Most of the posts I have written about austerity have been aimed at countering the idea that in a recession you need to bring down government deficits and therefore debt. But what if you accept all that (you are anti-austerity). Why should you care about debt at all? Why do we have fiscal rules based on deficits? Why not spend what the government needs to spend, and not worry that this resulted in a larger budget deficit?
The story often given is that the markets will impose some limit on what the government will be able to borrow, because if debt gets ‘too high’ in relation to GDP markets will start demanding a higher return. You can see why that argument is problematic by asking why interest rates on government debt would need to be higher. The most obvious reason is default risk. But for a country that can create its own currency there is never any necessity to default.
However there is another reason to demand a higher nominal interest rate on debt, and that is if you think there will be additional inflation in the country. Spending more without raising taxes will tends to increase inflation. But if the government or central bank is sure to raise interest rates to offset this inflationary pressure then the concern about inflation disappears.
In MMT inflation is also the fundamental constraint on how far you can raise spending without raising taxes. MMT also says that you do not need to worry about the deficit, but this is only true if - as they advocate - fiscal policy rather than monetary policy controls demand and inflation. Under MMT the link between the deficit and inflation is direct (assuming no change in the composition of either) .
When inflation is controlled using interest rates the situation is fundamentally different. There is now no single point at which the deficit is consistent with stable inflation. In the short term there are a whole range of interest rate/deficit combinations that keep inflation stable today (e.g. high deficit and high interest rates or low deficit and low interest rate). Does this mean we do not need to worry about the deficit and the debt it leads to because monetary policy will always take care of inflation?
The answer is no, if we think about dynamics. What happens if we choose a high deficit high interest rate combination because we want higher government spending without paying more in taxes? There are two important dynamic effects here. The most basic is that a high deficit raises the stock of government debt. Because of interest rate payments on that debt the deficit rises further. In addition raising interest rates to stop inflation will itself tend to raise debt interest payments. This is an unstable debt interest spiral. You cannot say why not fund the additional debt interest payments by creating money, because that will tend to reduce interest rates and raise inflation.
This means that over the longer term you have to adjust spending and taxes to keep government debt relative to GDP stable, That does not mean debt has to be stabilised at a particular level, but just that if there is not a compelling reason to do otherwise you need to keep debt stable rather than rising upwards. A recession is one such compelling reason, and there are others (like adding to the public sectors stock of assets).
Stability does not mean deficits have to be zero because we have to allow for the growth in GDP. The maths is simple (see ). Take the stock of debt to GDP as a fraction of GDP (say 0.8), multiply by the trend rate of growth of nominal GDP as a fraction (say 0.04), and you approximately have what the total deficit should be as a fraction of GDP to keep debt stable (0.032), which is a deficit of 3.2% of GDP. .
There is always the temptation for politicians to raise debt now, and let future governments stabilise debt at a higher level. In the past the US under Republicans and other countries (but not the UK) tended to let this happen in the 30 years before the GFC, and economists call it deficit bias. Fiscal rules began life because it was hoped they would reduce deficit bias.
So why not raise the level of debt by spending more for a period, and then stabilise it by cutting spending or raising taxes a generation later? Here we have to note that the stabilising deficit (the deficit that keeps debt to GDP stable) includes debt interest payment. What we call the primary deficit is the total deficit less interest payments, You should now be able to see the problem with allowing debt to increase and stabilising it later. If you raise the level of debt to GDP and then stabilise it, debt interest payments will be higher and the level of the primary deficit left over is smaller than the one you started with. This is one sense in which letting debt rise today takes from future generations. 
This is why it is never a good idea to increase the stock of government debt without good reason, as Trump is doing, because it either cuts spending or raises taxes in the long run. This logic does not mean that future GDP is any lower (although there may be other theoretical reasons why higher debt can reduce output), but it means that if debt to GDP is stabilised, debt interest rates will be higher and so something else has to adjust to compensate, which means higher taxes or lower spending. 
There is an important caveat to this dynamic, which becomes clear if you do the maths. You only get a debt interest spiral if the nominal interest rate exceeds the growth rate of GDP (call the difference between the two the ‘very real interest rate’). If the very real interest rate is negative, extra debt for a given deficit allows a higher primary balance. Journalists sometimes look at the level of debt interest as a share of GDP (currently 2% in the UK) and say government spending could be 2% of GDP higher (or taxes lower) if we didn’t have to pay interest on debt. But if you could somehow magic your debt to zero so debt interest rates were zero, the stabilising deficit would fall from a current level around 3% to 0, requiring a 3% fall in the primary balance. This reflects that the current very real interest rate is negative.
Does this mean we do not have to worry about the debt interest rate spiral, and therefore debt? Only if we know that the very real interest rate will stay negative. This is unlikely to happen, particularly if interest rates are having to rise to combat the inflationary effects of high deficits. Because debt levels should never be adjusted down quickly, it is best to act as if the very real interest rate will become positive at some point.
This is not the only reason why raising government debt to GDP in the long run can be detrimental, but this one is simple because it depends only on some basic economics, algebra and logic. This and other reasons will never be enough to justify cutting deficits in recessions, not even close. But being anti-austerity does not mean we can forget about debt completely, as long as we are using interest rates rather than fiscal policy to control demand. (On why you might want to do that see here.)
 G is government spending, T taxes, r is the nominal interest rate, and B the stock of debt. Little letters mean as a ratio of nominal GDP (Y). x is the growth rate of nominal GDP, delta means change in. We ignore money for reasons given in the text. The budget identity is
G - T + rB = deficit = delta B
So dividing by GDP gives
g - t + rb = deficit/Y
In continuous time (or approximately otherwise) we can write
deficit/Y = delta b + xb
So for delta b to be zero, deficit/Y = xb
Or equivalently g - t + (r-x)b = 0
 More strictly in this case it takes from future generations the benefits of public spending or adds to the cost of taxes, and transfers it to bond holders.