In an earlier post I went through the logic of why we do not think higher government debt necessarily causes inflation, even if that debt is denominated in nominal terms, as long as the central bank does not monetise that debt. As I argued there, talk of monetisation is largely unnecessary: we just need to say that the central bank uses interest rates to control inflation, and can therefore offset the impact of any increase in government debt.
However, as Mervyn King said, central banks are obsessed with budget deficits. This seems to contradict the previous paragraph. Are there some ways in which central banks would either lose the power to control interest rates, or be forced to abandon any inflation targets, as a result of fiscal policy?
In the previous post the thought experiment I considered was a sustainable increase in the level of government debt. By sustainable I mean that the fiscal authorities raise taxes (or cut spending) to service this higher level of debt. But suppose they do not: suppose the budget deficit increases because spending is higher, but there is no sign that the government is prepared either to cut future spending or raise taxes to a sustainable level.
In 1981 Sargent and Wallace published a well known paper which said that, in this situation, the central bank could in the short term control inflation, but in the longer term inflation would have to rise to create the seignorage to make the government budget constraint balance. In other words, to keep the economy stable the central bank would eventually be forced to monetise. This was later generalised by the Fiscal Theory of the Price Level (FTPL). If the government did not act to stabilise debt itself (which Eric Leeper called – a little oddly - an active fiscal policy, and which others - including Woodford, Cochrane and Sims - have called even more confusingly a non-Ricardian policy ), then the price level would adjust to reduce the real value of government debt. Fiscal policy determines inflation.
One of the critiques of this theory is that the government budget constraint appears not to hold at disequilibrium prices. See, for example, Buiter here, and a response from Cochrane. I do not want to go into that now. Let’s also concede that if the monetary authority does either follow a rule that allows the price level to rise (by fixing the nominal interest rate for example), or tries to move interest rates to both stabilise debt and inflation (as in my recent paper with Tatiana Kirsanova), then the FTPL is correct.
The case I want to focus on here is where the central bank refuses to do either of those things, but carries on controlling inflation and ignoring debt. Suppose the government is running a deficit which is only sustainable if we have a burst of inflation which devalues the existing stock of government debt, but the central bank refuses to allow inflation to rise. You can say it does this by fixing the stock of money, or by raising the rate of interest - I do not think it matters which. This is an unstable situation: interest payments on the stock of debt at the low price level can only be paid for by issuing more debt, so debt explodes. In this situation, we have a game of chicken between the government and central bank.
Now the game of chicken would probably end when the markets refused to buy the government’s debt. That would be the crunch moment: either the central bank would bail the government out by printing money, or the government would default, which forces it to change fiscal policy. But in Buiter there is an elegant equilibrium outcome: the market just discounts the value of debt by an amount that allows the central bank to set the price level, but for the government’s budget constraint to hold at that price level. We get partial default. This discount factor becomes the extra variable that solves for the tension that both fiscal and monetary policy are trying to determine the price level.
You could quite reasonably suggest that such a central bank could not exist, because the government has ultimate power. It can always instruct the central bank to monetise the debt. However suppose the central bank actually managed the currency for a whole group of nations, and could only be instructed to do anything if they all agreed to do so. Furthermore that central bank was located in the one country in that group that would never contemplate monetisation, so it would be immune to pressure ‘from the street’. That central bank should be pretty confident it could win any game of chicken. 
Has any of this any relevance to today’s advanced economies? It seems to me pretty clear that these governments are not playing any game of chicken. Quite the opposite in fact: they are being far too enthusiastic in doing what they can to stabilise debt, despite there being a recession. So we certainly do not seem to be in a FTPL type world. Instead monetary policy right now retains fiscal backing.
Yet in a way we are having the wrong conversation here. Rather than trying to convince central banks that their fears are groundless, we should be asking whether monetary policy should – of its own free will – raise inflation to help reduce high levels of debt. I agree with Ken Rogoff that it should, and have argued the case here. Yet however optimal such a policy might be, the chances of it happening in today’s environment are nil. It looks like we may have to go through a lost decade before we are allowed to contemplate such things.
 I guess a rationale for calling this fiscal policy ‘active’ is that stable regimes in Leeper require one partner to be active and the other passive. So in the normal regime monetary policy is active and fiscal passive, and this flips in a FTPL regime. In a FTPL regime, Ricardian Equivalence no longer holds (because taxes are not raised following a tax cut) – hence the label non-Ricardian.
 In this situation, would buying that government’s debt ‘show weakness’ in the game? If we follow Corsetti and Dedola and treat reserves as default free debt issued by the central bank rather than money, then not at all. Instead the central bank is giving the fiscal authority the best chance it can to put its house in order, by removing any bad equilibrium, but it retains the power to force default at any point. We no longer have Buiter’s method of resolving that game, but only because the central bank has the means which could force a win. As long as the government believes that the central bank would prefer the government to default rather than see inflation rise, the government should back down.