In a previous post I explained why, in a very simple setting, it was best to use lower interest rates to stimulate demand, but that both tax cuts and increases in government consumption could do this job as well, with welfare costs that were minor compared to the cost of inadequate demand. So, to use a bit of jargon, cutting interest rates is first best, but if that first best was not available because nominal rates had hit zero then fiscal policy should be used. If there was a financial constraint on the size of the stimulus, government spending was generally more effective than tax cuts.
What about unconventional monetary policy? There are two main kinds: forward commitment to above target inflation (and a positive output gap) in the future, and printing money to buy various kinds of assets (QE). In each case I want to compare the welfare costs of these policies with the costs of using fiscal policy. However there is also the issue of uncertainty of impact: we need to know how much of a policy measure to apply: this uncertainty issue was not critical in the previous post because we have a lot of evidence about the impact of conventional monetary and fiscal policy. I will consider each type of unconventional monetary policy in turn.
One way of stimulating demand when interest rates are stuck at zero is to promise a combination of higher than ideal inflation and higher than ideal output in the future. (This can be done either explicitly or implicitly by using some form of target in the nominal level of something like nominal GDP. For those not familiar with how this works, see here.) The cost of this policy is clear: higher than ideal future inflation and output. Once again, these costs can be worth it because of the severity of the current recession, which is why nominal rates are stuck at zero. Whether these costs are greater or less than the cost of changing government spending is debatable: a paper by Werning that I discussed here suggests optimal policy may involve both.
One issue that arises with this particular policy is the problem of time inconsistency. The central bank may promise to raise inflation above target in the future to help reduce the recession today, but once the recession is over will it keep to its promise? Will the public let it? If people think it might not then the policy will be less potent, which increases the uncertainty associated with the policy’s effectiveness. This is one reason why it may be useful to hardwire the policy by means of some nominal target. 
The other unconventional monetary policy is QE: printing money to buy assets. Now it could be that this policy is doing nothing more than signal forward commitment to lower interest rates in the future, which moves us back to the previous discussion. Suppose it is more than that. I think a largely unresolved problem is how distortionary this policy is.
For example, in one of the most popular models that has explored the effectiveness of QE by Mark Gertler and Peter Karadi, the central bank makes loans or buys government debt. In doing this it reduces a risk premium, which is welfare improving. This raises the obvious question of why QE is not permanent. The authors get around this problem by assuming that the central bank is less efficient than private banks in knowing which assets to buy. However I’m not sure whether anyone, including the authors, has any idea what these efficiency costs might be.
Perhaps these distortions are quite small. However this discussion illustrates a more serious problem with QE, which is that we still have no clear idea of its effectiveness, or indeed whether effects are linear, and what the best markets to operate in are. Announcements about QE clearly influence the market, but that could be because it is acting as a signalling device, as Michael Woodford has argued. Jim Hamilton is also sceptical. This strongly suggests that the uncertainty associated with the impact of QE is far greater than any uncertainty associated with either conventional monetary policy or fiscal policy.
Thinking about it this way, I cannot see why some people insist that unconventional monetary policy is always preferable to fiscal policy. In a comment on a recent Nick Rowe post, Scott Sumner writes “My views is that once the central bank owns the entire stock of global assets, come back to me and we can talk about fiscal stimulus.” What this effectively means is that it is better for one arm of the state (the central bank) to create huge amounts of money to buy up large quantities of assets than to let another arm of the state (the Treasury) advance consumers rather less money to spend or save as they like. This preference just seems rather strange, but maybe Lenin would have approved!
 If a temporary increase in government spending is in fact believed to be permanent, its effectiveness at stimulating the economy largely disappears, but this is not a problem of time inconsistency. Another difference is that governments are increasing and decreasing spending all the time, whereas it is much more unusual for an advanced economy central bank to deliberately create a boom.