## Wednesday, June 26, 2013

### Damn it, I hate it when my commenters upstage me

So my point has been that dropping the expenditure obscured the fact that Landsburg was just saying "income is income", which doesn't even amount to an accounting identity (for those of you who have been saying he's been confusing an identity for a behavioral law... a common though not universally applicable mistake).

No expenditures means no MPC which means we're not even talking about "the same logic as the Keynesian cross" anyway, but if you take his implied MPC you get the same result: income equals income (or if you make the mistake he did, income equals 0.99999999 times income).

But my point basically boiled down to "you don't knock the Keynesian cross by saying income equals income".

Commenter Malcolm gets to the point much quicker:
"I just posted this at Landsburg. This is all "a lot about nothing":

Sigh. This is worthless

If Y = E + L and E= .999999Y then L = .000001Y then
Y-E =L means
Y(1-.999999) =L which means that
Y = L/(.000001) which means that
Y = .000001Y/.000001
and all this means is that Y=Y. Hmmm."
Yep.

Some (edarniw, for example) think that my harping on the expenditure/income distinction and the MPC/income share distinction is beside the point and just adding extraneous complaints to Landsburg's post. It's not extraneous. Malcolm works out in the context of the problem why it's not extraneous and ALSO why I say that Landsburg has an implicit MPC of 1, not 0.99999999, even thought he solved the problem as if his MPC was 0.99999999.

Think of it this way: L pays E for a good or service. Some fraction of E's subsequent spending will go to L for a good or service that L produces. So L's consumption matters too, and if we're conflating income share and MPC the way Landsburg has chosen to that means MPC = 0.00000001 + 0.99999999 = 1.

Which gives you "income equals income".

Which is not any kind of argument against the Keynesian cross. It's an argument that leaves off half the Keynesian cross and any mention of investment which is the crux of the whole theory.

1. "And all this means is that Y=Y. Hmmm."

I think that is implicit in all these simple models that are based on accounting identities.

The question is what level will Y end up at given a change in G. I think Landsburg's point is that the multiplier that will drive the increase in Y is indeterminate in reality and probably much lower than many simple Keynesian models seem to suggest.

2. Landsburg has discovered reflexivity. Perhaps in few more years he will be on to symmetry and transitivity.

3. there are things that increase the multiplier like buying local

and things that decrease the multiplier like monopolies that pay their employees crap like walmart and things like gambling casinos

4. I tried to explain to Landsburg the distinction between spending and income and he simply didn't get it. He is convinced he has found some wonderful approach to make Keynes and the multiplier irrelevant. He is in love with his own insights and can not concede there is nothing there. By the way, he never posted my comment because he decided it was irrelevant. Go figure.

5. I gave it one last try at Landsburg. At least I am persistent:

One last try.

Why is this all worthless? Why is the conversation engendered by this fruitless?

I suspect that we all agree that adding apples to automobiles is
the wrong way to measure the output in the macroeconomy. 10 apples
and 1 automobile isn't equivalent to 1 apple and 10 automobiles. Output in macroeconomics isn't 11. By placing them all into dollar units I can compare and extra dollar of apples to an extra dollar of automobiles. On this we all agree.

When you write Y = E + L you are equating a unit of E to a unit of L. A one unit increase in E has the same impact as a 1 unit increase in L. But L, as we know, is insignificant compared to E.
By writing L as a stand alone variable you are mixing E and L which is as incorrect as mixing together apples and automobiles. How do we put them into comparable units? We can express each in terms of Y.

We know E=.99999999Y and L=.00000001Y. It should now be clear that the Landsburg multiplier is meaningless because of a math error.
By never scaling L in terms of E we create gibberish. Landsburg is insignificant; he is one 100,000,000th of the economy. By treating E and L as the same, it is as if there is an army of Landsburgs 100,000,000 strong. When the army gets bigger by one whole army we add 100,000,000 to Y. But L is an army of 1. Hence we need to scale everything down by 1/100,000,000.

So there's the math error. The Keynesian multiplier isn't subject to this critique because a unit of C is equivalent to a unit of I.

When Y= E + L and Y = .99999999Y + L increasing L by one is not the same as increasing E by 1 since E is huge and L is not.
So substituting for L into the Landsburg multiplier ( which he does not do) gives us Y = 100,000,000Y/100,000,000 = Y and the grand multiplier dissolves. In this world if we give L a unit of Y
(from somewhere) we have 1 more unit of Y not 100,000,000.

I have suggested this calculation elsewhere -- see my posts at Kuehne, Delong and Krugman.

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