Dynamic Macroeconomics

20.7.2 Monetary Policy at the Zero Lower Bound
As already mentioned, the theoretical possibility of a liquidity trap became a
reality in Japan during the 1990s, and in the other industrial economies in the
aftermath of the recession of 2008–2009, when short-term interest rates
touched the zero lower bound and in some cases became slightly negative for
a brief period.
The analysis of monetary policy at the zero lower bound became an active
area of research since Krugman [1998] studied it, prompted by the Japanese

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experience. Krugman used an intertemporal model of savings and investment
with and without price flexibility. Eggerstsson and Woodford [2003], Jung et
al. [2005], and others have since extended the analysis to new Keynesian
models.
To analyze the conduct of monetary policy at the zero lower bound,
consider the model consisting of 
(20.1)
 and 
(20.2)
, augmented for an external
finance premium, as in chapter 19. We abstract from productivity shocks to
focus on financial shocks. The modified model thus takes the form
where 
x
t
is, as in chapter 19, an exogenous external finance premium. This is
our financial shock.
Consider the impact of a large 
x
t
. To avert a recession would then require
a reduction in the central bank nominal interest rate 
i
t
that would make the
real interest rate plus the external finance premium equal to the natural
interest rate 
ρ
. Thus, the central bank nominal interest rate would have to be
If the shock to the external finance premium is large enough (i.e., if 
x
t
> ρ
+
E
t
π
t
+1
), then the central bank nominal interest rate ought to become negative.
If it cannot become negative because of the zero lower bound, then from
(20.44)
, a recession cannot be avoided.
Hence, the zero lower bound constraint (that the central bank cannot
reduce nominal interest rates below zero) results in financial shocks and also
other aggregate demand shocks, which could in principle be neutralized by
monetary policy, having real effects on output and employment. If the central
bank could fully adjust nominal interest rates below the zero lower bound,
negative aggregate demand shocks would not affect output and employment in
this model. It is only because nominal interest rates may hit the zero lower
bound that we end up with real effects for financial and other aggregate
demand shocks, even under the optimal policy.

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