Recessions and milder economic downturns are typically a result of insufficient aggregate demand for goods. The only way to end them is to stimulate demand in some way. That may happen naturally, but it may also happen because monetary policymakers reduce interest rates. How do we know we have deficient aggregate demand? Because unemployment increases, as a lower demand for goods leads to layoffs and less new hires.
A question that is sometimes posed in macroeconomics is whether workers in a recession could ‘price themselves into jobs’ by cutting wages. In past recessions workers have been reluctant to do this. But suppose we had a more prolonged recession, because fiscal austerity had dampened the recovery, and over this more prolonged period wages had become less rigid. Then falling real wages could price workers into jobs, and reduce unemployment. 
This is not because falling real wages cure the problem of deficient aggregate. If anything lower real wages might reduce aggregate demand by more. But it is still possible that workers could price themselves into jobs, because firms might switch to more labour intensive production techniques, or fail to invest in new labour saving techniques. We would see output still depressed, but unemployment fall, employment rise and stagnant labour productivity. Much as we have done in the UK over the last few years.
It is important to understand that in these circumstances the problem of deficient demand is still there. Resources are still being wasted on a huge scale. Quite simply, we could all be much better off if demand could be stimulated. How would central bankers know whether this was the case or not?
Central bankers might say that they would still know there was inadequate demand because surveys would tell them that firms had excess capacity. That would undoubtedly be true in the immediate aftermath of the recession, but as time went on capital would depreciate and investment would remain low because firms were using more labour intensive techniques. The surveys would become as poor an indicator of deficient aggregate demand as the unemployment data.
What about all those measures of the output gap? Unfortunately they are either based on unemployment, surveys, or data smoothing devices. The last of these, because they smooth actual output data, simply say it is about time output has fully recovered. Or to put it another way, trend based measures effectively rule out the possibility of a prolonged period of deficient demand.  So collectively these output gap measures provide no additional information about demand deficiency.
The ultimate arbiter of whether there is demand deficiency is inflation. If demand is deficient, inflation will be below target. It is below target in most countries right now, including the US, Eurozone and Japan. (In the UK inflation is above target because of the Brexit depreciation, but wage inflation shows no sign of increasing.) So in these circumstances central bankers should realise that demand was deficient, and continue to do all they can to stimulate it.
But there is a danger that central bankers would look at unemployment, and look at the surveys of excess capacity, and look at estimates of the output gap, and conclude that we no longer have inadequate aggregate demand. In the US interest rates are rising, and there are those on the MPC that think the same should happen here. If demand deficiency is still a problem, this would be a huge and very costly mistake, the kind of mistake monetary policymakers should never ever make.  There is a fool proof way of avoiding that mistake, which is to keep stimulating demand until inflation rises above target.
One argument against this wait and see policy is that policymakers need to be ‘ahead of the curve’, to avoid abrupt increases in interest rates if inflation did start rising. Arguments like this treat the Great Recession as just a larger version of the recessions we have seen since WWII. But in these earlier recessions we did not have interest rates hitting their lower bound, and we did not have fiscal austerity just a year or two after the recession started. What we could be seeing instead is something more like the Great Depression, but with a more flexible labour market.
 Real wages could also be more flexible because the Great Recession allowed employers to increase job insecurity, which might both increase wage flexibility and reduce the NAIRU. Implicit in this account is that lower nominal wages did not get automatically passed on as lower prices. If they had, real wages would not fall. Why this failed to happen is interesting, but takes us beyond the scope of this post.
 They also often imply that the years immediately before the Great Recession were a large boom period, despite all the evidence that they were no such thing outside the Eurozone periphery
 J.W. Mason has recently argued that such a mistake is being made in the US in a detailed report.