Granular Uncertainty and Disastrous Misallocation

We develop a general equilibrium model in which heterogeneous entrepreneurs produce output in the presence of financing constraints. We model granular uncertainty as the shocks that affect the uncertainty in future idiosyncratic productivity without changing the cross-sectional dispersion of productivity. These shocks give rise endogenously to rare disasters through credit misallocation. Intuitively, an increase in granular uncertainty exacerbates the misallocation of credit as productive entrepreneurs' self-financing ability through saving becomes weaker when their productivity becomes transitory. In the presence of financial frictions, the recovery from the state with large misallocation is slow. We propose an approximation method to solve the model without tracking the exact distribution of agents. We show heuristically and numerically that the covariance of cross-sectional wealth and productivity can accurately summarize the economy's aggregate states. Our approximation method provides a closed-form characterization for both the steady states and transitional dynamics of the economy