Default Risk and Aggregate Fluctuations in an Economy with Production Heterogeneity

We study aggregate uctuations in an economy where \u85rms have persistent di¤erences in total factor productivities, capital and debt or \u85nancial assets. Investment is funded by retained earn-ings and non-contingent debt. Firms may default upon loans, and this risk leads to a unit cost of borrowing that rises with the level of debt and falls with the value of collateral. On average, larger rms, those with more collateral, have higher levels of investment than smaller \u85rms with less collateral. Since large and small \u85rms draw from the same productivity distribution, this implies an insu ¢ cient allocation of capital in small \u85rms and thus reduces aggregate total factor productivity, capital and GDP. We consider business cycles driven by shocks to aggregate total factor productivity and by credit shocks. The latter are \u85nancial shocks that worsen \u85rmscash on hand and reduce the fraction of collateral lenders can seize in the event of default. In equilibrium, our nonlinear loan rate sched-ules drive countercyclical default risk and exit, alongside procyclical entry. Because a negative productivity shock raises default probabilities, it leads to a modest reduction in the number of rms and a deterioration in the allocation of capital that ampli\u85es the e¤ect of the shock. Th