17
4.4. Path Analysis
We study the relative importance of two channels using path analysis. This approach can be viewed as an extension of multiple regressions to decompose various factors affecting an
outcome into direct effects and indirect components. In this section, we decompose the relation between managerial ability and bank-loan spreads into a direct path between these two variables
as well as indirect paths through disclosure and fundamental channels, as shown in Figure 1. For parsimony, we employ a recursive all paths flow in only one direction path model with
observable variables. A direct path includes only one path coefficient while an indirect path includes a path coefficient between the source variable and the mediating variable, as well as a
path between the mediating variable and the outcome variable. The total magnitude of the indirect path is the product of these two path coefficients. In our study, the source variable is managerial
ability; the mediating variables are the disclosure and fundamental channels; the outcome variable is the bank-loan pricing. Accordingly we estimate the following model:
Cost of Debt = a + a
1
Managerial Ability + a
2
Future Fundamental
+ a
3
Disclosure + a
n
Controls
+
6 Future Fundamental =
β + β
1
Managerial A bility +
7 Disclosure =
+
1
εanagerial Ability + 8
In this model, the path coefficient a
1
is the magnitude of the direct path from managerial ability to bank-loan spreads. The path coefficient a
2
× β
1
is the magnitude of the indirect path from managerial ability to bank-loan spreads through the fundamental channel. Similarly, a
3
×
1
is the magnitude of the indirect path though the disclosure channel.
18 We use same four measurements used in cross-sectional analyses to represent the
disclosure channel Abnormal Accruals and PIN and fundamental channel Ohlson O and cash flow and model the four factors simultaneously as mediating variables. Table 6 summarizes the
results.
9
Columns 1 to 4 present the individual paths for each proxy for the two channels-one direct and one indirect. In Column 1, we use abnormal accruals as the only mediator between
managerial ability and cost of debt. The results indicate that the direct path between managerial ability and cost of debt is negative and significant, consistent with previous findings. The path
coefficient between managerial ability and the abnormal accruals is negative and significant, suggesting that higher managerial ability is associated with lower abnormal accruals. Moreover
the path coefficient between abnormal accruals and the offering yield is positive and significant, suggesting that high accruals relate to high cost of debt. This indirect path accounts for about
5.5 of the total impact of managerial ability on the cost of debt if the abnormal accrual is the only mediator.
Column 2 shows the role of PIN as a mediating factor. We find that that managerial ability is negatively associated with PIN, which is in turn positively associated with cost of debt. The
PIN account for 4.8 of total impact in this path. In column 3 and 4, we test the fundamental channel using Ohlson O and future cash flow as mediators, respectively. We find that more
capable managers are associated with high future cash flow and low bankrupt risks and that cash flow is the strongest path for managerial ability to affect bank-loan pricing. Ohlson O account
for 6.2 of total path and cash flow account for 37 of total path if we test them individually.
9
As all variables at path analysis are standardized, coefficients in Table 6 can not be compared directly to other tables. To make the presentation more readable, we also multiply the dependent variables by 100.
19 In Column 5, we model all four factors simultaneously as mediating variables. Cash flow
remains the strongest mediating factor. What is perhaps more informative is the proportion of the total managerial ability effect each mechanism achieves. Column 5 suggests that the fundamental
channel account for about 37 and disclosure channel account for about 6 of total managerial ability effects.
In sum, the path analysis indicates that both the fundamental and disclosure channels are effective channels through which managerial ability can affect cost of debt indirectly. Compared
with the disclosure channel, the fundamental channel is more significant.
4.6 Robustness Analyses
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