The magnitude and Cyclical Behavior of Financial Market Frictions

distributed log normally as

ln ω_it ~ N(—0.5σ²,σ2).

This assumption yields the following expressions for ψ(∙; σ) and ξ(∙; σ,μ):

ψ(ω_it;σ) = 1 — φ(^lnωi^t _σ ⁰∙^5σ2) — ω_it [1 — φ(^lnωi^t + ⁰∙^5σσ)

1 — ψ(ω,_t) — μφ(^lnωi^{t — 0}∙^5σ2) ,

where Φ(∙) denotes the standard normal cumulative distribution function.

Figure 2 considers the implications of varying the magnitude of financial market
frictions (μ = 0, 0.12, 0.24, 0.36), assuming a constant standard deviation of idiosyn-
cratic productivity shocks (σ = 0.28).⁷ As seen in the top left panel, the default
productivity threshold ω is relatively invariant with respect to μ over a consider-
able range of leverage. It is only for highly leveraged borrowers that increases in
bankruptcy costs generate significant differences in the default threshold. In this
case, an increase in μ causes a decrease in ω, because the optimal contract between
the lender and the entrepreneur stipulates a lower default threshold in order to reduce
the incidence of increasingly costly default. Despite the lower probability of default
(top right panel), the external finance premium schedule (bottom left panel) steepens
considerably, and the lender demands a wider credit spread (bottom right panel):
Intuitively, a higher external finance premium and credit spread at a given leverage
reflect greater bankruptcy costs in the event of default.

Note that the default productivity threshold ω is at the highest level (for any
leverage) when μ = 0. The frictionless case generates the highest and the steepest
default probability schedule, but because there is no dead-weight loss associated with
bankruptcy, the external finance premium is zero. The positive relationship between
leverage and credit spreads when μ = 0 reflects solely a higher probability of default
that comes with greater leverage, an implication, in turn, of an upward-sloping ω-
leverage schedule.

The effects of changes in the volatility of idiosyncratic risk (σ = 0.14, 0.28, 0.42)

⁷The calibration used by BGG corresponds to μ = 0.12 and σ = 0.28. When calculating the
annualized external finance premium and the annualized credit spread, we set the risk-free rate equal
to three percent.

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