Analysis of the relationship between Leverage and Profitability
After having covered the literature review, I shall now proceed with the quantitative analysis of the relationship between leverage and profitability. The explanatory variables presented in the following pages will be tested using the framework of the fixed and random effects.
The main source of data used in this dissertation is secondary data. This represents published data made available to the general public.
Financial ratios were collected from the annual reports of companies listed on the official market of the stock exchange of Mauritius (SEM). Most of the data was obtained from the handbook and fact book posted on the official webpage of SEM. Others were obtained from the Registrar of companies and from the internet.
Stata(2011 version) was used for the purposes of this study.
The sample consists of 37 firms. Given the restricted size of capital markets in Mauritius, all the firms listed on the official market are considered. This is because the listing requirements underlying the admission of any firm on the official market namely company size as measured by its market capitalization, its share issuance to the public, and that the company should have a good track record of its trading activities, should furnish documents that attest that the company is not being set up as a façade and should produce audited accounts and so on make the data so furnished more reliable. Indeed the listed firms have to abide by stringent rules and regulations and are closely monitored by the Financial Services Commission. Therefore it can be said that all firms listed on the official market and included in our sample are subject to uniform treatment.
The population consists of firms trading in various sectors of the economy namely the finance sector (banks, insurance companies), commerce, investments, sugar, leisure, transport, industry and mutual funds. Some firms were not included due to inaccessibility to annual reports for the period 2005-2009. After a screening of firms that have data available for the test period, the sample is reduced to 37 only out of 47. All figures were recorded at the domestic currency, Mauritian rupees. Those that published their accounts in some foreign currency had to be converted to Mauritian rupee using the exchange rate prevailing at the year end for each period.
PANEL DATA REGRESSION MODELS
For the purpose of this thesis, I will be using econometrics methodology namely panel regression. Some recent studies that have made use of econometrics are Kremp et al(1999) and Ozkhan (2001).Before deciding which technique to use it is important to distinguish the nature of the data being collected. In our case we have used panel data (also known as pooled or micropanel or longitudinal data); the same cross sectional unit (firm) will be measured over a period of time (5 years). Using panel data has a number of advantages namely:
This allows us to take stock not only of space but also the element of time which is an important parameter in finance.
Firms are not homogenous, the advantages of using this type of empirical data is that they take into account the unique characteristics displayed by each firm.
Econometricians also contend that panel data provides more information, more flexibility, less collinearity among others. “The combination of time series with cross-sections can enhance the quality and quantity of data in ways that would be impossible using only one of these two dimensions (Gujarati, 638)”.But they also have certain shortcomings which will be
Panel regressions allow researchers to analyse the dynamic changes occurring in the individuals or firms under study. In fact complex behavioral patterns are best explained by panel regression.
Panel data produces accurate results since data for thousand units can be compiled and examined.
In brief panel data encompasses many aspects that would otherwise be overlooked by using either pure cross sectional or time series data.
But among the drawbacks is the need to correct heteroscedasticity.
We have 37 firms and 5 time periods which add up to 185 observations and 37 regressions. If there are no missing values, the data set is called a balanced panel, but if there are missing values, the data set is referred to as an unbalanced panel. It is possible to run time series regression one for each firm but that would be a tedious job. We could also run 5 cross sectional regressions (one for each year).
There are three types of investment models namely the pre-neoclassical (Eisner and Strotz 1963;profit models), the neo-classical based on the static model of firm profit maximization and lastly the post-neoclassical (Tobin-Q model). The model used in the present study will be based on the neo-classical static model. The underlying assumption of the model is the irrelevance proposition put forward by Modigliani and Miller (1958). The dynamics of tax considerations are excluded because of the unavailability of data.
Yit= β1 + β2X2it + β3X3it+ µit where Y is the dependent variable, and X the independent variables; beta 1 is the intercept and the other betas are the estimators or slope coefficients ; u is the error term or residual that takes into account omitted variables and measurement errors; I stands for the ith firm and t for the time period. The X’s are assumed to be non- stochastic or fixed. It is also assumed that u follows a normal distribution with mean zero and variance .
The model used by Coleman(2007) meets the requirements and expectations of our analysis.
Before deciding on the technique to be used for estimating the model, it is important to understand the nature of the error term and the likelihood of correlation between the error term and regressors. The fixed and random effects take into account heteroscedascity in a set of random variables. But there is a dilemma to resolve, which of the two aforementioned techniques to use. The following notes will us in making the choice.
FIXED-EFFECTS MODEL (Covariance Model, Within Estimator, Individual Dummy Variable Model, Least Squares Dummy Variable Model)
The fixed effects can be used to analyse panel data.
The fixed effects model is used to analyse the relationship between the explained variable (profitability) and the explanatory variables (leverage) across firms. It caters for individual characteristics of each entity; how the capital structure of a firm may or may not affect its profitability. The choice of the estimation model will be guided by the assumptions made on the intercept, slope coefficients and error term. There are several possibilities namely that:
The intercept and slope coefficients are assumed to be constant over time and only the error term captures differences;
the slope coefficient is constant while the intercept varies over individuals;
the slope coefficient is constant and the intercept varies over individuals and time;
the slope coefficient and intercept vary over time; and the slope coefficient and intercept vary over time and individuals.
Under the first scenario all coefficients are assumed to be fixed and a simple pooled ordinary least square regression is carried out. It is assumed that all the slope coefficients are the same for all firms. It does not consider heterogeneity which is precisely what distinguishes panel data from others. It is obviously very unlikely to be the case. This may seriously alter the true relationship between the variables.
Fixed effects: Heterogeneity across firms
To include firm specific attributes in our analysis the Fixed Effects or Least-Squares Dummy Variable (LSDV) Regression Model can be used.
The model known as the Fixed Effect Model is shown below:
Yit= βii + β2X2it + β3X3it+ µit
The subscript I in the intercept shows that it varies across firms but is time invariant. Conversely, the regressors X are both firm and time variant. The coefficients of the regressors are however both time and individual invariant. Since each firm is unique its error term and intercepts should not be correlated with that of our firms. Otherwise, it is inappropriate to use this model. A dummy variable for every firm is included to account for firm specific characteristics. A dummy variable takes the values 0 or 1 to indicate the absence or presence of a certain effect that may influence the independent variable. By this way, the effect of each entity is estimated.
Considering the third case in which all the intercepts are allowed to vary both over entity and time, we add time effects to the above model. We control the time effects whenever it is believed that the occurrence of a certain event may impact on the dependent variable.Finally, in the last alternative “individual dummies are introduced in an additive manner.”(gujurati)
To choose between the use of the OLS with dummy variables and fixed effects using xtreg, the F-test is used to test whether the OLS or fixed effects is a better model. If the p-value is less than 0.05, then the fixed effects model is preferred. The latter is a quicker way of exploring data. Although the use of dummies is considered to be more informative, a too large number of dummies may create a large model where degrees of freedom become a source of concern.
Random Effects Model
The random effects model includes an error term that captures all unobserved but relevant explanatory variables that can be both time variant and time invariant. The dummy variable suggests that certain in Yit= βii + β2X2it + β3X3it+ µit
formation about the model is missing.
Instead of treating the intercept beta as fixed it is considered to be random. An error term is included for the intercept of each firm to reflect the differences between the firms.
β1i = β1 + αi i=1,2,…,N
Our model now contains two error terms: µit for the overall panel data and αi for individual or firm related differences. In the fixed effects model the intercept is assumed to be fixed for every intercept while the random effects model presumes that is the mean value for all cross sectional units and adds an error term to cater for the deviation from the mean value.
Breusch-Pagan Lagrange multiplier (LM) is used to test whether the random effects regression should be used or whether a simple pooled regression will suffice. Under the null hypothesis it is assumed that Var(u) = 0, that is there are no differences or panel effects across the firms. If this is the case that is if the null hypothesis is accepted we need to proceed with a simple OLS regression. The command used for this test in stata is xttest0.
Essentially a random effects model is used when the differences as measured by the error term across firms are uncorrelated with the regressors.
Choosing between the FEM and the REM:
At some point in the analysis, we will have to select the most appropriate model. The selection will be guided by the following criteria:
If the firm differences are correlated with the explanatory variables the FEM should be used. To understand why such correlation might arise we will take an example for illustration purposes. Suppose, a researcher wants to establish the consumption expenditure of a sample of workers in the same industry. The explanatory variables are income or earnings, inflation and so on. To account for individual/worker specific characteristics such as productivity, skills and education an error term is included. But these traits are also determinants of our X variable income. Hence correlation arises.
If the number of cross sectional units is large but the time period is relatively short, the choice will be determined by the nature of these units. Are they random or fixed values?
However to facilitate this process, a formal test has been developed and we will also rely on it for the purpose of this thesis.
To decide between the fixed effect or random effect the Hausman test is carried out. The latter postulates under the null hypothesis that the model is random effect against an alternative hypothesis that the model is random effects. If the error terms are correlated with the regressors the random effect will be used. Or if the p-value is significant (<0.05) the fixed effects will be used.
Since panel analysis is being used, the fixed effect or random effect model shall be used. We will proceed as follows:
We have to determine using the F-test whether to use the fixed effects model or the Ordinary Least Square regression (OLS).
LM test serves the same purpose. It provides guidance on the method to be used that is the random effects model or an Ordinary Least Square regression
Assuming the F-test and LM test indicate that the fixed effect and random effect respectively are more suitable, the Hausman test is carried out to ascertain whether a random effects or a fixed effects regression should be run.
The three models that have to be estimated are presented below:
ROEi,t =β0 + β1 STDi,t + β2 SIZE i,t+ β3TANi,t + µi,t
ROEi,t =β0 + β1 LTDi,t + β2 SIZE i,t+ β3TANi,t + µi,t
ROEi,t =β0 + β1 TDi,t + β2 SIZE i,t+ β3TANi,t + µi,t
Table 1: Definition of Variables
Net Profit before interest and tax over Total equity
Short Term debt to Total Capital
Short Term Liabilities over Total Assets
Long Term debt to Total Capital
Long Term Liabilities over Total Assets
Total Debt to Total Capital
Total Liabilities over Total Assets
Log of Sales
Fixed Assets over Total Assets
The descriptive statistics of the independent variables are shown in table . The mean is simply an indicator of the average; it is the summation of the values over the total number of observation. It can be seen that the mean of total debt amounts to 0.37 indicating that Mauritian firms are not so highly levered; only 37% of total assets is financed by debt. However, short term debt is mostly employed; as suggested by a mean of 0.24 against 0.14. This suggests a marked preference for short term debt, perhaps because short term debt is less costly and easily accessible. The figures for the standard deviation (which shows the dispersion around the mean) for the leverage measures are high enough to suggest that there is significant variation around the mean values. The significant difference between the minimum and maximum values of total debt hints that the leverage levels in Mauritius are unevenly distributed (skewed). Although an in depth comparison of capital structures across countries is not possible it is clear that the debt market in Mauritius is still a fledgling industry. Compared to its developed counterparts whose total debt ratio ranges from 50% to around 80%, Mauritian firms make scant use of debt. The banking system is dominated by a few large banks and the lending rates are far from being competitive. This prompts local firms to use internal funds in the first place.
The fixed assets constitute around 67% of the asset structure in Mauritius. Thus, the proportion of current asset held by listed firms can be interpreted to be relatively low. This is confirmed by the minimum and maximum values of 0.025 and 0.99 respectively. The firms in our sample have enjoyed satisfactory returns with a mean hovering around 0.13. The standard deviation of 0.23 lies within accepted ranges and suggests that overall firms have been reaping more or less the same returns. This result is supported by the corresponding range which is estimated to be around 3.23. The average annual sales growth of 2.4% indicates that the firms have been growing at a slow pace during the period of the study.
Return on equity-Y
Short term debt
Long term debt
Long term debt
Fixed assets to total assets
Long term debt
Fixed assets to total assets
The correlation coefficients in table are based on the whole sample with the regressors being short term debt, long term debt, size and tangibility. Short term debt is positively correlated with profitability, long term debt, total debt, size and is only negatively correlated with tangibility. Long term debt is also positively correlated with total debt, size and tangibility. Total debt is on the other hand positively correlated with size and negatively correlated with tangibility. Finally, size is negatively correlated with tangibility. Essentially, variables that are highly correlated (more than 0.75) should be removed from the model to avoid the problem of multicollinearity. They can be retained if the researcher intends to correct for multicollinearity. As shown in the table, multicollinearity is not a source of concern for most variables. But it can be noted that there is high multicollinearity between short term debt and total debt. This can be dealt with by regressing them separately.
This is in line with our empirical findings but a simple analysis of correlation using conventional matrix is not sufficient. For a more thorough investigation into the relationship between profitability and the leverage measures I will rely on the results of the panel regression. In particular the signs and values of the coefficients and the significance of the variables will be closely examined.
Panel Regression results
In this section, we will look into the effects of the different leverage measures on profitability separately because of the inherent differences among them while maintaining the same control variables each time. Accordingly, three sets of panel regressions have been generated. The signs and coefficients of the variables are reported as well as the estimates for the Hausman test, the Langrange multiplier test and the robust and heteroskedastic for the random effect and fixed effect respectively.
Analysis of relationship between profitability and Short Term debt
In the first instance we shall consider equation 1. The dependent variable is return on equity and the variable of interest is short term debt with size and tangibility as control variables.
We start by setting the data to panel. The note “strongly balanced” in stata means that that our data set is complete, there is no data missing and all variables have data for all years. We run a fixed effects model and save the estimates. Then a random effects model is run and again the estimates are saved. The Hausman test is then carried out. This test helps to select our model. Since prob>chi2=0.6652, the random effects model will be used. The Breusch-Pagan Lagrange multiplier (LM) determines whether an ordinary least square regression or a random effects regression must be used. Since prob>chi2=0.0000, the random effects regression itself is used. The results obtained have been tabulated as shown below:
Short term debt
Table 5.7: Hausman Test1
Hausman Statistic 
Breusch-Pagan Lagrange Multiplier (LM) Test 
Generalised Least Squares Results
Dependent Variable: CFP
Short term debt
R2 overall: 0.2544; Number of observations=185 ; Significant at 5% level
R2 shows the extent to which the regressors explain changes in the independent variable. The above R2 statistic indicates that short term debt explains only 25% variation in return on equity, that is profitability.
The regression coefficient shows the degree of responsiveness in the dependent variable (ROE), given a 1% change in the independent variable (short term debt). The regression coefficient beta indicates the magnitude of the change and the sign (positive or negative) indicates the direction of the relationship between the explained and explanatory variables. It follows that with a 1% change in short term debt, return on equity is likely to increase by 0.125%. It follows from the estimates that have been gathered that although short term debt positively impacts on profitability, its effect in absolute terms is negligible.
Similarly the coefficient value for the control variable size displays a positive influence on profitability. Surprisingly tangibility yields an inverse association.
The p-value is estimated from the t-statistic. When the p-value<0.05, the null hypothesis is rejected. The p-value indicates whether the independent variable is affected by all explanatory variables or only some of them. Furthermore, it reveals whether the variation in the regressor is significant or not. The smaller is this value the more significant is the variable in explaining changes in the dependent variable. The overall model is statistically significant. ( Prob>chi2=0.0000). Short term debt and size are found to be significant at 5% significance level.
There is a significant positive relationship between short term debt and profitability as evidenced by some empirical studies such as Taub (1995) and Abor (2005). This may be explained by the fact that short term debt is less costly so that increases in short term debt levels yield higher returns. This also suggests that profitable firms capitalize on their credit worthiness to secure debt at lower costs. Profitability is positively related to size of firm. This is consistent with the result obtained by Rajan and Zingales(1995) and Demstz and Lehn(1985).
However, contrary to our expectations tangibility is not only neagatively related with profitability but is also insignificant. By this, it is understood that even if firms have more collateral assets this does not necessarily entail that firms will employ higher debt levels. This runs counter to the predictions by Harris and Raviv (1990) Rajan and Zingales, (1995).Size is positively related and significant. This is in line with theoretical predictions by Titman and Wessels (1988) and Rajan and Zingales (1995)
Analysis of relationship between profitability and Long Term debt
Our second model consists of return on equity which is our regressand and our main regressor is long term debt. Size and tangibility are set as control variables.
Here again our data set is balanced. After setting the variables to fixed effects and random effects, the estimates are saved. The Hausman test reveals that once again the random effects model is suitable since prob>chi2 is 0.1712. So the data is set to random effects and the the Breusch-Pagan Lagrange multiplier (LM) is applied. It confirms that the random effects regression is more efficient for the estimation of the parameters than a simple OLS regression.. This is shown in the following tables.
Long Term debt
Table 5.7: Hausman Test
Breusch-Pagan Lagrange Multiplier (LM) Test
Generalised Least Squares Results
Dependent Variable: CFP
Long term debt
R2 overall: 0.2247; Number of observations=185 ; Significant at 5% level
The R2 shows that long term debt accounts for only 22% of the changes in profitability in Mauritian firms. Under this scenario, it is noticed that long term debt is inversely related with profitability. That is following a 1 % increase in long term debt, profitability is likely to decrease by 0.17%. Size yields a similar negative association. It can be observed that both long term debt and size are significant at 5% level.
This is in line with the theoretical predictions of the pecking order theory. Profitable firms prefer using internal sources of finance. This negative association may also be attributed to the fact that managing debt might be a costly exercise because proper management of portfolios requires recruiting skilled corporate officers. This reduces the profit margins of the firms. Ideally, firms should avoid being highly geared as this improves their credit rating. Higher leverage increases financial and bankruptcy costs. More debt is associated with lower profits since equity holders will also demand higher returns on their investments to compensate for increased default risk. Moreover, a quick glance at balance sheet figures confirms the stance of most local firms. They make little use of long term debt. The underdeveloped debt market may be responsible for this behavior. The results obtained clearly indicated an inverse relationship between leverage and profitability and therefore do not support the static trade off theory according to which profitable firms have a target debt level. From the statistical proofs gathered it can be inferred that the static trade off theory fails to explain leverage and profitability in Mauritius. Neither do firms rebalance their leverage position when earnings increase nor does profitability increase as debt levels increase. Considering the limitations which characterize the local debt market, the pecking order theory seems to fit the Mauritian context in that long term debt is negatively related to profitability. Moreover, most Mauritian firms are closely held family owned enterprises and they do not like the disclosure requirement of debt issues. Thus, they shy away from high leverage especially when their earnings can meet there needs adequately. . The predictions of agency cost also seem to tally with the results obtained. Given that most managers prefer to retain control over the firm out of fear that dilution might lead to building pressure from external investors, they will prefer retained earnings or short term debt such as trade credit and accounts payable over external funding. As a result as profitability goes up, managers shirk the use of debt.
The negative relationship between size and profitability under this model conforms to the positions held by theorists such as Williamson (1967).However, the static trade off and pecking order theories have both reported a positive relationship as they suggest that as a firm grows its credit worthiness improves and it can secure debt at lower costs. Surprisingly, tangibility has been omitted from the results because of collinearity.
Table 5.7: Hausman Test
Generalised Least Squares Results
Dependent Variable: CFP
R2 within: 0.1919; Number of observations=185 ; Significant at 5% level
Finally, we will take a look at the results for the last leverage ratio namely total debt. The dependent variable is return on equity and the variable of interest is total debt with size and tangibility as control variables.
The data is set to panel and Stata confirms that the data set is balanced. Like the previous panel regressions, once again we run a fixed effects and random effects models and save their estimates respectively. When the Hausman test is perfor