152 The Basics of financial economeTrics
leverage ratio for the 189 firms was zero (i.e., no leverage) to 99%. The data
also reveal that the leverage ratio is positively skewed (skewness of 83%)
and with a kurtosis of 252%. These statistical features of the data reveal
that the leverage ratio data are not normally distributed. As explained in
Chapter 4, a formal way of testing normality of data is proposed by Jarque
and Bera,^12 appropriately referred to as the Jarque-Bera (JB) test. In simple
terms, this test verifies whether the sample data have values of skewness and
kurtosis matching a normal distribution. If the distribution is normal, the
skewness and the excess kurtosis (or kurtosis of 3) should jointly be zero.
The calculated JB statistic^13 has a χ^2 distribution with 2 degrees of free-
dom (skewness being zero and excess kurtosis being zero). The calculated
JB statistic is 23.50 and the critical χ^2 with 2 degrees of freedom at a 5%
significance level is 5.99. Thus, the null hypothesis that the leverage ratio
data came from a normal distribution is resoundingly rejected.
Since the leverage data did not come from a normal distribution, the
use of classical regression analysis to explain the leverage ratio may not
fully describe important determinants of capital structure. In other words,
classical regression analysis may determine the leverage ratio at the mean,
but the analysis may not be useful in explaining the debt structure at the
top or the bottom quantiles of the leverage ratio. If an investment analyst
or chief financial officer is interested in understanding the determinants of
leverage across the entire distribution, then a quantile regression might be
an appropriate tool.
Capital structure studies show that companies with higher free cash flow^14
tend to have higher debt in their capital structure. The explanation offered for
such a relationship is that the owners by using debt are effectively reducing
the availability of cash for discretionary spending by the firm’s managers. It
is also argued that firms with a higher percentage of fixed assets tend to have
higher debt in their capital structure. The presence of fixed assets makes it
easier for the firms to borrow at a lower interest cost because these fixed
assets can be used as collateral. Thus, a priori one might expect a positive
relationship between a firm’s fixed asset ratio^15 and its leverage ratio. Finally,
it is also argued that capital structure depends on the size of the firm. Since
(^12) Carlos Jarque and Anil Bera, “Efficient Tests of Normality, Homoscedasticity and
Serial Independence of Regression Residuals,” Economics Letters 3 (1980): 255−259.
(^13) Standard statistical packages routinely provide the Jarque-Bera test statistic.
(^14) Free cash flow is the money available to shareholders after expenses are taken out
to maintain or expand the firm’s asset base. The formula is Free cash flow = Earn-
ings before interest and taxes − Change in networking capital − Change in capital
expenditure + Depreciation and amortization.
(^15) Fixed asset ratio is defined as fixed assets divided by total assets.