I've been trying to get my head around this over the last few days. Still not sure I'm there yet.
It seems to me that the effect of fiscal policy at the Zero Lower Bound in New Keynesian models is extremely sensitive to timing the exit. This isn't about finding "shovel ready" projects that can be started relatively quickly; this is about finding projects that can be stopped instantly.
"Better late than never" is OK for starting fiscal policy; it is not OK for stopping fiscal policy. If we believe simple NK models.
Take an extremely simple NK model where we ignore private investment and foreigners, so C+G=Y.
If the economy is above the ZLB, the central bank offsets fiscal policy, to keep inflation on target and output at potential, so C+G=Y=Y*. Any increase in G causes 100% crowding out of C, because the central bank makes sure it does.
But if the ZLB is a binding constraint, C+G=Y < Y*. The central bank wants to cut interest rates to keep output at potential and inflation on target, but can't.
Consider fiscal policy for an economy that is temporarily at the ZLB.
1. Changes in government spending.
It is (reasonably) well-understood that a permanent increase in G has no effect on Y. Because future C falls by the same amount that G rises, So current C falls too by the same amount, via consumption-smoothing. So current G goes up and current C goes down but current Y stays the same.
It is also (reasonably) well-understood that a temporary increase in G causes Y to rise by the same amount, because C stays the same (again via consumption-smoothing).
Now suppose that the increase in G is temporary, but G does not return to normal until "one period" after the economy lifts off the ZLB. So in that period immediately after the ZLB ends, the higher G causes lower C, which via consumption-smoothing reduces current C during the ZLB periods. It's exactly like a permanent increase in G.
If the government workers drop their shovels "one period" too late (or are expected to do so), fiscal policy will not work at all.
How long is "one period"? It's as short as you want it to be.
2. Changes in marginal tax rates.
Lump sum taxes have no effect in a simple NK model, because of Ricardian Equivalence.
Changes in marginal tax rates do have an effect in NK models: first because of standard supply-side reasons (incentive effects on labour supply); second because at the ZLB those supply-side effects will affect inflation and (with nominal rates at 0%) hence real interest rates.
At the ZLB, if you are doing a temporary change in marginal tax rates you want to increase tax rates, to reduce current Y* and so reduce the output gap and so increase inflation (i.e. reduce the amount inflation falls below target) and so reduce real interest rates (i.e. reduce the amount they rise) to increase current C (i.e. prevent it falling as much). See Gauti Eggertsson (pdf).
At the ZLB, if you are doing a permanent change in marginal tax rates (bear with me please) you want to reduce tax rates, to increase future Y*, and so increase future C by the same amount, and so increase current C by the same amount (via consumption-smoothing). There is no effect on inflation, because current C and current Y* change by the same amount, leaving the output gap unchanged.
Now suppose you do a temporary change to marginal tax rates but don't return them to normal until "one period" after the economy lifts off the ZLB. It's exactly like a permanent change.
It's not just the magnitude, but the sign of the tax rate multiplier that changes, if there is any (expected) delay in returning tax rates to normal.
That's what I call extreme sensitivity to timing.
3. God only knows what to make of all this.
Is it an artefact of this extremely simple version of the New Keynesian model? Is it an artefact of my discrete-time setup. [Update: maybe that's it. I'm thinking in discrete time rectangular steps, and maybe I should be thinking in continuous time triangular slopes. But all the same, it will still be very sensitive to timing the exit right.]
But if this simple version of the model is roughly right, the fiscal policy advice it gives cannot in practice be implemented. Governments can't usually stop doing things super-quickly.
Unless, maybe it requires some fancy footwork to coordinate monetary and fiscal policy?
But it's not enough to argue that the central bank can just delay raising interest rates for the same "one period". Because if you can do that, you don't need fiscal policy at all. Just tell the central bank to keep interest rates "too low for too long", to create the required amount of expected inflation.