Liquid equity and boom-bust dynamics

I develop and analyze a monetary model with liquid equity. Equity is a claim on the profits of firms acting as sellers in the search-and-matching market. Buyers in that market devote search to obtain matches with firms, and use the equity to relax a liquidity constraint. The dual nature of equity in the search-and-matching market entails a strategic complementary in search operating through buyers' liquidity constraint, and it gives rise to endogenous booms and busts. The economy is stable in an inflation-targeting regime if combined with asset purchases, meaning the government effectively puts a floor below the value of equity.