Model Specification And Diagnostic Tests

Published Date: 02 Nov 2017

The analysis chapter gives us an indication of the determinants of capital structure and firm performance in Mauritius. This chapter will consist of detailed analysis of our sample characteristics as well as test the hypotheses as set out in the methodology part.

STATA software (Edition 11, SE) has been used for the purpose of our study.

This chapter has been divided into different subsections where the first section gives a brief description of the variables, the second section considers the specification of the relationship to be tested and includes additional tests to ensure the model does not violate the main assumptions of the Classical Linear Regression model and the key findings of the regression models are reported in the subsequent sections.

Descriptive analysis of data

Variable

Observations

Mean

Standard Deviation

Minimum

Maximum

CS

151

25.20548

19.6393

0

95.99864

ROA

152

6.688734

8.571062

-22.0427

56.1252

OC

153

53.45069

20.34104

10.05

80.75

IO

152

8.604783

16.71406

0

76.077

Fsize

152

22.5624

1.578136

17.57454

25.97769

The mean leverage of firms is about 25 percent. This means that on average, the debt to equity ratio of firms in our sample is around 25 percent. Some firms also have a high gearing ratio of about 95 percent while there are some firms which have not contracted any long term debt ratio thus explaining the minimum value of zero. The high standard deviation is explained due to the high leverage of certain firms.

The return on assets has been used as a proxy for firm performance. On average, the return of firms is about 6.68 percent with a standard deviation of 8.57 percent. While some firms have earned high levels of profits, others have end up making losses. This therefore explains the minimum and maximum values.

The mean ownership concentration stands at 53.45 percent with a standard deviation of 20.34 percent. This means that on average, the top five shareholders own 53.45 percent of the companies’ total shareholding. Certain firms are highly concentrated firms whereas the others have a dispersed shareholding structure. The standard deviation gives an indication of the extent of variation in the sample.

The mean average of insider ownership is 8.60 percent with a standard deviation of 16.71 percent. Some firms have a high level of insider ownership as in certain companies the directors are the owners of the company while in certain companies the directors or managers do not hold any shares of the company.

Model specification and diagnostic tests

Capital structure Model

Specification test

A first glance, panel data analysis appears to be appropriate as our dataset includes both cross-sectional units and time series data. Panel data has the advantage that it allows us to control for variables that vary over time but not across companies, for example, government policies, or variables that we cannot explicitly measure such as difference in business practices across companies.

The two main techniques to analyst panel data include fixed-effects (FE) model and random-effects (RE) model. As Greene [2008, p.183] reports, "…the crucial distinction between fixed and random effects is whether the unobserved individual effect embodies elements that are correlated with the regressors in the model, not whether these effects are stochastic or not". In simpler terms, the RE model assumes the variations across the companies are random and not correlated with the independent variables included in the model, while under the FE model, the unique characteristics of each company may influence the independent variables" [1] 

According to empirical literature, the Hausman specification test is the preferred test when deciding between the use of the RE model or the FE model. Under the Hausman test, the null hypothesis is that the RE model should be used implying that the errors are not correlated with the regressors. Thus under the Hausman test,

HO = RE

H1 = FE

Table1: Hausman specification test

Variables

CS

Difference between RE and FE estimates

Standard Deviation

OC

0.1492992

0.1324432

IO

-0.228865

0.0626291

Fsize

-1.856948

1.947

ROA

0.0086875

0.0211675

Chi2 = 2.71 Prob>chi2= 0.6080

The Hausman test reports a p-value of 0.60. The p-value suggests that there is a 60 percent chance of rejecting the null hypothesis when in fact the null hypothesis is true. Since this is considerably greater than the conventional 5 percent significance level, we fail to reject the null hypothesis and conclude that the RE model is preferred over the FE model.

In order to ensure for the correct specification of our model, an alternative test has been run. The Breusch and Pagan Lagrangian Multiplier Test (LM) helps in choosing between the use of random effects regression or a simple OLS regression. The null hypothesis under this test is that there is no significance difference across companies, implying that there are no random effects. Results of the LM test are illustrated in the following table:

Table 2: Breusch and Pagan LM test

Coefficients

Variance

Standard Deviation

CS

391.9286

19.79719

E

77.35973

8.795335

U

338.195

18.39008

Var (u)=0 Chi2 = 228.56 Prob>chi2= 0.0000

Since the p-value is less than the 5 percent level of significance, we have significant evidence to reject the null hypothesis, thus confirming the presence of random effects in the model.

Having carried out the model specification test, additional tests are run to ensure the model is consistent with the assumption of the linear regression.

Multicollinearity

Multicollinearity arises when there is high degree of correlation between explanatory variables in a multiple regression. If the variables have a strong linear relationship, the estimated coefficients and t-statistics will not be able to remove the effect of each independent variable accurately on the dependent variable. Therefore we are more concerned with the degree of multicollinearity. The variance inflation factor (VIF) is used as an indicator to check for multicollineaity. As a rule of thumb, if the VIF value of a variable is greater than 10, it means the variable could be a linear combination of the other independent variables in the model. The following table illustrates the presence of multicollinearity in our model:

Table3: Multicollinearity

Variable

VIF

Tolerance = 1/VIF

Fsize

8.98

0.111344

OC

7.88

0.126851

ROA

1.53

0.655721

IO

1.34

0.744121

Mean VIF =4.93

Our independent variables individually have a VIF of less than 10 therefore explaining that our explanatory variables are not correlated. Furthermore, the reported VIF values do not exceed our "rule of thumb" thereby concluding that multicollinearity is not an issue.

Serial correlation

The standard error component of the panel regression assumes error terms are not serially correlated. However, this is often not the case for real-life data. For instance, when investment behavior of companies is being analyzed, an unobserved shock this period may have an effect on behavioral relationship over the next couple of periods (Balgati et al., 2008). That said, according to Balgati (2008) serial correlation is more likely to be an issue in macro panel data with long time series, over 20 to 30 years. Hence, we run the Wooldridge test to check for serial correlation and under the Wooldridge test, the null hypothesis there is no first order correlation. Results of the Wooldridge test are therefore shown in the following table:

Table 4: Wooldridge test for autocorrelation

F (1 , 19) = 3.473

Prob>F = 0.0779

Since the p-value, which is 0.0779 is greater than the 5 percent level of significance, we fail to reject the null hypothesis and therefore conclude that the data does not suffer from first order correlation.

Heteroscedasticity

The assumption behind Heteroscedasticty is that the disturbance term in the population model has a constant variance. When the disturbance term has a variance which is different from observation to observation to observation, this indicates that the variance is not constant and we therefore say that there is heteroscedasticity. Given that stata does not provide for tests to detect for heteroscedasticity in random effects model, we make use of the robust option to ensure that our model does not suffer from heteroscedasticity.

The above tests carried out for the capital structure model have also been run for the firm performance model in order to check for the specification of the relationship to be tested as well as to check whether the firm performance model satisfies the main assumptions of the Classical Linear Regression model.

Firm Performance Model

Specification test

Table 5: Hausman specification test

Variables

ROA

Difference between RE and FE estimates

Standard Deviation

OC

0.1189992

0.0772679

IO

0.0459992

0.1284896

Fsize

-0.3594629

1.8006

Chi2= 2.50 Prob>chi2=0.4745

The Hausman test reports a p-value of 0.47. The p- value states that the probability of rejecting the null hypothesis when in fact the null hypothesis is true is about 47 percent. Since the p-value is greater than the 5 percent significance level, we fail to reject the null hypothesis and therefore conclude that the RE model is preferred over the FE model.

The Breusch and Pagan LM test is also run for determining the choice for random effects regression or simple OLS regression and results of the test are shown in the following table:

Table 6: Breusch and Pagan LM test

Coeffients

Variance

Standard Deviation

ROA

74.83726

8.650853

e

38.50491

6.205232

u

15.09473

3.885194

Var(u)=0 Chi2= 19.59 Prob>chi2= 0.0000

We have significant evidence to reject the null hypothesis given that the p-value is less than the 5 percent significance level. Therefore we confirm the presence of random effects in our model.

Apart from the specification tests, the following tests have also been run in order to make sure that the model is consistent with the assumption of the linear regression.

Multicollinearity

Results for testing for multicollinearity are illustrated through the following table:

Table 7: Multicollinearity

Variable

VIF

Tolerance=1/VIF

OC

8.39

0.119137

IO

7.55

0.132456

Fsize

1.33

0.751656

Mean VIF = 7.56

OC high and age were dropped from our model. From the above table, we see that the mean VIF is less that the "rule of thumb" and we conclude that multicollinearity is not an issue. Moreover the independent variables are not correlated since they all individually bear a mean of less than 10.

Serial Correlation

In order to test for serial autocorrelation, the Wooldridge test is used and results are displayed as follows:

Table 8: Wooldridge test for autocorrelation

F ( 1 , 19 ) = 2.575

Prob>F = 0.1250

Referring to the above table we conclude that the data does not suffer from first order correlation since the p-value which is 0.1250 is greater than the 5 percent significant level.

Heteroscedasticity

A robust option is run in STATA to ensure that our model does not suffer from heteroscedasticity due to the fact that STATA does not provide for tests to detect for heteroscedasticity in random effects model.

The above discussed hypotheses have been tested using the random effects regression for the 2005 to 2012 dataset in order to report the results of the panel data analysis.

Findings

Capital Structure Model

Table 9: Results from findings

CS

Coefficients

Standard Deviation

P-Value

Variables

Normal

Robust S.D

Normal

Robust P-Values

OC

0.22409

0.143392

0.1443829

0.118

0.121 *

IO

-0.248714

0.1195376

0.1113493

0.835

0.823

FSise

2.00526

1.931718

2.012648

0.299

0.319

ROA

-0.1933368

0.1247705

0.1439345

0.121

0.179

Constant

-31.10297

45.0332

44.43418

0.490

0.484

Under Robust Regression,

R2 =0.071 Wald=8.17 Prob>chi2= 0.0855

*significant at 15 percent level of significance

The Wald test reported in the table above gives an indication as to whether all the coefficients in our model are jointly significantly from zero. With a p-value of 0.0855, our model is statistically significant at a 10 percent level of significance.

The overall R-squared of the model stands at 7 percent, which suggests only 7 percent of the variation in capital structure, is captured by our model. However, R-squared has been found not to be a good indicator of goodness of fit in panel data.

Turning to the individual influence of regressors on the dependent variable, it is shown from the above table that only ownership concentration is significant at 15 percent level of significance with a p-value of 0.121 while the other explanatory variables are insignificant in explaining the response variables.

Ownership Concentration and Capital Structure

From the above table, we see that there exists a positive relationship between ownership concentration and capital structure which is also confirmed by existing empirical research. A percentage point increase in ownership concentration will, on average, lead to a 0.22 percentage increase in capital structure, assuming all other things remaining constant. This is therefore given by the null hypothesis:

H1 : An increase in ownership concentration leads to an increase in the level of debts

The above hypothesis is confirmed with our sample since both ownership concentration and capital structure exhibits a positive relationship.

High ownership concentrated firms tend to have higher level of debt to equity ratio. This is because when ownership concentration is high in a firm, the impact on leverage is also high. A firm which has a high ownership will prefer debt financing over the issue of new equity in order to prevent dilution of share ownership as well as to maintain control over the firm. This is therefore in line with the tradeoff theory where large block holders prefer to issue debts than equity.

Moreover due to higher information asymmetry, the issue of equity becomes less popular and hence the issue of debts is preferred over that of equity. Moreover the issue of debts helps in reducing the agency problem as suggested by Pinegar and Wilbritcht (1989).

Insider Ownership and Capital Structure

H2 : Increase in the level of insider ownership leads to a decrease in leverage

The relationship between insider ownership and capital structure is negative although it is significant. Empirical studies also found that there is a negative relationship between these two variables. A one percentage point increase in insider ownership will on average, lead to a 0.24 percentage decrease in leverage, assuming all other things remaining constant. However given that insider ownership is insignificant, we therefore conclude that insider ownership does not help in determining the capital structure of a firm.

Firm Size and Capital Structure

H3 : Larger firms have higher level of leverage

There is also a positive relationship between firm size and capital structure. Thus a one percent increase in firm size will on average lead to a 2 percent increase in leverage assuming all other things remaining constant. Referring to previous studies, firms with higher growth opportunities tend to have a higher debt to equity ratio. This is because larger firms are less likely to default on payment. The positive relationship between the size of a firm and its capital structure is also confirmed with previous studies. However though firm size is a major determinant for the capital structure of a firm, yet it is an insignificant variable in our model for determining the leverage of a firm.

Return on assets and capital structure

Return on assets is found to be insignificant in determining the capital structure of a firm. However the relationship between return on assets and that of capital structure is negative confirming the pecking order theory. This is because firms prefer to use retained earnings for their financing activities followed by the issue of debts and finally they issue equity as a last option to raise finance.

Based on our sample, we conclude that ownership concentration is the only explanatory variable in determining the leverage of a firm.

Firm Performance Model

Table 10: Results from findings

ROA

Coefficients

Standard Deviation

P-Value

Variables

Normal

Robust S.D

Normal

Robust P-Values

OC

-0.660852

0.547494

0.0457039

0.532

0.148 **

IO

-0.342303

0.0487023

0.0423611

0.175

0.419

Fsize

-3.266795

0.6110301

0.9341613

0.000

0.000 *

Constant

84.20693

14.61082

22.15834

0.000

0.000

Under Robust Regression,

R2 = 0.3401 Wald = 15.46 Prob>chi2= 0.0015

*significant at 5 percent level, **significant at 15 percent level

The Wald test reported in the table above gives an indication as to whether all the coefficients in our model are jointly significantly from zero. Our model is statistically significant at the 5 percent level of significance since the p-value stands at 0.015.

34 percent of the variation in firm performance is captured by our model since the value of R-squared is 34 percent. However in panel data, r-squared is a good indicator for goodness of fit. However, R-squared in not a good indicator of goodness of fit in panel data.

While looking at the individual regressors on the dependent variable, it is shown from the above table that OC is significant at the 15 percent level of significance while Fsize is significant at the 5 percent significance level.

Ownership Concentration and Firm Performance

H4 : High ownership concentration improves performance

From the above table, ownership concentration performance is negatively related to firm performance. Thus, a one percentage point increase in ownership concentration will on average will to a 0.66 percent decrease in firm performance. However when OC high is included in the model, performance of the firm is also improved leading to a positive relationship. Results are shown in annex. When the shareholding of the top 5 shareholders exceeds 50 percent, the large blockholders are in a better position to influence management decisions. This therefore helps in solving the agency conflicts since the large shareholders will pressurize managers to work in the best interest of the companies rather than pursuing their own interests. This in turn explains the better performance when OC high is included in the model. However due to multicollinearity issue, OC high has been dropped since OC and OC high are highly correlated.

Firm size and Firm performance

There is a negative relationship between firm size and performance of the firms. A one percentage point increase in firm size will on average lead to a 3.26 percent fall in firm performance. This may be explained by the fact that as the firm grows in size it may experience diseconomies of scale. Moreover

the negative firm performance may also be due to the fact that the firms are unable to exploit the economies of scale.

Insider Ownership and Firm Performance

Insider ownership is insignificant in explaining the performance of the firms. However there is a negative relationship that exists between them. This may be the case as the proportion of shares that managers own in a company is relatively very low as compared to its share capital. Thus the interests of managers in the company are also very low and this in turn explains the negative relationship though insider ownership is insignificant in explaining the performance of firms.

In the firm performance model, we conclude that ownership concentration and firm size are the only two variables that are capable of explaining the performance of firms.