Public Investment, Time to Buid, and the Zero Lower Bound

Public investment represents a non-negligible fraction of total public expenditures. Yet, theoretical studies of the effects of public spending when the economy is stuck in a liquidity trap invariably assume that government expenditures are entirely wasteful. In this paper, we consider a new-Keynesian economy in which a fraction of government spending increases the stock of public capital–which is an external input in the production technology–subject to a time-to-build constraint. In this environment, an increase in public spending has two conflicting effects on current and expected inflation: a positive effect due to higher aggregate demand and a negative effect reflecting future declines in real marginal cost. We solve the model analytically both in normal times and when the zero lower bound (ZLB) on nominal interest rates binds. We show that under relatively short time-to-build delays, the spending multiplier at the ZLB decreases with the fraction of public investment in a stimulus plan. Conversely, when several quarters are required to build new public capital, this relationship is reversed. In the limiting case where a fiscal stimulus is entirely allocated to investment in public infrastructure, the spending multiplier at the ZLB is 4 to 5 times larger than in normal times when the time to build is 12 quarters