Following up on yesterday’s Keynesian Cross post:

1. The point, for those who missed it, is that using exactly the same reasoning that we find in Eco 101 textbooks to derive the Keynesian multiplier, we can conclude that sending all your money to me will make everyone rich. The conclusion is absurd; therefore the reasoning is invalid. And reasoning that’s invalid in one context is also invalid in another.
2. Some commenters thought that my version of the Keynesian cross argument was an unfair caricature. I invite those commenters to peruse some actual Eco 101 textbooks. For example, they might browse through the section labeled “The Income-Expenditure Model” in a widely used textbook called Macroeconomics. The authors are Robin Wells and Paul Krugman.
3. Let’s review the logic of that model. (See yesterday’s post for explanations of the notation.)

Step II: Throw in an empirical regularity (in this case C=.8Y).
Step III: Combine the two equations to get a third equation (Y=5(I+G).)
Step IV: Do a thought experiment involving a policy change (e.g. an increase in G) and predict the outcome by assuming that your equations will continue to hold after the policy change.

By contrast, my alternative model starts with an accounting identity (Y=L+E), throws in an empirical regularity (Y=.999999E), combines these equations to get a third (Y=1000000L) and then predicts the outcome of a thought experiment (send me your money!) by assuming that the equations will continue to hold. In other words, yes, exactly the same logic.

4. The problem with the Landsburg multiplier story is that after you send me your money, the equation Y=.999999E is not likely to remain true. The problem with the Keynesian multiplier story is that after you increase government spending, the equality C=.8Y is not likely to remain true. Why not? Well, for one thing, if the government buys you a bowl of Wheaties, you’re correspondingly less likely to go out and buy a bowl of Wheaties for yourself. For another, if the government spends wastefully, you, as a taxpayer, are going to end up poorer, which means you’ll probably consume less. The exact nature of the change depends on the exact nature of the government spending. But there’s surely no reason to buy into the model’s assumption that there will be no change at all.
5. What we have here is a particularly simple example of the so-called Lucas Critique, which was part of the revolution that swept through macroeconomics a few decades ago. Until then, it was routine in Keynesian macro models to assume that equations describing behavior would remain valid after a policy change. Lucas made the simple but pointed observation that this assumption is almost never justified.
6. None of this means that you can’t write down sensible Keynesian model with a multiplier; it does mean that the Eco 101 version of the Keynesian cross is not an example of such. This in turn calls into question the wisdom of the occasional pundit who repeatedly admonishes us to be guided in our policy choices by the lessons of Eco 101.
7. As I said yesteday, the idea for this post was not original with me; I’d thought that I vaguely recalled the source as Murray Rothbard. As some commenters pointed out, you can find the original here.
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#### 80 Responses to “Multiple Comments”

1. 1 1 Harold

I see, the target is not Keynesian multiplier per se, but the explanation of it in econ 101 textbooks. I think the first line of ysterdays post is a little misleading. Instead of “Todays lessson is about the Keynsian multiplier” it should have read “Todays lesson is about how Keynesian multiplier is erroneously explained in Econ 101 texts”. A valuable lesson, no doubt, but your first line got me off on the wrong foot thinking it was the multiplier, not the textbooks that were your target.

2. 2 2 Mike H

the equality C=.8Y is not likely to remain true. Why not? Well, for one thing, if the government buys you a bowl of Wheaties, you’re correspondingly less likely to go out and buy a bowl of Wheaties for yourself.

While the comment if the government buys you a bowl of Wheaties, you’re correspondingly less likely to go out and buy a bowl of Wheaties for yourself” is true, it doesn’t therefore follow that C=0.8Y becomes false if the government buys Wheaties – after all, presumably I have other things I’d also like to do with my money. Now I have free Wheaties, I’ll buy more milk.

It especially doesn’t follow that C=0.8Y becomes false if the government decides instead to fix bridges or buy trains. After all, most people spend precisely 0% of their money on public works, they can hardly spend less just because the government steps in.

Nonetheless, the policy probably will produce a change in my propensity to spend. Several reasons I can think of :

* my propensity to spend is not my marginal propensity to spend. However, if this were the only objection, we could run the same ‘accounting trick’ argument with dY = dC + dI + dG, and still get a multiplier.
* if the government spends, it must get the money from somwhere. The choice it makes may affect Y, dY, C or dC or all of the above.
— if the government raises personal taxes, then the stimulus is cancelled out by the tax. However, I’ve never heard Keynesians recommend tax-financed stimulus.
— if the government raises corporate taxes, presumably I goes down, and the stimulus is cancelled out by the tax. However, I’ve never heard Keynesians recommend tax-financed stimulus.
— if the government borrows money, this may raise interest rates, causing I do go down, so the stimulus effect is reduced by crowding out a la Ricardian equivalence. If, on the other hand, the government can borrow without raising interest rates (for example, during a liquidity trap). However, I’ve never heard Keynesians recommend stimulus outside liquidity trap conditions.
— the govt might also fund the stimulus through money-printing. I don’t have time to think about this right now.

3. 3 3 Harold

#2 See my comment 2 yesterday. Apparently if the stimulus is paid for by tax, then the multiplier is simply 1.
http://www.slideshare.net/lovgupta1/keynesian-multiplier-effects

This is also why Keynsians prefer spending to tax cuts.

4. 4 4 Harold

Another thought. If propensity to spend altered within the historical range as a response to the policy change, what would the multiplier be? From yesterdays post, this is approx 0.85 to 0.95.

For the stimulus dollar, the change doesn’t matter, only the new level. However, for every other dollar in the economy, there will be a reduction effect equal to the change in propensity to save. This could easily cancel out the multiplier for the stimulus.

5. 5 5 Steve Landsburg

Harold:

I see, the target is not Keynesian multiplier per se, but the explanation of it in econ 101 textbooks.

No, no, it’s far more than that. This textbook explanation really is a good representation of the traditional “old Keynesian” argument for the multiplier. Today we have “new Keynesians” who tell more plausible stories, but we also have occasional pundits who keep insisting that for many purposes, the old Keynesian ways of thinking are plenty good enough.

Steve,
aside from the theoretical derivation of the multiplier, do you think that as a practical matter it exists, even if it is unknowable and/or different depending on the economic context?

7. 7 7 Nick J

I see the point you’re trying to make, but I think you’re doing the Lucas critique a disservice if you argue it this way since this isn’t quite what it’s about.

The Lucas critique is a statement about relationships. It says that just because you’ve observed some empirical relationship in the past is no reason to expect it to continue once policy changes. In this case, there’s no reason to expect that people will continue to eat 80% of their income. It’s a subtle and profound point.

But I doubt there’s ever been an economist who ever lived who thought that because you observed some descriptive fact about the world that that fact would continue to hold forever. Examples include ‘My income is 0.01% of total income.’ I do see the point you’re making, but if you portray the Lucas critique as being a criticism of _that_ sort of thinking, then the Lucas critique seems to lose a lot of its brilliance.

8. 8 8 nobody.really

The point, for those who missed it, is that using exactly the same reasoning that we find in Eco 101 textbooks to derive the Keynesian multiplier, we can conclude that sending all your money to me will make everyone rich. The conclusion is absurd; therefore the reasoning is invalid.

Wait — the point was that the conclusion is absurd?

Oh. Well, when you get that check from me, just rip it up, ok?

9. 9 9 Andy B

Can you point to an instance where this example (static Keynesian multiplier) is incorrectly used? I do recall many Econ 101 references in his posts but never to this one. Thanks.

10. 10 10 Harold

Just checked “Macroeconomics” by Krugman and Wells. It is \$155.92, so I think I will give it a miss, and take your word that the above is a good representation.

Once pointed out, it seems obvious that we must be sure the policy has no effect on propensity to save to derive the magnitude of the multiplier. Many things that seem obvious when pointed out are difficult to see in the first place.* The textbooks should make it clear that this is required for the derivation to be valid. They should also provide an explanation of why this should be the case.

*(Quick example. Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married persdon looking at an unmarried person? Options are yes, no or need more information.)

Krugman’ Response
Karicature Keynesianism
Via Brad DeLong, Daniel Kuehn protests a really stupid argument by Stephen Landsburg; he does the work, and no need for me to follow up.

But let me note that Landsburg’s latest unfortunate intervention follows a well-trodden path: that of starting from the proposition that Keynesians are themselves really, really stupid — a proposition argued not by pointing to anything actual Keynesians say, but instead by presenting a caricature that supposedly is what Keynesians believe. Call it Karicature Keynesianism.

Anyone who’s followed the various attacks on yours truly knows what I mean: Keynesians believe that budget deficits never matter, that increasing demand can solve all economic problems, that there’s no such thing as a supply side to the economy, that more spending is always good. You can see it even in the comments to Kuehn’s post, with people expressing doubt about whether there’s crowding out in my textbook. Let me suggest a very difficult research project: how about actually looking at the book?

Now, to some extent Karicature Keynesianism involves extrapolating what people like me say about policy in a depressed economy with interest rates up against the zero lower bound and pretending that this is what we say in all situations. But where’s this urge to caricature coming from?

I’d say that it’s actually a form a flattery. If Keynesians had made a lot of bad predictions in recent years — if inflation or interest rates had soared, if austerity had produced prosperity — the other side could go after what we actually said and say. But reality, it turns out, has a well-known Keynesian bias. So the people who’ve gotten everything wrong are reduced to attacking an economic doctrine that has worked pretty well by misrepresenting that doctrine, and claiming that it’s stupid and absurd.

By the way, the man who really brought Keynesianism into the classroom — who was responsible for what we now call the “Keynesian cross” — was Paul Samuelson. And while arguing from the qualities of individuals isn’t the main way you should assess anything, still: maybe you think I’m stupid (a remarkable number of people apparently do believe that), but do you really imagine that Paul Samuelson was an idiot promoting a moronic set of ideas?

Anyway, as I said, ultimately being caricatured like this is a compliment.

14. 14 14 RJ

I posted a response in your former blog post on this, however there’s something still fundamentally wrong with your initial equation.

If E=0.99999999Y, then L=0.00000001Y. Plug the two values in and you get Y=0.99999999Y+0.00000001Y, which just says Y=Y. Even with your multiplier, it translates to Y=100,000,000*0.00000001Y which just says Y=Y.

This is nothing like the Keynesian cross.

15. 15 15 Jack

I am so confused.

16. 16 16 JohnW

RJ:

So you think that Y should not equal Y???

Do you know what an accounting identity is?

17. 17 17 RJ

John,

Yes, Y should equal Y. All this states is income equals income. This isn’t the same logic as when you derive the Keynesian cross. I suggest you go back to my former comment in SL’s earlier post on the subject.

18. 18 18 JohnW

You can do the same thing with the Y = C + I + G accounting identity.

Y = C + I + G
C = 0.8Y
I + G = 0.2Y
Y – C = I + G
Y(1-0.8) = I + G
Y = (I + G)/(1-0.8) = 0.2Y / (0.2) = Y

So income equals income. Identity!

What would you expect? Y ~= Y ?

19. 19 19 Steve Landsburg

20. 20 20 RJ

John,

No, no, NO! You’re missing the fundamental point when you derive the multiplier, it’s that you create a behavioral assumption about the real world that influences the accounting identities to hold.

Here’s how you *actually* do it.

Assume Y=Z (Income equals expenditure, not income equals income).

Z=C+I+G (We’re assuming a closed economy, but the logic is the same if you include net exports).

Define the consumption function as C=c0+c1(Y-T). (c0 is autonomous consumption and c1 is MPC)

Y=c0+c1(Y-T)+I+G

Do the algebra and you come up with…

Y=(1/1-c1)*[c0-T+I+G]

SL’s equation tries to create a multiplier from accounting identities alone, which you can’t do. They’re two completely different things.

21. 21 21 RJ

Correction!

The final equation after you do the algebra should read…

Y=(1/1-c1)*[co-c1T+I+G]

22. 22 22 JohnW

Steve:

No point, unless you count that an accounting identity is an identity. RJ seems to think that the fact that Y = Y somehow invalidates your logic.

Does what RJ is saying make sense to you?

23. 23 23 malcolm

John W:
The problem is that (I + G) is not a function of Y.
In the simple Keynesian cross model, I and G are exogenous variables.
Set I = 0 then G= .2Y. Do you really believe that? Do you believe that if consumers get happy and decide to spend more that Y will rise and G will rise also? Hmmm, that doesn’t sound right to me at all. You’re problem is that you substituted one too many times and ended up with something worthless.

24. 24 24 Steve Landsburg

RJ: Why do you find it surprising that you can use an accounting identity to derive another accounting identity? I agree that your calculation is nothing like the Keynesian cross. But it’s also nothing like the calculation in the post.

25. 25 25 RJ

SL: I’ve stated my main critique of your critique a few times in my posts. Also, the reason I went back and ‘simplified’ your initial formula was to show that you didn’t have a multiplier with the equation Y=100,000,000L.

26. 26 26 Gordon Landwirth

Steve,

As I implied at http://www.thebigquestions.com/2013/06/25/the-landsburg-multiplier-how-to-make-everyone-rich/#comment-103320, your argument seemed (and still seems) to be a straw man, although that is just intuitive on my part (and I can’t reference my old Macro 101 textbook because it didn’t make the cut at some point along the way of several moves over the years). I just find it hard to believe any economist or sensible person would advance the argument that such a ratio that is observed is, therefore, causal, such that increasing one factor would necessarily affect the others exactly to maintain the ratio.

Is there textbook material to that effect online to which you can link, rather than presenting your interpretation (the reasoning you are attributing to them), so someone without convenient access to an actual textbook can review it firsthand to try to assess if it actually reasons as you claim?

27. 27 27 Daniel

So here’s what I think Steve’s post is about.

1. The simple multiplier is inaccurate because of all of its simplifications.
2. Even though there are more plausibly written multiplier models, Krugman says that policy can be guided by econ 101

It just seems interesting that the multiplier that we would derive from the very simplistic form would argue for less stimulus to make up the output gap. The more complicated, lower multiplier, suggests that we need more stimulus to make up for the output gap.

So Steve, is your argument for more stimulus?

28. 28 28 Yancey Ward

Daniel,

Do you think it possible the multiplier of stimulus might always be below 1?

29. 29 29 Don Boudreaux

I take (perhaps mistakenly) Steve’s point to be the broad one that Keynesian analysis supplies far too flimsy a foundation upon which to build reliable guides to real-world policies. The very ignorance of the Keynesians regarding structural, micro issues – “ignorance” in the sense that Keynesians ignore these issues in order to focus on aggregate demand as the driver of economic activity – leads them to ignore many of the tradeoffs that reality inevitably imposes on the government and on the private sector even when a substantial number of assets (including labor) are unemployed.

Keynesian analysis can be gussied up, polished, spit-shined, and rendered into rococo equations adorned – in the style of Keynes himself – with all manner of opaque jargon. But at the end of the day it’s built on the implausible assumption that the chief cause of economic sluggishness is a stubborn superabundance of resources relative to demand. It is, at bottom, nothing more or better than old-hat mercantilism / businessman-in-the-Main-St. / politician-in-the-Pennsylvania-Ave. superstition that the only reason Mom&Pop Groceries or MegaDominant Corp. or “our economy” is doing poorly is because people aren’t spending enough money.

30. 30 30 Daniel

@ Yancey Ward,

I definitely think it’s possible. But I also think that the consensus is around 1.1-1.2 for liquidity traps in academic literature right now. My post was just poking fun at the fact that Landsburg is arguing with Krugman on the grounds that econ 101 is not a sufficient Keynesian model. The alternative Keynesian model which Steve admits could be correct would suggest that we need more government spending, not less.

31. 31 31 Daniel

@ Yancey Ward (continued),

Of course I also think that when Krugman is talking about econ 101 being a better policy guide than the one congress is currently using, he is saying that if congress was using an econ 101 textbook, at least they’d be getting the direction correct if not the magnitude, whereas right now he believes we’re going in the incorrect direction which is worse in this case than having the wrong magnitude, if Krugman is correct.

32. 32 32 Ken B

Krugman thinks Landsburg has presented a “Karicature” of an argument. That was Landsburg’s intent. His point could not be simpler: If you take two equations, one an identity and one not, and combine them, you cannot treat the new equation as an identity. The Old Keynesian argument did just that, and so did Landsburg’s.

33. 33 33 Daniel

@Ken B,

Why are we still worried about the Old Keynesian argument? Have you seen anyone lately advocating a multiplier calculated from the simple equation that Landsburg shows above?

34. 34 34 Andy Harless

Here’s the problem with the argument in this and the previous post: you don’t just “throw in” an empirical regularity; you make a behavioral assumption — in this case the assumption that the fraction of marginal income that people consume is exogenous. You might regard that as a bad assumption, and you can certainly make a case that it’s a bad assumption, but it’s not self-evidently ridiculous. Before considering the evidence, it’s plausible that people make short-run consumption decisions by a rule of thumb in which they consume a certain fraction of their marginal income. By contrast, I can’t even tell what behavioral assumption underlies the Landsburg multiplier. And when I try to think of a behavioral assumption that would explain the Landsburg multiplier, all the possibilities are self-evidently ridiculous.

(FWIW I don’t think the evidence supports the simple rule-of-thumb version of the Keynesian consumption function, but I do think it largely supports the modern “liquidity constraint” version, in which some fraction of agents consume 100% of their marginal income.)

35. 35 35 nobody.really

Yes, Y should equal Y.

Please – among Objectivists, we prefer so say A is A.

Then again, maybe you’re right after all. Spelling was never my strong suit….

36. 36 36 ThomasBayes

Okay, so everyone seems to agree that both analyses are absurd. But some people have said that there is a more sound way to derive the Keynesian multiplier. No one has said that about the Landsburg multiplier yet, but perhaps someone will. Why not test both of the theories?

Experiment 1: Give Landsburg \$10 or \$100 or \$1,000 or \$10,000 of additional income and see what happens to the nation’s total income.

Experiment 2: Have total government spending (federal, state and local) increase from \$5 trillion to \$6 trillion over a two-year period, then see how much total spending increases.

Some version of Experiment 1 probably happens every year at raise time.
Experiment 2 happened from 2007 to 2009. What did we learn?

37. 37 37 edarniw

@34

This is maybe the only legitimate criticism I’ve seen so far (most of the stuff by Kuehn goes off on some weird tangent). That is: in the first case you can argue that the second equation is a “behavioral” equation and in the second case the second equation is an “empirical regularity”. But I don’t think that it being an “empirical regularity” nullifies its case.

You can still demonstrate the absurdity with an example where there’s a clear “behavioral” assumption.

Example:

W = A + B

W=water in a cup
A=water poured in first 30 seconds
B=water poured after the first 30 seconds

Suppose we regularly observe that Jon, who’s pouring the water, fills about 80% of the final amount in the first 30 secs. As a result, we think that:

A=.8*W

Which implies W=5*B

Thus, we might (mistakenly) tell Jon that if he poured an additional ounce of water after the first 30 secs, total water in the cup would rise by 5 ounces!

38. 38 38 Daniel

The real argument is between a variable multiplier model that depends on lot’s of things and there is lot’s of evidence of it being above 1 in a liquidity trap, and those that believe the multiplier is less than 1 for whatever reason. Not some mythical super high at all times multiplier that Keynes never supported to begin with and is simply a way of introducing some basic math to freshman (and for which the simplifying of the assumptions behind it are clearly stated within the text).

As I stated before when Krugman talks about Econ 101 being a better guide to how fiscal policy should be decided than our current system, he’s arguing from a directional standpoint, not a magnitude standpoint.

Can we just call this for what it is. A light hearted attempt to poke fun at Krugman’s expense that went horribly, horribly wrong. . . for Steve.

39. 39 39 Steve Landsburg

edarniw: Very nice example.

40. 40 40 Daniel

@37,

That’s why we rely on both theory and empirical evidence to find answers, not either one alone.

41. 41 41 Mike H

Daniel Kuehn believes Landsburg is making some basic mistakes.

I haven’t wrapped my head around Kuehn’s points sufficiently well to post a coherent summary.

Also, Wikipedia’s article on the Keynesian cross seems relevant here.

42. 42 42 Capt. J Parker

Another way to make everyone rich.
Y=C+I+G
Assume:
I is exogenous
Government revenue =tY where t is the tax rate
then G=tY +Gd where Gd is deficit spending that is assumed exogenous
Also assume C=Co +CmYd – a pretty common Keynesian consumption function where:
Cm=marginal propensity to consume, Co is subsistence consumption and
Yd = disposable income = Y-tY = Y(1-t)
then:
Y=Co +CmY(1-t) +Gd +tY +I
do the math and:
Y= (Gd+Co+I)/((1-Cm)(1-t))
Where the Keynesian multiplier is 1/((1-Cm)(1-t))
So all you need do is make the tax rate t =99.9999999% and voila – infinite Y!
Note: this works even if the government runs a balanced budget (Gd=0)and Cm goes to zero in the process.

43. 43 43 Tom Dougherty

The multiplier equals 1/(1-MPC). In many textbook examples the MPC is .8, which gives a multiplier of 5. So, for every \$1 increase in government spending, output will grow by \$5. If such fantasies were really true what policies should the government pursue? Why the government should punish saving and further increase the MPC. If people consumed 90 cents out of every additional dollar earned the MPC would rise to .9 and the multiplier would increase to 10. That would mean an additional \$10 of GDP for every additional \$1 of government spending. But why stop there. We know with the IRS scandal, the NSA spying on everyone, and FBI drones flying over Americans that the government can get really draconian on the American people, so certainly it could force people to spend much more on consumption and come down hard on those who save. So, let’s put the multiplier to somewhere around .9999. For every \$1,000 earned you would be forced to spend \$999.90 and could only save 10 cents. But look at the multiplier now; it rises to 10,000. That will mean every \$1 increase in government spending will cause GDP to grow by \$10,000. Or a \$10 billion increase in government spending will cause GDP to grow by \$100 trillion. We could pay off the national debt, buy much of if not all of the worlds assets, we could take a vacation for the rest of our lives. And if we could get people to stop saving that last 10 cents and I know the government could (it is becoming very persuasive these days) the multiplier would rise to infinity. Therefore, each \$1 in additional government spending would increase the GDP by infinity. Now that we know how nasty saving is, if we would only consume every last penny earned the economy would become heaven on earth.

44. 44 44 RJ

edarniw

What you’ve mistakenly done in your equation is you’ve made both A and B endogenous variables. The reason government spending has more than a one-to-one effect on GDP via the multiplier is because government spending is assumed to be an exogenous variable (taxes and investment are also treated as exogenous). Thus, you’re equation is not analogous to how the Keynesian cross is defined or how the multiplier plays

There is a really bad misunderstanding of the multiplier and Keynesian Cross model here in general. These are elementary errors too that should be explained from the get-go when it is presented.

45. 45 45 RJ

*I’m re-posting this because of html errors.*

edarniw

What you’ve mistakenly done in your equation is you’ve made both A and B endogenous variables. The reason government spending has more than a one-to-one effect on GDP via the multiplier is because government spending is assumed to be an exogenous variable (taxes and investment are also treated as exogenous). Thus, you’re equation is not analogous to how the Keynesian cross is defined or how the multiplier works.

There is a really bad misunderstanding of the model here. These are elementary errors too that should be explained from the get-go when it is presented.

46. 46 46 RJ

Capt J. Parker,

You also commit the same error that edarniw made (which is surprising, considering it seems you understand the difference).

47. 47 47 Harold

#37. If we give give Jon the same time to pour, and a bigger jug, it is quite likely that we would get the result you describe. It depends on the way it is set up.

If we are more specific, and said that Jon must simply open a tap to allow the water to flow from a tank into a bucket and it empties in 1 min. We notice that 80% flows in the first 30 seconds. We adjust the size of the tank and tap so that the amount flowing in the second 30 seconds increases by 1. We find the total increases by 5 times.

48. 48 48 Harold

Correction – the total increases by 5 (or 5 times the increase inthe second 30 seconds)

49. 49 49 NickC

This fiscal multiplier comes from Froyen’s Macroeconomics:

dY = dG/((1-b)+i1c1/c2)

Where dY = change in total income
dG = change in government spending
b = marginal propensity to consume
i1 = interest elasticity of investment
c1 = increase in money demand per unit increase in income
c2 = decrease in money demand per unit increase in interest rate

Assuming some interest elasticity, the term i1c1/c2 decreases the multiplier. An increase in the interest rate (crowding out) that accompanies fiscal stimulus is what prevents us from unbounded riches driven by increased demand. The model only allows that increased government spending increases income up to some point of potential income, which is contingent on supply.

50. 50 50 Capt. J Parker

@RJ (45 and 46) Quoting RJ: “The reason government spending has more than a one-to-one effect on GDP via the multiplier is because government spending is assumed to be an exogenous variable”

This is clearly wrong because my model treats government spending as endogenous (except for Gd) and still gives you a multiplier.

I make a simple assumption of government behavior that government spends all of its tax revenue, tY, PLUS and an exogenously determined amount of deficit spending Gd. This assumption is well supported by how the US government actually behaves.

The error that I DO make, that you fail to grasp, is that I neglect the fact that the existing capital stock can only produce so much Y before it runs into trouble. But, that is not so much an error on my part as a limitation of the model which says nothing about how Y must be some function of the existing stock of capital.

51. 51 51 malcolm

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.

52. 52 52 Daniel Kuehn

@37 – I’m pretty sure @34 is making precisely the point that I was making.

I said you can’t confuse the income share with the MPC, and he says you can’t confuse an empirical regularity with a behavioral assumption, but we’re referring to the same thing. @34 is a great response.

I fail to understand how the reasoning of the Keynesian cross is bad here. The reasoning is fine. The problem is the input: a 0.99999999 MPC (or more accurately an MPC of 1, as I argued – in any case I agree with @34 that Landsburg is very confusing on this point).

53. 53 53 RJ

This is clearly wrong because my model treats government spending as endogenous (except for Gd) and still gives you a multiplier.

I was speaking of the Keynesian Cross model when I said the quote you highlighted in your post.

Even still, your model has a number of other errors that make it not analogous to the Keynesian Cross model. Your consumption function is incorrect, ‘t’ isn’t a tax rate but an absolute number representing total taxes.[Total] Government spending isn’t defined properly, it should be (if you want to use tax rates and deficit spending) Gd-tY, you cannot add total taxed income and government spending and call it total government spending. Also, government spending is still technically exogenous, what you’ve made is the tax rate endogenous and G is really public savings, not government spending. They’re two very different things.

The point of capital stock is irrelevant.

54. 54 54 Daniel

@50,

And in what world don’t Keynesians account for supply side constraints?

55. 55 55 Capt. J Parker

@ Daniel 50. If your question is in what world the econ 101 Keynesian cross model does not take into account supply side constraints, that would be this world.

56. 56 56 Daniel

@55

In the econ 101 books I read, they clearly state that aggregate supply is assumed to be horizontal in these cases. Which is the whole point in a liquidity traps that you seem to have missed.

57. 57 57 RJ

If your question is in what world the econ 101 Keynesian cross model does not take into account supply side constraints, that would be this world.

Then you do not understand the model.

58. 58 58 Capt. J Parker

@ Daniel (55) So, We agree! No supply constraints in the Keynesian Cross Econ 101 model.

@ RJ (53) Nope, my model’s fine. If government imposes a simple proportional tax rate t on all output Y then total tax revenue is tY. If government spends all the tax revenue it collects under this scheme and not a cent more on anything else then G=tY by definition. If Government decides to spend even more than it collects in taxes then G=tY + Gd where Gd is the amount of government spending G in excess of tax revenue tY. This is just accounting.

Why do you want to find fault with my model? It’s a big government Keyensian dream. It says that Uncle Sam can get as big a multiplier as he wants through taxing and spending AND it doesn’t have to worry about tax policy decreasing private marginal propensity to consume (Which Steve Landsberg is worried about.)
The simplest textbook Keynesian cross model says the multiplier =1/(1-MPC) Where MPC = marginal propensity to consume (I used the symbol Cm for MPC in my model.) If you can force MPC to be really close to 100% you can force the multiplier to be really big and hence Y to be really big. My model simply says government can, in fact, do all the forcing it needs to effectivly make MPC for the economy as a whole nearly equal to 100%. Government simply takes a whole lot of your money and spends it – no more lack of demand. Recession solved. This is exactly what guys like “pundit” are advocating. Are you saying they’re wrong? My model isn’t.

59. 59 59 Daniel

@58,

Um, no we don’t agree. Just because the model assumes something doesn’t means that it believes it always to be the case. Do you even understand abstraction. It seems like you don’t.

On the tax part. I wasn’t getting your exact reasoning until now, and now that I do what you’re saying sounds really, really stupid. Governments don’t set the rate that they take as a percentage of total income. They set the marginal tax rate. If income varies, it changes the total percentage of taxes the government takes in as a percent of income. Government budgets are set separately from this relationship.

60. 60 60 RJ

Captain,

If you’re to model government spending within the GDP accounting model, you cannot add tax revenue and deficit spending even under the assumption that all the tax revenue is spent. The reason is because you then cannot model government surpluses when analyzing public savings, which is pivotal to the Keynesian Cross model (which carries over to the IS-LM model). In order to do this, you need to make the effects of taxes upon GDP exogenous.

Why do you want to find fault with my model?

Because it’s wrong.

Are you saying they’re wrong? My model isn’t.

You do not understand the logic behind the multiplier or government spending during a recession. You need to read more into a macro textbook on the subject.

61. 61 61 Daniel

” This is exactly what guys like “pundit” are advocating. Are you saying they’re wrong? My model isn’t.”

And this little gem is just ridiculous. #”pundits” response yesterday. If you’re going to use this line of reasoning at least support it with language from any of “pundits” actual words instead of your fantasy world.

62. 62 62 RJ

Governments don’t set the rate that they take as a percentage of total income. They set the marginal tax rate.

Jeezus Christ! I spent the past 40 minutes looking at his equation because I ‘knew’ there was something else really wrong with it other than what I just said but couldn’t put my finger on it.

Good catch!

63. 63 63 Capt. J Parker

RJ 60 “If you’re to model government spending within the GDP accounting model, you cannot add tax revenue and deficit spending even under the assumption that all the tax revenue is spent. The reason is because you then cannot model government surpluses when analyzing public savings” I model G= tY + Gd if there is a surplus Gd is negative, if there is a deficit Gd is positive is there is a balanced budget Gd=0. deficit = expenditure – revenue. If deficit is less than 0 you have a surplus. Its an accounting identity my friend.

Daniel 59 “They set the marginal tax rate. If income varies, it changes the total percentage of taxes the government takes in as a percent of income.”
Here’s a Keynesian cross model that treats taxes the same way I do. (page 10).

http://faculty.haas.berkeley.edu/arose/Macro8.pdf

Here’s some data that says a proportional tax rate is a good model. Taxes as a percent of GDP stays pretty constant.

http://commons.wikimedia.org/wiki/File:U.S._Federal_Tax_Receipts_as_a_Percentage_of_GDP_1945%E2%80%932015.jpg

Quote: “Government budgets are set separately from this relationship.” Sad but true. That’s what Gd does in my model. Government can set G to any value it wants regardless of tax revenue. G=tY+Gd.

As far as “pundit” goes, all I claim is that he says we should increase G since that will increase Y and decrease unemployment. Am I wrong?

64. 64 64 Andrew_M_Garland

=== ===
Landsburg (above)
(4) The problem with the Keynesian multiplier story is that after you increase government spending, the equality C=.8Y is not likely to remain true.

(5) Lucas pointed out that equations describing behavior were unlikely to remain valid after a policy change.
=== ===

These above points are valid, but not the crux of what is failing in the analysis using the following equations.

1. Accounting Identity:   Y = C + I + G
2. Propensity to Spend C:   C = .8 * Y
3. Propensity to Spend I+G:   I+G = .2 * Y   “The missing equation”
4. Multiplier:   Y = 5*(I+G)
5. Conclusion:   Y increases by \$5 when G increases by \$1

The equations are correct, but the conclusion is wrong. Not slightly wrong because policy changes cause some slippage in the .8 factor. It is wrong in the sense of being absurd and illogical. Here is why.

Some equations are always true by definition. Cause and effect operate in both directions. As in the Accounting Identity, if you give me Y, I can give you C+I+G, and the reverse. Such identities are valid during change, regardless of equilibrium conditions.

Equilibrium Propensity to Spend C

Other equations are observed, like Propensity to Spend C. If you tell me Y (total income), it computes the likely personal consumption C. This observation depends on equilibrium, even if entirely true and reliable.

If Joe gets an unexpected \$1,000 bonus, he will very likely spend \$800 more. But, if Joe unexpectedlty spends an extra \$800, how likely is it that he will receive a \$1,000 bonus?

In the long term, in equilibrium, we might guess Joe’s income from what he spends, because we know that Joe usually spends .8 of his income. But we can’t know how a variation from equilibrium will work out. Maybe Joe will cut his spending after an \$800 splurge, or maybe he has correctly anticipated a future increase in income.

The cause and effect here runs strongly in one direction. More income will increase Joe’s spending. Forcing Joe to spend more is not going to increase his income (unless it forces him to take a second job).

The Propensity to Spend equation   C = .8 * Y   should have a big warning attached: “Only works from right to left if not in equilibrium”.

equilibrium Propensity to Spend I+G

The reasoning about the multiplier usually jumps over (3.) to the multiplier equation (4.). The “missing equation” is   I+G = .2 * Y. It has the same characteristics as Joe’s Propensity to Spend, namely it only works in equilibrium. When Y changes, it is quite likely that I+G will change. But, if we force a change in G, there is no mechanism which tells us how Y will change.

If Y (GDP) increases, then of course government spending will increase. But, merely increasing government spending isn’t likely to increase Y by a factor of 5. It will of course increase Y by definition, dollar for dollar.

The Multiplier

By omitting (3.) we get to the multiplier equation without much thought.
4. Multiplier:   Y = 5*(I+G)

There should be a warning “Only true in equilibrium. Sudden changes in Y are likely to affect (I+G), but not the reverse.”

An equation can be completely true in equilibrium, and entirely worthless when the prerequisites change. Equations are only a guide to further investigation. They don’t predict the future unless thay have been shown independently to do so, especially such simplistic ones as the Multiplier.

65. 65 65 Daniel

@63,

Your link is not a textbook. They seem like some professors slides. I’m not commenting on how good this professor is but textbooks have to go through many round of edits to correct for any errors.

If by taxes remain stable you mean fluctuate back and forth +/- 2.5% of income under specific policies (see other countries for much wider variation) than yeah I’d say it doesn’t fluctuate that much.

Anyway, let’s say that we do operate under your model. If we bring in aggregate supply, we disprove your theory that it can create infinite income. But the government can impose above full employment. See WW2. Keynesians aren’t advocating anything like this type of government involvement. We prefer a world where the government increases spending in times of severe trouble to push the private sector towards full employment. We want people to be able to keep as much of their money as possible because for most goods they are the best judge of what to buy, but we also believe in that there are circumstances where government can step in to help. I’m still not getting how yours or Steve’s caricature of Krugman resembles the real Krugman at all. Yes Krugman advocates more government spending at this time to push us towards full employment in a very particular circumstance.

I also reject the idea that Keynesians are necessarily big government. They advocate for stimulus in liquidity trap type recessions but they do not always advocate increasing the size of government. You’re describing a completely different group.

66. 66 66 RJ

I model G= tY + Gd if there is a surplus Gd is negative

Gd in your model cannot be negative. You stated it was extra spending on top of tax revenue that was collected and *automatically* spent.

deficit = expenditure – revenue. If deficit is less than 0 you have a surplus. Its an accounting identity my friend.

I believe it was I who explained this to you and suggested you model G in such a manner but you dug yourself into a hole when you claimed that tY was automatically spent as a part of government expenditure instead of treating tY as a separate concept of revenue in and of itself. How exactly can spending on top of automatic spending be negative?

Furthermore, the link you provided has a different multiplier even though it has a similar consumption function to yours. This is because, again, government spending is treated as an exogenous variable instead of some weird hybrid of the two. It (correctly) concludes if the tax rate goes up the multiplier will be weaker, contrary to yours that reaches a bizarre conclusion that if taxes goes up, then the multiplier will be greater.

Still not an analogous criticism.

67. 67 67 RJ

Come to think of it, I guess all Y*t represents for the consumption function is a flat-tax on income, so I can see the value in it with regards to the consumption function. Wonder though how it plays out when they get to the savings aspect of the model though…

68. 68 68 Capt. J Parker

Daniel (64)
I have no desire to caricature anyone. All I said about Dr. K is that he wants to increase Y by adding more G. From your comment I conclude you’re with him there. I’m with both of you in wanting to decrease unemployment. Being out of work is an awful thing to suffer through. I’m very unsure that Macro 101 has all the answers. Thanks for the discussion.

69. 69 69 Capt. J Parker

@ RJ (66) With the simplest Keynesian model the multiplier is 1/(1-MPC) if you can get MPC to approach 1 then you can get Y to get really big. My model simply says government can use its taxing power to take a portion of your income and spend it. This is like having you spend a greater portion of your income than you would have if left to your own devices. Your effective MPC has increased so the multiplier has increased. This should not surprise anyone. Taxes only decrease the multiplier if they don’t all get pumped back into Y by way of G. In other words taxes decease the multiplier if taxes do not increase G.
In the Berkeley slides they write:
Transfers + G = taxes + debt issuance + seigniorage
Now yes, I simplified by ignoring transfers and seigniorage and I wrote:
G = taxes + debt issuance But, taxes ARE tY and debt issuance IS Gd
so
G = tY + Gd But, They just fudge it and say G=Go WHY? Because they don’t want to deal with the fact their model (like mine) says we can tax our way to wealth. So, if you DO have a hard time believing we can TAX our way to wealth why don’t you have an equally hard time believing we can SPEND out way to wealth? For a government than never runs a surplus taxing and spending is the same thing.

70. 70 70 RJ

Oy vey, this is getting old.

For the last time, you cannot make government spending endogenous and expect your equation to be an analogous critique against the Keynesian Cross! The reason is because one of the purposes of the model is to find exogenous effects of government spending (and usually taxes, though not in the Berkeley model) and how it has more than a one-to-one effect on GDP via the multiplier.

Furthermore, and now I know why you made the mistake since you referenced the Berkeley page, G=tY+Gd is not treated as an accounting identity, it is used an equilibrium condition. This means one side is allowed to be larger in the other, which intuitively makes sense because government can collect taxes and not spend or issue debt at all and have a budget surplus. It seems to me the reason why the allowed for G=Go was to assume that government spending and revenue was in equilibrium.

I’m going to re-post a more organized explanation in the morning, for I am tired now.

71. 71 71 RJ

Screw it, no rest for the wicked. From the get go…

Not to beat a dead horse, but the problem with your model is one of endogeneity within government spending. The Keynesian Cross sets a behavioral relation to consumption, derives a multiplier and then attempts to explain other non-one-to-one exogenous effects on GDP, such as taxes, government spending, investment, exports, etc.

Two things uniquely wrong with your equation.

1) You mistakenly assumed an equation on the Berkeley page represented an accounting identity rather than equilibrium condition. This is why G=G0, I believe they are assuming it’s in equilibrium so that they *can* measure its effects exogenously. The reason I probably did not notice this earlier was because since you made the assumption that government automatically spends what it collects, through taxes or issuing bonds, I believed it could pass for an accounting identity. This irked me a lot because it didn’t allow for the possibility for public saving, which is sort of pivotal to the grander model that the Keynesian Cross is built into (IS-LM).

2) Even if it was an accounting identity, and I’m annoyed with myself that I didn’t think of this earlier, the whole point of every post myself, Khuen, Nick J, malcom and others have made against SL is that you cannot create multipliers from accounting identities! For this you need a behavioral relation.

72. 72 72 Capt. J Parker

RJ (70,71)

“You mistakenly assumed an equation on the Berkeley page represented an accounting identity rather than equilibrium condition.”

The eguation is an identity in the same way a “sources and uses of funds” eguation is and identity. Sources = Debt issuance + seigniorage + taxes,
Uses = G + Transfers. G of course if government purchase of goods and services just like C is private purchase of goods and services.

“Even if it was an accounting identity, and I’m annoyed with myself that I didn’t think of this earlier, the whole point of every post myself, Khuen, Nick J, malcom and others have made against SL is that you cannot create multipliers from accounting identities! For this you need a behavioral relation.”

Here are the behavioral relations that create my multiplier
C=Co + CmY
Gd is greater than or equal to zero.

73. 73 73 Capt. J Parker

RY (70,71) Ooops. Left out an important behavioral relation.
Goverment elects to collect taxes such that total taxes = tY

74. 74 74 RJ

Capt,

The eguation is an identity in the same way a “sources and uses of funds” eguation is and identity. Sources = Debt issuance + seigniorage + taxes,
Uses = G + Transfers. G of course if government purchase of goods and services just like C is private purchase of goods and services.

This is not what you have been stating. You’ve claimed:

If Government decides to spend even more than it collects in taxes then G=tY + Gd where Gd is the amount of government spending G in excess of tax revenue tY. This is just accounting.

I model G= tY + Gd if there is a surplus Gd is negative, if there is a deficit Gd is positive is there is a balanced budget Gd=0. deficit = expenditure – revenue. If deficit is less than 0 you have a surplus. Its an accounting identity my friend.

Are you actually interested in getting this correct or are you going to repeatedly be dodgy with your definitions in order to avoid being shown incorrect? If it’s the latter, I’m just cutting this discussion off.

(Also a tangential point, are you saying Gd, deficit spending on top of spent revenue, is the same as debt issuance? If so, you are vastly mistaken.)

75. 75 75 RJ

Actually, come to think of it, deficit spending on top of *spent* total revenue is technically debt issuance. So let me rephrase that question and ask “Are you saying saying deficit spending and debt issuance are the same thing?”

76. 76 76 RJ

Nvm, I noticed this right now.

Gd is greater than or equal to zero.

77. 77 77 Capt. J Parker

RJ Believe me, I’m open to the possibility that I’ve made a fundamental error but,I don’t believe I have. This is what I believe my overall methodology has been:
We all agree that Y=G+I+C for a closed economy.
If you add C=Co+CmY you can demonstrate a multiplier effect of 1/(1-Cm)for changes in exogenously determined Co, I or G.
You can demonstrate (as I have) that you get a multiplier of
1/((1-Cm)(1-t)) for changes in exogenously determined Co,Gd,I.
I believe G=Gd+tY is a perfectly good model for government spending based on 1)governments run deficits and 2)there is data (see 63) supporting a tY model for taxes. I still believe that a negative value of Gd if valid BUT in the hope of making progress I will, for the time being, narrow my claim that my model works perfectly well and is free of math, accounting or logical errors when Gd > = 0 If I am correct then my model and a Berkeley type model that includes taxes tY (but no transfers) will yeild the same equilibrium value of Y for a given I, Co, t, Cm and G. Since Gd is the input to my model, not G, you need to use the Berleley type model to calculate tY and then calculate Gd=G-tY and use Gd as an exogenous input to my model.you need to pick Co, Cm, I, t and G so that G>tY) Would that comparison lead to any progress? If not, we probably should call it quits. The argument that you can’t use an accounting identity to derive a multiplier doesn’t do it for me. My model uses at least one behavioral relation (C=Co+CmY) and at least one accounting identity Y=C+I+G. I don’t see any law of economics that says I can’t use an additional (pick one) behavioral relation, accountiing identity, sources and uses of funds equaiton, equilibrium requirement or whatever to change the form of the multiplier and still have a valid model. G=tY+Gd is right in the Berkeley slides in a more embellished form as I have shown.
“(Also a tangential point, are you saying Gd, deficit spending on top of spent revenue, is the same as debt issuance? If so, you are vastly mistaken.)” So, how does government spend more than it takes in revenue given that as I have said I am assuming seigniorage
is zero?

78. 78 78 RJ

Okay, now I can work with this.

I’m under the impression you’re critiquing the Keynesian Cross model by showing how the multiplier is trivial because any type of multiplier to support an absurd conclusion can be demonstrated via accounting identities. As pointed out earlier, this is incorrect as accounting identities by definition have to have equal values on each side at all time (example apples bought = apples sold is an accounting identity) and multipliers are derived by creating a behavioral relationship to show how one endogenous variable changes in response to a change in an exogenous variable.

Now, what you’ve done is made (part of) government spending endogenous and derived a multiplier to show logically how an absurd conclusion is reached and use it as a critique against the logic of how the Keynesian multiplier is derived. This isn’t a fair criticism, because the Keynesian cross assumes that government spending (and usually taxes, though the Berkeley model treats them endogenously to assume lump-sums) as exogenous. If you believe that this doesn’t accurately reflect the real world and believe government spending is in part endogenous, then that’s a whole separate debate and one I do not wish to spend time on at the moment. But you cannot critique the logic of deriving the Keynesian multiplier this way.

So, how does government spend more than it takes in revenue given that as I have said I am assuming seigniorage
is zero?

Deficit spending includes spending revenue and money from debt issuance; the only way I can see Gd, defined as money spent in excess of spent Yt, as tantamount with deficit spending is if we assume a government with a tax rate of zero. How can you negatively borrow?

79. 79 79 Capt. J Parker

RJ My model and a Berklely type model yeild identical equilibrium conditions. That holds true for both positive and negative values of Gd. I’ll mail you a spreadsheet that you can play with and see if you still feel my tax multiplier is absurd. Just email me at gilovepaulkrugman@gmail.com and ill send it. Honest injun.

If you do get on board with this model you can tell Dr. Landsberg he’s wrong – that you don’t care if the C=.8Y consumption model changes in response to goverment action. Government action can increase Y all the same and his Keynesian critique becomes irrelevant. (Sad he didn’t weigh in on this but, thems the breaks in blogland)

To your other issue: Deficit spending is the amount of spending IN EXCESS OF revenue. The amount of spending that equals revenue is just plain old spending. Negative borrowing is savings. Example: My personal sources and uses of funds looks like this:

Paycheck + borrowing = expenses

If Paycheck > expenses then borrowing by my definition must be negative, which means I am saving. I am running a surplus. I am not deficit spending.

RJ, I’m kind of cooked on this, I bet you are too. It’s been a nice, more or less civil discussion. My spreadsheet offer stands. Try it, you’ll like it. I wish you a nice weekend and Keynesian multiples for the future. Adios.

80. 80 80 Gordon Landwirth

Per my comment #26 regarding the Keynesian assertion Steve Landsburg implies is typically cited in intro Econ textbooks, can anyone link to textbook material online in which this assertion is made?

1. 1 The Landsburg Multiplier | Punto de Vista Economico