A Pure Test for the Elasticity of Yield Spreads



Table 9

Regressions of Changes in Default Rate of Corporate Bonds on Changes in Selected Nominal
Determinants -
AR-GARCH Estimation

Table 9 reports the results of the AR-GARCH estimation of regression model (6) in which the dependent
variable is the monthly change in the default rates from Moody’s. This regression model is of the
following form:

DR = β0 + β1YLT + β2 (YLT) 2 + β3Slope + β4I + ε,
where DR is the monthly change in the default rates, YLT is the monthly change in the nominal yield on
the constant maturity long-term Government of Canada (U. S.) index, (
YLT)2 is a convexity term, Slope
is the monthly change in the nominal spread between the constant maturity long-term Government of
Canada (U.S.) index and the three-month Treasury bill yield, and
I is the monthly nominal return on the
Toronto Stock Exchange 300 index (U.S. S&P 500 index).
t-values are in parentheses, m gives the degree
of the autoregressive process as determined by the stepwise autoregression method,
p and q are the
GARCH(
p,q) parameters, Norm. Test gives the p-value for the normality test for detecting
misspecification of the GARCH model, and finally LM gives the
p-value for the Lagrange multiplier test.
Panel A reports the estimates for historical tracing default rates of all North-American corporate bonds,
covering the 01:1980-12:2001 22 year period. Panel B outlines the results for the 01:2000-09:2004
period, in which forecasted default rates for only speculative bonds are used as dependent variables.

Panel A:

01:1980-12:2001____________________________________

Regression Coefficients

AR and GARCH Parameters______

Countries

β 0

β1

β 1

β 3

β 4

m p

q

Norm. Test R2

LM

U.S.

0.0002
(1.35)

-0.0001

(-0.27)

-0.0002

(-0.36)

0.0002
(0.44)

-0.0050

(-2.72)

1,2 0

1

<0.0001    0.16

0.0070

Canada

0.0001
(0.73)

0.0000
(0.14)

0.0000
(0.16)

0.0002
(1.25)

0.0000
(0.36)

11

1

<0.0001    0.13

0.0050

Panel B:

01:2000-09:2004

Regression Coefficients

AR and GARCH Parameters Goodness of Fit

Countries

β 0

β1

β 2

β 3

β 4

m p

q

Norm. Test R2

LM

U.S.

-0.0009

(-1.07)

-0.0020

(-0.78)

0.0070
(1.031)

0.0040
(1.04)

0.0080
(0.64)

--

-

-        0.05

-

Canada

-0.0009

(-3.21)

0.0037
(2.35)

0.0240
(4.57)

0.0006
(0.73)

-0.0007

(-0.12)

--

-

-        0.13

-

43



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