Optimal Public Expenditure with Inefficient Unemployment
基于匹配模型，推导出最优公共支出偏离萨缪尔森规则以缩小失业差距的公式，包含三个关键统计量：失业差距、失业乘数和公私消费替代弹性。
This article proposes a theory of optimal public expenditure when unemployment is inefficient. The theory is based on a matching model. Optimal public expenditure deviates from the Samuelson rule to reduce the unemployment gap (the difference between current and efficient unemployment rates). Such optimal “stimulus spending” is described by a formula expressed with three sufficient statistics: the unemployment gap, the unemployment multiplier (the decrease in unemployment achieved by increasing public expenditure), and the elasticity of substitution between public and private consumption. When unemployment is inefficiently high and the multiplier is positive, the formula yields the following results. (1) Optimal stimulus spending is positive and increasing in the unemployment gap. (2) Optimal stimulus spending is zero for a zero multiplier, increasing in the multiplier for small multipliers, largest for a moderate multiplier, and decreasing in the multiplier beyond that. (3) Optimal stimulus spending is zero if extra public goods have no value, it becomes larger as the elasticity of substitution increases, and it completely fills the unemployment gap if extra public goods are as valuable as extra private goods.