In mainstream macro today, Keynesian economics is synonymous with the macroeconomics of price rigidity. Most of the time I have no problem with that. All the evidence suggests there is significant inertia in aggregate prices, and it is very difficult to tell realistic stories about how inflation moves without taking this into account. Price inertia and imperfect competition are probably essential in understanding why output tends to follow aggregate demand in the short term.
My problem with identifying Keynesian economics with the macroeconomics of price rigidity is that it allows those who would like to ignore Keynesian theory with too easy an opt out. They can argue that, despite appearances to the contrary, prices are in fact pretty flexible. They then conclude that Keynesian economics is irrelevant. Unfortunately far too many academic macroeconomists appear to implicitly or explicitly take this view.
Is it logically the case that if prices are flexible Keynesian economics can always be ignored? The answer is simply no. Price flexibility alone does not ensure demand always moves quickly towards supply: it is the combination of price flexibility and monetary policy that does this. And when something goes wrong with monetary policy, price flexibility alone may not work.
We are living through exactly such a situation. It is not just the zero lower bound for nominal interest rates that is important here. It is also the fact that monetary policy has an inflation target rather than a price level target. After a large negative demand shock, demand can only be restored in the short term (for a given fiscal stance) by a large reduction in real interest rates. Real interest rates are nominal rates minus expected inflation. The zero lower bound stops nominal rates falling enough, and inflation targeting stops inflation expectations rising enough. No amount of price flexibility can change this. (For a more detailed discussion see here.)
Students often think that price flexibility must imply that output is supply determined, because if any workers were unemployed, nominal wages would continue falling until they were employed. But just imagine an economy made up of monopolistic competitors where production was linear in labour. In that economy firms would ‘determine’ a constant real wage through their mark-up, and no amount of nominal wage cutting would reduce real wages or increase employment.
Demand denial is the belief that we can always ignore aggregate demand when analysing short term movements in output and employment. It sometimes seems to be based on a view that price flexibility alone always ensures demand is sufficient for supply. It does not.