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 + β₁∆YLT + β₂ (∆YLT) ² + β₃∆Slope + 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.

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