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

4.1 Labor Market Equilibrium
In this section I solve for the wage w(k ′ , n ′ , b ′ , z) that is required by employees. Firms and employees agree
on wages at the same time as investment, hiring, and financing decisions are made. As the notation makes
clear, wages depend on all of the information that is available at that time. I assume that employment
agreements are long term, while wages are determined each period according to the state of the firm. The
worker will continue to work for the firm until he is laid off or leaves voluntarily. The terms of the employment
agreement are thus determined to meet a required level of lifetime (rather than single period) utility for the
employees. I assume that outside of default the firm fully insures its employees’ human capital, in the sense
that the employees’ lifetime utilities do not depend on the stochastic shocks. Several papers in the optimal
contracting literature have studied the optimal wage contract in a variety of economic settings (Harris and
Holmstrom 1982, Michelacci and Quadrini 2009, Berk, Stanton, and Zechner 2010, He 2011). In each setting
the optimal contract provides insurance to employees against adverse shocks to their human capital. This
result follows naturally from the inability of employees to diversify this risk away. While solving for the
optimal wage contract is outside the scope of this paper, I rely on these previous studies to motivate the
structure of the contract.
Employees are compensated for bearing risk through two channels. First, the contracted wage will respond
endogenously to the probability that a worker will be laid off in bankruptcy, thus compensating him ex
ante for bearing this risk. Workers may also be laid off outside of bankruptcy when the firm receives a
negative shock and needs to downsize. In this case, the firm pays each separated worker a severance payment
that compensates him ex post for the costs associated with unemployment. He (2011) finds such severance
payments to be optimal in a setting where employees can privately save. The severance payment is endogenous
and will be determined below.
Determination of the wage proceeds in two steps. Because firms cannot costlessly replace workers and
because workers cannot immediately find another job, there is a match-specific surplus associated with an
employment relationship. As is common in the labor literture, in the first step I use generalized Nash
bargaining to divide this surplus. The outcome of the Nash bargaining game is a market wage w0 which
provides the necessary level of lifetime utility to the employees. Since the firm cannot commit to paying
the market wage each period in perpetuity, the second step is to add a risk premium to the market wage to
account for the possibility that the worker is laid off. This second step produces the state-dependent wage
w(k ′ , n ′ , b ′ , z).
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