One
part of my earlier post
on monetary policy and austerity was a little cryptic. OK, it was largely unintelligible
to nearly everyone (see, for example, Arnold Kling here). My apologies. As it’s an important point, let
me elaborate. What I want to show is that with monetary policy aiming to hit some

*level*for nominal GDP (NGDP), if we are at the Zero Lower Bound (ZLB) for nominal interest rates today, austerity today will reduce welfare (by, in part, raising inflation tomorrow), and fiscal stimulus will increase welfare. I will not use maths, as even when I use the most simple of equations, my posts are described by well known blogging economists as nerdy.
Output
today depends on real interest rates today. Anything else that changes output
today is called a shock. There is no Quantitative Easing (QE). For simplicity we
will assume no direct linkage between output across periods. Inflation today depends
on output today, but also expected inflation tomorrow. Prices were on target yesterday, and let’s
assume that inflation the day after tomorrow is fixed. Now hit output today
with a negative demand shock, a shock which is not repeated tomorrow. If that
shock is small enough, we can offset it

*entirely*by lowering interest rates today. Inflation today is unchanged as a result. Nothing changes tomorrow. Everyone is happy: monetary policy has done its job, by lowering nominal and real interest rates today.
Now suppose
the negative shock today is so large, that even with nominal interest rates at
zero, output remains too low. This reduces inflation today. With a target for NGDP,
not only would this mean we missed our target today, but it would also mean
that we would miss our NGDP target tomorrow, because lower inflation today
would mean lower prices tomorrow if inflation tomorrow was unchanged. So
monetary policy cuts interest rates tomorrow in order to raise tomorrow’s
output and inflation. If this response is expected (we assume rational
expectations throughout) it does two things. It raises inflation today directly
(because inflation today depends on expected inflation tomorrow), and it
reduces real interest rates today (real interest rates today are nominal rates today
minus expected inflation tomorrow), which raises output today which in turn
raises inflation today. This is why NGDP targets can be very helpful to combat
the ZLB. If we instead targeted inflation, then monetary policy tomorrow might
do nothing, because policy would still hit the inflation target tomorrow.

Now suppose
that, despite relaxing monetary policy tomorrow, we still hit the ZLB today. Output
and inflation are too low today, even though we hit the NGDP target tomorrow.
There is absolutely no reason why this might not happen. Although inflation is
higher tomorrow to compensate for low inflation today, real interest rates today
are still not low enough to prevent output falling today. Sure, we could relax
monetary policy tomorrow by yet more (assuming we are not at the ZLB tomorrow),
and this could increase inflation tomorrow by enough to get real interest rates
low enough today. But that would mean we overshoot our NGDP target tomorrow.

So, we
hit the ZLB today, undershoot the NGDP target today, but meet it tomorrow. Now let
output also depend on fiscal policy, and add some austerity today. This reduces
output by yet more today. Interest rates are at the ZLB today, so monetary
policy today can do nothing about it. Lower output lowers inflation today still
further, but because this reduces the price level tomorrow, monetary policy
relaxes by more tomorrow. This is good, because higher inflation tomorrow
raises both inflation and output today, which

*moderates*the impact of austerity. But the end result must be that the net impact of austerity is to reduce output and inflation today, and raise inflation tomorrow. (If output and inflation are not lower today, inflation will not change tomorrow. But if inflation tomorrow is unchanged, why has austerity not reduced output and inflation today?)
That is
how a negative demand shock today, like austerity, can raise inflation
tomorrow. It only happens because we have a target for the level of NGDP,

__and__we cannot use interest rates to kill the impact of the demand shock today, because we are at the ZLB. But the latter is where we currently are, if you ignore QE.
It
follows directly that excess austerity today reduces welfare, even with NGDP
targets. We still hit the NGDP target tomorrow, but only by having additional
excess output and inflation tomorrow, and a bigger recession today. People are
clearly worse off both today and tomorrow.

This
little experiment also shows us why fiscal stimulus can be more effective than
a NGDP target at stabilising the economy at a ZLB. Just put the story in
reverse. Instead of excess austerity, now have a fiscal stimulus today
sufficient to get NGDP back to target today. As there is no shock tomorrow
(fiscal or otherwise), we also hit NGDP tomorrow. We are back to where we want
to be. Now the fiscal stimulus may have meant more government spending than we might have
wanted in the short term, so it’s not cost free. But in terms of output and
inflation, we are clearly better off as a result of the fiscal stimulus, even
though we have a NGDP target.