The Optimal Use of Government Purchases for Macroeconomic Stabilization

This paper extends Samuelson's theory of optimal government purchases by considering the contribution of government purchases to macroeconomic stabilization. We consider a matching model in which unemployment can be too high or too low. We derive a sufficient-statistics formula for optimal government purchases. Our formula is the Samuelson formula plus a correction term proportional to the government-purchases multiplier and the gap between actual and efficient unemployment rate. Optimal government purchases are above the Samuelson level when the correction term is positive — for instance, when the multiplier is positive and unemployment is inefficiently high. Our formula indicates that US government purchases, which are mildly countercyclical, are optimal under a small multiplier of 0.03. If the multiplier is larger, US government purchases are not countercyclical enough. Our formula implies significant increases in government purchases during slumps. For instance, with a multiplier of 0.5 and other statistics calibrated to the US economy, when the unemployment rate rises from the US average of 5.9% to 9%, the optimal government purchases-output ratio increases from 16.6% to 19.8%. However, the optimal ratio increases less for multipliers above 0.5 because with higher multipliers, the unemployment gap can be filled with fewer government purchases. For instance, with a multiplier of 2, the optimal ratio only increases from 16.6% to 17.6%