The macroeconomics of double pole dancing

The stupidest thing we do in macroeconomics is draw a downward-sloping IS curve. It's the stupidest thing we do, because we know it's stupid. (And I've done it hundreds of times.)

And because we do this stupid thing, we associate tight money with high interest rates. Unless of course we are someone like Scott Sumner, who never did get his head around the ISLM model, and so never made the false association between tight money and high interest rates. Come to think of it, I don't think Milton Friedman ever got his head around the ISLM model either, and he didn't associate tight money with high interest rates.

With an upward-sloping IS curve, and a vertical LM curve, because the central bank ought to make it vertical by targeting nominal GDP, everything falls into place. Tight money means shifting the vertical LM curve left, which causes interest rates (both real and nominal) to fall. Because you are moving down along an upward-sloping IS curve. Scott Sumner and ISLM: reconciled.

Why do we know it's stupid?

We know that investment is strongly pro-cyclical, more so than consumption. Even though consumption is larger than investment, the changes in investment over the business cycle are usually bigger than the changes in consumption.

And we know why too.

Who would want to invest in the depths of a recession?

In a recession, output is low, and so labour, or capital, or both, is idle.

If labour is idle, then the ratio of capital to employed labour is higher than normal, so the marginal product of capital is lower than normal, so the desired stock of capital is lower than normal, other things equal.

And if capital is idle, then the Marginal Revenue Product of capital is zero. Unemployed resources, whether labour or capital, are Zero Marginal Revenue Product workers or machines. Not because they can't produce any extra output, but because the firms can't sell the extra output that they could produce, so can't get any extra revenue from that extra worker or extra machine. So the desired stock of capital is lower than normal, other things equal.

In a boom, when labour and capital are fully employed, it's the exact opposite. Employment is high, so the ratio of capital to employed labour is low, so the marginal product of capital is high. And firms can easily sell the extra output produced by extra capital, so the marginal revenue product of capital is higher still.

For a given real rate of interest, the desired stock of capital will be higher in a boom than in a recession.

Investment is a flow, and the capital stock is a stock. If it weren't for adjustment costs, a small change in the desired stock of capital, above or below the actual stock of capital, would cause an infinitely large positive or negative flow of desired investment. So if the desired stock of capital depends on income, the marginal propensity to invest (the change in desired investment divided by the change in income) could be very large indeed.

We know this. There's nothing new here. The Old Keynesians knew this.

If the marginal propensity to consume plus the marginal propensity to invest exceeds one (mpc+mpi>1), then the IS curve is upward-sloping. That does not mean an increase in the rate of interest causes income to rise. It means an increase in the rate of interest causes income to fall and keep on falling. Equivalently, it means that an increase in income causes a rise in that interest rate at which desired saving would equal desired investment. Suppose income increased by $1, then desired consumption plus desired investment would increase by more than $1. So the real rate of interest would need to increase at the same time to offset it, and make sure that desired consumption plus desired investment rise by only $1.

Again, there's nothing new here. We knew all this.

So if business cycles are caused solely by monetary policy shifting a vertical (or at least steeper than IS) LM curve left and right along a fixed upward-sloping IS curve, we would see high real interest rates in booms and low real interest rates in recessions. Low real interest rates are caused by tight money. High real interest rates are caused by loose money. Which is what Scott Sumner says. And Milton Friedman said.

We all know that firms have a strong incentive to invest in a boom and not invest in a recession. And we know this is what they do. So we know that mpc+mpi>1 is a very plausible assumption, and one that fits the facts. So why don't we want to believe it?

1. Because mpc+mpi>1 makes equilibrium in the Keynesian Cross model unstable, and we don't like an unstable equilibrium, so we make the Keynesian Cross equilibrium stable by assuming mpc+mpi<1, and then use it to teach where the IS curve comes from. And mpc+mpi<1 gives us a downward-sloping IS curve.

2. Because we can't escape the "dominant discourse" (sorry) of monetary policy as setting a rate of interest. That's what central banks do. That's the monetary policy transmission mechanism. So the LM is horizontal. And if you have a horizontal LM and an upward-sloping IS it's an unstable equilibrium. All the dynamics are wrong. If you shift the LM up, by having the central bank raise the rate of interest, which is a tightening of monetary policy, income does not rise to the new ISLM intersection. It falls, and keeps on falling. The ISLM intersection tells you where the equilibrium is, but the economy won't go there. We don't like models like that.

We don't like models like that, but that doesn't stop them being true.

A central bank that conducts monetary policy by setting a (contingent) time-path for the nominal rate of interest is double pole dancing. It is balancing one pole upright, on the palm of its hand. And there's a second pole, balanced upright on the top of the first pole. And it has to dance like crazy, to try to keep both poles upright, and in about the position it wants them to be.

The first pole we know about. It's embodied in the Howitt/Taylor principle. The central bank sets a nominal interest rate, but what matters for consumption plus investment is the real interest rate. If the central bank sets the nominal interest rate too low, desired consumption plus investment will be too high, so inflation will rise, and expected inflation will rise, and the real interest rate will fall, and inflation will rise even more. It's unstable. So if inflation rises by 1%, the central bank must respond by raising the nominal interest rate by more than 1%, to bring inflation back down. It has to move the bottom of the pole (the nominal interest rate) by more than the top of the pole (the inflation rate) to keep the pole from leaning more and more.

The second pole is the result of the upward-sloping IS curve. Even if you ignore expected inflation, so that real and nominal interest rates are the same, the central bank can't hold the rate of interest constant and expect real income to stay constant. If the central bank sets the rate of interest a little bit too high, income won't just be a little bit too low, as it would be with a downward-sloping IS curve. Instead, income will fall, and keep on falling.

Take a bog-standard ISLM plus expectations-augmented Phillips Curve model. Make the LM horizontal because the central bank sets a (contingent) time-path for the nominal interest rate. Then assume mpc+mpi>1, so the IS curve slopes up. The central bank is then double pole dancing, trying to keep two poles balanced upright, one on top of the other.

That's why central banking is hard, if you set a nominal interest rate. And that's why things sometimes fall over.

Thanks edeast for this video link:

  

Comments

[Lee Kelly]

I'll get around to learning about the IS-LM model one of these days; then I'll know what you're talking about. Whether I'll know more about the economy, or just what economists think, is another matter.

[Greg Ransom]

Captial is not a stock. Read Hayek's "The Mythology of Capital" and the first few chapters of Hayek's "The Pure Theory of Capital" or Bohm-Bawerk's book "Capitaland Interest".

[Nick Rowe]

I was going to suggest Wikipedia on ISLM. But I skimmed through it, and found one howling error. It said that at any point on the IS curve there is no general glut. Which is total crap. I fixed that error. But there may be more.

Paul Krugman is better, but even he makes one mistake. He talks about 3 goods and therefore 3 markets. But it's a monetary exchange economy, so if there are 3 goods (output, bonds, and money) there are only 2 markets.

Dammit. Everybody teaches it. Nobody understands it. Except moi?

[Greg Ransom]

Producers will only chose longer production processes over shorter production processes if the longer process promises greater output.

What part of that don't you understand, Nick?

If there are increased resources devoted to increasing production, one aspect of that process will include shifting production to lengthier processes to achieve better output.

You will get different production processes in the FLOW of production, you will NOT simply have a larger "stock".

This is the fallacy of the "stock" -- ia brain dead notion contradicted by the fundamental facts of the logic of marginal
choice.

It's non-economic thnking at its worst.

And if the flow of capital has a shifting and flowing structure across relative prices / time, then you investment, interest, "stock of capital" story is bogus -- it's based on the iinability to think economically -- i.e. it's based on every fallacy post marginalist economic science was developed to do away with.

To strong? I don't think so.

[Nick Rowe]

Greg: IIRC I have read (decades ago) 2 out of those 3. The stock of produced means of production is a stock.

[Nick Rowe]

Greg: "Producers will only chose longer production processes over shorter production processes if the longer process promises greater output.

What part of that don't you understand, Nick?"

I don't understand how you can define "shorter" or "longer" independently of the term-structure of rates of interest.

Oh God. I wasted nearly a year of my life on Capital Controversies, when I should have been getting my bloody thesis written.

This is about the ISLM, and the effect of deficiences of effective demand for output on the demand for newly-produced investment goods.

Clower is the go to man. Not Hayek.

[edeast]

Can you explain the horizontal vs vertical LM? How does NGDP target affect the LM, vs the time-path contingent etc.....

[Kevin Donoghue]

"Unemployed resources, whether labour or capital, are Zero Marginal Revenue Product workers or machines. Not because they can't produce any extra output, but because the firms can't sell the extra output that they could produce, so can't get any extra revenue from that extra worker or extra machine."

Don't the poor guys who have to teach microeconomics get a bit cheesed off when you write this kind of thing? Between that and encouraging Scott Sumner to think that "we associate tight money with high interest rates" and that ignorance is strength, you really are doing a lot of mischief.

[edeast]

um thanks.

[Matt Young]

I get a little closer to getting the IS curve each time Nick brings up the subject.
My rule is a little simpler. When central banker lowers short term rates below real, investment bankers crowd around the short end sucking up subsidies, ignoring some of the long end. But within six two or three months bankers will build a hedging scheme to dissipate the liquidity.

When the central; banker raises short term rates above real, investment bankers tend to herd right, closer to the long end.

Central bankers can twist the curve for a while, but not much more.

[Joe]

"It said that at any point on the IS curve there is no general glut."

Isn't that because according to liquidity preference of the LM curve, the money market is always and everywhere in equilibrium because interest rates aren't sticky. Thus, if you're a quasi-monetarist, you would perceive IS/LM as implying that we are always in monetary equilibrium and thus there is never any glut, which is clearly impossible......

[Matt Young]

The curve is correct except, yes, the points are not equilibrium and we are only talking short term output and short term rates and we limit the integration cycle in computing real Y. Given these assumption then yes, a lowering of i below real gets more short term activity.

The LM curve adds in the effect on long term bonds, with all the dealers crowded initially around the short term liquity injection, the long bond gets monopolized and gains go up.
The single equilibrium point is when short term gains and long term gains, as a percentage of inventory, are about the same.
You have a two channel model, finance trades that happen frequently in small amount, and larger ones that happen less frequently.

[Nick Rowe]

Lee: click on the second link that edeast posts in his 04.08 comment. Read just the first part. It's my short synopsis of ISLM. (And the first link explains why the LM curve can be/is vertical.)

Kevin: you lost me there. Can you expand?

Matt: you are probably onto something there. But when central bankers try to twist the curve, and the commercial bankers respond, then real firms doing real investment respond too, don't they?

Joe: I don't think that's what they are thinking. People who think that all points on the IS curve are points where demand for newly-produced goods = supply are just confused. They don't get the distinction between quantity sold and quantity supplied. The IS curve shows points at which quantity demanded=quantity sold. But firms would nearly always like to sell more. But they don't produce more, because they can't find buyers.

[Kevin Donoghue]

Marginal revenue product = (marginal product of labour) x (marginal revenue). Profit maximization implies that MRP = wage, which is positive. The firm can get extra revenue from that extra worker. What you seem to be trying to say is that unemployed workers generate zero marginal profit. This is true, but trivial.

[Simon van Norden]

Nick: 3 goods means we can (if we want) talk about 3 markets -- it's just that one will be redundant. (We do that all the time in FX markets: happily talk about the market for EUR and the market for USD when they both could be the market in which we swap USD and EUR.)

That's not a mistake: that's a feature!

[Simon van Norden]

...and the downward-sloping IS curve is not the stupidest thing we do in macroeconomics; the Phillips Curve is way more stupidier.

It is an empirical relationship that doesn't work linking inflation to two variables we don't observe that relies on what Samuelson's textbook used to call a "Fallacy of Composition." That's not just stupidier, that's stupidierest!

[Patrick]

Ah, if only we the economy was so simple that could write out the Langrangian and beat it into submission with Pontryagin.

[Nick Rowe]

Kevin: "The firm *can* get extra revenue from that extra worker."

I strongly disagree! If the firm is sales-constrained, it can't.

Assume labour is the only variable input, Y=F(L), diminishing returns, and perfect competition, for simplicity. Profit maximisation only implies W=P.MPL if the firm is able to sell as much output as it wants.

Assume instead that there is a deficiency of aggregate demand, so the firm wants to sell output at the point where W=P.MPL, but can only find buyers for less than that, namely Y'. There is then a discontinuity in the labour demand curve at L', where L' is defined by Y'=F(L'). The labour demand curve follows the P.MPL curve until we get to L', then it is vertical. The MR curve is horizontal at P until we get to Y', then there's a discontinuity and it drops to zero. So MRPL=MR.MPL is zero to the right of that discontinuity.

But you knew this, I thought? Are we arguing at cross purposes?

[Nick Rowe]

Kevin: I'm just repeating Patinkin 1966(?) (2nd edition of Money Income and Prices) or Barro and Grossman 1971. The effective demand curve for a firm that is rationed in its sales because we have a Keynesian demand deficiency. Which is the ISLM world.

[Nick Rowe]

Simon: "3 goods means we can (if we want) talk about 3 markets -- it's just that one will be redundant."

I strongly disagree!

I know the usual story. In an economy with n goods, there are n markets, but we can make one redundant by Walras' Law.

And that usual story is totally wrong.

1. In a Walrasian economy with a central auctioneer, there is one market in which all n goods are traded simultaneously. That's the only economy where WL makes sense, but even then it only makes sense if demands and supplies are *notional* demands and supplies. "Notional" means "based on the assumption that the agent will be able to buy and sell as much of every good as he wishes". But if prices are not market-clearing, so some agents will be unable to buy or sell as much as they like, demand and supply functions will not be notional, because agents will take those additional constraints into account.

2. In a pure barter economy, where there exists a market in which any pair of goods can be traded, there are n(n-1)/2 markets.

3. In a pure monetary exchange economy, with n goods including the medium of exchange, there are n-1 markets. In each of those markets, money is traded against one of the non-money goods. And Walras' Law is totally messed up by the fact that there are n-1 different excess demands for money.

I did a long post on this a while back.

[Nick Rowe]

Simon: Here is one of my old posts on Walras' Law:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/04/walras-law-vs-monetary-disequilibrium-theory.html

[Phil Koop]

There is another reason why the FX comparison is misleading. If the CAD economy has n goods, then it has n-1 markets. If the USD economy has m goods, then the joint CAD/USD economy has n+m-1 markets, since there is a CAD/USD FX market. But if the EUR economy has k goods, then the joint CAD/USD/EUR economy nominally has n+m+k markets, because there are three FX markets (except that one of the three is redundant.) And if the JPY economy has j goods, then the joint CAD/USD/EUR/JPY economy nominally has n+m+k+j+2 markets, of which 3 are redundant. For joint economies with n currencies, the nominal markets grow as n choose 2, but the spanning markets as n-1. This is not the same thing as the Walrasian redundancy.

[Nick Rowe]

Phil: we are on the same page, I think. In the simplest model of forex markets, where there is only one reserve currency, there are n currencies and n-1 markets, and the reserve currency is traded in all markets, and each of the other currencies in only one. So the reserve currency is like "meta-money". It is the medium of exchange between all the other media of exchange.

If all the cross-markets actually existed, with no reserve currency, it would be like barter.

With subordinate local reserve currencies (Euro, pound?) it's more complicated.

[Lee Kelly]

My intuition here says that by holding the LM curve vertical (i.e. targeting NGDP), the central bank is keeping the equilibrium interest rate on money at zero.

Liquidity traps wouldn't be a problem if money had an interest rate of its own that moved up and down with other assets, because then the supply and demand for liquid assets would never become frustrated at the lower nominal bound. The demand for liquid assets would never spill over into money, and so money demand could never drive a wedge between saving and investment. All open market purchases would be about equally effective at stimulating nominal expenditures.

Another way to achieve a similar effect is to ensure the equilibrium interest rate on money never rises above or falls below its fixed value. This can be achieved by arbitrarily manipulating the supply of and, via expectations, the demand for money. In other words, money is neutral with regard to liquidity when the market clearing rate of interest on money is always equal to the nominal bound (which is arbitrarily fixed by the central bank). An excess supply or demand for money can literally be interpreted as a case when the market clearing interest rate on money is not equal to the rate imposed by the central bank (aka the "lower nominal bound").

[Kevin Donoghue]

Nick,
My apologies. I thought you were channelling Tyler Cowen, not Patinkin. Meanwhile I was thinking of Keynes, whose workers do not have zero MRP.

[Andy Harless]

I think you use the phrase "pole dancing" rather differently than it is usually used. Google "double pole dancing" (in quotes), and you get this blog post plus a bunch of YouTube videos of people pretending to be strippers.

The great paradox here is that cutting the interest rate causes the interest rate to be higher, in apparent contradiction to the definition of the word "cutting." I guess, given that the process isn't instantaneous, that one can resolve the paradox by saying that cutting the interest rate now forces you (if you're a rational central bank that wants to avoid hyperinflation) to commit to raising it later. Or one could say that the threat of cutting the interest rate causes it to rise. Ah, this is a chance for me to plug my newly relevant blog post from last year. I was talking about bonds in a liquidity trap, but it didn't occur to me at the time that the same logic applies to the federal funds rate during normal times: if the central bank can credibly announce a shift to looser Taylor Rule parameters, interest rates will rise specifically because the bank is threatening to cut them.

[Nick Rowe]

Lee: "My intuition here says that by holding the LM curve vertical (i.e. targeting NGDP), the central bank is keeping the equilibrium interest rate on money at zero."

The LM curve is defined as combinations of nominal interest rate (on "bonds") and real income at which the demand for money equals the supply of money. Implicitly it assumes the "bond" market clears. The normal assumption (though this can be relaxed) is that money itself pays no interest, so the interest rate on "bonds" is "the" opportunity cost of holding money. The slope of the LM curve depends on the relative demand and supply elasticities of money with respect to real income and the nominal interest rate. In principle, (unless one of the demand elasticities becomes infinite) the central bank can make the slope of the LM curve whatever it likes, by choosing its own supply elasticities.

Normally the ISLM model sees the central bank as shifting the LM curve by changing the supply of money. But it could also do it by changing the interest paid on money, which will affect the demand for money.

Kevin: that's a relief. But maybe I should have been more clear. I might edit the post at that point.

Andy: Yes. A *slightly* different meaning. One bank with 2 poles, rather than 2 girls with one pole. I was trying to get more hits for WCI, and bring in a wider audience! I just Googled "double pole dancing", and was pleased to see this post came top. Which suggests the competition must be rather weak. And oh dear, those videos are so hopeless. I think the video I've got here is much more fun to watch.

Agree with the rest of your comment. I liked that old post of yours.

[Determinant]

Right. Time for a dare.

You give me a posting slot and the ability to post a few graphs, and I will show you a model of a monetary economy that can exhibit three states: Supply Expansion (normal prosperity with investment), Demand Recession (monetary disequilibrium, balance sheet recession) and Supply Recession (supply contraction)

The kicker is that it features a Hayekian Triangle and I lifted most of it from Roger Garrison, a devoted Hayekian, but with one extra curve in the money market you can demonstrate a balance sheet recession and make the model completely compliant with Keynesian ideas.

Rate M for Mature, it features a Hayekian Triangle and a Production Possibilities Frontier. Devoted Hayekians should not look at it without adult supervision as it contains the obscene heresy of explaining Keynesianism with Hayekian precepts.

[Patrick]

Determinant: just create your own blog and post it there.

[Greg Ransom]

Non-permanent production goods must be replaced, usualy by production goods of a different technological form.

The valuation of the goods is forward looking, and production goods are never valued as a collective bundle, and how they cam to have a productive functional form is of no interest in the forward looking consideration of value and function.

The backward llooking perspective that identifies something as "capital" by looking backward at its causal history is non-economic thninking -- many "produced means of production" will have no value going forward, and a "stock" pf such things identified by past causal hisotry may have no value.

A good part of the Keynesian pathology derives from this backward looking "theory" of economic goods status and valuation derivation, i.e. its stuck on Ricardian/Smithan backward cost valuation theory (e.g. Kayenes' labor unit theory of capital value).

The idea that by looking backward we can identify a "stock of produced means of production" is the principle source od the "idle capital" fallacy that sees these as a stock that can magically have their old functional role and valuational significant if old aggreagate relations have been majically restored.

Imagine if biological science worked this way -- we could imagine the immune system building a "stock of produced means of immune response" to the flue bug of the past two or three decades -- but none of these will represent an immune response at all to the new variety of the flue coming next year in the flow of ever changing conditions. Past status doesn't give future status or future significance is a forward moving evolving and flowing system..

There IS no permanently significant "stock" of "produced means of production" and the problems math economists have in producing tractable equilibrium math constructs functionally accounting for this flow doesn't count against the real world, it counts against the academics gatekeepers demanding math models. When real scientists discover mathematically intractible phenomena in such domains as fluid dynamics, that don't pretend phenomena which does exist somehow does not exist.

Economists are not better scientists for pretending that phenomena which does exist does not exist, or for pretending it has magical valuational and functional significance which we know with certainty it cannot have.

Nick wrote,

"The stock of produced means of production is a stock."

[Nick Rowe]

Determinant: Dunno. If you, or anyone, thinks they have something good, you can always email it me. No promises though. Or, as Patrick says, start your own blog.

Greg: look, I understand all that. I think nearly everyone else does too.

In economics, bygones are bygones.

If we were born this minute, with all the capital goods that were produced in the past instead having fallen as manna from heaven, it would make no difference to today's equilibrium, which depends only on the present and the prospective future. The relevance of "produced" vs. "non-produced" factors of production is *not* whether they *were* produced in the past, but that more can be produced in the present and in the future. The difference between capital and land is not that one was produced in the past; it is that one can be produced in the present and future. If some of the current stock of machines is idle, we are less likely to want to produce more of those same or similar machines. If some of the current stock of manna-from-heaven land were idle, we would be less likely to produce more of that same or similar land, if we could produce more.

(There is a subtle exception to that, as Von Mises Regression Theory of Money implicitly recognises, with its implicit recognition of the past path of how we got to this point. In a world of multiple equilibria, then history my act as a focal point picking one of those many possible equilibria. For example, the current set of property rights is inherently backward-looking. I own what I own because I owned it in the past. It is extremely unlikely that we would recreate the current allocation of who owns what if our memories were wiped clean and we were to assign property rights anew. We keep promises (sometimes) because we made them in the past. We punish criminals because of what they did in the past. We want others to believe in future that how we will act depends on what will have happened in the past. My PhD thesis was an extended essay on how one can reconcile this fact that history seems to matter with the central vision of economics that bygones are forever bygones.)

Whether or not there were Cambridge UK Keynesian economists who failed to escape backward-looking theories of value into a Jevonsian forward-looking value theory, those economists are long defunct. Nowadays, the theory of investment and capital is all forward-looking Bellman equations. The current state variable may matter. The path by which we got to this current state variable does not. The war of 1871 is over. Your (my) side won. There is no need to re-fight that battle. Especially not against people on your own side. It was Japanese soldiers who disappeared into the jungle after WW2 and kept on fighting. Not American soldiers.

[Nick Rowe]

Here's a simpler version Greg.

"Produced" means of production doesn't mean "produced in the past". It means "those that can be re-produced in the present and future".

[Nick Rowe]

Economically speaking, antique furniture -- that cannot by assumption be reproduced today -- is land, not capital. If we suddenly forgot how to make new hammers, and could never figure out how to make them again in future, then hammers would become land too.

More generally, the extent to which goods produced in the past are capital rather than land depends on the elasticity of the current supply function of new goods and how close substitutes those new goods are for the old goods produced in the past.

[edeast]

I need help picturing this;" ...then the IS curve is upward-sloping. That does not mean an increase in the rate of interest causes income to rise. It means an increase in the rate of interest causes income to fall and keep on falling."

[edeast]

From Delong's interpretation of cochrane's paper through your old post,
"And so the higher the interest rate, the higher is the flow of spending needed to maintain bonds-spending equilibrium."

So, a raise in rates, requires the Y to increase, but doesn't cause it to, leading to the income death spiral?

[edeast]

Ok, I think I understand how you got the upslope IS from the steep AE line. What I don't understand is how a steeper than 45degree line can intersect the AD=Y, if there is some base (>0) exogenous demand.
Sorry, for the repeat comments, I'm playing catch up, on all that I've missed this summer.

[K]

But Nick, this is what I've been saying in our debate over the ketchup bottle. Crowding out is a form of tightening. Tightening reduces expected growth and inflation (the natural rate). (And therefore there is no positive feed back between government borrowing and inflation, ie no ketchup).

[Nick Rowe]

edeast: you are thinking it through exactly right. You just need to keep pushing your thoughts on the last step.

"What I don't understand is how a steeper than 45degree line can intersect the AD=Y, if there is some base (>0) exogenous demand."

Suppose the consumption function is the standard C=a+bY. So there's some base exogenous demand (a) for consumption. What about investment?

In a deep recession, nearly all firms might have a bigger capital stock than they desire. Desired investment is negative. They want to sell their machines back to the firm that produced them and sold them. But they can't. The firms that produced capital goods aren't buying them back. They want to convert the excess capital goods into consumption goods, so they can sell them to households, to satisfy that base consumption demand. But perhaps they can't. You can't eat machines. So there's a floor of zero on gross investment.

So, for low levels of income, where that zero lower bound on investment is binding, the AE curve follows the consumption function, and is flatter than the 45 degree line, and cuts the 45 line from above. Then at a certain level of income, the desired capital stock equals the actual, so desired investment becomes positive, and the AE curve is steeper than the 45 line, and cuts it from below.

This means the IS curve is U-shaped. But, in any economy where desired saving and investment are positive at full employment, we are on the upward-sloping part of the IS curve at around full employment.

(This is like the old multiplier-accelerator model).

The zero lower bound on investment won't be quite as sharp as that. Some firms will have positive desired investment even when others have negative. And machines wear out over time. And technology changes, etc.

[Nick Rowe]

K: Hmmmmmmmmm. Thinking.

[Nick Rowe]

K: If *this* what you were saying, then you were right: With an upward-sloping IS curve, that cuts full-employment income at an interest rate r*, where by definition r* is the natural rate, then an increase in G that shifts the IS curve right will cause a reduction in the natural rate.

Or, you might be talking about a long run growth model, of the AK sort, in which the natural rate of interest equals the long run growth rate (roughly). And an increase in G reduces I and Kdot and hence Ydot and hence r.

[Nick Rowe]

Scrap my above comment. The first bit is wrong. If the IS curve slopes up, an increase in G shifts the IS curve *left*. The natural rate still increases.

[edeast]

thanks,

Just trying to work through the bottom of the U. I gather it is where mpc+mpi=1.
With 2 intersections in the keynesian cross, ... by messing with the rates, eventually the curve would just touch the AD=Y line, and you would end up on the other path. Not sure how you swith paths, and what the correct interpretation of the AD=Y line being tangent to the AE curve would be.

Also other random info trying to get my head around. The expenditure multiplier goes negative when mpc+mpi >1.

[Nick Rowe]

edeast: "Just trying to work through the bottom of the U. I gather it is where mpc+mpi=1."

Yes, because the Old Keynesian multiplier is then infinite, so it only requires an infinitesimal drop in r to cause Y to change.

"Not sure how you swith paths, and what the correct interpretation of the AD=Y line being tangent to the AE curve would be."

Think of a ball on a locally flat surface, but that surface drops away downwards on one side, and gets slowly steeper upwards on the other side. Stable in one direction; unstable in the other.

"Also other random info trying to get my head around. The expenditure multiplier goes negative when mpc+mpi >1."

Yes. The change in *equilibrium* income divided by the change in G would be negative. But remember, we would never get to that new equilibrium (holding r and everything else constant) because it is unstable. Comparative statics results always have the "wrong" sign when the equilibrium is unstable.

[edeast]

This is slow slogging.

If you work this model out, how will this change your advice to Bank of Canada, for price level vs inflation target renewal?

[Greg Ransom]

Your dissertation sounds very interesting Nick. Is it possible to get a copy?

These sorts of issues were in dispute between Bohm-Bawerk and Menger, e.g. the role of law in the creation of the economic category of capital goods.

[Nick Rowe]

Greg: I published it as a book. http://books.google.ca/books?id=7nGBvAxWC6MC&pg=PA7&lpg=PA7&dq=Nicholas+Rowe+Rules+and+Institutions&source=bl&ots=j0604Avajf&sig=l5doYyJKlsrB2vo5fhFW1fTnuA4&hl=en&ei=M1NCTtmBEMOCgAfsuKGmCQ&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBoQ6AEwAA#v=onepage&q&f=false

It's a bit dated now, I think. Others have gone further in that direction (though I haven't followed the literature). It's sort of Austrian-friendly. Langlois cites it.

[nanute]

The reason there's no ketchup: Regan declared it a vegetable.

[Greg Ransom]

Thanks Nick. Terrific.

[Greg Ransom]

It look like we have more basic differences, Nick.

I'm a Wittgensteinian / Hayekian / Kuhnian on rules, were "rules" are mostly learned via imitation & trainings can't be reduced to anything else, most especially can't be cashed out in terms of "given" atomic entities and rules of logic or rationality.

The notion of the rational justification of rules and rule following at the most primitive levels is essentially nonsensical, radically violating all sorts of "knowledge problems".

At the most primitive level "rules" are ultimately "ways of going on together" which have no further grounding or justification.

(For Hayek on rules, see particularly Hayek's essays on rules, brain & social evolution in _Studies_ and _New Studies_, which are more significant on this topic than what is found in his books.)