Involuntary unemployment in economies with efficient risk sharing

We study economies where 'employment lotteries' determine random layoffs, and incomes for employed and unemployed agents allocate risk efficiently. We ask, for which specifications are unemployed agents worse off, a situation we call involuntary unemployment. We show unemployed agents are worse off iff an exogenous increase in wealth decreases aggregate unemployment. In a monetary economy, we show that in equilibrium the unemployed are worse off iff high inflation implies high unemployment. Our model also generates nominal wage stickiness as an equilibrium phenomenon. But neither involuntary unemployment nor nominal stickiness implies these economies are operating inefficiently or are out of equilibrium.