A Pure Test for the Elasticity of Yield Spreads

Y+ S        ∂S

...  ∂(Y-S)  Y(1 + — ) - (Y + S)     _

^dR = Y =     ∂ Y         = Y-1 ^dS _- Y -2 S

∂ Y    ∂ Y           Y²            ∂ Y

Thus, in equation (6) if the absolute spread is negatively related to the riskless rate
∂S

(— < 0), the relative spread will show a higher magnitude of negative relationship with
∂Y

interest rate. However, even if the absolute spread has no relationship with the riskless rate

(LS = 0), we can still find a strong negative relationship due to the negative sign of - Y²S in
∂Y

the above equation. Thus one should be cautious when analyzing the result of the relative
spread regression model.

Finally, the estimates for the coefficient c under regression model (2) for the entire
25-year sample period (Panel A of Table 3) and for the 01:1995-07:2001 period (Panel B of
Table 3) all remain negative and statistically significant. As in the analysis of absolute
spreads, the last result for relative spreads demonstrates that Longstaff and Schwartz's (1995)
asset factor is robust.

5.2 Duffee’s (1998) Model

Table 4 outlines the estimates for the Dufee (1998), regression model (3). In some
cases, we find that our SCM data set is characterized by the autoregressive nature of the OLS
residuals of regression model (3). This may be a function of liquidity in the underlying
Canadian bond markets, since Wagner, Hogan and Batten (2005) suggest - with respect to
German Eurobonds- that dependence in spread changes may result from a low liquidity in
the bond markets investigated as well a relatively illiquid corporate bond market compared
to the Government bond market. In our case, the order of the autoregressive process for the
residuals varies across the indices. To determine the correct autoregressive order, we apply a
stepwise autoregression method. In a number of cases, where the OLS residuals follow an
autoregressive process, they also exhibit non-constant volatility consistent with a GARCH
(1,1) process. In those instances, we apply a maximum-likelihood estimation procedure for a
combined autoregressive model and a GARCH (1,1) model. When the OLS residuals only

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