Productivity losses from financial frictions: can self-financing undo capital misallocation?

I develop a highly tractable general equilibrium model in which heterogeneous producers face collateral constraints, and study the effect of financial frictions on capital misallocation and aggregate productivity. My economy is isomorphic to a Solow model but with time-varying TFP. I argue that the persistence of idiosyncratic productivity shocks determines both the size of steady-state productivity losses and the speed of transitions: if shocks are persistent, steady-state losses are small but transitions are slow. Even if financial frictions are unimportant in the long run, they tend to matter in the short run and analyzing steady states only can be misleading.