Since the BGG model abstracts from various details of financial market behavior,
our estimation procedure incorporates time-specific industry and ratings dummies:
where RATINGit-1 denotes the set of dummies associated with bond portfolio credit
ratings at the end of period t - 1, and INDUSTRYit denotes the set of industry
dummies; the coefficients on these dummies are allowed to vary over time.20 The
stochastic disturbance cit is assumed to have zero mean and to be independent across
firms, but may exhibit time-varying heteroskedasticity; that is, E[cit] = 0, E[c2t] = ν2t,
and E[citCjt] = 0, for all i = j.
Rb
Rb
R it
R it
= RATING it-1 + INDUSTRY it + ett,
(12)
The rating dummies are included to control for liquidity factors that arise from the
fact that certain corporate bonds trade rather infrequently, implying a relatively thin
secondary markets for some securities.21 In such a case, a credit spread will include
a premium to compensate investors for the risk of having to sell or hedge a position
in an illiquid market. As shown by Delianedis and Geske (2001), this liquidity risk is
correlated with default risk and accounts for a significant portion of observed credit
spreads. Controlling for industry differences is potentially important because our
dataset, though rich in the cross-sectional dimension, spans a single business cycle
dominated by the bursting of the high-tech bubble.
Following this approach, the residual vector (c 11,... cntt) can be computed for any
given value of μ. Thus, for each time period, we start with an initial guess for this
parameter, and then utilize a standard optimization algorithm to obtain the NLLS
estimator μt that minimizes the sum of squared residuals.22
20Credit rating indicators are based on the average of the S&P ratings of the firm’s outstanding
bond issues, weighted by the market value of bonds. The resulting portfolio credit ratings were
condensed into nine categories: AAA, AA, A, BBB, BB, B, CCC, CC, and C. Industry effects are
based on the 3-digit North American Industry Classification System (NAICS).
21See Warga (1991) for a discussion of problems associated with high-frequency corporate bond
prices and the use of “grid-based” pricing.
22For each time period, we utilized an extensive grid of initial guesses to ensure that the NLLS
estimator reached the global minimum of the objective function.
22