We document two new facts about the market-level response to minimum wage hikes: firm exit and entry both rise. These results pose a puzzle: canonical models of firm dynamics predict that exit rises but that entry falls. We develop a model of firm dynamics based on putty-clay technology and show that it is consistent with the increase in both exit and entry. The putty-clay model is also consistent with the small short-run employment effects of minimum wage hikes commonly found in empirical work. However, unlike monopsony-based explanations for small short-run employment effects, the model implies that the efficiency consequences of minimum wages are potentially large.