中文摘要
本文提出了一种失业为非效率时的最优公共支出理论。该理论基于匹配模型。最优公共支出偏离萨缪尔森法则，以缩小失业缺口（当前失业率与有效失业率之差）。此类最优“刺激支出”可由包含三个充分统计量的公式描述：失业缺口、失业乘数（增加公共支出所实现的失业减少），以及公共消费与私人消费之间的替代弹性。当失业非效率地偏高且乘数为正时，该公式得出以下结果。（1）最优刺激支出为正，且随失业缺口递增。（2）当乘数为零时，最优刺激支出为零；当乘数较小时，其随乘数递增；在乘数适中时达到最大；超过该水平后，其随乘数递减。（3）若额外的公共品无价值，则最优刺激支出为零；其随替代弹性的增加而变大；若额外的公共品与额外的私人品同等有价值，则其完全填补失业缺口。
Abstract
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.