The optimal use of government purchases for macroeconomic stabilization

Abstract 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 sufficientstatistics 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%