Update: Continue reading, but then go to my next post to find out how it all turns out in the end.
Signs of fatigue are clearly evident and multiplying rapidly, so we had all better figure out and start executing our exit strategies from this convoluted, and at times acrimonious, debate about consumption smoothing. Things got started (two whole weeks ago!) when Simon Wren-Lewis picked on Robert Lucas for the following statement:
But, if we do build the bridge by taking tax money away from somebody else, and using that to pay the bridge builder — the guys who work on the bridge — then it’s just a wash. It has no first-starter effect. There’s no reason to expect any stimulation. And, in some sense, there’s nothing to apply a multiplier to. (Laughs.) You apply a multiplier to the bridge builders, then you’ve got to apply the same multiplier with a minus sign to the people you taxed to build the bridge.
and on John Cochrane for this statement:
Before we spend a trillion dollars or so, it’s important to understand how it’s supposed to work. Spending supported by taxes pretty obviously won’t work: If the government taxes A by $1 and gives the money to B, B can spend $1 more. But A spends $1 less and we are not collectively any better off.
Wren-Lewis made the following accusation:
Imagine a Nobel Prize winner in physics, who in public debate makes elementary errors that would embarrass a good undergraduate. Now imagine other academic colleagues, from one of the best faculties in the world, making the same errors. It could not happen. However that is exactly what has happened in macro over the last few years.
Paul Krugman followed up with a blast of his own at both Cochrane and Lucas, and John Cochrane weighed in, defending himself and Lucas. The battles among the principals were accompanied by various interventions on either (or neither) side by Brad DeLong, Scott Sumner, Nick Rowe, Karl Smith (to name just a few) and by responses and rejoinders by Cochrane, Wren-Lewis and Krugman. I got involved mainly because I was upset that my friend Scott Sumner seemed to be making arguments invoking accounting identities in ways that I thought were illegitimate and even nonsensical. Scott, though apparently intervening on the side of Lucas and Cochrane, denied that he was supporting their substantive position, a denial that I, though apparently intervening on the side of Wren-Lewis and Krugman, also made.
I am not going to repeat my previous arguments against Scott, which mostly involved denials that any useful implication can be inferred from an accounting identity. I will merely reiterate that I hate – despise — all accounting identities, and deny that they can ever have any substantive implications about anything, serving only one function, namely, to force us to obey the laws of arithmetic. OK, I got that out of my system, and now I feel well enough to go on.
The key passage that we have all been arguing was this one from Wren-Lewis’s original post:
Both make the same simple error. If you spend X at time t to build a bridge, aggregate demand increases by X at time t. If you raise taxes by X at time t, consumers will smooth this effect over time, so their spending at time t will fall by much less than X. Put the two together and aggregate demand rises.
But surely very clever people cannot make simple errors of this kind? Perhaps there is some way to re-interpret such statements so that they make sense. They would make sense, for example, if the extra government spending was permanent. The only trouble is that both statements were made about a temporary fiscal stimulus package.
My next step is a bit tricky because I am going to have to refer to Scott’s criticism of Wren-Lewis, which, I must admit, I still do not fully understand. But the gist of at least part of what Scott was trying to say — and he, as well as Karl Smith, has repeated it in responding to me several times — is that Wren-Lewis was trying to force Lucas and Cochrane to accept the validity of the Keynesian model, when they simply don’t accept the model. My basic response to that has been that you can’t have a discussion about the effects of a policy unless you have some (at least implicit) model from which you are deriving your conclusions. It is not enough to invoke an accounting identity from which no conclusions (as Scott agrees) can be deduced. My first attempt to specify some model from which we could deduce the position adopted by Lucas and Cochrane was not too successful. I suggested that what they had in mind was some sort of crowding-out effect, the increase in government spending and taxes causing private investment to fall. I then combined this effect with a consumption-smoothing effect to produce a small short-term increase in Y as a result of building the bridge. This was unsatisfactory, because it was ad hoc, and because, as commenter John Hall pointed out, the change in consumption ought to (and could) have been derived rather than just assumed as I had done.
But I realized when responding to Scott’s comment on my previous post, that there is a simple way to reconcile what Lucas and Cochrane are saying with the basic Keynesian model, which, after all, is just a tool of analysis compatible with a variety of substantive assertions about the real world. So it is not correct to say that it is an unfair imposition on Lucas and Cochrane to require their position to be expressed in terms of a Keynesian model that they obviously reject. The Keynesian model is pretty flexible, and, by appropriate assumptions, you can get almost any substantive implication you want. So how does one interpret Lucas and Cochrane? Simple. They believe that households are rational maximizers basin their consumption decisions on their expected future income stream and expected future tax liabilities. They therefore engage in consumption smoothing, so that current consumption is fixed and independent of variations in current income, such variations being capitalized into their expected future income streams. Thus, the MPC out of current income in such a model is 0.
In terms of the Keynesian cross, you have an aggregate expenditure line that is horizontal (reflecting a 0 MPC). The multiplier with respect to a change in autonomous expenditure is one. However, since all government spending must be financed eventually by taxes, Ricardian equivalence implies that the increase in G is offset by an equal reduction in C, reflecting the effect on consumption of expected future taxes. That is precisely what Lucas and Cochrane were saying in the quotations above. Wren-Lewis, in his criticism, accepted that position. His point was that if the increase in government spending is temporary, the increase in government spending in the current period will rise by more than the fall in consumption this period due to the effect of expected future taxes (or borrowing this period to pay part of the current tax bill). This is not necessarily the end of the story (though, with a bit of luck, perhaps it will be), but this is the framework within which the argument must be carried out. It has nothing to do with accounting identities.
PS By the way Nick Rowe apparently had this all figured out almost two weeks ago. He could have saved us all this agony. But the truth is we loved every minute of it.
Uneasy Money 
Scott will be here shortly to tell you that you have missed the point. He will probably say that you, like Simon Wren-Lewis, have failed to mention investment. He will pass over the fact that Lucas and Cochrane didn’t mention it either.
At times I’m reminded of Big Arnie as the Terminator: “It can’t be bargained with. It can’t be reasoned with. It doesn’t feel pity, or remorse, or fear. And it absolutely will not stop….”
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My bad, you did mention investment; but that won’t get you off.
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I really wish a good economist and communicator would start journaling the economic blogwars so the general public can understand what is going on. I mean, let’s be honest, sometimes, it feels as though telepathy is needed to understand what some people mean. But those arguments are supremely relevant to policy and it would be nice if the public at large learned what we are all learning. How many people do you think heard of the outcome of the Great Public Debt War of Early January 2012? A lot more than would have if you guys were arguing in journals, but still. Not enough.
@Kevin Donoghue:
As much as I love Scott’s blogging, I have to admit to say this really does sound like Scott Sumner. You have to imagine Arnold Schwarzenegger saying the following: “Targetting NGDP…” “Adopting Monetary Stance…” “NGDP Futures Market on Target…”
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David, Aren’t we back to square one? Where is the fall in investment, which would have to occur if there was consumption smoothing, AND if C fell, AND if we assume a balanced budget (as Wren-Lewis did)? It seems to me that you are repeating Wren-Lewis’s mistake here.
I interpreted Cochrane as arguing that private spending (not consumption) would fall by as much as G increased. Indeed right-wingers are obsessed with “crowding out” of investment, so I can’t even imagine how someone could assume they were holding I fixed and having all the adjustment in C. I think we all agree that consumers smooth consumption.
You say identities are only useful for showing someone got the math wrong. I say Wren-Lewis got his math wrong. The change in AD is the change in C+I+G, not the change in C+G. Yes, he could assume that I didn’t change, but then there’d be no consumption smoothing. So either his math is wrong, or there is no consumption smoothing.
BTW, I have a new post with some good quotes from Noah Smith.
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Based on David’s post:
Taking an extreme case of consumption smoothing so that current C stays the same no matter what the current Y, then all the components of AD (G, I and C and T) are fixed and the AD curve is a horizontal line. This means that when the govt spends its money it will simply have the effect of adding the full amount to both AD and Y (even though the G is fully funded by T) and we will have a new equilibrium to reflect that.
I think one has to accept an assumption that I is fixed for this to make sense. S will fall as a result of the consumption smoothing so I must be funded from money that was not previously being spent (ie from previously uninvested cash balances). As these cash balances are spent so AD and Y both increase. In the extreme case of consumption smoothing where the AD curve is flat this will be for an amount exactly equal to the tax.
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@Scott Sumner:
It seems to me this is all about money hoarding.
y = c + s
(y is my income, c my consumption, s is whatever I didn’t spend)
So
y = c + s
So now, there is a lump-sum tax t (since lump-sum taxes are the only ones that exist) and I smooth my consumption over let’s say 3 periods just to make things easy. (prime stands for ‘given the tax’)
y’ = y – t
c’ = c – (t / 3)
y’ = c’ + s’
So you solve for s’ = s – (2t / 3)
OK, so now we say that s = i + h (i is capital goods purchases while h is money hoarding) So now, the consumption smoothing is done partially by reducing your building of capital goods, but also by reducing your money holdings.
So now we aggregate. C falls by (T/3), but I falls by less than (2T/3). G goes up by T and so Y’ = C – (T/3) + I – ( 0. And voila, we get paradox of thrift, positive multipliers and all the Keynesian goodies.
What am I missing?
PS: I really want to be missing something because I really hate that result.
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I meant Y’ = C – (T/3) + I – ( < 2T/3 ) + T (since T = G)
as the last equation. I don't know why that didn't show up correctly.
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Scott: “Yes, he could assume that I didn’t change, but then there’d be no consumption smoothing.”
There’s the problem, Scott. You assume that consumption-smoothing means I changes. For Simon Wren-Lewis, consumption-smoothing merely means that consumers optimize in modern textbook fashion. (If I knew how to put an infinite-sum utility function in the comment box I’d do it now; please just take all that sigma-for-t-from-zero-to-infinity stuff as read.)
Consumption-smoothing (in the Wren-Lewis or textbook sense) does not require any change in C or I. Consumption-smoothing (in the Sumner sense) does require that. You are simply speaking different languages.
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In case that’s not clear: consumption does not change, according to Wren-Lewis, because optimal consumption does not change. That (if I understand his Oxford English correctly) is what consumption-smoothing means.
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Kevin, I may be confused, but right now I think, as you can see from my follow-up post, that without an MPC greater than zero, the Lucas argument can’t be refuted by consumption-smoothing. But if consumption smoothing implies an MPC equal to 0, then his result seems solid.
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Kevin,
I am on board with your statement, if you want to assume all agents are the same, but I would suggest considering separately what happens to the bridge-builders relative to everyone else.
There is actual actual consumption smoothing, because the bridge-builders are loaning money to the other taxpayers. It just washes out, leaving aggregate consumption and disposable incomes unchanged.
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D R,
You could approach it that way. But, if I were responding to Lucas and Cochrane, my point of departure would be Cochrane’s remark: “it’s important to understand how it’s supposed to work.”
If I start from there, what I need to do is show Lucas and Cochrane that “respectable” theory leads to BBM = 1 in a conventional, infinite-horizon utility-maximizing setup with Ricardian equivalence. For that purpose it’s better to think in terms of a representative agent, since that’s the shared language of New Keynesian and freshwater theorists.
Of course, the discussion is going nowhere because (a) Scott Sumner keeps dodging the fact that Cochrane is, by his own account, trying to explain a model in which stimulus actually does work; and (b) Cochrane himself seemed to forget about what “it’s important to understand” almost as soon as he set himself to explain it.
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Kevin,
I’m not arguing. I’m happy someone else seems to understand. I only think it’s useful for dealing with that dodge that there is no change in disposable income, and therefore no smoothing.
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Kevin, No need to apologize, we are all improvising. I think we are having trouble at least partly because we aren’t making clear all of our implicit assumptions, so we aren’t controlling for everything that can change. But I must admit that I still have to sort things out.
PrometheeFeu, This is a work in process, at least for me. I got involved because Scott pushed a button when he invoked an accounting identity as if that could prove anything about a theoretical model. So for the time being, I think it is premature to think about any implications for this discussion which is operating, for the most part, at a pretty high level of abstraction.
Scott, If you interpret consumption smoothing as households deciding how much to consume in the current period based on their expectation of permanent income, all changes in income in the current period can be treated as transitory and therefore result in corresponding changes in saving, making the MPC equal to zero. In that world, if you have an equilibrium in the current period that for some reason is below full employment income, one has to ask what is the correct assumption to make about households’ consumption in the current period. Do they treat equilibrium income in the current period as permanent income or do they treat equilibrium income at full employment in the next period as permanent income. If the former, then you can get an equilibrium with at the current income level, but that seems inconsistent with the assumption that long-run full employment equilibrium prevails in the future and that households are smoothing consumption based on that expectation. On the other hand, if consumers are consuming now based on the expectation of future income is at the full employment level, then why is current income less than full employment in a simple model with no investment and foreign trade sector and a balanced budget. So I don’t know how to set up a model that simultaneously corresponds to all the assumptions that we are trying to make here. My head is hurting me.
More responses to other comments will follow later.
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“If you interpret consumption smoothing as households deciding how much to consume in the current period based on their expectation of permanent income, all changes in income in the current period can be treated as transitory and therefore result in corresponding changes in saving, making the MPC equal to zero.”
This seems to assume that “all changes in income in the current period” also do not change “expectation of permanent income.” If the government takes from A to give to B in the current period, it seems A’s current and permanent incomes rise, while those of B fall. In an effort to smooth consumption by a factor of F, B loans some of the money back to A. We find the MPC=1/F.
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Whoops. Obviously, A’s income falls and B’s rises…
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Scott, A lot has happened since I read your comment, and I got myself all tied up in knots. To respond again, there is no reduction in savings because income keeps expanding with reduced saving (and increased spending) until incomes rise to fund investment with saving. Now Lucas and Cochrane could still reject the model, but not on the basis that the increase in government spending is matched by an increase in taxes either now or in the future, because that result only follows for permanent equal increases in government spending that must be funded by matching taxes that must be paid now or must generate savings now to pay for them in the future. Crowding out could occur, but that argument only works for an increase in government spending sufficiently large to cause a significant increase in Y. In the neighborhood of the initial equilibrium at least you can ignore crowding-out effects. As I showed in my post yesterday going through the exercise for a two-period model, if I doesn’t change, there is consumption smoothing between the two periods. Consumption is equal in the two periods, so there is smoothing.
Rob, The point is not that current consumption doesn’t change but that consumption after the increase in government spending and taxes is equal in the two periods of a two-period model, which is what I showed in yesterday’s post. What you left out is that the consumption line has to shift to reflect the adjustment in desired consumption based on the current period tax obligation that won’t exist in the next period.
PrometheeFeu, There is a depletion of assets in the current period to finance an increase in consumption. Any increase in income is saved once consumption plans have been revised to reflect the increased tax liability in the current period only. So saving s increase dollar for dollar with the increase in current period spending.
Kevin, There is an ambiguity here. Consumption in the current period does change relative to the equilibrium in the absence of increased government spending. But reoptimization is based on an equality of consumption between this period and succeeding periods. My initial response to you was completely wrong because I confused myself about what the MPC is. I forgot the distinction between a movement along the consumption line which is horizontal given that MPC = 0. However, the increase in taxes in this period induces a reoptimization that caused the consumption line to fall, but by less than the increase in government spending. The corresponding decrease in savings implies a net increase in aggregate spending that is saved funding the planned investment that is assumed not to change. (But as pointed about to Scott above, for sufficiently large changes it would be hard to argue with a straight face that there is no effect on interest rates and investment).
D R, Good point about the distributional effects, but aggregate consumption does fall because even the bridge builders are hit with an increase in taxes. The previous reply to Scott which you quoted is withdrawn.
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