A Pure Test for the Elasticity of Yield Spreads

of Equation (5) to incorporate Moody’s default rates:

∆DR = β₀+ β₁∆Y_LT +β₂(∆Y_LT)²+β₃∆Slope+β₄I+ε       (8)

where ∆DR is the monthly change in Moody’s default rate and the remaining variables are as
defined above.

We initially assume that Moody’s trailing twelve-month all corporate default rates, serve
as a good proxy for expected future default probabilities, and therefore use these default
rates in regression model (6). This sample covers the 12:1979-11:2001 period. Noting that
these are ex post default rates, we then use Moody’s monthly speculative- grade default rate
forecasts (12:1999-11:2004), which may serve as a better proxy for expected default
probabilities.¹⁸

Note that, in 2001 81.2% of the number of defaults in Moody’s default universe
occurred in North America (U.S. and Canada). Thus, these default rates also reflect the
Canadian default experience. However, most of the North American defaults (77%) are those
of U.S. companies. Thus, we also apply regression model (6) with U.S. data replacing the
Canadian data to proxy the independent variables. Following Collin-Dufresne et al. (2001)
we use the following proxies: the 10-year benchmark Treasury yield represents the level of
the term structure; for the slope we use the spread between the 10-year and 2-year
benchmark Treasury yields; and finally we use returns on the S&P 500 index.

The results are reported in Table 9. In panel A, which reports the results using historical
Moody’s trailing twelve-month all corporate default rates, we find that when U.S.
determinants (term structure components and asset returns) are used, the stock index return
coefficient is significantly negative. This is expected since higher stock returns imply higher
asset returns and lower default rates. At the same time, the term structure variables are not
statistically significant. When Canadian data are used instead, we find that none of the
independent variables are statistically significant. This is also expected, since most of the
defaults are attributed to U.S. rather than Canadian companies.

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