The (Keyenesian) multiplier effect. Easily debunked?

Economics Economics Questions
1

I have a really basic question and I don’t have time to go to the economics textbooks to check details. So I’m hoping someone can please shed some light on this.

Basically the story goes…

If the government spends X , then there will be m*X increase in GDP. (Fiscal multiplier effect)

I assume the number “m>1” is the multiplier that is estimated empirically and takes into account crowding out, etc. (Multiplier is because of money changing hands more than once)
When I learned this multiplier it was generally assumed that this somehow made government spending more preferable.

Isn’t it the case that if an individual spends X the same thing will happen? Or is there some magic that happens when you collect taxes? Why does it matter that the government spend the money? I don’t see what the trick is, is it so easy to debunk this? Please let me know if you have a reference to a discussion of this.

And most of all, what happened to assessing things based on opportunity cost, rather than some gdp accounting?! (rhetorical question)

2

Ordinarily, yes…

Because the context is that of a recession.

3

So you are saying that the idea is:

There are unused resources/gap in demand? And that’s why gov should spend money.

But even if that was true, why wouldn’t individual’s spending the money lead to the same thing? I’m saying IF they were to spend it, not that they will (according to the theory they are not going to).

We can discuss how you get the spending out there, but I don’t see why money coming from the government is so special compared to private sector money.

Did I understand your answer correctly?

4

Yes, that’s right - IF they were to spend it. I believe Hazlitt discusses this in The Failure of the “New Economics”.

5

All that matters within the Keynesian model is that money is spent, not who spends it. So you’re perfectly right that individuals spending money should have the same effect. C+I+G+(E-M)=Y. It doesn’t matter where the spending comes from, it just has to come from somewhere. This is why (contra many conservative and more than one libertarian strawman) oftentimes Keynesians propose a variety of tax-breaks. Indeed that was a large part of the 09 stimulus package.

The reason why government spending is supposed to be especially effective is that the government has an incentive to have no propensity to save and therefore it can activate the multiplier. This is why Keynes advocated the “treasure chest” idea of the government saving a huge amount of money during the boom period and then when the depression hits it uses this money in order to boost back up aggregate demand.

6

Just spend money, you dumbies! You’re wasting time while you could be saving the economy!

7

Neodoxy,

Thanks, I see that the whole argument is actually about what causes the recession. But I gather that any Keyenesian would have to agree that a recession does not imply the need for government action. In fact there may be a perfectly Keyenesian private sector solution :wink:

Is it not the case that the spending multiplier is less than the tax multiplier? So tax cuts would provide a smaller stimulus (in the short run, because we don’t care about the long run). This I believe is due to the propensity to save/consume, like you mentioned. I believe this was the argument they give for stealing money and spending it on whatever they fancy, since government can create additional demand through the difference in multipliers.

Again, there may be a perfectly private section analog to this. Just have the mafia extort the money out of the private sector and spend it.

8

Forum deleted my post. Argh! That’s it, I’m making my own forum.

For your convenience, here are the two articles I included in my post that got eaten:

http://mises.org/daily/3290

http://mises.org/daily/3155

I’m not going to rewrite everything I did, but the gist of it is that government is not able to specifically target idle resources. Furthermore, there are resource misallocation arguments. And let’s not forget who caused the recession in the first place.

9

http://bastiat.mises.org/2012/11/fiscal-stimulus-or-fiscal-depressant/

10

The Keynesian fiscal “multiplier” is actually mathematical nonsense.
In the multiplier chapter of his “General Theory” book, Keynes said that income Y, equals consumption C, plus investment I:
Y = C + I
He said his investment “multiplier” k, is the change in income ΔY, over the change in investment ΔI:
k = ΔY/ΔI
Say that:
Y = C + I
10 = 9 + 1
and add a $1 investment increment ΔI, to I:
Y = C + I + ΔI
9 + 1 + 1 = 11
So ΔI = $1, ΔY = $1, and
k = ΔY/ΔI = 1/1 = 1
That’s all there is to it. There is no fiscal “multiplier”.
There are actually 2 values for k, and Keynes used the wrong value.
The marginal propensity to consume determines how income is allocated to spending, but is irrelevant to the effect of spending on income.

What Keynes did was:
Y = C + I
10 = 9 + 1
Y = k I
10 = 10 x 1

And then:
Y = C + I + ΔI
9 + 1 + 1 = 11
Y = k I + ΔI
10 x 1 + 1 = 20
The 20 comes from illegal addition before multiplication.

Y = C + I = kI
So both equations must give the same answer. Y = kI is derived from Y = C + I, so it must give the same answer as Y = C + I.
Y = C + I + ΔI = k I + ΔI
Y = 9 + 1 + 1 = 10 x 1 + 1 = 11

You can’t have Y vary both linearly and geometrically with respect to I, unless the “multiplier” is 1 … no multiplier at all.
And unless the $1 you add is a no-offset $1, charity from another country, there is no gain from the govt spending.

Keynes was very clever and didn’t show his math. He instead used a confusing word problem. Basically a version of Three Card Monte.

I have more about this in Pt 1, Fiscal Multiplier Debunked on Tugwit.blogspot.com

11

Hey, did Caplan ever get back to you about your mathematical tricks?

12

Since that post came out with no paragraphs, I will try it again:

The Keynesian fiscal “multiplier” is actually mathematical nonsense.

In the multiplier chapter of his “General Theory” book, Keynes said that income Y, equals consumption C, plus investment I:

Y = C + I

He said his investment “multiplier” k, is the change in income ΔY, over the change in investment ΔI:

k = ΔY/ΔI

Say that:

Y = C + I

10 = 9 + 1

and add a $1 investment increment ΔI, to I:

Y = C + I + ΔI

Y = 9 + 1 + 1 = 11

So ΔI = $1, ΔY = $1, and k = ΔY/ΔI = 1/1 = 1

That’s all there is to it. There is no fiscal “multiplier”.

There are actually 2 values for k, and Keynes used the wrong value. The marginal propensity to consume determines how income is allocated to spending, but is irrelevant to the effect of spending on income.

What Keynes did was:

Y = C + I

10 = 9 + 1

Y = k I

10 = 10 x 1

And then:

Y = C + I + ΔI

9 + 1 + 1 = 11

Y = k I + ΔI

Y = 10 x 1 + 1 = 20

The 20 comes from illegal addition before multiplication.

The 2 equations can be set equal to each other:

Y = C + I = kI

So both equations must give the same answer. Y = kI is derived from Y = C + I, so it must give the same answer as Y = C + I.

Y = C + I + ΔI = k I + ΔI

Y = 9 + 1 + 1 = 10 x 1 + 1 = 11

You can’t have Y vary both linearly and geometrically with respect to I, unless the “multiplier” is 1 … no multiplier at all. And unless the $1 you add is a no-offset $1, charity from another country, there is no gain from the govt spending.

Keynes was very clever and didn’t show his math. He instead used a confusing word problem. Basically a version of Three Card Monte. I have more about this in Pt 1, Fiscal Multiplier Debunked on Tugwit.blogspot.com

13

Since it’s relevant to the thread - this means that private consumption and investment also shouldn’t really have a multiplier, correct?

14

Neodoxy,

Keynesians say that since the tax cut multiplier b/(1-b), is one less than the government spending “multiplier” 1/(1-b)

(1/(1-b)) - (b/(1-b)) = (1-b)/(1-b) = 1

that “proves” that government spending is better for the economy than tax cuts.

That comes from disguising the “saved” fraction of disposable income (1-b)Yd as a+I+NX, and disguising tax T, as G.

It’s another kind of Keynesian math fraud. I have more about it in Pt 2, Fiscal Multiplier Debunked.

Scroll down about 2/3 of the way to The Bogus Tax Cut “Multiplier” (TCM)

Tugwit

15

It’s inappropriate for government to invest someone else’s money. It’s inappropriate and astronomically more inefficient.

16

Wheylous,

I never heard back from Caplan. And I don’t use math tricks. I show the ones Keynesians use.

I did get a reply from a Keynesian professor. I had asked him: In the GDP equation:

Yt = C + I + NX + G

Where is tax? It seems kind of curious to have the GDP equation and no mention of tax doesn’t it? I mean what is it that govt spends?

He went off on a big diversion and didn’t answer. So I emailed back and asked him again. First, he was unable to find tax in the GDP equation. Then he said it was in C.

Tugwit

17

That’s not the point. I want Tugwit’s mathematical reply.

18

Wheylous,

If that was meant for me, yes, there is no Keynesian “multiplier” for any kind of spending. Each $1 of any kind of spending is just addition. Each $1 is spent multiple times, but there is no way to calculate some fantasy value for the jobs it will create, or what the increase in total national income will be, or especially to say that $1 of govt spending returns (according to the Obama administration) $1.50, so deficit spending pays for itself with money left over.

For a marginal propensity to consume = b, you can derive a 1/b “multiplier” for consumption spending, and I do that in Pt 1 Fiscal Multiplier Debunked on Tugwit.blogspot.com . The 1/b “multiplier” is just as legitimate as Keynes’ 1/(1-b) “multiplier”, and 1/b is actually required to avoid the Keynesian infinity, for when investment is zero. The problem is that you can’t use the investment “multiplier” for consumption, and you can’t use the consumption “multiplier” for investment. For a $1 increment of consumption, the marginal propensity to consume is 1, and 1/b = 1/1 = 1. For a $1 increment of investment, the marginal propensity to consume is zero and 1/(1-b) = 1/(1-0) = 1. No multiplier for either consumption or investment. That’s why the marginal propensity to consume is irrelevant to the effect of spending on income. It only applies to the allocation of income to spending.

In Pt 2, Fiscal Multiplier Debunked, I show the absurdity of the Keynesian “multiplier process” story. Scroll about 1/4 to 1/3 the way down the page to: The Absurd “Multiplier Process” Story.

Tugwit

19

Tugwit , really big thanks!

This is exactly what I was looking for. I remembered there was some funny math with the tax multiplier difference. I’ll take a look at the site a bit later.

20

You don’t need mathematics to dispute or disprove it. A dollar spent by government at most is a dollar spent by government. The question is does it expand productivity and create wealth? In virutally all cases the answer is no.