A Pure Test for the Elasticity of Yield Spreads



Table 5

Regressions of Changes in Nominal Yield Spreads of SCM Long-Term Corporate Bond Indices on
Changes in Selected Nominal Determinants -

AR-GARCH Estimation

Table 5 reports the results of the AR-GARCH estimation of regression model (4) in which the dependent
variable is the monthly change in the nominal yield spread. This regression model is of the following
form:

δS = βj + ^'\YLT + β2 (δYLT) + fakSlope + β4I + ε,
where S is the monthly change in the nominal yield spread, Ylt is the monthly change in the nominal
yield on the constant maturity long-term Government of Canada 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 index and the three-month Treasury bill yield, and
I is the monthly nominal return on the
Toronto Stock Exchange 300 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 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

β 3

β 4

m

p

q

Norm. Test

R2

LM

AAA

-0.0101

(-1.51)

-0.1547

(-11.06)

0.0614
(3.80)

-0.0887 ■

(-7.40)

-0.0055

(-3.61)

1, 2, 4

1

1

<0.0001

0.22

0.0004

AA

-0.0063

(-1.47)

-0.1196

(-9.67)

0.0429
(4.40)

-0.0679

(-6.90)

-0.0050

(-4.68)

1, 2, 4

1

1

0.0018

0.23

0.0067

A

-0.0067

(-1.07)

-0.1208

(-8.86)

0.0600
(5.59)

-0.0541

(-5.06)

-0.0058

(-4.66)

1, 2

1

1

0.0021

0.20

<0.0001

BBB

0.0029
(0.21)

-0.1467

(-3.82)

0.0447
(1.58)

-0.0701

(-2.67)

-0.0109

(-3.30)

-

1

1

<0.0001

0.15

-

Panel B

: 01:1995-07:2001

Regression Coefficients

AR and GARCH Parameters

Goodness of Fit

Index

β 0

β1

β 2

β 3

β 4

m

p

q

Norm. Test

R2

LM

AAA

N/A

AA

-0.0154

(-0.85)

-0.1676

(-2.02)

0.2605
(1.31)

-0.0041

(-0.08)

-0.0070

(-2.31)

-

-

-

-

0.16

-

A

-0.0001

(-0.00)

-0.1817

(-2.29)

0.0541
(0.29)

-0.0041

(-0.08)

-0.0063

(-2.17)

-

-

-

-

0.13

-

BBB

0.0047
(0.14)

0.0510
(0.43)

-0.0081

(-0.03)

0.0141

(0.18)

-0.0132

(-3.03)

-

-

-

-

0.16

-

39



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