Optimal Public Expenditure with Inefficient Unemployment

This paper 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 gap between the current and efficient rates of unemployment). Such optimal “stimulus spending” is described by a formula expressed with estimable sufficient statistics: the unemployment gap, the unemployment multiplier (the effect of public expenditures on unemployment), and the elasticity of substitution between public and private consumption. Using the formula, we obtain four results. (1) When the unemployment multiplier is positive and unemployment is inefficiently high, 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 increasing in the elasticity of substitution between public and private consumption. In particular, it is zero when extra public goods are useless, and it completely fills the unemployment gap when extra public goods are as valuable as extra private goods. (4) The formula for optimal stimulus spending remains the same whether taxes are distortionary or not. *Pascal Michaillat: Brown University, http://www.pascalmichaillat.org. Emmanuel Saez: University of California– Berkeley, http://eml.berkeley.edu/∼saez. We thank George Akerlof, Steven Coate, Emmanuel Farhi, Xavier Gabaix, Roger Gordon, Yuriy Gorodnichenko, Nathaniel Hendren, Henrik Kleven, Michael Peters, David Romer, Stefanie Stantcheva, Matthew Weinzierl, and participants at many seminars and conferences for helpful discussions and comments. This work was supported by the Center for Equitable Growth at the University of California–Berkeley, the British Academy, the Economic and Social Research Council [grant number ES/K008641/1], the Institute for New Economic Thinking, and the Sandler Foundation.