Using our estimates of the bankruptcy cost parameter μt and the corresponding
solutions for the default productivity threshold ω*t and the standard deviation of
the idiosyncratic productivity shock σ*t, we can calculate the model-implied recovery
rate. This provides an alternative metric by which to evaluate the BGG model and the
quantitative relevance of bankruptcy costs during the last economic downturn. Figure
8 shows the evolution over our sample period of both the average actual recovery rate
at default and the average model-implied recovery rate, defined as
(1 - μt) Rk (Bit-1 + Nit-1)
Bit-1
× E [ωit I ωit < ω*t] ,
(13)
where E [ωit ∣ ωit < ω*t] is the expected realization of the productivity disturbance ωit
conditional on being on default.25 The model-implied recovery rate is much higher
than the actual recovery rate on corporate bonds, particularly so in the pre-recession
period. As shown in the next subsection, the exclusion of credit rating effects gen-
erates bigger estimates of the bankruptcy parameter μt and, consequently, smaller
model-implied recovery rates. Qualitatively, however, actual and model-implied re-
covery rates behave similarly even in this benchmark case, decreasing before the
economic downturn and rising since 2001. Importantly, the model-implied recovery
rate in the case without bankruptcy costs (μ = 0) is unrealistically high and displays
no cyclical pattern. This implies that a substantial degree of financial market frictions
is a necessary ingredient if one wish to explain the recovery rate on corporate bonds
during the last recession.
An important advantage of our strategy of estimating a structural model is that
we can derive firm-specific estimates of the unobservable external finance premium.
Movements in the external finance premium over the business cycle reveal how endoge-
nous developments in financial markets work to amplify and propagate shocks to the
economy. In fact, with procyclical borrowers’ net worth—due to the procyclicality
of profits and equity valuations—the external finance premium will move counter-
25Assuming ωit is log normally distributed, we can write this conditional expectation as
→ φ(
E [ωit 1 ωit < ωit] — /
φ(
ln ω*t
σ
0.5 σ^t
.*
it
ln ω*t +0.5 σff
σ,,
it
To obtain Rk we multiply the model-implied external finance premium [ɪ] . by the gross risk-free
rate Rt , which is assumed to be constant at an annual rate of 3 percent.
26