There is a great deal of discussion about the appropriate goals for monetary policy. Should it just be targeting inflation, or should central banks also include the output gap in their objective function? Perhaps they should target nominal GDP. However, hardly anyone would dream of suggesting that monetary policy should help reduce government debt, by lowering interest rates or raising inflation. It is just accepted that we should only use costly (in welfare terms) increases in taxes, or costly cuts in government spending, to achieve debt reduction.
What I have called the consensus assignment for economies with their own currency is that the central bank stabilises demand and inflation, and the government through fiscal policy manages government debt. The first part of that assignment does not work at the zero lower bound (ZLB), although some economists find it difficult to admit this. But equally there are circumstances where the second part of the assignment is far from optimal, and where it is useful to have the central bank help reduced debt. Circumstances like when debt is much too high.
If we just think about the macroeconomics, where a benevolent policy maker operates both monetary and fiscal policy, then the reason is straightforward and pretty obvious. When debt is high, reducing real interest rates is a pretty effective means of getting debt down. If government debt is about the same size as annual GDP, then a reduction in the real interest rate on government debt of 1% is equivalent to raising taxes by 1% of GDP. If debt is only half the size of GDP, the same reduction in real interest rates is only equivalent to increasing taxes by half as much. The larger the stock of debt, the more effective interest rates are compared to fiscal instruments in reducing debt.
Will reducing interest rates to cut debt not allow inflation to rise? Of course we are compromising our control of inflation. Fiscal instruments can be used to reduce this cost: if we cut government spending as well as cutting interest rates, the net effect on inflation may be small. But the key point is that inflation is not the only thing that matters. Raising taxes or cutting spending to reduce debt is costly too. So it may be better, in terms of social welfare, to let inflation rise for a time to get debt down than to have taxes rise to do the same.
At this point you are probably thinking isn’t the whole point about the consensus assignment that monetary policy is much better at controlling inflation than fiscal policy? Yes it is in our benchmark models, but only when debt is not a problem. If we had some fairly painless way to control debt (i.e. lump sum taxes), then outwith the ZLB, monetary policy is indeed the best way to control inflation. But suppose instead that debt is much too high, and we need to bring it down (and there are no lump sum taxes). Suppose, as suggested above, that monetary policy is also the best way of getting debt down. In that case we are in a different world where comparative advantage applies.
If you are still having difficulties with this - and because the consensus assignment has become such a consensus you might well be - imagine if debt was ten times GDP. In that case it is so much easier to get debt down by reducing real interest rates, it would be crazy not to. Any advantage monetary policy had in controlling inflation would pale into insignificance. If monetary policy is only a bit better at controlling inflation and much better at controlling debt, the latter should have priority.
So if I’ve convinced you this is possible, what about in more realistic situations. Here I can say two things. First, in quite a lot of the DSGE work I have done with my co-author Campbell Leith, we found situations in which monetary policy was useful in reducing debt when debt was high. Here high meant something like 50% of GDP, which is pretty standard today. Second, in the real world there have been occasions when monetary policy was linked quite closely with getting debt down, such as after the second world war. (See, for example, Charles Goodhart here.)
The reason why the idea of adding debt reduction to monetary policy’s tasks seems so taboo today is that we are concerned about the non-benevolent government. A government that spends too much and taxes too little can create ‘fiscal dominance’, and an inflation rate that is permanently too high. In extreme cases it can lead to hyperinflation. As is so often the case with fiscal policy (like the specification of fiscal rules), it is the non-benevolent policy maker which determines how we think about things.
To some it will seem obvious that this should be so. Politicians can be trusted to do the wrong thing, particularly if it is in their interests. There are plenty of examples where this has happened in the past. However, many of us have been arguing that governments today seem if anything too eager to use fiscal policy to get debt down. We seem to have a twisted sort of fiscal dominance, where governments are reducing debt too rapidly, the economy is suffering as a result, yet monetary policy cannot effectively counter because we are at the ZLB. It therefore seems a little odd to be arguing that monetary policy cannot help bring debt down, because that would let fiscal policy makers off the hook. In countries like the UK, USA or the Netherlands, there is no hook, but policymakers are taking unpopular measures to get debt down nevertheless. Would they really do a complete about face if monetary policy lent them a hand?
Now with short interest rates at the ZLB, and in the US and UK with Quantitative Easing directly reducing interest rates on government debt, it would appear as if there is no conflict at the moment between keeping inflation on target and reducing real interest rates. (Although this does not stop some getting very worked up when the central bank helps to reduce current borrowing.) However there are two parts to real interest rates. To the extent that monetary policy could be more expansionary today, but at the cost of higher inflation, it could be helping to reduce debt. If it is not, and the government is benevolent, monetary policy is probably behaving sub-optimally.
 These are taxes which have no impact on incentives, and so do not reduce output when raised. Although Miles Kimball has written what seems like a lament to their absence, when Mrs Thatcher tried to introduce them in the UK it led to her downfall.
 This is also true if we are quite happy to let debt permanently rise and fall in response to shocks, as Eser et al show.