A theory specifies that the leverage ratio of a firm increases with its firm siz

Question

A theory specifies that the leverage ratio of a firm increases with its firm size, decreases with market-to-book equity ratio, and increases with profitability. Using Ordinary Least Squares estimation based on 20 firm observations to test this theory, a regression equation is written as: L = 0.411+ 0.0235, – 0.547(MIB), + 0.102EPS, + residual, (0.055) (0.009) (0.201) (0.075) R = 0.02 where L; is the book value of debt divided by total assets of firm i, Sj is the log of total sales of firm i for measuring firm size, M/Bis the market value of equity divided by book value of equity of firm i, and EPS, is the earnings per share of firm i for measuring profitability. The figures in parentheses below the coefficient estimates are estimated standard errors. 2.1) How should you write the population model? Explain the meanings and predictions of each of the parameters according to the theory (i.e., the intercept term, and slope coefficients) in the regression model. [20%] 2.2) Given the coefficient estimates and standard errors (in parentheses), test the null hypothesis that B2 is zero or positive against a suitable alternative hypothesis with a significance level of 5%. Also explain your finding. [20%] 2.3) Suppose that the theory does not predict the direction of the relation between the firm leverage ratio and its market-to-book equity ratio. Would you test a set of null and alternative hypotheses for B2 different from what you did in b)? If so, how would this affect the test result? Note that you are required to answer the hypotheses, the test procedures, and the effect on the test. You do not need to carry out the test. [10%]

Explanation / Answer

2.1 here the population model is :

L^ = 0.411 + 0.023 S - 0.547 (M/B) + 0.102 EPS

Here we can interpret all coefficient here.

Here intercept term means that if the firm has no sales & no Market to book equit ration and zero EPS then it has book vlueof debt = 0.411

Similarly, if we increase the log value of total sales by one unit, it will increase the book value of debt of that firm by 0.023 units.

If we increase market value of of equity divided by book value, that will decrease the book value of debt of any given firm by -0.547 units.

if we increase the EPS of any form by one unit, it will increase the book value of debt of that firm by 0.102 units.

2.2 Here

2 = 0

2 > 0

Here test statistic

t =  ^2  / se(2) = -0.547/ 0.201 = 2.7214

Here for dF = 20 -1 = 19 and alpha = 0.05 and one tailed test

tcritical = 1.7291

so here t > tcritical so we shall reject the null hypothesis and can say that the the regression slope is positive here.

2.3 Here the hypothesis will change as now we want to know that is there any relation between these two given variables.

Here the hypothesis are

2 = 0

2 0

Here we will again calculate the test statistic

t =  ^2  / se(2) = -0.547/ 0.201 = - 2.7214

Here for dF = 20 -1 = 19 and alpha = 0.05 and two tailed test

tcritical =2.029

now we can see that l t l > tcritical so we shall reject null hypothesis again.

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