve conflicts of interest that may arise between shareholders and managers. Indeed, in case of debt issuance, the leader is forced to face the payments of annuities [START_REF] Jensen | Theory of the firm: managerial behavior, agency costs and ownership structure[END_REF], to be more efficient [START_REF] Grossman | Corporate financial structure and managerial incentives[END_REF], limit discretionary behavior on Free cash flow [START_REF] Jensen | Agency costs of free cash flow, corporate finance and takeovers[END_REF][START_REF] Stulz | Managerial discretion and optimal financing policies[END_REF]) and finally to stop the current operations of the company and opt for liquidation [START_REF] Harris | Capital structure and the informational role of debt[END_REF]. Therefore, it is expected that the use of debt serve as a true substitute for control exercised by the Boards. In this sense, [START_REF] Bathala | The determinants of Board composition: an agency perspective[END_REF] found that the proportion of external directors on the Board is inversely related to debt. The ownership structure and the quality of financial reporting are not the only factors that can influence the cost of corporate borrowing.

Other elements such as the size of the company and the stock exchange listing may also be involved in determining the structure of the cost of debt of a firm. The size of the company can influence the structure of the board i.e. the ownership structure. Indeed, large companies are generally characterized by high visibility and great complexity and therefore can be expected to have a different structure of the board of the small businesses.

Previous studies have shown that the size of the board is positively correlated with that of the company [START_REF] Yermack | Higher market valuation of companies with a small board of directors[END_REF][START_REF] Denis | Ownership and board structures in publicly traded corporations[END_REF][START_REF] Godard | Les déterminants du choix entre un conseil d'administration et un conseil de surveillance[END_REF]. In the same alignment, [START_REF] Rediker | Boards of directors and substitution effects of alternative governance mechanisms[END_REF] and [START_REF] Denis | Ownership and board structures in publicly traded corporations[END_REF] found a positive impact of company size on the independence of the board. Since the cost of debt is correlated with company size and it is correlated with the ownership structure. So the ownership structure itself can affect the cost of debt of a company. The stock market listing may also affect the characteristics of the board. Thus, on the stock market listed companies are more visible to the public and therefore they could offer more seats on the board and representatives of the public interest. Moreover, these companies are generally characterized by higher agency costs than other companies and therefore they tend to have more outside directors on the board. In this respect, the necessary company information is available to all actors on the market and mainly financial institutions.

In this case, the quality of information on companies can play an important role in the cost of debt of these. [START_REF] Bowerman | the effect of corporate social responsibility disclosures on share prices in Japan and the UK[END_REF] investigate whether corporate social responsibility disclosure (CSRD) is associated with firms' market values in order to assess whether CSRD provides incremental value relevant information to investors. They used a modified [START_REF] Ohlson | Earnings, Book values, and dividends in equity valuation[END_REF] model which is a widely accepted equity valuation model in accounting research. Their empirical findings show that investors in the UK consider CSRD information in the total information set they employ for their investment decision-making, whereas Japanese investors do not appear to find that CSRD provides incremental information over and above financial information to assist in their valuations of firms. These empirical results have implications for investors and regulators, specifically around the management, control and governance of firms. [START_REF] Lawrence | Giving institutional theory a critical edge: A study of systems change in a Fijian housing authority[END_REF] use critical theorizing of institutional theory to find how the Housing Authority of Fiji's mission of providing housing to low income earners was obscured. The changes in Housing Authority of Fiji's accounting and management system came from pressure from donor agencies such as Asian Development Bank and the World Bank. The top management employed power to implement commercial accounting and control systems. The consultants and people brought from the private sector to carry out changes towards business routines were 'carriers of change' at Housing Authority. [START_REF] Lawrence | Giving institutional theory a critical edge: A study of systems change in a Fijian housing authority[END_REF] show that the changes in the organization systems resulted in the organization losing sight of its original idea which was to assist the underprivileged people who were locked out of the housing market place.

Methodology

Sample

Our goal in this paper is to validate the research proposal from the theoretical part. The data used in the empirical work has been extracted from the annual reports of the companies' database used in our study and the Stock Exchange of Tunisia (SET). Thus, our sample included major companies in Tunisia (28 banks) during the period from 2007 to 2015. The study we develop concern the companies presented in Table 1.

Model

In our work we used a model for measuring the impact of the ownership structure and the quality of financial reporting. This model includes the following variables:

 𝑪𝑫 𝒊𝒕 (The Cost of Debt): the ratio between total debt and total assets of firm i at time t. Debt is measured by financial leverage is total liabilities divided by total assets. This measurement is also used by [START_REF] Agrawal | Firm performance and mechanisms to control agency problems between managers and shareholders[END_REF] and [START_REF] Fernandez | Alternative internal controls as substitute of the board of directors[END_REF].

 DIV it : This is the company's information disclosure index i at time t.

 LNASSET it : This is the logarithm of the total assets of firm i at time t. The size could be an important determinant of the performance of a company. This measure is used in several studies as [START_REF] Mak | Changes in Ownership Structure and Board Structure after an Initial Public Offering[END_REF].

 ROA it : it is the ratio between net income and total company assets i at time t.

 ROE it : it is the ratio between gross operating surplus and total assets of firm i at time t.

 DIR it : is the percentage of capital represented by business leaders i at time t. This variable is measured by the percentage of capital held by the CEO and, if applicable, the CEO of the company. This measure has been used in previous writings including those of [START_REF] Rediker | Boards of directors and substitution effects of alternative governance mechanisms[END_REF] and [START_REF] Fernandez | Alternative internal controls as substitute of the board of directors[END_REF].

 INST it : is the percentage of institutional shareholders of the company i at time t. We measure this variable with the proportion of shares held by institutional investors. In this study we considered as institutional investors, banks, investment companies, insurance companies and social security funds. This variable was measured in the same way by [START_REF] Bathala | The determinants of Board composition: an agency perspective[END_REF].

 CONC it : it's business capital concentration i at time t. It is a dummy variable equal to 1% if the largest shareholder is greater than 50% if it is not equal to 0. This variable is measured by the percentage of capital held by the largest shareholder. This measure is also used by [START_REF] Bathala | The determinants of Board composition: an agency perspective[END_REF].

 ACCT it : this is the measure the company's total accruals i at time t. This variable equal to the difference between net operating income and operating cash flows.

For the empirical analysis we chose a model to test the impact of the ownership structure and the quality of financial information on the cost of the debt of a company. Indeed, the model to be estimated is as follows: Where, 𝛼 𝑖 denotes the coefficients of all explicative variables (i = 1, …, 8),𝛼 0 represent the constant, i is the index of each firm (i = 1, …, 28), t is the year (t = 1, …, 9), and 𝜀 𝑖𝑡 is the error term.

𝑪𝑫 𝒊𝒕 =
Thus, all data used in the calculation of variables are obtained from annual reports of the companies used in our study and the data published by the Stock Exchange of Tunisia (SET).

Empirical analysis

In this section, we will try to analyze and interpret the different results obtained from the estimates made on the model used (CD).

First, we will specify the type of estimate is a regression on panel data. Our choice is justified by the presence of two dimensions in the data used; the first is the time (a period of 7 years) and the second is individual (our sample is composed of 28 Tunisian companies).

Table 2 summarizes the descriptive statistics for each variable used in our estimates .The CD variable, which expresses the cost of debt of Tunisian companies, can reach a maximum value of 0.83. As the minimum value is 0.41. His risk is measured by the standard deviation is 0.133 which is pretty important. The results for the other variables are presented in Table 2.

Moreover, the results show no coefficient exceed the tolerance limit (0.7), which does not cause problems in estimating the model. We present the results of the estimation of the model (CD) in Table 4. We note that the panel structure is homogeneous. So we can apply the method of ordinary least square which allows a better fit by minimizing the sum of squared residuals. Thus, we estimate the CD model as dependent variable.

The empirical results of the estimated model by the OLS (Ordinary Least Squares) for the measurement of the impact of the ownership structure and the quality of financial information on the cost of debt of Tunisian companies are reported in Table 5.

We also conducted a test of the unit root panel data. Thus, we used the test Levin Lin Chu.

The null hypothesis of this test is H0: all series are non-stationary and the alternative hypothesis is H1: all series are stationary. The acceptance or the rejection of the null hypothesis is based on the value of the p-value. This value is compared to a 10% threshold. If the value of the p-value is less than 10%, then we reject H0 and the value of the p-value is greater than 10%, then we accept H0. Table 4 summarizes the results of study of the stationary different variables. In our case, we notice that all the variables used herein lower pvalue at 10%. In this case, one rejects H0 and thereafter all these variables are stationary. For the dummy variable (CONC), we assume that this variable is stationary. In our model, we found that the probability of Hausman test is less than 10% (0.0844), so the fixed effects models are preferable to random effects.

In addition, we conduct further tests to demonstrate the validity of our models and to justify the significance of the estimates. We test the correlation between the explanatory variables and residue. This type of test is based on the value of (Prob> chi2). If this probability is less than 5%, so we accept H0 which verifies the absence of correlation between the residuals and the explanatory variables. If this probability is greater than 5%, in this case there is a correlation between the waste problem and the explanatory variables that we must fix it.

In the estimated model, the probability value (Prob> chi2) is less than 5%. So we do not have problems of correlation between the explanatory variables and residue.

For CD model, the probability value (Prob> Chi2) is less than 5%. In this context, there is not a problem of correlation between the explanatory variables and residue. These values are presented in Table 5 summarizes the estimates made on the model chosen. The significance test of the model is based on the probability of Fisher. We notice all the Fisher probability values are less than 5% in all estimates of both models. So, we can remark that the five estimates of each model are globally significant.

In addition, the coefficient of determination for the estimated model is greater than 0.70. In this case, the estimated model is characterized by a good linear fit.

Table 5. Results of estimation

The fourth variable (ROE) has a positive and significant impact on a threshold of 10% on the cost of debt. So the relationship between the disclosure and the cost of debt is positive for the case of the financial performance of the company as measured by ROE ratio. Then, the increased level of financial performance induces an increase in the cost of debt of a company

The fifth variable (ACCT), which measures the value of total accruals has a positive impact but not significant on the cost of debt. So the relationship between the disclosure and the cost of debt is positive for the case of the ACCT variable. So, the augment in the level of the value of accruals resulting in an increase in the cost of debt of a company

In the second case, we sit down to test the existence of positive relationship between the concentration of ownership (CONC) and the cost of debt. We find that the variable CONC has a positive and significant impact on a threshold of 1%. That is to say that the percentage of shareholders in the company's capital plays an important role in increasing the cost of debt.

In the third case, we test the existence of a negative relationship between participation of institutional investors (INST) and the cost of debt. We remark that the INST variable that measures the percentage of institutional shareholders in Tunisian firms has a negative and significant impact on a threshold of 1% on the cost of debt. That is to say that the percentage of institutional shareholders in the company's capital plays an important role in reducing the cost of debt.

In the fourth case, we test the existence of a negative relationship between managerial ownership (DIR) and the cost of debt. We show that the DIR variable that measures the managerial stake in Tunisian firms has a negative and non significant impact on the cost of debt. That is to say that the involvement of managers in the company's capital plays a sometimes non-existent role in reducing the cost of debt.

After analyzing the results obtained from the estimation of the model for measuring the impact of the ownership structure and the quality of financial information on the cost of debt for the case of Tunisian firms, we can conclude that the ownership structure and the quality of financial reporting play a dominant role in the evolution of the cost of debt of Tunisian companies. Thus, we can find that there is a positive relationship between financial communication (DIV, LNASSET, ROA, ROE, and ACCT) and the cost of debt in the case of Tunisian firms. Also, we find a positive relationship between the concentration of ownership (CONC) and the cost of debt.

Conclusion

The main objective of this paper is to examine empirically the relationship between of the boards with other internal governance mechanisms such as ownership structure, quality of financial information and the cost of debt. To do so, we employ a sample of 28 Tunisian listing companies during the period from 2007-2015.

The empirical results show that the value of the assets has a positive impact on the cost of the debt of the Tunisian firm. The level of performance of each firm (ROA and ROE) influences positively the cost of debt of listing Tunisian firms. In addition, there is a positive relationship between the concentration of property and the cost of debt. There, too, a negative relationship between the participation of institutional investors and the cost of debt. Finally, there is a negative relationship between the managerial ownership and the cost of debt. Our empirical results are in conformity with the previous literature, especially, for the case of emerging countries.

The results of this paper suggest that it would be worth encouraging the development of alternative mechanisms for the decrease of information asymmetries between lenders and borrowers in order to guarantee firms' access to better credit terms. One potentially effective mechanism would be to encourage analyst coverage in order to diminish the average cost of corporate debt when the development of market tools to address information asymmetries problems is impeded by the characteristics of the institutional and legal setting.

Table 1 . List of firm (2007-2015)

 1

	Air liquide	ARTES	SFBT	SOTRAPIL
	Alkimia	Essoukna	SIAME	SOTUMAG
	Assad	GIF filters	SIPHAT	SOTUVER
	Tunisie lait	ICF	SITS	STEQ
	SIMPAR	Magasin general	SOMOCER	Tunisair
	Adwya	Monoprix	SOPAT	TPR
	STIP	Poulina	SOTETEL	Electrostar

  𝜶 𝟎 + 𝜶 𝟏 𝑫𝑰𝑽 𝒊𝒕 + 𝜶 𝟐 𝑳𝑵𝑨𝑺𝑺𝑬𝑻 𝒊𝒕 + 𝜶 𝟑 𝑹𝑶𝑨 𝒊𝒕 + 𝜶 𝟒 𝑹𝑶𝑬 𝒊𝒕 + 𝜶 𝟓 𝑫𝑰𝑹 𝒊𝒕 + 𝜶 𝟔 𝑰𝑵𝑺𝑻 𝒊𝒕 + 𝜶 𝟕 𝑪𝑶𝑵𝑪 𝒊𝒕 + 𝜶 𝟖 𝑨𝑪𝑪𝑻 𝒊𝒕 + 𝜺 𝒊𝒕

Table 2 . Descriptive statistics

 2

	Variables	Observation	Mean	Max	Min	Std Div	Skewness	Kurtosis
	CD	252	0.7572006	0.836772	0.4083131 0.1333252	2.319716	23.8936
	DIV	252	0.482446	0.7222222 0.2142857 0.1339269 -0.2239395 1.963432
	LNASSET	252	4.729896	5.736108	3.62447	0.4658897 -0.7396421 2.953065
	ROA	252	0.0093889 0.0291264 -0.1035052 0.0118462	-6.63919	60.45131
	ROE	252	0.0267582 0.0487229 0.0063502 0.0097373 -0.0479703 2.418214
	DIR	252	0.4088346 0.6363636 0.0714286	0.147494	-0.2515029 1.787143
	INST	252	0.2551459 0.5941176 0.0536316 0.1296333 0.3261328	2.115759
	CONC	252	0.5357143	1	0	0.5	-0.143223	1.020513
	ACCT	252	802570.2	6467555	-3084839	1290409	1.590546	7.170016

Table 3 . The matrix of correlation

 3

		CD	DIV	LNASSET	ROA	ROE	DIR	INST CONC ACCT
	CD	1.0000
	p
	DIV	0.1092	1.0000
	p	0.128
	LNASSET 0.2339	0.2296	1.0000
	p	0.001*	0.021**
	ROA	0.0280	-0.0624 -0.0782	1.0000
	p	0.696	0.385	0.276
	ROE	0.3779	0.0577	0.2910	0.2273	1.0000
	p	0.000*	0.422	0.000*	0.001*
	DIR	0.1365	0.0352	0.4243	0.0080	0.2488	1.0000
	p	0.056*** 0.624	0.000*	0.912	0.000*
	INST	-0.2075	0.1060	-0.4156	0.0485	-0.2642 -0.0577 1.0000
	p	0.004*	0.139	0.000*	0.500	0.000*	0.422
	CONC	0.0130	-0.0381 -0.0474	-0.0035 -0.0352 -0.0307 0.0421 1.0000
	p	0.856	0.596	0.510	0.962	0.625	0.669	0.558
	ACCT	-0.0780	0.0756	0.2893	-0.0028 -0.0870 0.2773	0.1138 -0.0354 1.0000
	p	0.277	0.292	0.000*	0.969	0.225	0.000*	0.112	0.622
	Note: Significant value at a threshold, (*) 1%, (**) 5%, and (***) 10%

Table 4 . Unit root test

 4 In this test the p-value is compared to 10%. If p-value <10% therefore we reject H0 and p-value> 10% then, we accept H0. With H0: all series are non-stationary.The choice of model to estimate is based on the comparison of the probability of the Hausman test compared a 10% threshold. If the probability of the test is less than 10%, in this case we will choose the fixed effects model. So, if the probability of Hausman test is higher than 10%, so we will choose the random effects model.

	Variables	Statistic	p-value
	CD	-3.5395	0.0002
	DIV	-2.8474	0.0022
	LNASSET	-1.7158	0.0431
	ROA	-4.3599	0.0000
	ROE	-4.4979	0.0000

Model with fixed effect Note: Significant value to a threshold, (*) 1%; (**) 5% and (***) 10%. The Wall of test is used to test the correlation between the explanatory variables and residue. Comparing the probability of (Prob> chi2) to a threshold of 5% with H0: no correlation between the variables used and residue. If (Prob> chi2) <5%, then we accept H0.

In the first case, we sit down to test the existence of a negative relationship between financial information (DIV, LNASSET, ROA, ROE, ACCT) and the cost of debt. Thus, financial communication is measured by five variables: DIV, LNASSET, ROA, ROE and ACCT.

For the DIV variable, it has a positive but not significant impact on the cost of debt.

The second variable, LNASSET, also has a positive and significant impact on a threshold of 1% on the cost of debt. So the relationship between the disclosure and the cost of debt is positive for the case of company size measured by the logarithm of total assets. Subsequently, he increased level of asset values led to an increase in the cost of debt of a company

The third variable (ROA) has a positive and significant impact on a threshold of 1% on the cost of debt. So the relationship between the disclosure and the cost of debt is positive for the case of economic business performance measured by ROA ratio. Subsequently, the increase in the level of economic performance led to an increase in the cost of debt of a company.