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

By Hafedh Bouakez, Michel Guillard and Jordan Roulleau-Pasdeloup

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.

It surprises Europeans that the US has not taken advantage of a deep recession and very low interest rates to renew its crumbling infrastructure. After all, this seems like a greate opportunity for some intertemporl substitution of government expenses. The key is likely in the American distate for public deficits. Yet, given that the stimulus money was decided anyway, why not focus on public infrastrucutre? This paper shows that the returns could have been very large. Unfortunately, I am not quite convinced of the results. Indeed, using a log-linearization in the context of a highly non-linear situation like the ZLB can yield misleading results. In addition, the log-linearization is taken around the deterministic steady-state, which is quite far from the ZLB under stochastics and the approximation error could be large even if there were no linearity issue.

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