The flaw in the argument central banks have used to justify the rates first, QE later exit plan

Two posts ago, I mentioned that the basic plan central banks had for withdrawing stimulus was to go first with rates, and then scale back QE.

That plan was based on wanting to avoid the risk that, if another recession came along, QE balance sheet shrinkage would have to be reversed to respond [interest rates being still trapped at the floor].  And that was motivated by central banks wanting to avoid relying on QE to be the marginal tool of stimulus that rises or falls with the progress of the economy.  Which in turn relied on the worry that this instrument was least well understood.

That logic goes back to an old paper from 1967 by Brainard [Bill, a different Brainard from the Lael currently on the FOMC].  In that paper, he showed that in a simple example with one instrument, one goal variable, and one shock, the more uncertain was the multiplier that connected the instrument to the goal variable, the less the instrument should be used to respond to the shock, for fear of injecting more variance into the goal than was saved by responding.

The intuition extends to multiple instruments.  If you have several instruments to counter a shock, respond most with the one whose effect is most certain.  If you are baffled, but happen to know the algebra of filters or forecasting or portfolio choice, there is a read across.  The more uncertain the link between the indicator and the variable to be forecast, the less weight you should put on it.

The evidence thus far is that what matters above all [if anything] is the stock of QE.  Applying the Brainard logic leads us to the conclusion that in the face of more multiplier uncertainty about QE, central banks should adjust the stock away from its base or rest point by less.

You can think of central bank behaviour before the crisis as a way of paying heed to this advice in an extreme way:  they used rates only, and left QE well alone, and only deviated from this when there was no way of lowering rates further.

On the way out of the crisis, and the period during which interest rates are constrained, the priority - from a perspective of eliminating the effects of multiplier uncertainty - should be to get the level of QE back to base as quickly as possible.  That means winding down QE first, and worrying about rate increases later.   The rest point for QE after the crisis - as Bernanke and others have written - may well be higher than before.  But we can be confident that it lies below current stocks.  And that therefore the Brainard logic would mean withdrawing QE-imparted stimulus first.

An important detail overlooked here is that the original Brainard logic did not cater for a situation where one instrument was constrained [as interest rates are by their effective lower bound].  I doubt this would overturn the basic point.  Even if it did, central bank rationale would not be rescued, since they were building from the floor-free intuition too, only incorrectly.

Could the central bank plan be rationalised by believing that the dominant effect of QE was via flows only?  No.  Suppose that there is some reputational cost to QE, and that balance sheets have to be scaled back so that they can subsequently be rebuilt again in a future crisis.  The optimal thing to do would be to very slowly shrink the balance sheet just as soon as the economy was buoyant enough such that the effect of keeping rates at their floor imparted a small stimulus to offset the shrinkage flows.  So, once again, we don't get to anything that looks like the Fed or other central bank plans for exit.

The only way to rationalise what the Fed is doing and what the BoE said they would do is to assume that they believe that the costs of reversing interest rate moves are less than the costs of reversing a QE balance sheet shrinkage.  But there is no real evidence to back up such a belief, and I don't recall a policymaker having asserted it.