David Glasner writes:
It must have been a good feeling when Scott Sumner saw Karl Smith’s blog post last Thursday announcing that he had proved that Scott was right in asserting that Simon Wren-Lewis had committed a logical blunder in his demonstration that Robert Lucas and John Cochrane made a logical blunder in denying, on the basis of Ricardian equivalence, that government spending to build a bridge would be stimulative.
. . .
In Karl’s nonsense result, savings is not equal to investment (because investment has not changed while savings has fallen by 1) and expenditure is not equal to income (because DC + DG + DI > DC + DS + DT). This is just the ABCs of comparative-statics analysis.
Now in a subsequent post, Karl seems to have retracted his “proof,” admitting:
S = –1 is not allowed [because investment has not changed].
I took Scott’s point to be that one must invoke the old Keynesian model in order for Wren-Lewis to have been correct. Its not simply that once one acknowledges consumption smoothing that even a child can see Cochrane was wrong.
The reason I take this to be his position is because in his very first post on the matter Scott states:
As it is, Wren-Lewis and Krugman are showing they don’t understand that not everyone agrees with the Keynesian model, and also that they don’t even know how to defend their own model. It does no good to “refute” Cochrane with an example that implicitly accepts the crude Keynesian assumption that savings simply disappear down a rat-hole, and cause the economy to shrink.
My sense was that – intentionally or not – Scott was being beat up upon for his lack of comfort with Mathematics. Which is never a reason to beat up on anyone. Indeed, Scott wrote
In a perfect world I’d lay out a concise logical proof that Simon Wren-Lewis and Paul Krugman are wrong. And number each point. They’d respond saying which of my points were wrong, and why. Then I’d reply.
Which is indeed ideal. Rather than just shooshing him away, one could reply as Glasner did to me
In Karl’s nonsense result, savings is not equal to investment (because investment has not changed while savings has fallen by 1)
In which case I would demand that you tell me why investment cannot change.
At this point someone is likely to invoke the IS curve and investment’s indifference to anything but the interest rate. To which Scott or I could respond: so what you are saying is that if the Old Keynesian model is TRUE then it is TRUE.
While that statement is undoubtedly correct, its not immediately obvious why it should be compelling Cochrane or anyone else who rejects the Old Keynesian model.
Now, instead one could have said: Look if you go through a chain of reasoning you will see that you get qualitatively the same results from an Old Keynesian model as you do from an intertemporally optimizing rational agent model, which we all [For Better or Worse] take seriously.
However, you’d also have to give up on simply saying that Cochrane is willfully ignorant of Macro 101.
I understand Brad’s point on Lucas but I am still not sure how I feel about that.
Just as a note on the use of Mathematical language. I said
Let . . DS = –1
Some folks then wanted to ask why this would make any sense or if it jived with a more general model of the economy. However, that’s not how proofs work.
One can’t simply ask“well why should that be”
It should be because in a proof I am effectively God and I can “let” anything I want unless the statement itself is contradictory. So, I cannot let X be a stone so heavy even an omnipotent being could not lift it, since those concepts are grammatically contradictory.
However, I can certainly let X be the day last year when I was crowned by all mankind as the Emperor of Ice Cream. Sadly, in this case, X is the empty set.
Its important that proofs work that way because in an elegant proof it should be clear which let is doing the heavy lifting at each stage. And, ideally there should be no extraneous “lets” to confuse the matter.
Then one can easily say “Ah this entire logical argument depends crucially on that one assumption right there.”
Then we can all at least agree on what precisely we disagree about and hopefully move forward from there.