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.

我们提出了一个具有非自愿失业，市场不完整和名义刚性的模型，其中政府支出的影响取决于国家。政府购买的增加增加了总需求，拉紧了劳动力市场并减少了失业。反过来，这降低了失业风险，从而降低了预防性储蓄，从而导致私人消费的反应比具有完善保险的模型更大。随着消费冲击，高消费家庭在总人口中所占的比例增加，通过构成效应进一步扩大了产出乘数。这些特征，加上劳动力市场上的相应摩擦，在衰退中产生的乘数明显大于在扩张中的乘数。由于低迷时期的求职者比扩张时期的大，