We propose a model with involuntary unemployment, incomplete markets, and nominal rigidity, in which the effects of government spending are state-dependent. An increase in government purchases raises aggregate demand, tightens the labor market and reduces unemployment. This in turn lowers unemployment risk and thus precautionary saving, leading to a larger response of private consumption than in a model with perfect insurance. The output multiplier is further amplified through a composition effect, as the fraction of high-consumption households in total population increases in response to the spending shock. These features, along with the matching frictions in the labor market, generate significantly larger multipliers in recessions than in expansions. As the pool of job seekers is larger during downturns than during expansions, the concavity of the job-finding probability with respect to market tightness implies that an increase in government spending reduces unemployment risk more in the former case than in the latter, giving rise to countercyclical multipliers.