The magnitude and Cyclical Behavior of Financial Market Frictions

4 Estimation Methodology

As discussed in Section 2, the bankruptcy cost parameter μ determines the magnitude
of financial market frictions in the BGG framework. Recognizing that this parameter
may exhibit substantial temporal variation, we use the cross-section of firm-level
observations for each time period t, and apply non-linear least squares (NLLS) to
obtain the value of μ_t that minimizes the sum of squared deviations between observed
credit spreads and those predicted by the model. In implementing this procedure,
we allow the idiosyncratic shock variance, σ_it , to vary across firms as well as time
periods.

For any given value of the bankruptcy cost parameter, the predicted credit spread
of a given firm i at time period t is computed as follows. First, using the observed
leverage ratio and expected default probability, the following two equations can be
solved to obtain values for the default threshhold ω,_tt and the idiosyncratic shock
variance σ_it :

where [B/N]_i,t-1 denotes the firm’s leverage at the end of the previous quarter, and
EDF_i,t-1|_t denotes the probability (as of the end of quarter t - 1) that firm i will
default in quarter t. Under the assumption of log-normality of the idiosyncratic
shocks, the functions ψ and ξ are given by equations 7 and 8, respectively, while Φ
denotes the standard normal cumulative distribution function.¹⁹

Next, the predicted credit spread [R^bit/R_it]* is obtained by evaluating the follow-
ing expression using these values of ω*_t and σ*_t together with the observed leverage

r R^b 1 ∙  ₌             ^ω*tψ' (^ω*t ; σ*t ) (1+ [ N ] it-1)

_ ^r J it      ^ψ(ω*_t; ^σ*)^ξ(ω*_t; ^σit^, μt) - ^ψ(ω*_t; ^σ*t)^ξ(ω*t; ^σ*t^, μt)

¹⁹ To match the one-period nature of the BGG framework, we convert the MKMV year-ahead
expected default frequency (EDF_it|_t+1...t+4) to a quarterly basis using the simplifying assumption of
a constant hazard rate over each four-quarter horizon; that is, EDF_it|_t+1 = (1+EDF_it|_t+1...t+4)^1/4-1.

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