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

a function of debt, while the solid line plots total interest expense as a function of debt. As debt increases
both labor expenses and interest expense increase in a convex fashion. This reflects the increasing risk of
default as debt increases.
Figure 6 plots the firm’s marginal cost of debt, the derivative of the plots in Figure 5. The solid line
plots the marginal interest expense, the dashed line plots the marginal labor expense, and the dotted line
plots the sum of the two, or the total marginal cost of debt. In a model that ignores labor the optimal debt
policy would be determined by the solid line. Accounting for labor, the dotted line determines the optimal
level of debt. The absolute magnitude of labor related distress costs, and hence the difference between the
dotted and solid lines, will depend on how heavily the firm relies on human capital to produce. Thus, the
figure illustrates that ignoring labor related costs of distress leads to understatement of the costs of debt and,
therefore, overstatement of optimal debt levels.
An important feature of the model is that wages increase as firms approach distress, following the pattern
of interest rates. At first glance, this result seems to be at odds with the data. For example, Figure 1
shows that on average wages dip very modestly preceding a separation event. The workers represented
in the figure were part of mass layoffs, so the firms involved were likely in distress. There are, however,
several factors to consider here. First, my model abstracts from any incentive effects of distress. Workers
are assumed to always work while they are employed. In reality, workers for distressed companies may not
be as productive as those employed by healthy companies. Second, all workers are homogeneous in my
model. In reality, distressed firms are likely to lose their best employees, those who can most easily find a
different job, while retaining those who would have a more difficult time finding alternative employment. The
more relevant comparison, then, is what happens to productivity-normalized wages for distressed firms. If
worker productivity in distressed firms drops more significantly than do wages, then these firms still are more
burdened by labor related costs in distress. Finally, in the case that wages do actually decline in distress even
when properly measured, this would amount to an additional cost of distress borne by employees, for which
they would demand compensation ex ante. With competitive labor markets, the firm will end up paying
employees for bearing this risk one way or another.
5.3 Cross-section of Labor Intensity
As was shown above, firm leverage decreases significantly with labor intensity. In this section I evaluate the
model’s ability to match this empirical fact. In the model, labor intensity is controlled by the parameter αn.
Table 5 shows the leverage generated by the model when this parameter is varied over a range of values. The
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