Nick Rowe makes a couple of simple points around my post yesterday. Let me start with the issue of whether helicopter money (HM) is ‘permanent’ or not. (Alas I cannot match Nick’s admirable brevity.)
Permanent or temporary?
Think about a really simple world, where the ratio of money to prices is always the same in the long run. In this world we have a short run recession accompanied by deflation, and nominal interest rates have hit the buffer of zero (or wherever). The inflation target is 2%, and the central bank will never let inflation go above 2%. However because interest rates have hit zero, it cannot do the reverse and prevent deflation by conventional means.
If in this world the monetary authority gives away some new money (helicopter money, or HM) to stimulate the economy, is that new money permanent or temporary? Let’s think about what happens without HM. Prices fall or stall for a while, and only when the recession ends does inflation go back to 2%. Now compare this to what would happen if the central bank does HM, and this was successful at raising inflation much more quickly to 2%. That means that the price level will in the long run be permanently higher than if the central bank had done nothing. As a result, at least some of the additional money created to end the recession quickly will be created permanently relative to the no money creation case.
So to the extent HM works, and stops deflation, it involves permanently creating some money. That permanent money creation does not mean that inflation has to be above target, but rather it stops inflation being below target.
But there is absolutely no reason to limit HM to the amount by which money will be permanently higher, because that will almost certainly be insufficient to end deflation. Money will need to overshoot its permanent long run level in the short term.  There is nothing wrong in temporarily creating additional money to get us out of a recession. The only issue of any interest in all this is whether unwinding any temporary money creation requires the central bank or the fiscal authorities to do anything unusual (see below)
Will the temporary money be spent?
But if you just give people additional money temporarily, will that mean it is just saved? This is a variant of the Ricardian Equivalence issue, and the real world answer is the same: all the evidence is that quite a lot of it will be spent. I would argue there are two main reasons for this: some people are credit constrained (and HM is like a bank manager that says yes), and others do not know how the money will be payed back (it could be through lower public spending).
What about governments: will they try to offset conventional (cheque in the post) HM by raising taxes, or not increase spending as a result of ‘democratic helicopter money’ (see my last post)? We need to go back to why we need HM in the first place. We need HM because governments are not undertaking the fiscal expansion through borrowing that they should do in a recession where interest rates hit their lower bound. To know how governments will respond to HM, we need to know why they will not undertake this fiscal expansion.
The real fear of too much government debt
Suppose governments have convinced themselves that any additional spending paid for by borrowing is ruled out by worries over the amount of government borrowing. Their fears about borrowing are genuine, and this fear is acting like a constraint stopping them from doing what they otherwise would like to do. So what happens if the central bank does conventional HM, or says to the government you can spend more (or cut taxes) without having to borrow in the short term. Central banks are removing the constraint that governments have (almost certainly) imagined. There is therefore no reason why governments should either try and offset conventional HM, or not spend the democratic variety.
But if HM is temporary, borrowing will have to increase at some point. It is easy to get lost in the institutional detail of the many ways this can happen, so let’s just pick one. Once the recession is over, the central bank worries that there is too much money in the system, and they do not have enough financial assets to mop it all up. They ask the government to recapitalise the central bank, which just means that the government gives the central bank some financial assets in the form of government debt. That means more government borrowing.
Will the government worry about this, and therefore try to reduce its borrowing to offset HM? I would suggest the government will almost certainly not do this. The reason is that governments have convinced themselves that the problem is not the long run position of the government’s finances, but the level of debt and the deficit right now. How do I know this? Because if the problem was the long run position of the government’s finances, they would spend now to end the recession quickly, and then cut the deficit once we were away from the interest rate lower bound. That is the obvious optimal intertemporal policy mix. The fact that they do not do this suggests some imagined short run constraint.
You can also look at what governments undertaking austerity do. They are quite happy to cut deficits through privatisation, which almost surely increases future deficits. They embark on all kinds of fiscal tricks that simply shift revenues into the short term, or shifts spending into the long term. In other words, fiscal plans operate under a short term deficit constraint, and democratic HM relaxes that constraint.
Using a fear of debt as a cover for shrinking the state
Suppose governments do not really believe that their own borrowing has to be reduced right now, but are using public anxiety over public debt (with phrases like the government has maxed out its credit card) as a pretext to cut public spending. Short term borrowing is not really a constraint, but governments just pretend it is to achieve the goal of a smaller state. Such a government would almost certainly use any democratic HM to cut taxes, so the distinction between conventional and democratic HM is not central. Would this government use HM as an excuse to cut spending by yet more, thereby offsetting the benefits of HM?
The great advantage a central bank has is speed. It takes time to put new fiscal plans into effect, but money can be created overnight. So if the government plans to cut spending by more as a result of HM, the central bank can just offset the demand impact of those additional spending cuts with yet more HM. If you think such a game cannot go on forever you are right, but it does not have to. Once the recession is over, monetary policy can offset the impact of spending cuts on demand using interest rates in the normal way.
In this situation, both the central bank and government are happy. The central bank, by using HM in potentially unlimited amounts, can end the recession quickly. The government that wants to use the deficit as a cover for cutting public spending has succeeded in doing so, perhaps by more than they had thought possible. That might upset you because you do not want a smaller state and resent voters being tricked into allowing it to happen, but I personally would prefer that to a prolonged recession every time. 
 Macroeconomists sometimes say that in a recession the public’s demand for money increases, or there is an excess demand for money. To a non-economist, of course, that just sounds silly.
 Remember that HM does not stop a benevolent government doing the right thing and enacting a fiscal stimulus. It is a fall back to stop a malevolent government crashing the economy in pursuit of an ideological goal.