Credit-crunch dynamics with uninsured investment risk

I study the effects of credit tightening in an economy with uninsured idiosyncratic investment risk. In the model, entrepreneurs require an equity premium because collateral constraints limit insurance. After collateral constraints tighten, the equity premium and the riskiness of consumption rise and the risk-free interest rate falls. I show that, both immediately after the shock and in the long run, the equity premium and the riskiness of consumption increase more than they would if the risk-free rate were constant. Indeed, the long-run increase in the riskiness of consumption growth is purely a general-equilibrium effect: if the risk-free rate were constant (as in a small open economy), an endogenous decrease in risk-taking by entrepreneurs would, in the long run, completely offset the decrease in their ability to diversify. I also show that the credit shock leads to a decrease in aggregate capital if the elasticity of intertemporal substitution is sufficiently high. Finally, I show that, due to a general-equilibrium effect, there is no \"overshooting\" in the equity premium: in response to a permanent decrease in firms' ability to pledge their future income, the equity premium immediately jumps to its new steady-state level and remains constant thereafter, even as aggregate capital adjusts over time. However, if idiosyncratic uncertainty is sufficiently low, credit tightening has no short- or long-run effects on aggregate capital, the equity premium, or the riskiness of consumption. Thus my paper highlights how investment risk affects the economy's response to a credit crunch.