The 2007-8 crisis in the U.S. lead to a steep recession, followed by aggressive policy responses. Monetary policy went full tilt, cutting interest rates rapidly to zero, where they have remained since the end of 2008. With conventional monetary policy seemingly exhausted, fiscal stimulus worth $787 billion was enacted by early 2009 as part of the American Recovery and Reinvestment Act.
Unconventional monetary policies were also pursued, starting with “quantitative easing”, purchases of long-term bonds and other assets. In August 2011, the Federal Reserve’s FOMC statement signaled the intent to keep interest rates at zero until at least mid 2013. Similar policies have been followed, at least during the peak of the crisis, by many advanced economies. Fortunately, the kind of crises that result in such extreme policy measures have been relatively few and far between. Perhaps as a consequence, the debate over whether such policies are appropriate remains largely unsettled. The purpose of this paper is to make progress on these issues.
To this end, I reexamine monetary and fiscal policy in a liquidity trap, where the zero bound on nominal interest rate binds. I work with a standard New Keynesian model that builds on Eggertsson and Woodford (2003). In these models a liquidity trap is defined as a situation where negative real interest rates are needed to obtain the first-best allocation. I adopt a deterministic continuous time formulation that turns out to have several advantages. It is well suited to focus on the dynamic questions of policy, such as the optimal exit strategy, whether spending should be front or back-loaded, etc.
It also allows for a simple graphical analysis and delivers several new results. The alternative most employed in the literature is a discrete-time Poisson model, where the economy starts in a trap and exits from it with a constant exogenous probability each period. This specification is especially convenient to study the effects of suboptimal and simple Markov policies—because the equilibrium calculations then reduce to finding a few numbers—but does not afford any comparable advantages for the optimal policy problem.