The Optimal Use of Government Purchases for Macroeconomic Stabilization

This paper extends Samuelson’s theory of optimal government purchases by accounting for the contribution of government purchases to macroeconomic stabilization. Using a matching model of the macroeconomy, we derive a sufficient-statistics formula for optimal government purchases. The formula implies that the deviation of optimal government purchases from the Samuelson level is proportional to the elasticity of substitution between government and personal consumption times the government-purchases multiplier times the deviation of the unemployment rate from its efficient level. Hence, with a positive multiplier, optimal government purchases are above the Samuelson level when unemployment is inefficiently high and below it when unemployment is inefficiently low. We calibrate the formula to US data. A first implication is that US government purchases are optimal with a small multiplier of 0.04; if the multiplier is larger, US government purchases are not countercyclical enough. Another implication is that optimal government purchases should increase during recessions. With a multiplier of 0.5 the optimal government purchases-output ratio increases from 16.6% to 20.0% when the unemployment rate rises from the US average of 5.9% to 9%. With multipliers higher than 0.5 the optimal ratio increases less because fewer government purchases are required to fill the unemployment gap: with a multiplier of 2 the optimal ratio only increases from 16.6% to 17.6%; this is the same increase as with a multiplier of 0.07.