Quantile Regressions 153
larger firms tend to have diversified investments and easier access to capital, it
would be easier for these firms to borrow at a favorable interest rate. Hence
one expects a positive relationship between large capitalized firms and debt.
Here we define the size of the firm by its market cap and since market cap is
given in millions of dollars, it is normalized by taking its logged values. The
source of firm-specific data on free cash flows, fixed asset ratio, and market
capitalization for 2010 was obtained from Bloomberg Financial.^16
The first task is to run a multivariate regression to determine the factors
that influence the debt ratio. The result of this classical regression analysis was
Leverage Ratio = 0.23 + 0.00006 Free cash flow
- 0.57 (Fixed Assets/Total Assets) − 0.05 log(Market Cap)
The free cash flow term is not statistically significant. The t-value for the
market cap factor is −8.7. The relationship between between the firm’s size
and leverage ratio, instead of being positive, is negative and different from
what is hypothesized. It shows that large cap firms in the petroleum industry
have lower debt ratio than small cap firms. This finding could be unique to
this industry. Finally, the results show that the fixed asset ratio is statistically
significant with a t-value of 6.92. This shows that the firms with a higher
ratio of fixed assets tend to have a higher leverage ratio.
Since a classical multivariate regression only captures the mean change,
the above results may not be informative and may not provide a complete
view of how capital structure is determined. Quantile regressions provide a
complete view of the factors that determine the capital structure. The fol-
lowing quantile regression model is estimated:
Qτ(Leverage Ratio) = Free cash flow + Fixed Assets/Total Assets
+ log(Market Cap)where Q is the quantile and τ represents the quantile levels. The selected
quantile levels are 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90.
The results of this quantile process, presented in Table 7.3, show the
leverage ratio for different quantiles. The results indicate that free cash flow
has very little effect on the leverage ratio across all quantiles. The results also
show that the fixed asset ratio is statistically significant across all quantiles
and the coefficient is monotonically increasing. This finding indicates that
firms with a higher ratio of fixed assets tend to have a higher leverage ratio.
Instead of a positive relationship between the market cap and the lever-
age ratio, the relationship is negative across all quantiles implying that as