A Pure Test for the Elasticity of Yield Spreads



Table 4

Regressions of Changes in Absolute Yield Spreads of SCM Long-Term
Corporate Bond Indices on Changes in Government of Canada Yields -
AR-GARCH Estimation

Table 4 reports the results of the AR-GARCH estimation of regression model (3) in
which the dependent variable is the monthly change in the absolute yield spread. This
regression model is of the following form:

S' = β0 + β δ YT-bill + β2sloPe + ε,
where S is the monthly change in the absolute yield spread, Yτ-buι is the monthly
change in the three-month Treasury Bill yield, and
Slope is the monthly change in the
spread between the constant maturity long-term Government of Canada index and the
three-month Treasury bill yield.
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 the entire sample,
covering the 08:1976-07:2001 25-year period. Data during this sample period are
dominated by corporate bonds carrying a standard call provision. Panel B outlines the
results for the 01:1995-07:2001 sub-period, in which bonds carrying the doomsday call
are expected to dominate all indices.

____________________________Panel A: 09:1976-07:2001_________________________

_________Regression Coefficients

AR and GARCH Parameters_______________

Index

β 0

β1

β 2

m

P

q

Norm. Test

R2

LM

AAA

-0.0027

(-0.51)

-0.0442

(-2.51)

-0.0806

(-4.25)

1, 2, 4

1

1

<0.0001

0.19

<0.0001

AA

-0.0074

(-1.82)

-0.1231

(-8.72)

-0.1893

(-12.56)

1, 2, 4

1

1

0.0005

0.18

<0.0001

A

-0.0063

(-1.13)

-0.1011

(-6.22)

-0.1514

(-8.16)

1, 2

1

1

0.0001

0.16

<0.0001

BBB

0.0025
(0.18)

-0.1244

(-3.26)

-0.1996

(-4.72)

-

1

1

<0.0001

0.09

-

Panel B

: 01:1995-07:2001__________

Regression Coefficients

AR and GARCH Parameters

Goodness of Fit

Index

β 0

β1

β β2

m

P

q

Norm. Test

R2

LM

AAA

N/A

AA

-0.0076

(-0.48)

-0.1732

(-2.34)

-0.1751

(-2.44)

-

-

-

-

0.08

-

A

-0.0016

(-0.11)

-0.1519

(-2.17)

-0.1645

(-2.42)

-

-

-

-

0.08

-

BBB

-0.0037

(-0.15)

0.1361

(1.21)

0.0947
(0.87)

-

-

-

-

0.02

-

38



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