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"And don't say that anyone else has got it wrong until you say what your implicit benchmark assumption is and what his implicit benchmark assumption is."

I'm afraid that commandment gives an unfair advantage to the guy who won't say what his assumptions are. For that reason the anti-obscurantists will find it necessary to say things like: you may be assuming A or possibly B, but either way you're wrong.

Can you summarize briefly how an open versus closed economy affects the balanced budget multiplier?

Great stuff. Seems to be another example of traditional macro oversimplifying things. And, as often is the case, it oversimplifies things in a manner that common sense would suggest might be problematic: Does it matter what the government spends on? Yes. Of course, one needs to be an expert on these complex models to find their mathematical faults!

Kevin: Hmmm. You have a point. But, you could say instead: "You haven't made explicit your implicit assumption, and nobody should take you seriously until you do!"

Notice by the way how I worded my bit about the implicit Keynesian assumption. My original draft accused Keynesians of implicitly assuming government expenditure is useless. Then I edited it to read: "If Keynesians were implicitly assuming that government expenditure is totally useless, that assumption would give you standard Keynesian multipliers, but maybe other assumptions would too."

JKH: "Can you summarize briefly how an open versus closed economy affects the balanced budget multiplier?"

An open economy will generally have a smaller multiplier than a closed. Depends on the exchange rate regime too.

Ken: thanks! Yep, we sometimes get so caught up in our Celestial Emporium that we don't see things that aren't in the taxonomy.

Nick, excellent post. A good way to start the morning. Thanks!

Kevin: I think some sort of strong separability assumption might also give you standard Keynesian multipliers, but I can't quite get my head around it.

I suppose that if you asked the early Keynesians what they were assuming about just what goods G consists of in their models, they would say it's a public good of some sort. Surely that would be Samuelson's answer? (Yes, I do remember his objection to sentences like that; it doesn't stop me writing them.) So probably the most natural assumption is that C and G are complements. The utility I derive from my bicycle would be considerably increased if I lived closer to the Phoenix Park.

Kevin: I would say your bike is more like I, not C, in which case we get a bigger multiplier. Suppose instead it really is a C. You buy a new bike every year, and it wears out from you riding it in the park. Then G is a complement to both current C and future C. It increases the MU of both. So it doesn't make you want to consume more today (it doesn't affect the MRS between present and future C).

(Isn't a park land? If so, the government buying land does not count as G at all, since it's not a newly-produced good. That would reduce the multiplier, or even make it negative).

But yes, it matters a lot what the government buys. And some sort of publicish good makes sense. (What was Samuelson's objection?)

I am still not sure of the time variable. Do the agents measure time or do they measure event sequences? An important distinction. Does the statement "When grow up", mean in ten years, or when I graduate, find a job, then get married? If bankers measure time, but agents measure sequences, then one would expect the financial crisis about every generation.

Thanks. That helped advance my understanding

Thanks Greg and David! David: see, your rabbits are breeding like mad in these comments, what with Kevin's example(s).

Matt: I think the time variable that matters is this: how long does the increased government spending last relative to how long the recession lasts? I should probably have said more about this, but couldn't get my head around it. I *think* I am implicitly (oh dear!) assuming that the increased government spending never lasts longer than the recession. (And in 4, where I look at the preponed government spending multiplier, and explicitly assume G is reduced below normal after the recession ends.)

Isn't a park land? If so, the government buying land does not count as G at all, since it's not a newly-produced good.

The expenditure on maintaining roads, cycle-paths, flower-beds and suchlike is included in G. Of course you're right that the bike is I, the consumption is a non-market activity.

What was Samuelson's objection?

"Surely no sentence that begins with the word 'surely' can validly end with a question-mark?" He was a witty bastard.

Kevin: ROFL. That was not at all what I expected. I thought I was going to get some deep or picky insight into Samuelsonian public goods!

In Keynes about 1930 it was building houses ....

In Krugman in the early 00s it was building houses ....

"I suppose that if you asked the early Keynesians what they were assuming about just what goods G consists of in their models, they would say it's a public good of some sort."

Everybody check my Update on 2b.

Nick what about the non-tax/non debt, monetary/fiscal policy. Multiplier on useful gov projects, while meeting the monetary disequilibrium. or does re, apply to printing money somehow.

Nobody should ever talk about "the" government spending multiplier without at least saying something about what that government spending is on.

What you mean is, "Nobody who believes in full Ricardian equivalence should ever talk about..." etc.

This is a fair criticism of Krugman, DeLong etc., since they have written on various occasions that the multiplier is greater than zero even with full Ricardian equivalence. But I don't think they actually beleive -- most Keynesians certainly don't believe -- in full Ricardian equivalence. So your argument from (2) on is a good debating point but is not really going to the substantive questions at stake. The substantive Keynsian argument is perfectly compatible with some consumption smoothing -- Keynes himself argued quite strongly that temporary tax changes would not be effective in shifting consumption -- but not with the strong form of the PIH you are using.

In a one-good world where Keynesian policy makes sense, the government buying you groceries does *not* lead to an offsetting fall in your own grocery purchases. Maybe you were credit-constrained, and would have moved more of your purchases forward in time if you could. (Do people experiencing temporary unemployment reduce their private consumption? Um yeah.) Maybe you don't realize, or are uncertain about, the implications of today's grocery handout for your future income. (Lucas is not the last word here.) Maybe you have routine grocery-purchasing habits, that are slow or costly to change. Etc. But the general assumption of Keynesian policy is that there is some dependence of consumption on current income as well as on permanent income.

That said, I think your argument here is useful in that it helps move the argument from whether/how fiscal policy would work in a counterfactual world of Ricardian equivalence and strong PIH, to how/whether it works in the real world.

I mean, just look at the world outside. The huge premiums people pay to move consumption forward -- credit card rates averaging 15%; payday loans; etc. -- tell us that Ricardian Equivalence is very far from a good working assumption.

"Now make one change: assume consumption smoothing (i.e. consumption depends on permanent disposable income) and full Ricardian Equivalence (so it doesn't matter whether the increase in government spending is tax-financed or bond-financed). "

The simplest way to do it would be to change ordinary Old-Keynesian equation
Y = mpc*(Y-T) + I + G
into
Y = mpc*E[Y-T] + I + G
where E[.] represents expected value function. In this transformation, mpc becomes the key variable of smoothing -- you can't just assume it equals 1 as Nick did in 2b.
If you take the expected value of both side of this equation, you obtain
E[Y] = E[I + G - mpc*T]/(1-mpc)

To conduct Comparative Statics, you compare this to
E[Y] = E[I]/(1-mpc)

Therefore, it's the estimation of E[G-mpc*T] that determines the effect of the fiscal policy. If you think E[G]=0 (or worse, E[G]<0), it surely could be negative. (Note that you don't have to resort to utility function etc in this simple estimation.)

"But government spending in this case is just a transfer payment, in kind rather than in cash. The government takes your cash, goes to the supermarket, and does your shopping for you, and gives you what it bought for you and what you would have bought for yourself. Clearly it makes no difference to anything. The multiplier is zero."

As I commented before, I think I=S theory mainly concerns GDI=GDE aspect of the "Principle of equivalent of three aspects", i.e., equation of GDP(Gross Domestic Product) = GDI(Gross Domestic Income) = GDE(Gross Domestic Expenditure). So I think, in this case, transfer payment can be safely counted in, although normally it isn't included in GDP. And the multiplier could be larger than zero in this case, if the government used all the cash which you would have partly saved.

Nick, re the Old Keynesian assumptions, specifically "the present value of taxes needed to finance that increased government spending," aren't you assuming a gold standard or some other form of hard currency? Most large, developed economies operate soft currency systems today, no?

Few economists would make a Ricardian assumption that, under a gold standard, the PV of new additions to the stock of monetary gold today would eventually have to be paid back by re-burying an equivalent amount of gold at some point in the future (regardless of duration). So why do economists reflexively make that assumption about a unit of sovereign currency that has come into existence via deficit spending?

Operationally, as far as adding to the supply of net (not gross) financial assets, a fiscal deficit it isn't much different than a CB paying interest on reserves, or even Friedman's old k% rule (side note: http://www.creditwritedowns.com/2012/01/milton-friedmans-1948-functional-finance-proposal.html). Why don't most economists argue that 100% of the dollars issued via monetary policy need to eventually be recovered via taxation?

Should CBs also have an intertemporal constraint imposed upon them?

If it's inflation, shouldn't that be the relevant one for fiscal deficits too?

"It's the implicit assumptions that get you"

Yes--which is surely a reason to do the math, rather than not? (this is basically a shorter version of my comment on your follow-up post) Yes, it's possible to make implicit assumptions even when doing math. But surely it's *much* easier to do so when reasoning purely verbally. Math may be an imperfect check on our pre-mathematical intuitions--but it's surely better than no check at all.

Which isn't to say that one can't use one's pre-mathematical intuitions as a way to alert oneself to (possible) implicit mathematical assumptions. If the math gives you a non-intuitive result, one reason might be that your intuitions are bad. The other reason might be that there's some implicit assumption in the math that you don't yet recognize.

[Posted by: JW Mason | January 17, 2012 at 12:56 PM] "I mean, just look at the world outside. The huge premiums people pay to move consumption forward -- credit card rates averaging 15%; payday loans; etc. -- tell us that Ricardian Equivalence is very far from a good working assumption."

JW, I'd argue Ricardian Equivalence is n/a to a sovereign govt (though Nick and others have claimed that RE and MMT go hand-in-hand, so I might be misinterpreting one or the other?), at least as long as there's any kind of output gap.

It clearly does apply to debtors who are mere currency users though. If my debts aren't denominated in a currency I issue, then deficits today will have to be repaid out of future consumption. The premium you point out might imply positive future income expectations. Of course, it might imply financial duress (and hope of improved fortunes), bankruptcy intentions (much harder these days in the US), flight plans, or some combination of them. But all of those could be viewed as having a Ricardian aspect to them. None of them are 'free.'

You also have to wonder how much credit demand there is at those high rates. Not sure their existence reflects on people's Ricardian or non-Ricardian tendencies. Banks' risk aversion and cruelty, definitely. :)

"An open economy will generally have a smaller multiplier than a closed. Depends on the exchange rate regime too."

Fallacy of composition. The ceteris paribus requires that all open economies engage in fiscal expansion. Otherwise it is trivial but hardly an answer to the question being asked.

JW: suppose that half the population follows Ricardian equivalence and the other half consumes hand-to-mouth. Then the multiplier is (roughly, I think) halfway between the old Keynesian and the full consumption smoothing case. So once you've done both extremes, the middle real world case drops right out, as an average.

himaginary: I think we are in agreement in your first part. But I don't get you on the second part. Why should we say that GDP has changed if I give the government $20 and it buys my groceries for me?

Art: I'm not assuming the gold standard. I am assuming the Intertemporal Government Budget Constraint, and bond-financing (not money-financing of deficits). And the IGBC only bites if the real interest rate exceeds the growth rate in the long run. That's all part of the underlying assumptions of Ricardian Equivalence, which I'm assuming explicitly.

Jeremy: sometimes the math can reveal the implicit assumptions in your intuition (it happened to me once). But just as often, your intuition can reveal the implicit assumptions (or rather, what they *mean*) in your math. That's happened to me a lot more.

Sergei: I disagree. If all countries in the world do the same fiscal expansion, the multipliier is the same as in a closed economy. The world is closed. Maybe i totally misunderstood you.

It clearly does apply to debtors who are mere currency users though. If my debts aren't denominated in a currency I issue, then deficits today will have to be repaid out of future consumption.

Not necessarily. Any unit facing interest rates below the growth rate of its income can run a Ponzi game indefinitely. Defaults can also be important. But even leaving those possibilities aside, there's no reason to think that this always or even usually is the *binding* constraint on borrowing. Some large proportion of households and firms would like to move more future expenditure into the present than the financial system allows them to. Some other large fraction of units make spending decisions based on some behavioral rules that weigh current income, wealth and some benchmark, and don't really involve intertemporal tradeoffs at all.

You also have to wonder how much credit demand there is at those high rates.

$650 billion outstanding credit card debt in the US, at an average interest rate of over 12%. So, kind of a lot. Do you really doubt that if households could borrow at the same rate as the government, they would be moving a lot more consumption forward?

Even if you grant the assumption that people know the true distribution of their future income, which I absolutely do not, PIH is irrelevant if most people can't get onto their desired curve.

I still do not get it.

What if the government only redistributed money. This should not change aggregate private income, and thus not consumption (given some assumptions), whether there is or is not consumption smoothing. Or do I get this wrong?

What if the government could find some, otherwise unemployed, people and force them to build a pyramid for free. Assume the pyramid is worth X $ to the people in the economy.

If I understand point 2 correctly, consumption will in fact decrease if there is consumption smoothening.

Why?

The argument “If government spending rises permanently by $100, then taxes also rise permanently by $100, consumption drops permanently by $100, and the multiplier is zero.” looks strange. if the multiplier is zero, the multiplier sure is going to be zero. But what if the multiplier is one – i.e. “ If government spending increase by $100 and this increase some peoples income by $100 and taxes rise by $100, consumption stay the same, and the multiplier is one.”

I am sure that I miss something obvious, but I have a hard time to identify it. I guess that it is somewhere in “2c. The longer the duration of the increased government spending, the bigger the present value of the taxes needed to pay for it,”, where I would assume that someone else is getting those taxes as income.

nemi: OK. I wasn't clear enough. Let me try it this way: it's like when you try to solve an equation by guessing that the answer is x=5, then checking to see if the equation is true when you set x=5.

Let us conjecture (guess) that Y stays the same. Then Y-T falls by $100. Therefore C falls by $100. Therefore C+G stays the same. Therefore Y stays the same. Yes! Our guess checks out OK!

(This way of solving for an equilibrium normally works fine. The only time it fails is where there are two or more possible equilibria. I am implicitly assuming there was only one.)

@Nick

But does it not work perfectly well with another guess?

Let us conjecture (guess) that Y increase by 100. Then Y-T stays the same. Therefore C stays the same. Therefore C+G increase by 100. Therefore Y increse by 100. Yes! Our guess checks out OK!

If i start out by guessing that Y change by 10000/-100/X, can i not still make the same line of argument.

nemi: yep. But there was presumably something else, outside my simple assumptions, like a Phillips curve, or productive capacity, making that original level of Y an equilibrium.

there was presumably something else, outside my simple assumptions, like a Phillips curve, or productive capacity, making that original level of Y an equilibrium

Whoa, wait a minute, you can't do that!

The entire logic of the multiplier is that government spending can raise output. If you stipulate that output is fixed, then of course the multiplier is zero. But then it's your "something else" that is doing all the work.

JW: sure. But in the long run, and we're talking about the long run in that case, it *is* only the supply-side that pins down output. And what we are trying to see is if there might be a permanent excess demand for output if government spending increased, that would require an increase in the rate of interest to equilibrate the economy. And what this shows is that an increase in G would not create an excess demand for Y, and so would not require an increased interest rate. Another way of saying this is that if it weren't for the supply-side, so if long run output were purely demand-determined, output would be indeterminate. That's normally what you get with an mpc=1 anyway.

In the short run, it's different. If a temporary increase in G causes excess demand at a given level of Y, then we know Y and/or r will increase to eliminate that excess demand.

But you and nemi were exactly right to make that critique. I've been thinking it over this last couple of hours, trying to get my head clear on it. It's exactly at the root of one of the problems of Woodford's paper. He just *assumes* that it is C that is pinned down by "something else" in the long run. So when G rises, Y=C+G must rise by an equal amount! My assumption that Y is pinned down by the supply-side in the long run makes much more sense than his assumption that C is pinned down. If C were pinned down (there's no I or NX in his model) then government spending would have zero opportunity cost even in the long run!

In the short run prices and or wages are sticky, so an excess demand for Y will cause Y to rise (if interest rates don't rise). In the long run prices and wages are flexible, so any excess demand for Y must result in an increase in r or hyperinflation.

OK, this is helpful. But the whole reason anyone talks about stimulus is the assumption that long-run output is not fixed. If you believed it was fixed, there'd be no reason to propose a stimulus.

You'd be on better footing (tho I still wouldn't agree) if you said long-run *potential* GDP was exogenuously fixed. But aggregate deviations from potential are not fixed (tho they should be negative.)

But yes, in an economy with excess capacity government spending has no (direct) opportunity costs, it's mobilizing resources that would otherwise be wasted. That's the whole point of it!

I'm not sure what you mean by "excess demand for Y"? And sticky prices are not a necessary condition for demand constraints, I think we can agree on that?

JW: people talk about short run fiscal policy, because short run output is not fixed (at "potential", though I dislike that word, precisely because you can go temporarily above "potential"). Long run is different.

JW: "I'm not sure what you mean by "excess demand for Y"?"

?? People want to buy more newly-produced goods and services than firms want to produce and sell (at existing prices, interest rates, etc.).

"And sticky prices are not a necessary condition for demand constraints, I think we can agree on that?"

That depends on the model, and on monetary policy, etc.

I would like to redeem my handle, with a semi-useful comment.

Getting rid of semantic paradoxes(like samuelson's), requires the separation of the target and descriptive language.(object and metalanguage) Tarksi.
http://en.wikipedia.org/wiki/Semantic_theory_of_truth#Tarski%27s_Theory

Yet another fun fact I've learned in my travails down here, in a bin of formalisms.

[Posted by: JW Mason | January 17, 2012 at 04:55 PM] "Any unit facing interest rates below the growth rate of its income can run a Ponzi game indefinitely."

The econ profession has co-opted 'Ponzi' in a rather dissociative way. There's nothing unsustainable (barring a significant decline in income without an offsetting net asset position) or fraudulent in this example. Not sure why it's called 'Ponzi.' In any case, if an individual or H/H (since those are the units we're talking about) could manage to continuously refinance without ever making an interest payment (a highly unrealistic assumption in the real world, and theoretically requires an infinite number of lenders who are indifferent to this action), the debt would still eventually come due, as both people and their estates are finite. At some point, someone's going to have to make good on it, and that will involve someone foregoing some amount of consumption, whether borrower or lender. I don't think you have to subscribe to the PIH to accept the fact that most individuals understand this.

"Some large proportion of households and firms would like to move more future expenditure into the present than the financial system allows them to....Do you really doubt that if households could borrow at the same rate as the government, they would be moving a lot more consumption forward?"

Agreed, and no.

"$650 billion outstanding credit card debt in the US, at an average interest rate of over 12%."

I should have said actual credit extended, which has been stagnant in the US for some time (Nov might be a turning point, although based on PDI and saving trends, some of that could be desperation-driven). Maybe it's as much a supply issue, but it's not unreasonable to think there's a demand impact from those high rates, pessimism about availability even at those high rates, changes in behaviors, etc. If you subscribe to the idea of a H/H balance-sheet recession, it seems pretty certain the demand curve would shift inward, regardless of what's happening w/ supply. And lenders have been talking about poor demand for some time now.

Nick: "I'm not assuming the gold standard."

Understood. My point is that some of the conventional assumptions are analogous to saying that, under a gold standard, all gold would eventually have to be re-buried (~"paid back"), which no one in their right mind would ever say (though perhaps those who owned and loaned gold and gold-linked currencies entertained the idea in the late 1840s and mid-to-late 1890s!?).

Sure you've heard these, so my apologies in advance. With a soft currency, net (or vertical) financial assets come about (assuming a closed economy) via:
1) CB interest on reserves
2) Int pmts on sov debt
3) Sovereign budget deficits (in a somewhat roundabout way in the US, for purely legislative reasons)

With a hard currency (let's say gold), and again assuming a closed economy, NFAs come about via additions to the stock of monetary gold.

Can we say with a straight face that the IGBC applies equally to both systems, instead of just the latter?


Nick, on a related note, I came across your attempt last April to construct an IS-LM model of MMT, thanks. This seems like an appropriate place to point out a particular aspect of IS-LM application that doesn't seem to reflect reality.

In addition to P and AD curves, the model assumes a CB "off camera," right? For example, a textbook typically says something like, "as the CB expands the money supply, it drives the rate of interest down and shifts the LM curve outward."

But with a soft currency:
(1) M is not the only form of "M" (i.e., NFAs). Interest-bearing sovereign liabilities are too. Both are analogues to specie under a gold std (of course, int-bearing sov liabilities did not constitute NFAs under a gold std).
(2) CBs don't (they can't possibly) expand the supply of NFAs under conventional operations, i.e., rate targeting, which merely shift the existing mix of NFAs. In conventional rate targeting, every open market operation is a credit transaction of some sort. No dNFA.

In other words, when IS-LM (or the LM curve specifically) implies that the rate of addition to NFAs impacts the rate of interest r, which impacts liquidity preference or similar, that's all fine and good. But we're playing fast and loose when we assume that it works just as well in reverse, i.e., "CB changes its target for r, which impacts MS, which shifts LM."

It might *look* like that's happening as long as private credit (gross financial assets?) is (are) expanding the MS. And with Baby Boomers moving through their household formation and peak earning years from the 1970s thru around 2000, it sure did. But during most of that time, the actual stock of NFAs was determined solely by net fiscal deficits (assuming a closed economy still, though incorporating the US current account would make the case even more emphatically).

Tying that back to my first question, can we still assume in good faith that only M adds to NFAs, while B just crowds out the 'competition'? And if not, what use is the IGBC, at least as currently formulated? I'm not arguing that there's no constraint on fiscal deficits (or interest pmts by a sovereign or a CB), just that the orthodox assumption that all (or any subsequent) budget deficits must be offset by taxes in the future is exceedingly rigid and (seems to me) misguided. Even under gold, which unlike soft currency NFAs *is* of finite supply, people didn't think this way.

[Posted by: Art Patten | January 17, 2012 at 11:40 PM] "the orthodox assumption that all (or any subsequent) budget deficits must be offset by taxes in the future is exceedingly rigid and (seems to me) misguided. Even under gold, which unlike soft currency NFAs *is* of finite supply, people didn't think this way."

Sorry, this was confusing. Under gold, people may have appropriately thought of govt budget deficits in this way. But they did not think of specie (which constituted the NFAs of a gold std) in the way we think about sovereign liabilities today, i.e., as having to be "repaid."

In other words, the IGBC is fine under a gold standard. But maintaining the M and B bifurcation after moving to a soft currency seems more than a little pointless and confusing.

People want to buy more newly-produced goods and services than firms want to produce and sell (at existing prices, interest rates, etc.)

OK. But the reason why I'm confused is that, in a situation where a fiscal stimulus was on the table (and in most other situations, probably, but that's neither here nor there) we generally think firms would like to sell more than they actually are selling, at the given prices, interest rates, etc. (I'm sure I've seen you write practically that sentence, more than once.) So there shouldn't be any question of excess demand, at the margin.

"If all countries in the world do the same fiscal expansion, the multipliier is the same as in a closed economy. The world is closed."

If all economies are open, and only open economies can have import leakages due to fiscal expansion, then multiplier in an open economy can not be generally lower than in a closed one. It should be the same on average.

Or the question is rather about the definition of "generally". I guess your "generally" is biased to unemployment whereas my generally is biased to the real full employment because full employment is the goal for fiscal expansion. You can not apply "full employment goal" to one country only, then assume that other countries engage in fiscal contraction and calculate multiplier of that fiscal expansion. You compare apples (expansion) to oranges (contraction).

Nick@04:38 PM:
Transfer payment is usually made from rich to poor. So, as far as the money which rich people would have saved is used for the purchase of the good which poor people couldn't have afforded previously, overall mpc goes up, and the multiplier becomes larger. In other words, the multiplier of the transfer payment could be larger than zero.

Nick at 17/01 08.52:
"In the short run prices and or wages are sticky, so an excess demand for Y will cause Y to rise (if interest rates don't rise). In the long run prices and wages are flexible, so any excess demand for Y must result in an increase in r or hyperinflation.".
Was it fast typing or do you really means hyperinflation which come not from excess demand but from a breakdown in supply?

himaginary: "Transfer payment is usually made from rich to poor."
in most real economies. transfer mostly slushes between the middle-class and the upper-lower class.

Art: "At some point, someone's going to have to make good on it, and that will involve someone foregoing some amount of consumption, whether borrower or lender. "

If we lived in a world where housing prices only went up, which was a good approximation until the most recent episode, this would not be true. Asset prices rise, borrowing rises, when time comes to liquidate, the asset is sold, pays off the borrowing, which the new owner borrows to buy it. The only consumption foregone is by some heir that inherits less than the gross estate but that is hardly foregone as it is all they could expect. The buyer may in fact be the heir. Borrowing does not necessitate foregone consumption when it is good debt.

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