2 The Theoretical Framework
In an influential recent paper, BGG embed the costly-state verification (CSV) debt
contracting problem of Townsend (1979) and Gale and Hellwig (1985) into a dynamic
stochastic general equilibrium model with money and sticky prices. In the CSV
framework, there are “bad” states of the world in which it is optimal for a firm to
default on its debt obligations. Agency costs arise because limited liability creates
an incentive for a firm to default in “good” states. To ascertain whether the true
state of the world warrants default, a lender has to pay a cost. Because borrowers
have insufficient wealth with which to finance their investment projects, a lender will,
in equilibrium, demand an external finance premium (cost of external funds less the
opportunity cost of internal funds) in order to be compensated for this verification
cost.
In general equilibrium, the CSV framework gives rise to a financial accelerator.
The key factor in the amplification mechanism is the negative relationship between
the leverage of borrowers (the ratio of debt to net worth) and the external finance
premium. Reflecting shocks to return to capital and to ex post real borrowing costs,
net worth moves procyclically, causing countercyclical swings in the external finance
premium. Because of these endogenous fluctuations in net worth, movements in the
external finance premium are highly persistent, and fluctuations of macroeconomic
variables are magnified and propagated through the economy. In the remainder of this
section, we present the formal details of the debt contracting problem and examine
its comparative statics.
2.1 The Debt Contracting Problem
At the end of period t - 1, an entrepreneur who manages firm i purchases (homo-
geneous) capital to be used in production during period t. Ex ante, the revenue
expected from the investment project is given by RtkQt-1Kit,whereKit is the quan-
tity of capital that the entrepreneur purchases at unit price Qt-1 (measured at the
end of period t - 1 relative to the price of the final good), and Rtk is the aggregate
gross rate of return on capital investment.4
4Following the BGG convention, the time subscript on capital denotes the period in which the
capital is actually used. We assume that when making the investment decision, the entrepreneur
takes Qt-1 and Rtk as given. In general equilibrium, of course, both the price and the return on
capital are endogenous.