The magnitude and Cyclical Behavior of Financial Market Frictions

old, the entrepreneur will be faced with negative profits and will declare bankruptcy,
leaving the proceeds of the project—net of bankruptcy costs—to the lender.

The default productivity threshold in the debt contract ω_it is defined by

R'B- 1 = ωR Qt-1 Kit

and implicitly determines the contractual interest rate R_i^b_t :

Thus, under the incentive-compatible debt contract, the entrepreneur’s expected
profit will be given by ψ (ω_it ) Rk Q_t-1 K_it, where

∞

ψ ( ω_it )=/ ( ωit - ω_it ) f ( ω ) dω.
Jitit

Note that if ω_it < ω_it, the entrepreneur declares bankruptcy and simply walks away
from the project with nothing. The expected return to the lender under such a
contract can be expressed as ξ (ω_it ; μ) RkQ_t-1 K_it, where

In equilibrium, therefore, the optimal debt contract negotiated at the end of period
t - 1 specifies the amount Bit-1 that the entrepreneur can borrow along with the
default productivity threshold ω_it, so as to maximize the expected return of the
investment project, subject to the constraint that the lender earns the risk-free rate
Rt:⁶

^{ψ (ω}it ) Rk ⁽Bit-1 ⁺ Nit-1⁾

ξ(ω_it; μ)Rk (Bit-1 + Nit-1) = RtBit-1.

⁶ See BGG for additional technical details that guarantee a solution without credit rationing and
that ensure entrepreneur’s participation in the project. We checked our numerical results to make
sure that they are consistent with all the assumptions of the BGG framework.

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