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. I don’t begrudge Scott such innocent pleasures, and I feel slightly guilty for depriving him of that good feeling, but, you know the old saying: a blogger’s gotta do what a blogger’s gotta do. For any new readers who haven’t been following this twisted tale of claim and counterclaim, charge and countercharge, response and rejoinder, see my three previous posts (here, here, and here, and the far from comprehensive array of links in them to other posts on the topic).
My main problem with Scott’s argument against Wren-Lewis was that, at a crucial stage in his argument, he relied on the national income accounts identity that savings equals investment. Now in the General Theory, Keynes himself also asserted that savings and investment were identically equal and made a rather strange argument that the identity between savings and investment had a deep economic significance because there had to be an economic mechanism operating to ensure the ultimate satisfaction of the identity. That was a nonsense statement by Keynes, as pointed out by Robertson, Haberler, Hawtrey, Lutz and others, because if two magnitudes are identically equal, there is no possible state of the world in which the two magnitudes would not be equal, so there obviously is no mechanism required (or possible) to ensure equality between the magnitudes. The equality is simply a consequence of how we have defined the terms we are using, not a statement about what can or cannot happen in the world. The nonsense statement by Keynes did not invalidate his theory, it merely meant that Keynes was confused about how to interpret his theory.
I cannot resist observing that this is just one example of many showing that the notion that the original intent of the Framers of the Constitution has any special authority in Constitutional interpretation and adjudication is totally wrong, based on the misconception that the original inventor, discoverer, or articulator of a concept has any power to control its meaning and interpretation. Keynes, let us posit, invented the income-expenditure theory. But his understanding of the savings-equals-investment equilibrium condition of the theory was obviously wrong and defective. The Framers of the Constitution may have invented or may have first articulated any number of concepts mentioned in the Constitution, e.g., the prohibition against cruel and unusual punishment, due process of law, the right to bear arms, equal protection. That they invented or articulated those terms first does not give the Framers ownership over the meaning of those terms in the sense that their understanding of the meaning of those terms cannot establish an immutable understanding of what the terms mean any more than Keynes could impose the notion that savings is identically equal to investment simply because he provided the first articulation of a model that hinged on the equality of savings and investment. Sorry for that digression, but I just couldn’t help myself.
Now back to Scott. Based on the presumed identity between savings and investment, Scott asserted that the reduction in savings by which households would seek to smooth their consumption in response to a temporary increase in taxes would necessarily imply a reduction in spending on capital goods (i.e., a reduction in investment). But savings and investment are not identical; their equality is a condition of equilibrium. If savings fall, there has to be an economic mechanism (perhaps, but not necessarily, the one posited by the Keynesian model) that restores equality between saving and investment. The equality cannot be established by invoking an identity between savings and investment that is purely conventional and is the result of a special definition that ensures the equality of savings and investment in every conceivable state of the world, a definition that drains the identity of any and all empirical content.
Here’s what Karl Smith had to say on the subject on his blog:
Scott says
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
Karl’s notation is a bit cryptic. This is how I understand it:
DY = change in Y (income)
DC = change in C (consumption)
DS = change in S (saving)
DT= change in T (taxes)
DG = change in G (government spending)
The first equation says that a change in income can be decomposed into a change in consumption plus a change in savings plus a change in tax payments. This is derived from the definition of income in the income-expenditure model, namely that income is disposed of either by spending it on consumption, paying taxes or saving it. There is nothing else (in the model) that one can do with his income.
The next equation simply makes the substitution of G for T, which in the example under consideration were assumed to change by equal amounts.
The symbol “Λ” means something like “and furthermore,” so that we are supposed to assume that DG > 0, i.e., that government spending has increased. Then we are given another assumption, -DC < DT, which means that, because of consumption smoothing, the temporary increase in taxes is not financed entirely by a reduction in consumption, but partly by a reduction in consumption and partly by a reduction in savings, so that the reduction in consumption is less than the increase in taxes. This is Karl’s rendition of Simon Wren-Lewis’s argument that a temporary increase in taxes to finance the construction of a bridge would imply an increase in Y because G will increase by more than C falls. Karl continues:
Which is false.
Proof by example:
Let DG = DT = 2, DC = -1, and DS = –1
Here Karl is saying let us assume that G and T both increase by 2. That part is fine. The problem is what comes next. He assumes that to finance the increase in taxes, consumption goes down by 1 and savings goes down by 1. Why is that a problem? Because he is reasoning in terms of an accounting identity rather than in terms of an economic model. Wren-Lewis was making an argument in terms of the implications of the income-expenditure model which consists of (yes!) definitions, causal or empirical functions (consumption, investment, etc.) and an equilibrium condition. The change in income cannot be derived from a simple definition, it is derived from the solution of the model. The model has a solution. You can solve for Y by taking the initial conditions and the empirical functions and applying the equilibrium condition. You can also express the equilibrium value of Y in a single equation as a reduced form in terms of all the parameters and initial conditions. If you want to solve for DY in terms of a change in one of the other initial conditions, like G and T or consumption function, you have to do so in terms of the reduced-form equation for Y, not in terms of the definition of Y. Doing that leads to the nonsense result that, I am sorry to say, Karl arrives at below.
Then both inequalities are satisfied and by the first equation.
DY = –1 –1 + 2 = 0
Which is what we were required to show.
It’s a nonsense result, because his solution does not correspond to the equilibrium condition of the model, which is either savings equals investment or expenditure equals income. 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].
Karl actually has interesting things to say about how to think about the effects of an increase in government spending and taxes in terms of a neo-classical analysis which is worth reading and thinking about. But the point is that to make any statement about the consequences of a change in the initial conditions or parameters of a model, one must reason in terms of the equilibrium solution of the model, not in terms of the definitions within the model, and certainly not in accounting identities that are completely separate from the model.
Finally, just one comment about Lucas and Cochrane. As Karl points out in his more recent post, Lucas and Cochrane offered reasons for rejecting the stimulative effect of building a bridge that were themselves couched in the very terms of the Keynesian income-expenditure model that they were criticizing. Thus, Lucas offered as his explanation for why building the bridge would have no stimulative effect that the increase in spending associated with building the bridge would be offset by a reduction in consumption associated with the taxes needed to finance the bridge as if that were an obvious internal contradiction within the model. Karl suggests a better response that Lucas and Cochrane might have given, but their response was simply an attempt to show that there was some gap in the logic of the model. That is why they invited such a brutal counter-attack from the Keynesians.
PS Have a look as well at Brad DeLong who has a new post quoting Paul Krugman quoting Noah Smith on the dangers of accounting identities, and also quoting moi.
PPS Just to be clear, as Scott notes in a comment below, Noah did not mention Scott in his post.
Uneasy Money 
The Keynes -> Constitution analogy doesn’t work. Keynes was trying to describe the world around him and we may borrow and discard ideas from him at will. The constitution is a legal document that some statesmen agreed to, and later generations inherited that agreement along with the option of amending it. If someone claimed it didn’t mean what people previously thought it meant, that would be treated like someone changing the terms of a contract and would lead to a big court battle. Altering purely descriptive accounts of the world just leads to different and possibly interesting theories.
I like Christopher Green’s paper on constitutional indexicals. It contains seven different possibilities for what we should consider “the constitution” to be, of which he favors “the original textually-expressed meaning or Fregean sense” over (among others) original expected application/ultimate purpose.
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All this argument is very interesting. I agree with You David. By the way, i just like to notice that MY=PT is an identity. And an abused incentity, I would say. Not less than S=I, for example.
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David, You still don’t seem to realize that if A is defined as being equal to B, then it is in fact equal to B, no proof is required. I certainly understand that a few economists, including yourself, prefer to define S and I in such a way that they aren’t equal by definition. But you cannot rewrite history. The standard defintion of S&I in all the textboks I know of is that they are equal by definition. So your really should be criticizing the profession (including Krugman), not me specifically. (Although I certainly don’t mind, it’s flattering to be targeted by so many distinguished bloggers!)
So we need to discriminate between your claim that it would be better to define S in such a way that it doens’t equal I by definition, and your claim that I have made some sort of logical mistake. If I’ve made that mistake, then so has Wren-Lewis, as he also claims S=I is an identity. Indeed if you were correct, his “proof” would be nonsense, but for different reasons that I claimed it was nonsense. Think about it. He claims if C falls by less than G rises, then Y must have risen. But why? If you are right that identities are irrelevant, then what possible reason would there be for us to assume that Y has increased, just because C fell by less than G increased? Isn’t there an identity looming in the background of that claim?
Suppose I defined Chinese exports to America as Chinese goods that are successfully shipped to America. And I defined American imports from China as goods successfully shipped from China to the US. Would you object to me claiming that those two quantities are equal by definition?
You also seem to imply that Noah Smith’s post was directed at me. That’s not the case, indeed he told me that he didn’t think I made the mistake you seem to think I made. So citing his post doesn’t really advance your claim.
And finally, your mathematical proof a few posts back assumed the S=I identity. Why did you do that? What role did that play in your proof? Why didn’t you simply end up saying “anything can happen, since S doesn’t equal I, and C+I+G doesn’t equal GDP.” Instead you produced a specific numerical answer. But why?
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BTW, I fail to see where Karl Smith “retracted” his proof. Wren-Lewis claimed that saving fell, and yet his model assumes that investment is constant. That’s Karl’s point. That’s a contradiction if S=I, an identity Wren-Lewis acknowledged he accepts in a later post. Again, these are the facts:
1. Wren-Lewis claims S=I is an identity
2. Wren Lewis implicitly assumed I is constant
3. Wren-Lewis implicitly assumed S had fallen.
Which of those three statements about Wren-Lewis do you believe is false? To me, they are all obviously true. You may not believe S=I is an identity, but Wren-Lewis most certainly does. You’ve written a lot on this issue, but I don’t see where you’ve addressed my claim that Wren-Lewis contradicted himself.
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I’m not convinced that point 2 is correct.
In this post (http://mainlymacro.blogspot.com/2012/01/savings-equals-investment.html) Wren Lewis writes
“So if people consume less (C falls), but investment in new capital (DK) stays the same, measured investment rises because firms accumulate inventories of the goods that consumers did not buy (DS rises).”
I interpret this to mean that when savings rise or fall, investment rise or fall with it. In other words it is only investment in new capital that remains fixed. Wren Lewis goes on in that post to explain the Keynesian mechanism that brings S back in line with the original I.
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RE: last post, I meant point 2 of Sumner’s 3 facts about Wren-Lewis’s views.
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rob, It would be even more wrong if Wren-Lewis claimed I rose. He’s claiming S fell, and he’s also claiming S+I is an identity.
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BTW, A few months back Brad DeLong did a post claiming the equation: MV=PY was the quantity theory of money. So I’m not sure he’s the go to guy on accounting identities. (In fairness, I assume DeLong does know the difference, but probably just slipped up in that post.)
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David, I reread your post and I now think you completely misunderstood my argument. You say this:
“Now back to Scott. Based on the presumed identity between savings and investment, Scott asserted that the reduction in savings by which households would seek to smooth their consumption in response to a temporary increase in taxes would necessarily imply a reduction in spending on capital goods (i.e., a reduction in investment). But savings and investment are not identical; their equality is a condition of equilibrium. If savings fall, there has to be an economic mechanism (perhaps, but not necessarily, the one posited by the Keynesian model) that restores equality between saving and investment. The equality cannot be established by invoking an identity between savings and investment that is purely conventional and is the result of a special definition that ensures the equality of savings and investment in every conceivable state of the world, a definition that drains the identity of any and all empirical content.”
You seem to be implying that I believe that if people try to save less, then investment must decline. But I never said anything of the sort, nor do I believe that to be true. What I said is that if actual saving declines in the new equilibrium, then actual investment must decline. And Wren-Lewis agrees with me on that point. So I think you misunderstood my argument. I was very clear that it’s possible that people might try to save less, but end up saving exactly the same amount as before, with no change in I. Indeed that is a very standard interpretation of the Keynesian model. But that wasn’t Wren-Lewis’s assumption. He assumed people actually did save less.
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David, Brad DeLong quotes you as saying the following:
“When Scott says he can derive a substantive result about the magnitude of the balanced-budget multiplier from an accounting identity between savings and investment, he is making a theoretically ungrammatical statement.”
I think it’s from an earlier post.
Accounting identities tell us NOTHING about multipliers. My argument is that anyone else making claims about multipliers must not violate accounting identities in their reasoning process. The S=I accounting identities allows the multiplier to be zero, one,100, or a million. It tells us nothing about the multiplier. If you think I did make that claim, then please quote the paragraph where I made it, so I can apologize. I’m certain you will not be able to do so, because the paragraph doesn’t exist. Only a complete idiot would claim you can prove behavioral realtionships with accounting identities.
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RE: “It would be even more wrong if Wren-Lewis claimed I rose. He’s claiming S fell, and he’s also claiming S+I is an identity.”
In the article I quote from he is looking at the opposite case (to this long running discussion) where S increases.
In regard to the effect of an increase in T he’s claiming that if S falls then I will fall with it (if you include inventories), and that as a result of falling inventories I will then increase again (via the mechanism he described in his post). until I = S at the original level of I, which will be at a higher level of C.
He is saying that I=S , but that at least initially I is variable and depends upon S.
I can see many things wrong with this analysis but I just don’t see the internal contradictions in his position that you have focused on.
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Teageegeepea, Excuse me, but the constitution is a legal document that is like many other legal documents interpreted by the courts and the courts have a whole slew of criteria upon which to base their interpretations. The question is which criteria should they choose. Where is it written that one method of interpretation is legally acceptable and another is not. You are begging the question by asserting that original intent has some special legal standing, when obviously it does not, unless you believe that Justice Scalia is intrinsically more credible than any of the other justices who have served on the court. If the Framers believed that blacks are not deserving of equal rights of citizenship, what possible relevance would that have to us in deciding the meaning of the equal protection clause?
Scott, I absolutely deny that E is defined as equal to Y or that I is defined as equal to S. Look at the Keynesian cross and tell me where you see E defined equal to Y. If that were the case, all you would have is a 45-degree line. The only equality between E and Y, or between I and S is the equality associated with an equilibrium condition. Any reference to an accounting identity between I and S can only mislead. I agree that many textbooks pay absurd lip-service to the notion that there is an identity between I and S or between E and Y, but they usually avoid any explicit argument based on such an identity and restrict themselves to arguments in terms of equilibrium solutions. But you are right, I am just as upset with everyone else as I am with you. You just had the misfortune of making an explicit argument using the I = S identity which caught my eye and got me started on this tirade.
Specifically on Wren-Lewis, he follows the convention of an ex post identity between I and S, but he tries to avoid the absurdity by stating the equilibrium condition in terms of planned saving and planned investment. He introduces the totally unnecessary and confusing unintended inventory adjustment as the means for achieving ex post equality as if it was necessary to provide an economic mechanism to ensure that a tautology is satisfied. (Is there an economic mechanism operating to ensure that M = Y/M?) As I recall you stated explicitly that saving is spending on capital goods. That’s taking the identity to a higher level.
You said:
“Indeed if you were correct, [Wren-Lewis’s] “proof” would be nonsense, but for different reasons that I claimed it was nonsense. Think about it. He claims if C falls by less than G rises, then Y must have risen. But why?”
If C falls by less than G, then at the moment the change occurs, E > Y. In the income-expenditure model, when E > Y, Y rises. When Y rises, E rises, and the process continues until E and Y are again equal at a new higher level.
“If you are right that identities are irrelevant, then what possible reason would there be for us to assume that Y has increased, just because C fell by less than G increased? Isn’t there an identity looming in the background of that claim?”
No identity. Just an equilibrium condition.
You asked:
“Suppose I defined Chinese exports to America as Chinese goods that are successfully shipped to America. And I defined American imports from China as goods successfully shipped from China to the US. Would you object to me claiming that those two quantities are equal by definition?”
Chinese exports are the same physical thing as American imports, so it’s perfectly natural to say that they are identical. Savings is income not spent by households and investment is spending undertaken by businesses, so, on their face, they are different physical magnitudes. In the income-expenditure model, the equality of the two magnitudes is the condition for the model to be in equilibrium.
Scott, I didn’t mean to imply anything about Noah Smith’s post in relation to you. I just was referencing Brad DeLong who linked to Krugman who linked to Noah Smith. I’m sorry if I made it appear otherwise. I don’t know why you think that I ever assumed that S = I is an identity. Can you give me an exact citation? I use I = S as an equilibrium condition not an identity.
Here’s what Karl Smith said:
“The 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 –1 so that the multiplier would be zero.
This is supposed to motivate you to tell me why I can’t do that.”
You said:
“Wren-Lewis claimed that saving fell, and yet his model assumes that investment is constant. That’s Karl’s point. That’s a contradiction if S=I, an identity Wren-Lewis acknowledged he accepts in a later post.”
It’s not his model, it’s the simple income-expenditure model, and with a fixed level of investment expenditure exceeds income, raising income and expenditure until a new equilibrium is reached at which income and expenditure are equal at a new higher level with savings again equaling investment. This is the point that you don’t seem to understand and this is where you are reasoning in terms of an identity rather than the equilibrium condition of a model. I agree that Wren-Lewis, following decades of bad precedent, mistakenly acknowledges an ex post identity between savings and investment relying on misguided notion of unintended inventory investment, but he wisely does not allow that identity to affect his solution of the model. When it counts, he properly disregards the identity. You, on the other hand, focus on the identity and forget about the equilibrium.
You said:
“You seem to be implying that I believe that if people try to save less, then investment must decline. But I never said anything of the sort, nor do I believe that to be true. What I said is that if actual saving declines in the new equilibrium, then actual investment must decline. And Wren-Lewis agrees with me on that point. So I think you misunderstood my argument.”
I must have misunderstood. But you seem to be interpreting Wren-Lewis to mean that the quantity of savings would go down in the new equilibrium rather than that the savings schedule as a whole shifts down. His original argument was pretty vague and qualitative, so I don’t know how you can be so sure what he meant.
Scott, The statement that Brad quoted was from my previous post “Why Am I Arguing with Scott Sumner?” Here’s one passage that I found problematic.
“First recall that C + I + G = AD = GDP = gross income in a closed economy. Because the problem involves a tax-financed increase in G, we can assume that any changes in after-tax income and C + I are identical. Checkmate in four.
Suppose that because of consumption smoothing, any reduction in after-tax income causes C to fall by 20% of the fall in after-tax income. Then by definition saving must fall by 80% of the decline in after-tax income. So far nothing controversial; just basic national income accounting. Checkmate in three.
Now let’s suppose the tax-financed bridge cost $100 million. If taxes reduced disposable income by $100 million, then Wren-Lewis is arguing that consumption would only fall by $20 million; the rest of the fall in after-tax income would show up as less saving. I agree. Checkmate in two.
But Wren-Lewis seems to forget that saving is the same thing as spending on capital goods. Thus the public might spend $20 million less on consumer goods and $80 million less on new houses. In that case private aggregate demand falls by exactly the same amount as G increases, even though we saw exactly the sort of consumption smoothing that Wren-Lewis assumed. Checkmate in one.
Those readers who agree with Brad DeLong’s assertion that Krugman is never wrong must be scratching their heads. He would never endorse such a simple error. Perhaps investment was implicitly assumed fixed; after all, it is sometimes treated as being autonomous in the Keynesian model. So maybe C fell by $20 million and investment was unchanged. Yeah, that could happen, but in that case private after-tax income fell by only $20 million and there was no consumption smoothing at all. Checkmate.”
When I responded to this passage in my earlier post “I Figured Out What Scott Sumner Is Talking About,” I made the assumption that to keep income constant it was necessary to assume that private investment fell by an amount sufficient to keep income from rising after the increase in government spending and taxes. I now think that was the wrong strategy. Lucas’s assumption that there is a dollar for dollar reduction in private consumption means that the MPC is 0. So my assumption that it was a reduction in private investment that held income constant was not the right one to capture what Lucas was thinking about. Nick Rowe had the right intuition, and got the right result that the multiplier for temporary government spending would be between 0 for a permanent increase in spending and 1 for a momentary increase in government spending. You get a smaller multiplier than is implied by the conventional Keynesian model, but it’s bigger than the Lucasian multiplier of 0.
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David –
I really should clear this up. I do NOT think that Scott was trying to make an “argument from accounting identity.” In the first post where he mentioned S=I, Scott was obviously *not* trying to claim that S=I implies a fiscal multiplier of zero. He was using S=I to help him demonstrate that consumption smoothing does not imply the smoothing of total private expenditure. That point is correct. It was not an argument from accounting identity, but rather the use of an accounting identity to illustrate the difference between two concepts (smoothing of consumption and smoothing of total private expenditure), and thus does not violate my Principle #4
Best,
Noah
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S=I David, We’ll just have to agree to disagree on the S=I question. But I strongly disagree on the statement that Brad quoted. The passage you just provided not not involve me making any such error, as I MAKE NO CLAIM AT ALL ABOUT THE ACTUAL SIZE OF THE MULTIPLIER (sorry for the caps, but I want to emphasize this point. I’m perfectly happy conceding that S=I is consistent with a multiplier of 1, or zero, or any other number. Indeed I provided two examples in my critique of Wren-Lewis, a multiplier of 1, and one of zero. Either one could occur. And I showed that if it were zero, he was wrong to criticize Cochrane ,who also claimed it was zero, and if it were one then there was no consumption smoothing, as C and I didn’t change in equilibrium. I think most people now accept that. I didn’t mention other multipliers, like 1/2. But if it were 1/2, then he would have been wrong to ignore the change in saving and investment in his critique of Cochrane.
You say that Wren-Lewis was right to claim that an increase in G+C was the change in AD in equilibrium. I think that’s wrong if C changed and there was also consumption smoothing. Because a change in C, plus consumption smoothing, implies that S and I also changed in equilibrium.
I also disagree with your comment about household saving and business investment. Investment includes household investment (which is huge) and saving also includes business saving (which is huge.)
Again, definitions are definitions. It’s not a matter of right and wrong, but useful and non-useful. The textbook definition may not be useful, as you seem to claim, but it certainly can’t be viewed as wrong, if there is no conceivable act of aggregate saving that doesn’t result in identical investment. If an act looks like household saving (say putting the money in the bank) but does not result in an immediate investment, then it’s not really saving in an aggregate sense, rather it’s a loan of money from the household to the bank. No net national saving in that case.
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Scott and David,
I think you are both missing something crucial here. dS (change in saving measured in dollars) may equal dI (change in invesment measured in dollars) but it is rare that Savings = Investment across the time continuum. The reason is very simple – the value of an investment may change independently of the savings used to finance it.
Meaning that it may initially cost $1 million to inititally construct the bridge, but that does not mean the bridge is worth $1 million 20 years from now (or even 6 months from now). It may be worth more or it may be worth less.
Or another way to look at it is, what happens if $1 million is not used to construct a new bridge, but instead to tear down an existing bridge? In that case, the rubble that is left is surely worth less than the money used to create the rubble.
The reason that S = I is wrong is that it tries to hold the value of the investment fixed to match the fixed value of the savings.
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Hoo boy. Market Monetarists are smart, but movement-wise, you are dunderheads.
Market Monetarists are currently drowning in a whirlpool of side-arguments—-even after Krugman allowed that monetary policy could snuff out fiscal stimulus (obviously).
At that point Market Monetarists should have built a platform with Keynesians on board, on the practical position that smaller fiscal stimulus is needed if monetary policy is aggressive.
Market Monetarism will ramp up fiscal stimulus, thus requiring less deficit spending (and hopefully none).
Instead the MM movement is lost (temporarily I hope) in a sea of acrimony.
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David,
I simply cannot find any way of thinking about things where Y does not = E. Can you give an example of how that can be ?
I can see easily how S may not equal I (you simply need to have either some investments coming out of cash holdings, or some some savings going into cash holdings) but even when S does not equal I, I think Y still equals E (Y and E will both go up or down by the amt that the cash balances decrease/increase).
When individuals have lower post-tax income they can rearrange between consumption and savings, or they can consume more than they earn by dipping into cash balances.
In a non-Keynesian model the switch to more consumption will tend to depress investment, but the increased velocity of money if cash holding are reduced to fund the increased consumption may spur additional investment as supply increases to match the higher demand.
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Benjamin, you have to remember that we are nerdy economists. We live for these discussions (even though this particular one is not too interesting to me…). Unlike the policy makers the Market Monetarist bloggers actually insist on understanding what we are advocating. Only by debating – also with each other will we really understand.
But agreed…I am also getting pretty tired of this discussion;-)
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Rob, I don’t follow your discussion of Wren-Lewis. You are being distracted by irrelevant discussions about some adjustment process. All that matters in this model is the final equilibrium. Inventory adjustment doesn’t matter to the final equilibrium.
Noah, When I mentioned your blog in passing, I didn’t mean to attribute to you any position regarding Scott’s argument. I looked quickly at your post earlier and found no reference to Scott, so I made no assumptions about what you were thinking. I take a harder line on identities than you do. All identities are good for is to check that your arithmetic is right. Otherwise, an accounting identity provides no substantive information about the behavior of a model.
Scott, What bothered me was your assertion that if consumption went down by 20, then savings would go down by 80 which would mean a reduction of investment by 80 because reduced savings leads to reduced investment. You have to find equilibrium income first and then you can infer what happens to savings. You just seemed to be pulling numbers out of the air and drawing conclusions about them without showing that you were talking about an equilibrium.
A change in C with consumption smoothing implies that income rises. Isn’t that the point? Nick Rowe also found that income rises with consumption smoothing.
Are you sure that household investment is treated as investment rather than consumption in the Keynesian model? Business saving is a category in the national income accounts not in the Keynesian model in which saving is undertaken strictly by households. But I could be wrong.
I did not say that any definition was wrong. What I did say was that certain definitions don’t fit with the structure of the Keynesian model. And a definition that treats saving as the same as (or identically equal to) investment is at odds with the logic of the model which is that the equality of savings and investment is a condition of equilibrium not an identity. Therefore you can’t assume that any saving by households is the equivalent of spending on capital goods, which is a claim that I think you made.
You said:
“if there is no conceivable act of aggregate saving that doesn’t result in identical investment.”
Either I completely misunderstand what that means or it is totally wrong even under a very liberal interpretation of the verb “result in.” How could you possibly tell if an act of household saving (putting money in the bank) does or does not “result in” an immediate investment. And why would the identical act by a household be categorized differently depending on what that bank rather than the household decided to do with the household’s money?
Frank, The Keynesian model does not directly take into account capital gains or losses on existing assets. Those capital gains or losses may be significant, for example affecting consumption decisions by households that have been either enriched or impoverished by changes in the value of their assets.
Benjamin, I knew you would be upset by this little dust-up. Just think of it as a minor distraction on the road to the future Market Monetarist Majority.
Rob, Suppose households decide to buy more stuff. They go to the stores and spend more (expenditures rise) and businesses produce more. The revenue of business firms rises, but they don’t pay workers any more, workers salaries being fixed in the short term. Perhaps they have to hire more workers or pay overtime, but it is safe to assume that the incomes received by households from businesses don’t increase immediately to match the increase expenditures by households and receipts by business firms. Over time, increased expenditure will make its way back to households and as it does households will further increase their spending. So during the period of adjustment to the new equilibrium level of consumption, expenditures and incomes will rise but expenditure will run ahead of income. Gradually income will catch up to expenditure and the rise in expenditure and income will cease and income and expenditure will equal each other and will remain stable until there is some other disturbance to equilibrium.
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David,
I don’t understand your response to my comment. I was just agreeing with you that I does not always equal S (and describing a situation where this would be the case) and asking for clarification on where E may not equal Y as I still can’t see how this can be.
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“Frank, The Keynesian model does not directly take into account capital gains or losses on existing assets. Those capital gains or losses may be significant, for example affecting consumption decisions by households that have been either enriched or impoverished by changes in the value of their assets.”
David,
What you are describing is a balance sheet recession – what we are still going through. And the way the federal government gets an economy out of a balance sheet recession is to sell liabilities with a high real value. Those federal government liabilities become private sector assets. This is what is missing from the Keynesian model – double entry bookkeeping and capital markets.
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David Glasner you said, ” I use I = S as an equilibrium condition not an identity.”
I think I agree with you on the main point, I don’t like this definition of savings as spending on capital goods either. However you lost me on the quote above-what is the difference between and equilibrium condition and an idenitty?
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Mike,
An equilibrium condition is different from an identity in terms of stability.
Imagine a ball perfectly balanced at the top of a peak. It has reached a position of equilibrium, but there are forces operating on it that are trying to push it out of this state. When it is perfectly balanced, those forces counteract each other, but the introduction of another force (wind, earthquake, etc.) quickly takes the ball out of its current state of equilibrium to a state of motion.
And so, dS (change in savings) can equal dI (change in investment) over short time periods, but whether S = I holds depends on how unstable the value of the investment is.
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I think the Keynesian cross has a path to equilibrium implicit within it.
Imagine the cash flows in an economy – income->expenditure->income and so on. At each point individuals hold cash balances defined as funds neither consumed not invested. Cash balances will change whenever income differs from the expenditure in the next step ( For example: If income of 10000 is followed by spending of 9000 then cash balances have increased by 1000). Savings (S) is defined as any money that an individual does not consume from income.. If any of these savings do not become investments then they will get added to cash balances. Cash balances change whenever I does not equal S.
The 45 degree line then just shows that as cash balances (defined as above) decrease so AD (and S and I) must increase. At any point on the line where AD=Y then it is easy to see that S=I also.
Each point on the “Aggregate Demand” can be broken down into I and C. If a changed consumption function causes C to change then the process back to a new equilibrium as follows:
At each given level of AD the composition between I and C changes. As a result, at the starting AD then I can no longer be equal to S. If I is no longer = S then money must move in or out of cash balances (as explained above) which will cause AD to rise or fall as the money from the cash balances is spent. As AD changes Y moves with it until we get to a level of Y where I = S and (as its assumed in the consumption function) I will be at its initial level.
In more detail: Assume C increases and S decreases causing I > S. There will spending from cash balances. Each item bought with money from cash balances will cause Y to increase , If at this higher level of income there is still excess cash balances (because I still does not equal S) then more things will be bought from cash balances until excess cash balances are eliminated at the point where I=S again. The only time lag will be how long it takes to spend sufficient money to bring cash balances down. The effect that this process will have on RGDP Is indeterminate but as AD has increased but I stayed he same one suspects some inflation.
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Rob, That’s just what I was trying to explain. An increase in consumption expenditures by households does not identically equal an increase in household income. Expenditures by households on the stuff sold by businesses are constituted by a different set of transactions from those by which households derive income from the sale or rental of productive services to businesses. In equilibrium (with unchanging income and expenditure) even though the magnitudes are not identical they are equal. But in the course of moving from one equilibrium to another expenditure and income will not be equal. Income tends to lag slightly behind expenditure.
Frank, Surprise. I actually agree with you.
Mike, An equilibrium condition describes a situation in which two different magnitudes are in balance with no tendency for either to change. But the whole point of an equilibrium is that it is special, there are opposing forces that are just in balance. If you say that two magnitudes are identically equal, then the notion of an equilibrium in which opposing forces have achieved a balance is ruled out by assumption. Think of the water level in a bath tub. It is in equilibrium if it is constant. The water level (forget about evaporation) could change either because water is going down the drain or because water is pouring in through faucet. If the rate of flow through the drain equals the rate of flow through the faucet, the water level will be in equilibrium. Now if water going down the drain is recycled back into the faucet, the equilibrium will tend to be preserved. But if the recycling process takes time, there may be periods of time when water is flowing out faster than it is pouring in and the water level will be changing Frank provides another very good example of what equilibrium means.
Rob, I think that you are basically on the right track. The Keynesian cross suppresses asset (including cash) holding. But it is definitely in the background and to tell the story adequately you need to bring assets into the picture.
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David,
Just wanted to thank you for running this blog and your diligence in responding to comments (which in my case sometimes have a tendency to be just “thinking aloud” and drift off-topic – a habit I will try and address in the future.)
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Rob, Thanks for your kind words. Remember also that part of the fun of blogging is the freedom to think out loud
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