A Structural Model of Human Capital and Leverage - Duke ...

severance payment in the period he is laid off. This assumption is made for tractability, since alternatively
I would have to solve a dynamic consumption-savings problem with stochastic labor income. The severance
payment as specified provides an upper bound on what the severance payment would have to be if the agent
were to dynamically smooth his consumption. Rather than complicate the model by embedding a dynamic
consumption-savings problem in the current framework, I perform sensitivity analysis by exogenously varying
the severance payment to ensure that this assumption does not drive my results.
4.2 Debt Market Equilibrium
In this section I characterize the endogenous default condition for the firm as well as the corresponding
interest rate r(k ′ , n ′ , b ′ , z). Default in the model is endogenous, with firms choosing to default whenever is is
in shareholders’ best interest. In default firms are liquidated, with bondholders receiving all of the proceeds
after employees are made whole, and equity holders are left with nothing. 7
As is common in the previous literature, I assume that when a firm defaults it incurs a deadweight cost
that is a proportion ξ1 of its capital stock. Bondholders’ recovery can then be written as
R = (1 − τc)π ′ + τcδkk ′ + (1 − ξ1)(1 − δk)k ′ . (23)
Consistent with the previous literature, I assume that the tax benefit of debt is lost when the firm defaults.
In addition to the standard default costs, a proportion ξn of employees lose their jobs in default. As is
well documented in the labor literature, job loss is costly to employees. The loss of human capital associated
with the unemployment caused by default augments the costs of default. Firms that rely more heavily on
human capital in the production process face higher overall default costs and will therefore optimally choose
to use less leverage than firms who rely less on human capital.
Default in the model occurs any time that the equity value function equals zero. Since the value function is
increasing in the productivity shock and in net worth, there exists an endogenous critical value zd(k ′ , n ′ , b ′ , z)
such that the firm defaults if and only if z ′ < zd. Given this definition, the firm’s conditional default
probability can be written as
pd(k ′ , n ′ , b ′ � zd
, z) =
z
Γ(z, dz ′ ). (24)
7 The assumption that firms are liquidated in default is made for simplicity and is not crucial. In practice, default is more
likely to result in renegotiation or reorganization than liquidation. What matters in the model is that there are costs associated
with default. The parameters that determine default costs are set in the calibration to reflect actual costs observed in default
consistent with the prior literature, rather than the potentially larger costs associated with liquidation.
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