This paper shows that when unemployment is inefficient, optimal public expenditure deviates from the Samuelson rule to reduce the unemployment gap. Optimal stimulus spending depends on the unemployment gap, unemployment multiplier, and an elasticity of substitution.
This paper explores how the optimal replacement rate of unemployment insurance varies over the business cycle in the United States. It finds that the optimal replacement rate is countercyclical, just like the actual replacement rate.
This paper develops a New Keynesian model in which the government multiplier doubles when the unemployment rate rises from 5% to 8%. The multiplier is so countercyclical because in bad times, on the labor market, job rationing dwarfs matching frictions.