Involuntary unemployment and the business cycle

Can a model with limited labor market insurance explain standard macro and data jointly? We construct monetary in which: i) the unemployed are worse off than employed, i.e. unemployment is involuntary ii) force participation rate varies business cycle. To illustrate key features of our model, we start simplest possible framework. then integrate into medium-sized DSGE show that resulting does as well existing models at accounting for response macroeconomic variables to policy shocks two technology shocks. In addition, these three