A number of us are highly critical of moving to austerity so early in the recovery from the Great Recession. Market Monetarists (MM) argue that this criticism is unfounded, because monetary policy can offset the impact of austerity on demand. Not when interest rates are at the Zero Lower Bound (ZLB), the critics of austerity respond. The ZLB is not a problem, MM reply.
I want to make a couple of observations. First, MM often imagine that they invented this offset argument. However it forms a key part of the austerity critics’ original objection. If the impact of fiscal consolidation on output is always the same, then the reasons for postponing deficit reduction until the recession is over become significantly weaker.  The whole point is to postpone deficit reduction until when the ZLB constraint no longer bites. At that point, monetary policy can offset the demand impact of fiscal consolidation, whereas at the ZLB it cannot (according to the austerity critics). Monetary offset is built into the austerity critics’ main case.
Second, if you are a fiscal policy maker, and you want to take the MM argument seriously, you have to believe two things. First, that monetary policy is capable of offsetting the impact of austerity as much now as later. Second, that this is actually what monetary policy makers will do. If you believe the first, but are not sure about the second, then fiscal consolidation now is a mistake. Sure, you can blame monetary policy makers for not offsetting when they could, but if you knew this might happen then you hold some responsibility.
This second point exposes how weak the MM argument is at the ZLB. They have to argue not only that unconventional monetary policy could offset fiscal contraction at the ZLB, but also that it will. We see immediately that the issue of NGDP targeting is beside the point. Central banks at the moment are inflation targeting, and are likely to continue to do so, so enacting fiscal contraction in the hope that they might change is highly irresponsible.
So the MM argument that the ZLB does not matter has to rely on Quantitative Easing (QE). But here there is a basic problem that MM has never to my knowledge answered. Just how much QE do you do to offset any fiscal contraction? We have no real idea, because we have so little experience. Lags between policy actions and reactions are such that we cannot just say whatever it takes, because we might have lost a lot of output (or created a lot of inflation) before policy makers get it right. In reality, policy makers are likely to be cautious, so almost certainly they will not offset enough, even presuming that QE is capable of offsetting completely. So once again, being realistic about what we know and what monetary policy makers will do, fiscal contraction at the ZLB is irresponsible. (I have talked about this in more detail before.)
These are abstract arguments, but they can be applied to two real examples. First the Eurozone. Here we currently have no QE. We should have QE - indeed I have argued we should think about having helicopter money, but to presume that these things would happen just when they are required would be highly unrealistic. It would also be silly to assume that the ZLB was never going to bite when the new fiscal regime was put together following the crisis. So fiscal contraction in the Eurozone is a major problem and highly irresponsible whichever way you look at it.
In the UK it is often argued that 2010 austerity was not a problem, because given the rapid inflation that happened in 2011, if austerity had not happened, the MPC would have raised interest rates. However that is an argument made with hindsight . It has no bearing on whether austerity was a good policy choice when it was enacted in 2010. In 2010 inflation was not expected to rise to 5%, so the coalition had no reason to believe that the ZLB constraint would cease to bite in 2011 (assuming that it did). Instead to justify 2010 austerity we have to assume that, if the 2010 forecast proved over optimistic (which it did), QE would have been applied to the required degree to get the economy back on track. Given the uncertainties noted above, that would have been a foolish assumption to make. So 2010 austerity was a costly policy choice which reflects badly on those who made it.
So to conclude, the monetary policy offset argument is not a problem for critics of austerity at the ZLB but a key part of their argument. To believe that monetary offset will continue to apply to the same extent at the ZLB, you have to make quite unrealistic assumptions about what policy makers are capable of doing with Quantitative Easing, and also about what they will actually do.
 Convexity of the social welfare function would still be an argument to wait until the recession was over, although to set against that is the point that if the long run desired position involves some level of debt, the longer you leave deficit correction the more adjustment you have to make. This post discusses an IMF exercise which plays around with such things, but ignores the key ZLB argument.
 Even with hindsight I would argue it has little purchase, as the period during which 3 members of the MPC voted for higher rates lasted only 4 months in 2011. There is also an issue about whether the inflation caused by the VAT increase was really seen through by policy makers.