Scott says
Regular readers are sick of this, so just take a vacation and come back next week. I keep being told that no one’s interested even as I have record volume of viewers. (Didn’t Yogi Berra say “nobody goes there anymore, it’s too crowded.”) I’m interested, and I’m the one who decides.
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. . . .
Perhaps I can help.
Wren-Lewis said:
DY = DC + DS + DT = DC + DS + DG Λ DG > 0 Λ -DC < DT ==> DY > 0
Which is false.
Proof by example:
Let DG = DT = 2, DC = -1, and DS = –1
Then both inequalities are satisfied and by the first equation.
DY = –1 –1 + 2 = 0
Which is what we were required to show.
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Thursday ~ January 19th, 2012 at 8:38 am
Kevin Donoghue
Clicking on the link I see that Simon Wren-Lewis actually wrote:
“If you spend X at time t to build a bridge, aggregate demand increases by X at time t. If you raise taxes by X at time t, consumers will smooth this effect over time, so their spending at time t will fall by much less than X. Put the two together and aggregate demand rises.”
I can see ways to quibble with that but I can’t see that they amount to much. I’ve lost count of Scott Sumner’s posts on this and he doesn’t seem to be getting any closer to a worthwhile critique. Maybe the ‘point’ is that Wren-Lewis is implicitly assuming a model without capital accumulation, so that dI=0, or something of that sort. But would anything much change if he dressed up the idea in a fancier model?
Thursday ~ January 19th, 2012 at 9:22 am
Joe
What they are saying is that the increase in spending is exactly offset by the combined reduction in consumption and savings. If savings is equal to the demand for investment, then it’s a wash.
They are taking Says Law (S=I) and twisting it into “the supply of savings = the demand for investment”. That requires a redefinition of supply and demand.
Friday ~ January 20th, 2012 at 7:30 pm
Mike Sax
Joe in this endless, senseless debate what you say actually makes sense. Sumner is cheating in some way comparing apples to oranges. When you call him on it he claims that proves you don’t know about the accounting identity S=I
Thursday ~ January 19th, 2012 at 12:46 pm
Karl Smith
Yes Wren-Lewis could simply say DS = 0 and his statement would be true. But he did not and as it stands his statement is false.
Friday ~ January 20th, 2012 at 9:32 am
D R
Nor did Cochrane say anything about dS. Is his “theorem” thus disproved?
Thursday ~ January 19th, 2012 at 11:42 am
TheMoneyIllusion » Go bother Karl Smith for a while
[...] he just endorsed my argument on consumption smoothing. So I’m done. If you have complaints, go put them in his comment [...]
Thursday ~ January 19th, 2012 at 12:01 pm
Mr. Violet (@EuropeanViolet)
Karl, I’m going OT as usual, but I am still thinking about the obesity epidemic, if I understood well you suggested it could be a molecule. Well, what about a combination of molecules? Could be a combination of molecules used in order to make the cattle growing faster AND some kind of chemical preservatives used for bread, so that combining them in a Hamburger… well, actually if they are molecules getting stored in fat tissue you don’t even need to combine them in the same meal…
If it was that the case, the difference in the spreading of the epidemic among US, UK and the rest of EU for example should be explained in terms of different molecules given to the livestock or used in bread or some kind of threshold value for one of them or for their combination. This could be also explain why these side effects weren’t detected: the molecules were tested alone.
Thursday ~ January 19th, 2012 at 12:47 pm
Lord
The refutation: DC’ = DC + DS, -DC’ DY > 0
Didn’t you think of this?
Thursday ~ January 19th, 2012 at 2:24 pm
Karl Smith
For an implication to be true there must exist no counter-example. A single instance of the antecedent being true and the consequent being false renders the entire statement false.
Thursday ~ January 19th, 2012 at 2:37 pm
Lord
The lt sign was elided. -DC .lt. DT I just refuted your interpretation of Wren consistent with what he wrote. Your counterexample is no longer valid.
Thursday ~ January 19th, 2012 at 2:43 pm
Lord
Make that -DC’ .lt. DT.
Thursday ~ January 19th, 2012 at 3:59 pm
D R
Wren-Lewis did not intend for it to be an implication. He was trying to offer a counter-example to Cochrane. You cannot disprove a counter-example with another counter-example.
[The fact that you, Sumner, and others (including myself) erroneously assumed investment was part of his example is an entirely different matter.]
Thursday ~ January 19th, 2012 at 4:11 pm
Karl Smith
RE: Lord
Yeah, but how can DC’ lt DT possibly be a consistent interperation of what he said. Indeed, I don’t even think its what he meant, which I’ll address in another post.
Thursday ~ January 19th, 2012 at 4:38 pm
Lord
Entirely consistent. DC’ and DT are the immediate change, but DC’ is only a small part of a total DC” which occurs only over the fullness of time due to consumption smoothing. One can argue that spending a lump sum now and amortizing the cost doesn’t really work since they are equal present values, but that isn’t really true in a ZLB situation.
Thursday ~ January 19th, 2012 at 4:45 pm
D R
dS = 0
This follows from:
Y = C+G
Yd = Y-T = C+G-T = C
Sp = Yd-C = 0
Sg = T-G = 0
S = Sp+Sg = 0
Thursday ~ January 19th, 2012 at 1:26 pm
D R
Yes, if you read Wren-Lewis to have spouted nonsense rather than asking what he was trying to say, his argument is not merely confusing, but illogical as well. I tip my hat to you, sir.
Thursday ~ January 19th, 2012 at 3:03 pm
rob
Wren-Lewis says “their spending at time t” , not their combined C + S at time t. Savings is not spending, but is equated to I and I consists of a combination of Investment spending and changes in inventory,
Thursday ~ January 19th, 2012 at 3:23 pm
rob
So spending does increase, just inventories get run down and this reduces I down to the level of S
Thursday ~ January 19th, 2012 at 3:35 pm
D R
Actually, Wren-Lewis has now made it explicit that in intended no investment at all. S=I=0 at all times.
It was our mistake. It’s not like he said before that X=M=0 either. But somehow we all seemed to understand that.
Thursday ~ January 19th, 2012 at 4:23 pm
Lord
In these simplified models, saving is just spending on investment goods and both are a form of consumption. His is even simpler than that if assumed zero.
Thursday ~ January 19th, 2012 at 6:39 pm
D R
Well, technically, saving can be loaning to other agents. But in the aggregate, that’s correct.
Which is yet another reason why that no-change-in-ex-post-Yd argument is bogus.
Thursday ~ January 19th, 2012 at 3:04 pm
tom
Karl you are biased. We are talking about depressed economy and not that multilpier is always positive (at full employment it is certainly not positive).
Here is my argument:
1) dY=dC+dS+dT and 2) dY=dC+dI+dInventories +dG
If dG=dT=2 and dC=dS=dInventories=-1 and dI=0 then:
in the first period dY=0 BUT in the second period dI=1 (firms want to replenish inventories) and from 2) dY=1 and this implies from 1) that dS=1.
So multiplier is positive
Thursday ~ January 19th, 2012 at 7:52 pm
tom
Here is another version of my proof:
Y= C+G+I+Inventories AD=C+G+I
If dG=dT=2 and dC=dS=dInventories=-1 and dI=0 then:
in the first period dY=0 but dAD=1. Because dAD>dY firms invest to replenish inventories so Y increases by dInventories=1 and AD doesnt change. So in the end AD=Y at the higher level with multiplier>0
Saturday ~ January 21st, 2012 at 5:28 pm
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[...] point that I had hoped to make clear with my little proof was that Wren-Lewis does not constrain savings. I specifically set the change in savings equal to [...]
Sunday ~ January 22nd, 2012 at 2:33 pm
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[...] 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 [...]
Tuesday ~ January 24th, 2012 at 4:16 am
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[...] Economics | by Karl Smith 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 [...]
Tuesday ~ January 24th, 2012 at 1:41 pm
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[...] by various interventions on either (or neither) side by Brad DeLong, Scott Sumner, Nick Rowe, Karl Smith (to name just a few) and by responses and rejoinders by Cochrane, Wren-Lewis and Krugman. I got [...]