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1. The fact that two models come up with the same answer in a particular case tells you nothing at all. As Majikthise and Vroomfondel pointed out, it’s not possible to determine the question uniquely if all you know is that the answer is 42. The same goes for G=4, Y=8 etc. If the models came up with the same answer in all possible cases that would be interesting, because your model is easier to solve.

2. Neither model is ‘wrong’ any more than Ricardo’s wine-and-cloth model is wrong. I don’t think your model is all that useful. I’m not sure about Woodford’s; I’d prefer something simpler and I’m sure he would too. As to whether a model incorporates money, I suspect that for any monetary model you can create, somebody can create an observationally equivalent model which is non-monetary. Would that bother you?

3. I know of no simple criterion for determining whether a model is Keynesian. Neither model is Marshallian or Walrasian, that’s for sure. Keynes would probably wonder why on earth anybody would be interested in such a question. For me, one of the funniest lines in his correspondence is: “What I am trying to say is really very simple and cannot possibly require all this exegesis.”

1. There must be a range of cases where his and my model come up with the same answer. I could change my production function and labour supply function and still get the same answer. So would he. In both cases, we always (I think) come up with a balanced budget multiplier of one as long as we hold monetary policy constant. We have different definitions of what "holding monetary policy constant" means, of course. He defines it as holding r constant and I define it as holding MV constant. Both models only work within a range (there's a maximum level of employment in his model equal to the perfectly competitive equilibrium past which firms would ration sales, just like my L=8). In fact, I'm a bit stuck trying to think of an example where our models would give different answers, though there must be some.

Plus, if you built two totally different models, and asked both models the same question, and both models came up with exactly the same answer: 42.00000, and that answer was independent of any of the parameter values in either model, wouldn't that be an incredible fluke? Only here it's 1.00000, so I don't think we have found the meaning of life. More likely, both models have simply "discovered" the same statistical artifact.

Fair enough, but there's an infinite set of models for which BBM=1 is the "natural" answer. If Y = C + I + G then dY/dG = 1 + dI/dG + dC/dG. So all you need is a set of assumptions which ensure that there is no crowding out. The Old Keynesians got that result by assuming involuntary unemployment and an obliging central bank. Woodford gets there by a different route. It all boils down to BBM = 1 <=> d[I+C]/dG = 0.

Kevin: OK. But there's an implicit assumption of monetary exchange in all New Keynesian models, because otherwise people would barter their way to the efficient level of output regardless of monetary policy or imperfect competition. Woodford's model assumes that government spending and taxes have no monetary implications, so they are like barter. My model makes both those assumptions explicit. All models that get dY/dG=1.0000 are rigged. Maybe my model just makes explicit how his is rigged?

Put it another way: in all models where the balanced budget multiplier is one, the only thing that is really happening is that the government is telling the unemployed they have to build something like pyramids that are outside the model but still counted as part of GDP. All the rest of the model, whether it's MV=PY, C=a+b(Y-T), or the whole New Keynesian shooting match of imperfect competition, Euler equations, and Calvo Phillips Curves, is totally irrelevant.

Simply redefine Employment Insurance benefits as wages the government pays you for undertaking job search, so it gets counted as G rather than a transfer payment (negative Taxes), and there's your balanced budget multiplier.

No, you can get d[C+I]/dG = 0 without invoking tyranny. There need be no telling the unemployed what they have to do. All the rulers need say is we propose to raise taxes to pay for the fleet that you bastards won't build for yourselves because of the free-rider problem. We'll have a referendum: vote Yes for taxes and a fleet, vote No for neither. Now if there are unemployed resources, C=C(Y), I=I(r) and the central bank is willing to freeze r then BBM=1.

Of course Keynesian economics leaves the politics and the composition of G out of the story. That doesn't mean that the story must be one of compulsion. It could be, of course.

Kevin: OK. You are right. But you only get strict d(C+I)/dG=0 if the thing they build has zero effect on the marginal utility of consumption and the marginal efficiency of investment. So the utility function must be separable in the fleet. Agreed. (But notice how G does not appear in Woodford's agents' utility functions, so he is implicitly assuming it's pyramids).


I have not read Woodford (yet), but let me wade in here briefly.

First, on your property [2]. C+I is defined as output that is produced and sold for "money." For a monetary theorist, you are rather vague about how you define money here. Are these transactions cash purchases? Is there another subset of goods purchased with credit? Or did you mean to define C+I as output produced and *exchanged* on a market (which is how I would define GDP); whether or not money (cash) mediated the exchange?

Second, wrt your experiment of the government conscripting labor to produce G. Note that your story here in no way relies on outdated concepts like "involuntary" unemployment or "sticky prices" or whatever. Suppose people want to work 8 hours a day, but that the government forces them to work 10. Now, in terms of GDP, what are we talking about here? It seems to me that the distinction is between actual and measured GDP.

If the output produced by this forced labor is truly worth X (people would be willing to buy it), then we add X to our measure of GDP and the actual multiplier is 1. If X is considered waste, the actual multiplier is zero; although the measured multiplier is 1.

Or have I missed something in this discussion?

David: M is cash, and C+I are purchased with cash. There is no market in which goods are exchanged for other goods (barter) or credit. People meet anonymously in the forest where it's dark and they can't see each other's faces and they buy and sell haircuts.

I wanted the model to have something that looked like Old Keynesian involuntary unemployment. Depending on the utility function, the government might be able to force them to work 10 hour days. But past a certain point people would choose to produce and consume fewer haircuts if the government makes them build more pyramids.

If the government of Canada pays more than the going wage for labour, it's still all counted in G. In this case, since everybody is a self-employed hairdresser, the real wage is 1. Statistics Canada measures the labour at the wage of employed workers, even if the government could get the labour for less, because the government does not undercut the market. It just pays an imaginary wage and gets it back immediately with imaginary taxes so the velocity of the government's imaginary tax and spend is infinite. Just like corvee labour.

"Or have I missed something in this discussion?"

Maybe that my model is supposed to be a monetarist parody of New Keynesian models, and you are asking some rather serious micro-theoretic questions about it ;-)

[edited to fix typos NR]

Nick rolled.

Actually, it doesn't matter how Statistics Canada values the pyramids (as long as it's above zero), provided it values the taxes the same way. And it has to value the taxes the same way, because otherwise the government accounts won't balance, since the government issued no bonds or new money to pay for the pyramids. The balanced budget multiplier is still one, even if you halve the value of the pyramids and the taxes.


Here is my model.

There are 8 workers producing output for themselves.
There are 2 workers who are doing nothing, even though they could be doing what the other 8 are doing (these 2 are non-optimizing, say).

There is no money.

The government forces the two unemployed workers to work; the government pays them wages equal to their output (collects taxes in the form of their output to repay in the form of wages).

The government balanced budget multiplier is one.

This is not rocket science.

I find the cases where different models agree to be very interesting. The boundary conditions where they agree/disagree are especially interesting, as they illustrate what conditions or policy choices we have to make to ensure that we get the behaviour we want. Engineering classes focus on these boundary conditions.

I am also convinced that monetarist models and [New] Keynesian models don't disagree as much as talk past each other. One focuses on supply, the other on demand. If you admit that both supply and demand can be problems, and then go on to admit that there can be both demand recessions and supply contractions, you get much further ahead. Your policy suite is enhanced and you have much more clarity about what tools are appropriate for the occasion.

Given that you tax and pay the people who do the government investments (and keep r constant instead of M - you know, like in a real world recession), is your model that unrealistic?

Is your problem that the labor supply in fact would be very elastic?
Is it that G would be such a perfect substitute to personal consumption?
Is it that you think real world G is absolute crap, and that its contribution to GDP is deeply misleading?

If all the above - could you put some number w.r.t. to how much each factor is reducing the "true" multiplier (e.g. since X$ G only is worth 0.8X$, the multiplier should be discounted by 20 % because of this).

I really can’t see why someone would think that the multiplier would be significantly below 1 in a recession.Given rigidities, liquidity constraints and excess capacity, I really can´t se how you could have it below one.

Determinant: "I am also convinced that monetarist models and [New] Keynesian models don't disagree as much as talk past each other. One focuses on supply, the other on demand."

One correction here. Both monetarist and Keynesian (at least New Keynesian) models are very much demand side models of short run fluctuations. It's just that they think of demand a bit differently. (And a lot less differently nowadays than the differences between old monetarists and old keynesians).

nemi: By the way, if you read Matt Rognilie's comments on the Woodford post, and my responses, you can see where we "addressed/solved" the problem you raised in my earlier post on multipliers.

"I really can’t see why someone would think that the multiplier would be significantly below 1 in a recession.Given rigidities, liquidity constraints and excess capacity, I really can´t se how you could have it below one."

In Canada, even if we accept a basic New Keynesian model, it's not obvious to me that it is above zero. The Bank of Canada doesn't hold M constant or r constant. It holds the inflation forecast constant. Over the last few years though I have hedged my bets. A temporary fiscal expansion during the worst of the recession seemed to me like fairly cheap insurance. And, as far as I can see, most of the stuff the government bought seemed reasonably sensible, and was mostly just bringing forward expenditure that would have been made sooner or later anyway.

But why would (moderate amounts of) G have any significant effect on inflation in a recession (when you have unemployment and excess capacity)?
Do you think recessions generally (or this one in specific for, say, the US) are due to structural factors?

Surely, the fear of restrictive monetary policy can’t be your main reason for thinking that fiscal policy will be ineffective?*
(you probably already written a post on it - and if so - do you remember the name)

*Yes, I read the Samuelson quote.

PS: I just realized that when I think about a “depression”, I generally visualize a really bad one (the great depression is a walk in the park compared to the one I´m thinking about). I then take whatever results I get from that thought experiment and apply them to lesser depressions/recessions – but this is of course really idiotic.

If I think about a economy where the unemployment only increased by, say, 3 percent – I can definitely see why you would except a close to zero multiplier.

I will reevaluate and come back

If everyone was working 4 hours what's the problem? If half are working 8 and half not working at all, then there is a really big problem, one even this policy could address.

"And, as far as I can see, most of the stuff the government bought seemed reasonably sensible, and was mostly just bringing forward expenditure that would have been made sooner or later anyway."

'Sooner or later' we will all be dead. There is no evidence that the Harper govt would have brought forth the stimulus package had they been in possession of a majority. Most likely we would have seen austerity and more economic decline. Instead they were forced to dance the Keynesian dance, and that's a good thing.

nemi: by assumption (and because that's what it says it is doing, and because I once tested to see if it was in fact doing what it said it was doing and I couldn't easily reject that hypothesis), the Bank of Canada sets monetary policy so that its expectation of future (2 year ahead) inflation will be 2%. If the Bank of Canada saw that an increase in government spending would increase aggregate demand, the Bank of Canada would simply tighten monetary policy by an equal offsetting amount to prevent aggregate demand increasing and prevent inflation deviating from 2%.

So fiscal policy would only increase real output if:

1. The Bank of Canada made a mistake and underestimated the amount of tightening it would need to offset it. (But then it would have to overcorrect later, plus it would be equally likely to make mistakes in either direction).

2. There are lags, and fiscal policy can affect AD more quickly than the Bank can respond.

3. For some reason the Bank of Canada cannot loosen monetary policy as much as it wants to (e.g. Zero Lower Bound) and so won't tighten when fiscal policy loosens.

Lord: It's still a problem if they all want to work 8 hours a day. It's just that the problem is spread out.

richard: I very distinctly remember the opposition complaining about the increase in the deficit that the Conservative government was creating. This is evidence against your assertion, and you have given no evidence in favour of your assertion.

And this is a blog post about the theory of balanced budget multipliers. Not about people's views on Stephen Harper.

Nick, I like these recent posts quite a bit, but haven't had time to focus. My preference is to look at things from a AS/AD perspective, which means a multiplier of one when holding MV constant implies a shift in AS. Then the question becomes how to think about this "supply shock." Is it a typical supply-side mechanism, or what looks like a demand mechanism, having mysterious supply-side-like effects.

Is the intuition behind your corvee labor example something like this:

1. Put a head tax of $1000 on all adult males.
2. Force all adult males to build dikes at gunpoint.
3. Pay them each $1000 for their work.

Or just do number 2, and skip steps one and three, which cancel out.

In my simple example, doing just 2, and doing 1,2 and 3, are basically identical. It seems to me you are saying do #2 in this post, and then arguing that Woodford's plan doesn't differ in its essentials from doing 1, 2, and 3. In which case it's pretty much like doing just #2.

BTW, Don't all models with the price level have "money" in the sense of medium of account, even if there is no medium of exchange? I'm thinking of reserves, which I believe exist in Woodford models. Otherwise what is the "price level" measured in terms of?

Scott: There are no reserves in the model. Just (sticky) prices all denominated in the unit of account. No interest free money at all.

Interesting, depending the on real value we ascribe to Pyramids, there would be a wedge between the gdp deflator and other 'market-basket' based measures of the price-level as a consequence of fiscal stimulus.

So suppose the CB was targeting nominal output, 'G' always contributes to nominal output but the wastefulness of 'G' can be directly harmful. Quite differently from the old Keynesian claim about digging holes, hole digging would lower real output.

That sounds pretty darn obvious when phrased in those terms.

There is no nominal anchor. Just stickiness (however little) and a CB controlling the inflation rate. But the initial price could be anything.

And I realize that you'll object that in all real economies the value of the unit of account is determined (roughly) by the quantity. That's because the money demand is similar in those economies because they all have similar money creation technologies. But it's the price level that determines the quantity via the money demand (velocity), not the other way around. And since it's extraneous, the quantity is not defined in the model. And I know you don't agree with this view. I'm just letting you know how I think most New Keynesians would see it.

"This is evidence against your assertion, and you have given no evidence in favour of your assertion."

You raised the issue (stimulus spending), not me. As to the nature of this blog post, you seem to have some difficulty in reconciling reality with your theory, which explains the vigorous backpedalling above.

Pyramids have value. Most people are proud of their cities cathedral and military citadel , even outdated when built ( Québec City 's a good example). The best modernequivalent to the Pyramids, the race to the moon, is still viewd with pride and nostalgia.
Even the ancient Egyptians used the pyramids for a nascent tourism industry. Is the feeling at seeing the pyramid worthless? Then why do we do it?

Nick: I tend to side with Richard. A discussion of reality is useful. But maybe on a separate specific thread.


Aren't you rather weakening the plausibility of the NK view by suggesting that they have to belief that the direction of causality ALWAYS runs from prices to money? It's a bit like weakening the plausibility of monetarism by requiring that they ALWAYS have causality running from money to prices or that they always used a vertical LM curve.

W Peden: I don't think so. There is so much debt, so little money. The impact of real rates on the economy is quite obviously enormous, whereas the magnitude of the effect of nominal rates on the demand for money (total quantity of seignorage) is minuscule. We are talking many orders of magnitude. And in lots of countries, (e.g. Canada, Australia, UK, NZ) we don't even have reserve requirements (and in fact we pay interest on the reserves we do have). The CB's of those countries manage fine with no currency other than a bit of paper money. And when you consider that the principal uses of paper money (organized crime and tax evasion) are the least sensitive to rates, I think it gets very hard justify a significant role for money/nominal rates. Seriously, as Matt asked in his post, how much would you change the average quantity of cash *in your wallet* because the CB changed the short rate by a few percent? Now compare the impact on your behaviour if your mortgage rate changes by the same amount.


I suspect we're in a confusion here about the word "money", since I agree with you if we're talking about cash i.e. the narrow monetary base.

K, If the price level determines the quantity of money, then how do you explain currency reforms?

And did the rise in prices during the 1500s cause Columbus to discover America in 1492, thus leading to a huge increase in gold and silver stocks?

And how about that German hyperinflation?


Money was tight during the German hyperinflation- just look at the interest rates during that period!

W. Peden, Have you been reading Joan Robinson again!

Scott Sumner,

Actually, my favourite Joan Robinson line right now is "John (Maynard Keynes) never took the 20 minutes needed to understand the theory of value." Keynes acted as one of the referees of her book on... The theory of value.

Then there's Wynne Godley getting invocking Keynes as an authority on wartime taxation through inflation-


- and Roy Harrod's classic quote at a lecture-

"I have searched through his (Keynes's) writings very carefully, not long ago- for the purpose of discovering anything he had to say about what we call 'cost push inflation'. I could find only one short passage in Keynes, just a couple of short sentences, where he said... Of course the wage-earners might demand more than the corresponding rise in their productivity; might demand more and get more... You can find these words if you search; I ought to give you chapter and verse, but I have not put down the page reference; they are there all right."

Who says that Cambridge produces slavish followers of Keynes?!

(The Robinson and Harrod stories are from Tim Congdon's "Keynes, the Keynesians and Monetarism".)

Scott: there are different regimes of money. In ours the quantity of money is whatever is determined by liquidity preference vs tbill interest. Nobody oversupplies money like Weimar or the Spanish armada. It's more like a largely irrelevant appendix. If rates go up, people will switch their (minuscule quantity of ) money to tbills and vice versa. But the money itself is nothing.

W Peden: Assuming the interest rate largely follows the policy rate you can't count M1. It's just bank debt. "Money" must be interest free for the quantity theory to work.

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