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

employees who likely suffer more significant losses from displacement. Couch and Placzek (2010) find more
modest results that they argue are more consistent with results from different data sources, time periods,
and geographic regions. They find that six years after separation displaced workers are still suffering 15%
wage loss. Since all jobs are identical in my model, I need to choose a low probability of successful search to
approximate the magnitude of earnings losses from these studies. I thus set pe = .3, which implies that earn-
ings on average are 8.4% lower six years after separation. This parameter should not be interpreted literally,
since the probability of finding a job during a year of unemployment is clearly greater than 30%. Rather, it
should be interpreted as a parameter that controls how costly an unemployment spell is in expectation.
Notice from equation (15) that hiring costs η, the unemployment benefit wu, and the market wage w0
are determined only up to a scaling constant. I therefore set these parameters to deliver a market wage of
1. Hiring costs η are set equal to .75, which implies that hiring costs are three-quarters of a worker’s annual
payroll. (Hamermesh and Pfann 1996) review the research on estimates of direct costs of labor adjustment
and report that some studies find external costs up to one year’s payroll for a worker. They also report that
these costs increase rapidly with the skill of a worker, being low for high-turnover, low-skilled workers and
high for low-turnover, high-skilled jobs. My model is motivated by the importance of human capital in the
production process, so I choose the hiring costs to wage ratio to be in line with what it would be for relatively
high-skilled workers. The unemployment benefit wu is set equal to .5, which approximates the stated goal of
the unemployment insurance system to replace half of a worker’s wages. Given these values, the employees
bargaining power θ is set equal to .6811, which sets the market wage w0 to 1. Finally, I choose log utility to
represent the workers’ preferences, which represents a very conservative level of relative risk aversion.
5.2 Numerical Solution and Baseline Results
Since the model has no closed-form solution, I solve the model using value function iteration. Specification
of the state space requires grids for the control variables {k ′ , n ′ , b ′ } as well as a grid for net worth ω and a
grid for the productivity shocks z. The dimensionality of the state-space is rather large for this problem,
restricting the number of grid points that can be used in each dimension. The state space for z is especially
expensive computationally since both z and its lagged value are needed to calculate the firm’s realized net
worth. As such, I use 9 grid points for z in the interval
22
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.