# Panel Regression Model with Random Effects

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## EMPIRICAL FINDINGS

This chapter aims to show the reader the empirical results of the study including the descriptive statistics, correlation between variables and panel regression models, both pooled regression model and panel regression model with random effects.

Descriptive Statistics

Basic features of the data are described using descriptive statistics. Simple summaries about the sample and the measures are provided. The following table shows the statistical information for 2005-2013 for both dependent variables and explanatory variables with regard to number of observations, mean, standard deviation and maximum and minimum values.

LEVERAGE 1

The table shows that LEV1 has a mean of 0.636851. This implies that 63.69% of the average firm total assets is finance by total debt. The companies in this sample are more leveraged compared to US companies with 29% as reported by Frank and Goyal (2009) and 35.5% of Norwegian companies as pointed out by Nilssen (2014).

LEVERAGE 2

The average LEV2 is 0.129326 indicating that the average company in the sample has a short debt level of 12.93%. Comparing this with the average LEV1, it implies that family firms in the OECD countries finance their assets using more long debt than short term debt. There is a slight difference in standard deviation for both dependent variables.

### PROFITABILITY

The sample shows average profitability of 8.27% which is considerably higher than the mean of 6.55% for Norwegian firms reported by Nilssen (2014). Frank and Goyal (2009) found mean of 2% in their research on US companies. Song (2005) reported profitability mean of 8% and a standard deviation of 0.28. The standard deviation is 0.08, this implies less variability compared to Norwegian firms and Swedish firms.

TANGIBILITY

This variable has a mean of 0.259222. It is less than average of 0.35 reported by Frank and Goyal (2009). In comparison, Nilssen (2014) got an average tangibility ratio of 0.395, which is higher than this sample. Furthermore she got a standard deviation of 0.30 which is significantly higher than the standard deviation of 0.164 from this sample.

LIQUIDITY

Liquidity has an average of 0.177931 and it can be interpreted as how much the average company is able to meet short term financial obligations. This ratio implies that for every 1 unit of current liabilities, a firm has an average of 0.178 units of current assets to cover short-term liabilities. This means that the family firms in OECD countries need to improve the level of current assets so that they can meet short term obligations. Nilssen (2014) achieved a liquidity ratio of 1.71 which indicates that Norwegian firms are better at meeting their short-term obligations.

GROWTH

This variable has an average of 2.937993 which indicates that the market expects future growth for the companies included in the sample. The mean of 1.84 was found by Nilssen (2014) for Norwegian firms, and the mean of 1.74 discovered by Frank and Goyal (2009) for US firms.

SIZE

The table shows the average size of 1.331689 with standard deviation of 0.997. Nilssen (2014) used logarithm of sales as a proxy for size, discovered mean of 14.3093 and standard deviation of 2.0045. This means that Norwegian firms have large differences in size between them compared to family firms in OECD countries.

DEBT-TAX SHIELD

This variable has a mean of 0.371891 and a standard deviation of 2.088. This indicates that 37.19% of taxable income from debt on family firms on OECD countries is reduced on average. This is achieved through claiming allowable deductions such as mortgage interest which reduce the family firms’ taxable income for a given year or defer income taxes into future years.

### NON-DEBT TAX SHIELD

Non-debt tax shield has a mean of 0.042. This is slightly lower compared to mean of 0.049 obtained from Nilssen (2014). The same applies to the standard deviation from her research, which is 0.036 and about 0.005 higher than what was detected in this sample. The non-debt tax shield is achieved through claiming allowable deductions such as depreciation and amortization which reduce the family firms’ taxable income.

Correlation Analysis

The correlations between dependent variables and independent variables are presented in the table below.
In the correlation matrix, levels of significance at 1%, 5% and 10% are denoted by **, *, respectively. The table shows there is slightly strong correlation between leverage 1 and leverage 2 because both ratios are based on debt of the company. The correlation between most variables are relatively low. Profitability is significantly correlated with both leverage 1 and leverage 2. This agrees with the pecking -order theory that profitable firms prefer to finance internally. Asset tangibility is negatively correlated with both leverage ratios contrary to the trade-off theory. Firms’ liquidity is positively correlated to both leverage ratios but only significant with leverage 2. This also supports the idea of trade off theory on relationship between firms’ liquidity and leverage. Growth is positively correlated to leverage 1 and negatively correlated with leverage 2. Both leverage ratios are positively correlated with firms’ size. As firm gets larger, their debt also increases. Leverage 1 and leverage 2 are significant at 5% and 1% respectively. This agrees with trade-off theory. Leverage 1 is negatively correlated with debt-tax shield while leverage 2 is positively correlated with debt-tax shield. The former is in contrast to what we expected while latter agrees with the trade-off theory. Non-debt tax shield is positively correlated to both leverage ratios contrary to what we expected. There is a significant positive relationship between non-debt tax shield and both leverage ratios.

Pooled Regression Model

Panel Least Squares analysis was conducted on the two models, on with leverage 1 as dependent variable and the other with leverage 2 as dependent variable with explanatory variables Profitability, Asset Tangibility, Growth, Size, Debt Tax Shield, Non-Debt Tax Shield and Liquidity. Level of significance at 1%, 5% and 10% are denoted by **, *, respectively The two models are significant since the probabilities of F-statistics are less than 1%. F-statistic values for model 1 and model 2 are 46.17976 and 26.46967 respectively. The higher the F-value, the more of the total variability is accounted for in the model implying that model 1 has more explained variability than model 2. According to Koop (2013), R-squared measures the explanatory power of the model and indicates how the variance in the dependent variable can be explained by the independent variables. The results show that R-squared for model 1 is 0.277652 while that of model 2 is 0.180542, meaning that 27.76% of the variation in model 1 is explained by significant explanatory variables while only 18.05% of the variation in model 2 is explained by the significant independent variables.

Interpretation of Coefficients.

The results from the table above show that there are some differences in the magnitude of the coefficients for both models. While interpreting the coefficient of one variable, other variables are kept constant (ceteris paribus).

Profitability

Model 1: Leverage 1
There is a negative relationship between leverage 1 and profitability. 1 unit increase in profitability, leverage 1 decreases by 1.067 units. The coefficient is significant at 1% significance level.
Model 2: Leverage 2
The regression results show that there is a negative relationship between leverage 2 and profitability. The results also indicate that when the profitability increases by 1 unit, leverage 2 decreases by 0.684 units. Like in the model 1, the coefficient is also significant at 1% level.

Asset Tangibility

Model 1: Leverage 1
The regression indicates that there is a negative relationship between asset tangibility and leverage 1. 1 unit increase in the ratio of fixed assets to total assets leads to decrease in 0.098 units in leverage 1. Tangibility is significantly different from zero at 1% level of significance.
Model 2: Leverage 2
The results show that there is also a negative relationship between leverage 2 and tangibility. The coefficient is not significant at 1%, 5% and 10% significance level.

Growth

Model 1: Leverage 1
There is a slight positive relationship between growth and leverage 1. Growth is not significantly different from zero at 1%, 5% or 10% significance level.
Model 2: Leverage 2
Unlike the model 1, the results show there is a slight negative relationship between leverage 2 and growth. Also in this model, growth is not significant at 1%, 5% or 10% significance level.

Size

Model 1: Leverage 1
A positive relationship was found to exist between size and leverage 1 according to the results in the table above. When size increases by 1 unit, leverage 1 also increases by 0.0198 units. The coefficient is significant at 1% level of significance.
Model 2: Leverage 2
The regression results show that there is also a positive relationship between size and leverage 2. 1 unit increase in size causes leverage 2 to increase by 0.022 units and the coefficient is significantly different from zero at 1% level of significance.

Debt-Tax Shield

Model 1: Leverage 1

Non-Debt Tax Shield

Model 1: Leverage 1
The regression results show that there is a positive relationship between non-debt tax shield and leverage 1. 1 unit increase in non-debt tax shield will result into a 0.351 increase in units of leverage. The coefficient is significantly different from zero at 5% level of significance.
Model 2: Leverage 2
There is a positive relationship between leverage 2 and non-debt tax shield. When non-debt tax shield increases by 1 unit, leverage 2 increases by 0.569 units. Non-debt tax shield is significant at 1% level.

Liquidity

Model 1: Leverage 1
The results obtained a positive relationship between liquidity and leverage 1. The coefficient in not significant at 1%, 5% or 10% significance level.
Model 2: Leverage 2
A positive relationship exists between leverage 2 and liquidity. The results indicate that 1 unit increase in liquidity will cause the leverage 2 to increase by 0.2005 units, while the coefficient is significantly different from zero at 1% level.

#### Panel Regression Model with Random Effects

The analysis explores how firm-specific factors affect firms’ level of leverage by using panel regression model with random effects. Interpretation of the coefficients in a random effects model is different from the panel least squares as the coefficients include both within-entity and the between-entity effects, Nilssen (2014). When interpreting the results, the coefficient will represent the average marginal effect of explanatory variables over dependent variable, when explanatory variable changes across time and between firms by 1 unit. It means that the random effects regression model does not only predict change over time but also it takes into account the difference between units. Model 3 and model 4 are both significant since the probability of F-statistics are less than 1%. F-statistic values for model 3 and model 4 are 14.25108 and 12.44125 respectively. The higher the F-value, the more of the total variability is accounted for in the model implying that model 3 has more explained variability than model 4. R -squared measures the explanatory power of the model and indicates how the variance in the dependent variable can be explained by the independent variables. The results show that R -squared for model 3 is 0.106040 while that of model 4 is 0.093837, meaning that 10.60% of the variation in model 3 is explained by significant independent variables while only 9.38% of the variation in model 4 is explained by the significant explanatory variables. This shows that there is a small difference between the models and the ability of the explanatory variables to explain variation across firms. Conclusively the explanatory variables can explain 1.22% more of the variation in model 3 than that of model 4. There is a negative relationship between debt-tax shield and leverage 1. The coefficient is not significantly different from zero at 1%, 5% or 10% significance level.
Model 2: Leverage 2
A positive relationship exists between leverage 2 and debt-tax shield. Debt-tax shield is not significant at 1%, 5% or 10% significance level.

1 INTRODUCTION
1.1 BACKGROUND
1.2 PROBLEM STATEMENT
1.3 PURPOSE
1.4 RESEARCH QUESTIONS
2 THEORETICAL FRAME OF REFERENCE
2.1 CAPITAL STRUCTURE
2.2 THEORIES OF CAPITAL STRUCTURE
2.3 DETERMINANTS OF CAPITAL STRUCTURE
3 METHOD
3.1 Research Design
3.2 Research Strategy
3.3 Sampling and Sample size
3.4 Description of Variables
3.5 Data Analysis Techniques
3.6 Pooled Regression Model
3.7 Random Effects Model
3.8 Limitations
4 EMPIRICAL FINDINGS
4.1 Descriptive Statistics
4.2 Correlation Analysis
4.3 Pooled Regression Model
4.4 Panel Regression Model with Random Effects
5 ANALYSIS
5.1 Profitability
5.2 Asset Tangibility
5.3 Growth
5.4 Size
5.5 Debt -Tax Shield
5.6 Non-Debt Tax Shield
5.7 Liquidity
6 DISCUSSION
6.1 Conclusions
6.2 Limitations
6.3 Further Research
GET THE COMPLETE PROJECT
Determinants of Capital Struc-ture in family firms An empirical evidence from OECD countries