Firm dynamics, dynamic reallocation, variable markups, and productivity behaviour

I analyze two opposing effects of firm dynamics on productivity over the business cycle. Consider net exit, on the one hand it reallocates resources to incumbents whose productivity improves through scale economies, on the other hand it reduces the competitive pressure incumbents face which depresses productivity. Contrarily net entry strengthens competition, thus increasing productivity, but worsens incumbents' scale economies, thus decreasing productivity. I outline a theory that focuses on two industrial features (1) slow firm entry/exit and (2) firm pricing that depends on the number of competitors. In this environment a negative shock strikes incumbents due to slow exit responses. This weakens their scale thus worsening productivity but the effect recedes as exit occurs which reallocates resources to incumbents. However, the remaining firms face fewer competitors and thus charge higher markups which damages productivity. I analyze this trade-off between productivity improving resource reallocation and productivity degrading market power, by developing a continuous time, analytically tractable DGE model of endogenous firm entry/exit and endogenous markups.