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

Positive dividends are subject to taxation at a rate τd. Letting φi be an indicator variable for equity issuance,
net dividends received by shareholders are given by
The firm uses capital and labor to produce output
d = dg − (1 − φi)τddg − φiΛ(dg). (5)
f ′ = z ′ A · F (k ′ , n ′ ) ν . (6)
The function F is strictly increasing and concave in both arguments and is homogeneous of degree one. I
assume that ν < 1 so that the output function exhibits decreasing returns to scale. This is consistent with
empirical observations on the growth dynamics of firms, namely that small firms grow faster than large firms.
A is simply a scaling constant that is used to set the steady state value of capital to one in each simulation
below.
period
Operating profits are equal to output less wages and a fixed cost of production that must be paid each
π ′ = f ′ − w(k ′ , n ′ , b ′ , z)n ′ − f0. (7)
Wages are agreed upon at the beginning of the period and, like the interest rate, are an endogenous function
of all information that is available at the time they are agreed upon. Wages are subject to two sources of
risk. First, since wages are a fixed claim it is possible that the firm will not be able to pay the promised
wages in some states, a situation that I refer to as wage default. Second, when the firm defaults on its debt
obligations, a proportion of employees lose their jobs. As will be shown below, unemployment is costly to
the workers, so wages will reflect both the possibility of wage default and of unemployment due to financial
default. Accounting for labor in the production process introduces operating leverage in the profit function in
the form of wages which are fixed in the short run. This operating leverage can crowd out financial leverage.
The amount of labor-induced operating leverage varies in the cross-section with the wage bill w · n, or labor
intensity, of the firm. Thus, the more a firm relies on labor for production, the less financial leverage it will
use. The function w will be derived in the following section.
Capital depreciates at a constant rate δk, and depreciation and interest expense are tax-deductible,
10