Still angry about Sumner's analytical garbage
Even after writing it in pedantic logical symbols, I'm still upset by the analytical garbage that Sumner is foisting on the world. But I think you can see where Sumner does his slight of hand if you realize he means two different things by "independent central bank". One is "independent central bank" the other is "monetary policy is effective". In Sumner's monetarist view, these two statements are identical. An independent central bank has effective monetary policy. In the Keynesian view, they are not. A central bank can be independent, but the zero lower bound means monetary policy is ineffective.
Here's Sumner's characterizations in terms of monetary policy effectiveness:
Keynesian: Fiscal austerity is contractionary at the zero bound regardless of whether [monetary policy is effective].
Market monetarist: Fiscal austerity is contractionary if you lack [effective monetary policy]. Fiscal austerity would not be expected to have much effect if you have [effective monetary policy], due to monetary offset.
Note that the monetarist view is the only one that continues to makes sense with this replacement. That's because "zero lower bound" means "monetary policy is not effective" in the Keynesian view:
Keynesian: Fiscal austerity is contractionary [when monetary policy is ineffective] regardless of whether [monetary policy is effective].
Which means we can actually shorten this:
Keynesian: Fiscal austerity is contractionary [when monetary policy is not effective].
Market monetarist: Fiscal austerity is contractionary if you lack [effective monetary policy]. Fiscal austerity would not be expected to have much effect if you have [effective monetary policy], due to monetary offset.
Then there is fact that the modern Keynesian view actually believes in monetary offset when you're not at the zero lower bound ... that is: "away from the zero lower bound" and "monetary policy is effective" mean the same thing. So let's add that piece on ...
Keynesian: Fiscal austerity is contractionary [when monetary policy is not effective]. [Fiscal austerity isn't contractionary when monetary policy is effective.]
Market monetarist: Fiscal austerity is contractionary if you lack [effective monetary policy]. Fiscal austerity would not be expected to have much effect if you have [effective monetary policy], due to monetary offset.
These two statements effectively say the same thing! So how do Sumner and Sadowski view them as different? Because they don't believe you can make the replacement:
"zero lower bound" = "monetary policy is not effective"
But that's the entire liquidity trap model!
That's why they can keep in countries that aren't at the ZLB in the final graph -- zero lower bound has nothing to do with monetary policy effectiveness.
That's also happens to be the reason they think they can throw out the countries without independent central banks! They think they can take the "regardless" out of the Keynesian formulation and say that it must be true if the central bank is independent. But then they believe that monetary policy is effective if the central bank is independent. So they've constructed a contradiction:
Keynesian: Fiscal austerity is contractionary [when monetary policy is ineffective] [if][monetary policy is effective].
It's all because Sumner and Sadowski believe:
"zero lower bound" = "monetary policy is not effective" is FALSE"independent central bank" = "monetary policy is effective" is TRUE
That is to say, they assume the market monetarist model! In the Keynesian model:
"zero lower bound" = "monetary policy is not effective" is TRUE"independent central bank" = "monetary policy is effective" is ambiguous
In order to make this true or false, you need to add a bit about the ZLB.
"independent central bank" and "ZLB" = "monetary policy is effective" is FALSE"independent central bank" and not "ZLB" = "monetary policy is effective" is TRUE
But then market monetarists don't think the ZLB is important, so they don't see the problem with leaving it off!
And round and round we go ...
The only way to make sense of this is that Sumner and Sadowski don't understand the liquidity trap model. Krugman understands the monetarist model -- it's the one he uses when you're away from the ZLB!
...
PS. You can replace independent with "awesome"
Keynesian: Fiscal austerity is contractionary at the zero bound regardless of whether you have an [awesome] central bank.
Market monetarist: Fiscal austerity is contractionary if you lack an [awesome] central bank. Fiscal austerity would not be expected to have much effect if you have an [awesome] central bank, due to monetary offset.