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A reswitching post - awesome. I worked through it when I was writing my thesis, and I even taught it once or twice. I remember almost nothing of it. I wonder if I have my lecture notes somewhere.

Stephen: Thanks! It made my brain hurt. I am very impressed you once worked through it. And taught it!!! How come? How did you discover it? (I don't remember it being on the course outlines at UWO in my day, but that might be just my memory.

My thesis was on investment, so I ended up reading a lot on how capital stocks are measured. A nasty, thorny thicket that literature turned out to be.

Aha! Yep. It sure is.

I think I missed the punch line.

Sorry, that was a joke. I missed the whole article. So the capital controversy could have been an anything controversy.

You are referencing Descartes Rule of Signs for real polynomial roots.

Edeast: Yep. Capital, food, swallows.

Lord: Aha! Good find!!

This was the clearest description of re-switching I've ever seen.

God, the amount of time we spent on the reswitching controversy in advanced macro back in the early 1970s. I don't remember very much of it (but I think I still have a book about the whole thing--Some Cambridge Controversies in the Thoery of Capital, by Geoffrey Harcourt, which you, too, can experience (http://www.amazon.com/Some-Cambridge-Controversies-Theory-Capital/dp/0521096723/ref=sr_1_fkmr0_1?ie=UTF8&qid=1345257808&sr=8-1-fkmr0&keywords=come+cambridge+controversies+in+the+theory+of+capital).

1. Suppose the price of fertiliser goes down, holding the prices of all the different types of food constant. Will the farmer use more fertiliser? Maybe. Probably yes. He certainly won't use less fertiliser.

2. Suppose the current 1-period rate of interest goes down, holding constant all future 1-period rates of interest. (So the term-structure twists). Will the farmer invest more this period? Maybe. Probably yes. He certainly won't invest less.

1 and 2 are formally identical.

Indeed; I suspect 1 and 2 are identical and both 'wrong', at least by the lights of the reswitching controversy. Namely, 1 is plausible but does not follow from core assumptions on consumer behavior. It has to be imposed as an aggregate assumption.

There is a whole rhetorical dust-up as to whether Giffen goods and other failures of the law of demand (aka where 1 is false) is an appropriate analogy to reswitching - in both there is a perverse equilibration that messes with 'nice' behavior, but Giffen goods are largely easy to detect, have straightforwardly unlikely theoretical requirements, and don't seem to exist, but reswitching is hard to detect, has utterly confusing theory, and who knows about existence...? The Sraffians straightforwardly exist that it is prevalent and the neoclassicals say it is rare at best, in the absence of empirics, and the burden of argument is obviously on the other side, etc. etc.

David, the Sonnenschein-Mantel-Debreu theorem is often cited as an "anything goes" result, showing that violations of the law of market demand are always possible. Yet such violations are unlikely to occur in the real world, since they depend on pathological interactions between substitution and distribution effects. Informally, suppose that folks with highly income-elastic food demand happened to hold a long position on fertilizer, as part of their endowment. (They might have no motive to hedge that position, because there is no uncertainty inside the model: we are doing comparative statics). Then as the price of fertilizer falls, these folks' endowment becomes less valuable and their demand for food falls, so food production falls in turn and so does fertilizer use. This might count as a violation of the law of market demand, but it shows how contrived such violations can be.

I definitely don't understand the roots of the debate, but I'm somewhat surprised to learn that it all just hinged on an absurd misconception about the term structure of interest rates. My understanding - and maybe I'm totally wrong - is that neoclassical theory held that the profit rate was meaningfully explained as the "marginal product of capital."
Leftists (Cambridge UK), while taking offense to the fact that this was easily conflated with the marginal product of *capitalists*, further objected that the theory was circular and meaningless. I have no idea how these ideas were presented in the '60s, but my modern/finance perspective is that returns (ie profits from capital) are determined by the risk tolerances of investors, rather than their marginal contribution to output. I.e. investors make money because they are scared, nothing to do with their fearless advancement of "technology." (Maybe we should revisit the fallacy of the Cruesonia plant here).  I *thought* that was what was at the core of the debate, but I'll admit that I hadn't fully understood the reswitching dispute, nor is it clear to me the extent to which it was critical in the Cambridge UK critique of the neoclassical view of capital.

Is it really the case that Solow and Samuelson were made to issue contrite retractions when all that would have been required is a statement that "obviously profits/rates aren't the same in all periods, and to the extent that we ever wrote that, it was just a convenient..."

Lord: Decartes' rule of signs"

Cool! Never seen that. Was going to pipe in with my "discovery" of a proof that you were right, Nick (see last comments in previous post), that oscillation of the sign of terms is in fact a *necessary* condition for having n positive real roots. Oh,well...

but I'm somewhat surprised to learn that it all just hinged on an absurd misconception about the term structure of interest rates.

IIRC, the issue was capital aggregation. Due to re-switching, you cannot aggregate capital based on market price, because demand for capital A and capital B changes when interest rates change. But interest rates are themselves determined from the market price of capital. So there is no well-defined way of aggregating heterogenous quantities of capital, or there might be multiple ways of doing this that give different answers, each equally valid. But then you cannot say "as the quantity of capital increases, the return on capital falls" because you are unable to define "quantity of capital".

See, e.g. http://en.wikipedia.org/wiki/Cambridge_capital_controversy

As someone who studied reswitching with Don Coffin (above) and later published on it in JET (1983), I think there are some things missing from this post, interesting as it is. The most important is what is key to reswitching, namely a time pattern of returns to a technique that is complicated over time in the sense of having some non-monotonicity. These can arise in environmental examples where there may be costs up front then positive returns but then delayed costs. Or at least in comparing two techniques there are relative changes over time the pattern of net benefits. These are what bring about the phenomenon.

The immediate relevance here is that I do not see any of that going on in these agricultural examples. I doubt they exhibit reswitching or even more garden variety capital-theoretic paradoxes.

Which brings me to a second point: what about the term structure of interest rates? Maybe I missed it, but I think what is potentially interesting there is when we get inversions of that structure, or better yet, non-monotonicities such as we are currently seeing in many countries, with minimum interest rates (in some cases nominally negative) for bonds of about two years in maturity. I suspect that such shifts in patterns can bring about some curious and apparently paradoxical shifts of relative rankings of techniques that have complicated time patterns of relative net returns.

Oh, and the bottom line from my old paper was that when reswitching can occur, discontinuities can occur in optimal time paths of growth for capital-labor ratios. This result was inherent in some of the models put forward during the original debates by such figures as Garegani and Pasinetti, although they did not pursue the full implications of it, although Pasinetti in particular seemed more aware of this possibility.

but my modern/finance perspective is that returns (ie profits from capital) are determined by the risk tolerances of investors, rather than their marginal contribution to output.

OK, but orthodoxy says that returns are a function of *both* preferences and real physical returns -- where the preference curve is tangent to the production frontier curve. It is not one or other. And re-switching calls into question the physical side of things -- what is this aggregate production function, and how do you define the "K" that goes into it in a way that is independent of preferences, so that you have two independent curves that can jointly determine the equilibrium profit rate and quantity of capital employed. If the production side is itself a function of preferences, then you have an under-determined system and you are back to Sraffa's view that the profit rate is exogenous.

If you throw all that overboard and say "it's only preferences", then you are not taking the neo-classical side of the argument, which is basically "we don't care about logical problems in passing from micro to macro such as re-switching". It is possible, at least conceptually, to aggregate consumption goods, but it is not conceptually possible to aggregate capital goods.

I think "we don't care" is a legitimate view to take, but it is not compatible with a demand for microfoundations.

I may be completely wrong, but I think that once you conceive of capital as time, of time as uncertain, of uncertainty and risk-bearing being related with returns, and of there being no meaningful difference between quantity of capital and value of capital, all this fades away?

I thought Hicks had solved this for us for the certain view of the world, and Fischer Black solved this for the uncertain view of the world?

I am full on board with K's finance view of the world. Too many people pay lip service to 'capital is just the PV of expected future returns' and then try to ground those expected returns into some function of the current physical stock of capital, which pushes them back into the capital is buildings and factories view of the world. Expectations and uncertainty is all that matters, and the 'quantity' of capital is stochastic.

Nick:

Let me create an aggregate investment demand schedule that slopes up. There are two kinds of farmers in the world. Those who have cash and those who don't. They're competing for the same market of final output. When the price of fertilizer goes down, the cash-rich farmer does not buy more fertilizer, because even the cash-deficient farmer can now buy fertilizer and the rich farmer will have to fight harder in the marketplace. But when the price of fertilizer goes up, the cash-deficient farmer is priced out, and the cash-rich farmer loads up, creating sustainable advantage. The actions of the cash-rich farmer dominate those of the cash-deficient farmer. The investment demand schedule slopes up.

When firms finance the bulk of investment out of retained earnings and large incumbents dominate new/small busineses, this can easily happen.

rsj: thanks! I was trying to be as simple and clear as possible. That's the only way I can understand things.

david: Ooops! Yep. I forgot about Giffen goods!

rsj: "IIRC, the issue was capital aggregation. Due to re-switching, you cannot aggregate capital based on market price, because demand for capital A and capital B changes when interest rates change. But interest rates are themselves determined from the market price of capital. So there is no well-defined way of aggregating heterogenous quantities of capital, or there might be multiple ways of doing this that give different answers, each equally valid. But then you cannot say "as the quantity of capital increases, the return on capital falls" because you are unable to define "quantity of capital"."

That's basically my "IIRC" too. And I'm saying it seems to me you can't aggregate "food" either, for exactly the same reason. So when farmers charge us for what they call "food", it's really all just mystification and exploitation and them grabbing part of the surplus.

Barkley: JET! Wow. I can't even read that journal. Thanks for saying the post is interesting. But I don't *think* it's missing *some* of the bits you say it's missing.

"Or at least in comparing two techniques there are relative changes over time the pattern of net benefits. These are what bring about the phenomenon."

" Maybe I missed it, but I think what is potentially interesting there is when we get inversions of that structure, or better yet, non-monotonicities such as we are currently seeing in many countries, with minimum interest rates (in some cases nominally negative) for bonds of about two years in maturity. I suspect that such shifts in patterns can bring about some curious and apparently paradoxical shifts of relative rankings of techniques that have complicated time patterns of relative net returns."

Yep. That's something it would be interesting to explore, but I didn't explore it here. You didn't miss it.

"Oh, and the bottom line from my old paper was that when reswitching can occur, discontinuities can occur in optimal time paths of growth for capital-labor ratios."

That's interesting. I think a closely related thing is that you might get weird fluctuations in the optimal time path for output. I was sort of getting at that in my Robinson Crusoe example. But then I wonder if those fluctuations couldn't be smoothed out by using a *mix* of the two techniques, and slowly changing the mix over time. (You farm half the land using the old technique and the other half with the new technique.) That is the question that I (or someone else) really should explore next (though it's maybe already been done somewhere). Take a reswitching example, then explore the optimal mix of the two techniques over time in a GE example. For example, if the switch causes ultra low output in the third year after the new technique is introduced, then just introduce the new technique slowly over time to more and more of the economy, to smooth out that low spot.

I wish I had spent more time talking to Luigi Pasinetti on this stuff when I had the chance. But I was a new prof, trying to teach 3 new courses, and get my thesis done. Stuff happens.

"But then I wonder if those fluctuations couldn't be smoothed out by using a *mix* of the two techniques"

I wonder if those discontinuities don't go away once you realize that that the present production decisions are made based on expectations of uncertain future paths, and that those expectations always change *continuously* unless the underlying stochastic output processes themselves have discontinuities.

I am intrigued by the implications of re-switching for the simple productivity/policy discussions that suggest that current low interest rates should solve our investment problem and hence productivity problem. If the issue is expectations about future harvests and markets as well as interest rate evolution, it seems to me that some of the simplistic policy pronouncements of various central bankers, finance ministers and other talking heads get problematic.

I just realised: you can always make food prices look like a geometric series as you move along the alphabet. Just choose different units for different foods to make it happen.

Im not sure this matters but in combinatorics they don't even bother solving for x, or r of your polynomials. Just use them as a clothes line for generating sequences of numbers.. Aka generating functions. Anyway changing the units seems valid, it's the coefficients that matter.

And then if you have n terms in your polynomial,where n is infinite, you switch to Having a power series. Hey is that the problem with aggregation, the fact that we don't subdivide a category to infinity. Because apparently you need power series to overcome some of zeno's paradoxes. Maybe its the same problem.

For a real world example of what is involved, Raymond Prince and I published a paper on this in 1985 in Growth and Change. We looked at numbers available then to compare cattle grazing and strip mining of coal in the US Southwest. We determined that switch points occurred at 2% and 7% roughly for real discount rates. In between coal mining was more profitable while in the higher and lower ranges it was cattle grazing. Driving this was high upfront costs for coal strip miniing that made it unprofitable at the higher rates, and then assuming somebody made them pay for the delayed cleanup costs, those delayed cleanup costs made it relatively unprofitable at the much lower rates.

A warning from this, identified by others prior to us, such as Herfindahl and Porter, is that one cannot necessarily and unambiguously say that lower interest/discount rates are necessarily "more conservationist."

As I understood it, the capital values depend on the interest rate structure which the creation of capital itself changes.

Nick,

And I'm saying it seems to me you can't aggregate "food" either, for exactly the same reason. So when farmers charge us for what they call "food", it's really all just mystification and exploitation and them grabbing part of the surplus.

I'm sorry, I missed this part. I thought you were saying that the supply curve of different types of food dependent on the interest rate. We can still aggregate consumption, at least conceptually, by the market price, say using a laspeyeres index. We would not be able to do this if the interest rate was a function of the price of food because then we would have a loop a la capital. But just saying that the interest rate influences the relative supplies of foods (say like the weather) does not in and of itself create a self-referential loop.

Lord: "As I understood it, the capital values depend on the interest rate structure which the creation of capital itself changes."

True (for the economy as a whole). But it will also be true for food. The value of chalking the fields depends on the food price structure. And chalking the fields changes the relative supplies of different foods, and will change relative food prices.

rsj: if we can aggregate apples today and bananas today, we can aggregate apples this year and apples next year.

My disaggregated foods example was supposed to ignore time. Fertiliser affects output today only, so interest rates don't matter. (Yep, not a great example to illustrate the idea).

Barkley: I think those are good examples. If there are costs at the beginning, and none at the end, it's simple investment. With costs at the end, and none at the beginning, it's like negative investment. And with both, it's some sort of mixture.

Implicit in this though, is the question: what is the alternative? Is the alternative not mining at all? Or is it waiting till next year to mine? I expect the answer is: whatever happens to be the next best alternative.

Which makes me think (though I don't think it's an entirely original thought): what's underlying all this stuff is the concept of "joint production". Sheep: wool and meat. Investment: output next year and the year after. Car: new car and 1-year old car and 2-year old car...etc. And cost of production theories cannot handle joint products. I should probably do a post on this.

Actually, a better example than fertiliser and food would be sheep. Suppose the farmer switches to a different breed of sheep, that produces more meat, less wool, more fertiliser, etc. You cannot define the benefit of the new breed of sheep independently of the relative prices of meat, wool, and fertiliser. Therefore sheep are an illusion.

if we can aggregate apples today and bananas today, we can aggregate apples this year and apples next year.

Let me try again.

Re-switching is important because it is the non-trivial portion of a two part argument. The first (trivial) part says that the price of a capital good is the interest rate (or one over it). The second (non-trivial) part part is re-switching, which says that the relative prices of capital goods are also a function of the interest rate.

The attack against aggregation requires both parts.

So what is your equivalent attack against consumption aggregation? What is trivially true for capital goods is not true for consumption goods. You need more than just the re-switching part of the argument.

rsj: "The first (trivial) part says that the price of a capital good is the interest rate (or one over it). The second (non-trivial) part part is re-switching, which says that the relative prices of capital goods are also a function of the interest rate."

First. That should be interest rates, plural.

Second: let's try it with sheep. The first (trivial) part says that the price of a sheep is the sum of the prices of the various joints of meat and wool. The second (non-trivial) part part is re-switching, which says that the relative prices of different breeds of sheep are also a function of the relative prices of the various joints of meat and wool. (Merinos produce lots of wool but not so good on the meat.)

Ritwik,

Capital is not time. When an entrepreneur decides to create a firm that sells, say, on line ticketing services, then he needs many ingredients. He needs to hire and train people, acquire land, buy servers, routers, write software, and create relationships with the relevant gatekeepers that control access to the payment system or to local vendors.

You can say that this process requires time just as it requires the ability to bear risk, the ability to hire talented people, the ability to see profit opportunities and access to credit relationships.

But the resulting capital of the firm -- the collection of software, hardware, land, specialized skills, and the supporting infrastructure -- is not equal to "time" anymore than it is equal to market insight or the ability to bear risk.

That is a category error. And the whole point of the re-switching debate is that these issues do not go away once you aggregate by market price.

let's try it with sheep. The first (trivial) part says that the price of a sheep is the sum of the prices of the various joints of meat and wool. The second (non-trivial) part part is re-switching, which says that the relative prices of different breeds of sheep are also a function of the relative prices of the various joints of meat and wool. (Merinos produce lots of wool but not so good on the meat.)

No problem, you can still aggregate based on price in that example.

The thing is that with consumption goods you can always argue that the ratio of market prices of two consumption goods reflect some sort of indifference between the two goods as a result of consumer preferences. And this allows you to, at least conceptually, aggregate based on price by letting one of the goods be a numeraire.

So the consumer is the aggregator of consumption.

Then to prevent something like re-switching, you only need downward sloping marginal utility of each good + non-satiation. Perhaps you need some other things -- you know better than I.

You do not care about non-convexities across time because consumption goods are not aggregated across time. They are assumed to be consumed in each period. If a good provides future consumption but is sold today, then it is a capital good by definition even if it is just a piece of paper that says "bananas tomorrow". The "tomorrow" turns the paper into a bond rather than a consumption good. If it is possible to purchase the good but not consume it in the same period as it is purchased, then it's not a consumption good.

But with capital, you can have these non-convexities that prevent the investor from being as effective an aggregator as the consumer. The investor can still try to aggregate, but there may not be a unique ratio of prices, there may be multiple ratios, leading to multiple definitions of quantity.

rsj

When the stock market says that Apple is worth \$600 billion (assume no debt), it is aggregating by market price. If I now say that the value of the firm's assets, and hence capital is \$600 billion, at this moment, what mistake am I making?

Ritwik, the mistake would be putting 600 billion, divided by some aggregate deflator as the value of K into a production function that determines the quantity of output produced by Apple. We do need some production function in order to make things work, and we try to relate interest rates to the rental rate on this K and whatever preferences we have.

The whole problem of the valuation of multiple production goods across time in the "Robinson Crusoe" case with NO money just if the "problem of interest" as posed by Bohm-Bawerk. (Not one good, not two goods -- multiple production goods).

Here's the key issue -- no one will extend the length of a production process unless it promised superior output, and most production goods can be used in various ways taking various lengths of time to produce alternative outputs.

The pricing of borrowed money in the real world, ie interest rates in the actual world, is related to the theoretical problem of "interest" as first clearly articulated by Bohm-Bawerk -- but anyone who knows their history of economic thought knows that these are two different questions.

@anon

David, the Sonnenschein-Mantel-Debreu theorem is often cited as an "anything goes" result, showing that violations of the law of market demand are always possible. Yet such violations are unlikely to occur in the real world, since they depend on pathological interactions between substitution and distribution effects.

I am curious as to whether "unlikely to occur" has been rigorously quantified anywhere in the literature. It is easy to find neoclassicals asserting that the interaction is rare and heterodoxist asserting that it is common.

@Greg Ransom

I dare you to define "the length of a production process"!

Greg: "The pricing of borrowed money in the real world, ie interest rates in the actual world, is related to the theoretical problem of "interest" as first clearly articulated by Bohm-Bawerk -- but anyone who knows their history of economic thought knows that these are two different questions."

The difference is: in the theoretical Robinson Crusoe case, there is one person, who only has to "coordinate" his actions with Nature. In the real world there are two or more people, who also have to coordinate their actions with each other, as well as nature. Right?

"Here's the key issue -- no one will extend the length of a production process unless it promised superior output,..."

That's not quite right. We store apples for later consumption, even though we know the apples won't multiply in storage, and some will go bad. The real 6-month rate of interest, deflated by apple inflation, is negative.

david: A farmer has the choice of different crop rotation techniques. There are (at least) three different crops in each technique, and maybe fallows too, where there is no crop.

We could say:

1. "No farmer will switch to a technique that produces lower quality of food unless it produces higher quantity of food".

2. "No farmer will switch to a technique that produces food later unless it produces a higher quantity of food".

ISTM you need a price/interest rate index in both cases, to define "quality", "later", "quantity". And you need to talk about preferences.

(You maybe don't disagree).

rsj: assume sheep produce 3 different cuts of meat: rack is best and dearest, leg is second best, shoulder is worst and cheapest. Different breeds of sheep produce different quantities of the three cuts. Let r represent the discount rate as you move to the next lower quality of cut. So the relative price of leg to rack is 1/(1+r), and the relative price of shoulder to rack is 1/(1+r)^2.

Then as r changes, you can get re-switching of breed of sheep.

BTW: TypePad seems to be playing up. If your comment doesn't immediately appear, go backpage, forward page, and re-post.

Nick,

" So the relative price of leg to rack is 1/(1+r), and the relative price of shoulder to rack is 1/(1+r)^2."

I don't get it. So all of this depends on some arbitrary exogenously imposed set of price constraints? So why do we care?

Same goes for capital. Different capital has different rental rates, and those rates vary feom period to period. We know that from MPT. So why the obsession over *the* interest rate? Also it's really confusing to use the word "interest" for expected profit. Let's use "interest" for debt, and profit for capital in general.

@Nick Rowe

I don't disagree. But your modus ponens is another's modus tollens, and it is hard to intuit "later" and "quantity" in a straightforward way. And of course the price vector isn't independent here.

K: "I don't get it. So all of this depends on some arbitrary exogenously imposed set of price constraints? So why do we care?"

You get it.

david: "But your modus ponens is another's modus tollens,..."

Took me a while to figure that one out, but I think I get it. But nobody ever says "you can't define "sheep" independently of the price vector", and takes that as a starting point to talk about the distribution of income between shepherds and everyone else.

"You get it."

:-)))

Ok, but then which part *didn't* Samuelson, Solow et al get at first? Did they really write multi-period models with flat term structures, and think that would work? What was Samuelson's (flawed) "non-reswitching" theorem all about, and what was he trying to prove? Why the big fight over nothing? (These guys weren't stupid.)

K: Dunno. I don't get it.

Maybe they thought that under constant returns to scale it ought to be possible to determine relative prices independently of preferences based on technology alone???

I blame Marshall. Not 100% sure why, but I still blame Marshall. He tried to downplay 1871. If Jevons had been a better swimmer, and hadn't died young from drowning (1882) this would never have happened.

If you produce sheep under constant returns to scale, using labour only (assume land is free), then you can pin down the value of sheep from technology only, but you need preferences to determine the relative prices of wool and meat, which are joint products. If the shepherds need to wear woolen cloaks to look after the sheep (so the shepherds don't freeze), you get production of sheep by means of sheep. You can't talk about the cost of producing a sheep independently of the relative prices of wool and meat, which depend on preferences. With two different breeds of sheep, you can get reswitching of breeds of sheep.

@Nick Rowe

You need to poke the hornet's-nest of the heterodox more often! The post-Keynesians will not generalize the Cambridge aggregation problem too much - they have their own aggregates to think about, after all. But the econophysicist guys will talk about instability of price tâtonnement and anything-goes and Sonnenschein-Mantel-Debreu until your ears fall out.

I regret to inform you that people who say "you can't define 'sheep' independently of the price vector" do exist. Usually it's 'deserved' labour wages or somesuch rather than ruminants, though. Grandiose charges that the entire price system fails to reflect individual productivity and contribution in any way are limited to the more frothy types. But they do exist.

Wasn't the great dream of the Sameulson era an easily-computable, stable, and unique general equilibrium?

I'm a little reminded of Nick's old fish-don't-see-the-water-they-swim-in post. The first and second welfare theorems didn't even exist back then, guys.

Nick - totally off topic - do you have a post where you explain what the optimal NGDP target growth rate is?

2 very good comments david. Your parting sentence, "The first and second welfare theorems didn't even exist back then, guys." came as a shock. "But we've always known about the first and second welfare theorems! After all, once you've seen an Irving Fisher diagram, and just added a few more dimensions, they're obvious!" Hmmmmm.

Frances: I don't. Maybe Scott Sumner has one. Anyway, it's 5%. Because it's been 5% in the past!

David,

"I'm a little reminded of Nick's old fish-don't-see-the-water-they-swim-in post."

My ultimate question is not "why were they so stupid?" On the contrary: there seems to be a general implication (see eg the wiki on the CCC) that the neoclassicals just acknowledged their mistake, but then proceeded to blissfully ignore it from there on. But then, apparently Samuelson completely revised his seventh edition to expunge all relevant errors. So the real question is, is the current theory subject to related flaws or not? Is there something deeply misguided about the current conception of capital, or are we fine now, having moved on and accepted a more modern (MPT?) perspective on aggregation as well as the possibility of the existence of multiple equilibria. Can I safely go back to work now? Or am I blissfully (but dangerously) ignoring some fatal flaw?

Well - it was certainly widely suspected to be true. But the possibility that simple price competition might be 'destabilizing' in some sense kept lurking, and the Depression lent motivation to the suspicion, and a lot of errors we recognize easily today - confusion between statics and dynamics, between a movement along a locus of points and a shift of the curve itself, assorted aggregation fallacies (the variety with openly problematic empirical consequences!) - kept allowing arguments to reach other conclusions. I think the most important work was in clarifying exactly what assumptions led to exactly what conclusions. That took until Arrow et al.

... progress in which was promptly halted when it was perceived that the great general equilibrium project had failed, so there's that.

Nick, if I was a finance minister grilling you on the subject of NGDP targeting, that's the question I'd ask (i.e. what's the optimal target and why). Got to get back to work - urgh.

@K

On the contrary: there seems to be a general implication (see eg the wiki on the CCC) that the neoclassicals just acknowledged their mistake, but then proceeded to blissfully ignore it from there on.

That's not really fair. It is quite easy to suppress aggregation problems: simply bite the bullet and insert assumptions on aggregate behavior. It's not like the core four assumptions that underpin S-M-D (of which the CCC is plausibly merely a special case) are perfectly and reliably true anyway. I discover local non-satiation of preferences every time I watch a barrage of TV advertisements.

If you can't derive the law of demand, just assume the law of demand. I mean, it's useful to investigate what happens without it - we don't want to commit the sin of Euclid's Fifth Postulate again - but some brilliant people already did explore the forbidden land and they tell us that Anything Goes there. That's not terribly useful.

Samuelson wanted a Grand Unified Economics: A implying B implying C implying D. Well, we found that B can't imply C. That still leaves us with all of partial-equilibrium micro and representative-agent macro. You just have to keep in mind that "microfounded" has a very restricted meaning in this context, that you are asserting that it is okay to aggregate K and L along state borders, and individuals into firms, and... etc. And that it is not okay to aggregate individuals into (say) social classes of differing consumption/production behavior, or into bank/non-bank groups as the post-Keynesians occasionally do, or into alternative national/ethnic/etc. identities as your politics dictates, etc.

And do keep in mind that the choice of the artifice of a pure exchange static economy to represent what is important and interesting about actual economies rather than, say, any of the game-theoretic alternatives that proliferated during the 1980s is itself a choice (remember the individuals-into-firms bit?).

All these at least partly reflect political choices rather than objective assessment, if only because counterfactual-via-econometrics is so dependent on theory to begin with. Okay, it's not very comforting to say that you shouldn't worry about capital aggregation because you have so much else to worry about, but it really is quite true. Modern mathematical economics in all its convex-set, fixed-point glory dates to the 1950s, it's still young, there are minefields everywhere.

George Selgin argues in "Less Than Zero" that around 2% would be best, because that would result in the least long-term disruption of price signals since gradual low deflation would reflect the tendency of the economy to become more productive over time.

Bill Woosley has some interesting counter-arguments that I've forgotten.

Those would be the first two people whom I'd ask.

K

There's an old Tyler Cowen post, on how Solow/ Samuelson basically conceded everything from a technical standpoint, but carried on as the overall implication for capital theory was 'meh', because capital markets - which the MIT neoKeynesians paradoxically refused to analyse properly - ensured that the neoclassical pov was empirically 'right' (or at least could not be refuted without showing capital market disequilibrium).

http://marginalrevolution.com/marginalrevolution/2007/05/was_there_anyth.html

I tend to agree with his judgement.

Eventually, as rsj mentioned, the problem may yet come down to 'what deflator to use for asset prices', but the Cambridge debates did not even begin to talk in terms of asset prices and capital markets homogeneity in the face of capital heterogeneity. The closest was when Samuleson offered the Bohm Bawerk defence of 'capital is time', without fully understanding its implications.

And you're right, 'interest rate' is an improper term. The term I prefer is Keynes's MEC (I prefer to call it the efficiency of marginal capital, EMC), or Fisher's rate of return over cost. Nick blames Marshall for the confusion, but I think the problem is much deeper. It is the 'economics' view of capital, which is still coming to terms with the fact that the capital markets know a way - right or wrong - to aggregate Apple's engineers, product managers, brand name, goodwill and vending machines without necessarily bothering about the price of any of these individual assets, or without jumping from one root of the underlying equation to the other (stochastic capital and stochastic MEC erase even that problem). It's a view of the world that laughs at Jim Bullard when he says that the productive capacity of an economy declines in a wealth shock, and which believes that Tyler Cowen's 'we are not as wealthy as we thought we were' is about reduced household consumption.

Again, at the risk of sounding like a broken record, I thought Hicks had basically solved this even for the economics view of the world by 1973 in his Capital and Time, or in 1974 in his 'Capital controversies - ancient and modern', when he noted that firm investment is on the whole not so much about buying a thing as about increasing longevity, about buying 'time'. I thought it was a particularly novel (and true) take on the Austrian conception without getting bogged down in the messiness of 'the average period of production' and such-like. But then, what do I know.

Modern theory, btw, seems to completely ignore capital theory. AFAIK, Jorgenson's neo-classical take on Tobin's q and various varieties of the AK growth model using Cobb-Douglas rule the roost. Capital asset pricing is about partial equilibrium and debates about market efficiency, capital theory be damned.

Again, John Geneakopolos comes to mind - he presented CAPM as GEI and GEI research as revealing how financial capital and real capital are different - but I can't quite parse him yet.

K + Nick,

1) Re-switching, as a concept, has nothing to do with a multiplicity of rates. It has to do with a multiplicity of production techniques as interest rates, however defined, change (it is called "re-switching" because you are "switching" to a technique and then switching back).

2) And for the same reason, there is no need to bring in bond/equity distinctions. Nothing to do with re-switching.

3) The political-economic cheap shots are not helpful, either.

Let's keep it simple and talk about re-switching, mK?

Nick, re: the lamb shoulder discounted by preferences -- are you saying that preferences are changing? I would be happy to only consider models in which they don't change. But if you want to think of your preference discount changing, causing the same re-switching that would occur as a result of rates changing, then fine, then I agree that similar aggregation problems exist in that sense.

In any case, you are really hitting the same problem, as changing preferences for one type of lamb meat over another will cause changing techniques and will hit capital, as what we really need to aggregate is what goes into the production function -- capital and labor.

Whether or not re-switching itself is important (I suspect it is not), what *is* problematic is how we aggregate production, believing that everything is produced in one giant real process and then an auction is held in which prices are applied.

What I suspect is the true insight here is that the production process itself is a function of expected and present prices. This goes back to the dispute about whether aggregate supply is exogenous or not or whether you get that nice hyperbola where total output is always the same as long as prices are flexible. Re-switching is one of several lines of attack on the notion of this aggregate supply curve.

Ritwik,

The definition of capital is independent of what motivates capitalists. We need a function f(K,L), or some mathematical equivalent to this. The change in K has to map to net investment. If you choose to aggregate K by market price, then the wild swings in market price clearly don't correspond to wild swings in K, so you must add a deflator. But that deflator will not work for individual firms, some of whose market value is rising and for others its falling even as the underlying book value is moving in yet another direction.

You need a different deflator for each firm. Meaning that you've achieved nothing -- you've added a million new tweak parameters, one for each firm, without any theory that predicts what they will be in response to a change in the overall price level.

This problem is not solved.

Nick,

The alternative to the mining was cattle grazing, assumed to have a steady flow of real net income over time. Looking at the broader agricultural example you have been dealing with, while sheep may not be a part of it, there are plenty of areas of agriculture that do exhibit the sorts of complicated time patterns of returns that can lead to the sorts non-monotonicities that lead to multiple roots and all those other tricky problems people have been discussing. Some of these end up in more garden variety oddities as backward-bending supply curves in fisheries and forests and some other items, as well as cycles in production with lags (see cattle and pigs), in come cases even arguably chaotic dynamics.

Let us be clear. The real problem arising from the reswitching controversy was not that particular phenomenon but the broader matter of non-monotonic demand and supply functions of various forms of assets. Samuelson among others was quite clear about this. Also see Burmeister and others. While many argue that physical and financial capital are distinct, they are not necessarily so, although I am not going to argue that the turmoil we have seen in financial markets arises from paradoxes of capital theory.

To Greg Ransom: It is my understanding that it was Hayek's awareness of some of the complications arising from complicated time patterns of returns that led him The Pure Theory of Capital to pull back from the old Bohm-Bawerkian conceptualization of there being an well-defined "average period of production" that clearly defines or measures "capital as time" in some general sense.

rsj

Say,

Y(t) = EMC(t)K(t)
I(t) = Y(t) - c(t)K(t)
K(t+1) = K(t) + I(t)

Book values don't matter, only market prices do. The deflator that we use for K(t) is the same as the deflator for Y(t). Have different deflators for individual firms. Let the deflator for each firm be the same as the deflator for its output. Let the deflator itself be stochastic! Why s that a problem?

(As an aside, why is the multiplicities of deflator for output itself not an issue? There are multiple own rates of interest. And there are multiple own rates of inflation. And there are multiple own rates of growth. No one seems to bother much about these millions of own rates when constructing national income accounts. Or when measuring inflation. So why only for capital?)

Why can't the wild swings in market prices correspond to the wild swings in capital? Do market prices really have 'wild' swings? Again, I don't wish to push the point too much - because I don't necessarily believe in this model fully - but Fischer Black basically pooh-poohed Shiller's results by saying that he is surprised stock prices are not more volatile, given the massive uncertainty and heterogeneity of expectations. Say that the 'true capital' is between 1/2 and 2 times of the market capital 99.99% of the time.

Is this an incoherent or tautological model? Or one with millions of tweak parameters? I don't think so. In the simplest form, it has two parameters for the rate of return and no more tweak parameters than any other aggregate model.

I don't completely believe this model. I think liquidity preference makes the cost of capital sticky, so that the ex-ante cost of capital itself may diverge from the ex-ante efficiency of marginal capital, even if the ex-ante vs ex-post differences may be explained by a stochastic error term. I think financing patterns and dislocations may divorce ex-ante savings from ex-post savings. And I tend to believe that the wealth curve is an LM curve, not an AS curve. And I think the model is too aggregated.

But as a benchmark to begin from and explain divergences from, I'd rather begin with this and a properly specified asset pricing model than with any other constructions.

Barkley: I tend to agree with your 10.17 comment (i.e. it makes sense to me).

One small point. When you say "The real problem arising from the reswitching controversy was not that particular phenomenon but the broader matter of non-monotonic demand and supply functions of various forms of assets." I would replace "assets" with "goods". I really wish I could come up with a better example than "sheep" to illustrate my point. Because sheep are an asset, and produce future wool and lambs. So sheep are still too much like capital. I want a good that you produce *now* and that produces 2 or 3 different goods *now*, and them immediately dies. So that time and interest rates have nothing to do with the value of my good. Sheep live too long for my purposes. Maybe a "dead sheep"?

rsj: "Nick, re: the lamb shoulder discounted by preferences -- are you saying that preferences are changing?"

Well, let me say that the change in relative prices of various cuts of meat should be understood in the same way that the change in rates of interest is understood. It *might* be a change in preferences that caused interest rates/relative meat prices to change. Or it might be something else. Or we might just be doing a stability experiment to see which way demand and supply curves slope.

... mutton?

david: No, because sheep=mutton+wool! Maybe dead sheep = mutton + sheepskin?

The other trouble with mutton: I don't think anybody eats it nowadays. At least not knowingly. It's all lamb. I wonder what they actually do with mutton? Does the old metaphor "mutton dressed as lamb" still work?

I'm just doing a new post on sheep.

Nick Rowe,

"I wonder what they actually do with mutton?"

Cook it thoroughly and call it lamb.

Trivia: by virtue of its importance in the cuisine of South Asia and the very very high population densities there, mutton is probably the meat with the most consumers worldwide (although very little of it is eaten per consumer there).

Aha! W Peden + david = "Cook it thoroughly, add lots of spices, and call it 'lamb curry'" That makes perfect sense. International trade explains why I don't see mutton.

Notice how we talk about cow's milk, beef curry and ox tail! The language of food is a very complicated affair.

One of the horrifying things about living in England after being raised in Scotland was the dearth of sheep products of all kinds. I don't know how bad it is in Canada, Nick; my main memory of Canadian food was having oatcakes and cheese on the flight over from the States, which was a wonderful taste of home after almost a month in Boston.

Lamb is difficult here. There's a little bit of Canadian lamb, fresh, but more expensive, and only some times of the year in some stores. (This is not sheep country, maybe the winters, or coyotes??) You can get NZ or Oz lamb legs, loin or shoulder chops, frozen, most supermarkets (not all). In Oz they sold great bags of kidneys. Extremely rare here. I wonder if it's culture, rather than climate/coyotes? Germans don't like lamb IIRC. But there are so many immigrants from so many lamb-eating countries?? Brits, Irish, French, middle east, south asia. Dunno.

Part of the food language complication is due to the Norman conquest, I think. If it's running around in the field it has an Anglo Saxon (i.e. German) name. If it's on the table, it has a French name? Cow/kuh beef/boeuf? Old hare = hare = Haas (German). Young hare = leveret = lievre (French)? (My pet theory.)

Nick, you can imagine a dictator forcing two or more people to coordinate there actions, so the number of people isn't sufficient to identify the problem.

The real issue is that in the real world there is money & there are assets, there is credit, there are lenders & borrowers, there are taxes & government, there are banks & central banks & there rival perceptions/judgements, there are laws, regulations and price controls, etc., etc.

The existence of all of these create price ratios and alternative costs across time for things that are not time-consuming production goods -- money and credit for example are not production goods.

For example, changing cash balance preferences, ie "Liquidity preferences" is just one element which effects interest rates, which isn't directly a product of valuational relations among alternative time-consuming and alternative output producing production goods.

Nick writes,

"The difference is: in the theoretical Robinson Crusoe case, there is one person, who only has to "coordinate" his actions with Nature. In the real world there are two or more people, who also have to coordinate their actions with each other, as well as nature. Right?"

Nick, your argument here make no economic sense to me.

Greg wrote: "Here's the key issue -- no one will extend the length of a production process unless it promised superior output,..."

Nick wrote: "That's not quite right. We store apples for later consumption, even though we know the apples won't multiply in storage, and some will go bad. The real 6-month rate of interest, deflated by apple inflation, is negative."

We prefer 5 apples in April to 10 apples in September.

Hayek goes through all of his in the paper in which he introduced time dating & intertemporal equilibrium to economics "Intertemporal Price Equilibrium and Movements in the Value of Money" (1928). Hayek was specifically looking at the winter demand for agricultural products that were costly to store, on analogy with the geographical pricing problem of goods were costs to transport were included in valuational relations.

Then there are Scotticisms here up north e.g. brambles instead of blackberries, neeps instead of turnips, finkadella for meatballs.

There's also the old Oxford common-room philosophy puzzle-

- which perhaps says more about Oxford philosophy than either language or food.

(Just noticed that the beginning of that conversation is at the end of this video: http://www.youtube.com/watch?v=KLVbxg5zZuo)

Nick writes,

"The difference is: in the theoretical Robinson Crusoe case, there is one person, who only has to "coordinate" his actions with Nature. In the real world there are two or more people, who also have to coordinate their actions with each other, as well as nature. Right?"

Nick, the issue of coordinating actionsbecomes truly relevant the the problem of the price determination of interest only once the number of individuals and the sophistication of the society increases to the point where money and credit are required to facilitate coordination.

"@Greg Ransom

I dare you to define "the length of a production process"!"

It takes 30 minutes to make a kid's bow & arrow out of sticks and twine.

Length defined.

So what's the issue?

Nick -- 5 apples in February is a superior product to 10 apples in September.

(of course, in these sorts of numbers, in this example we are assuming the background world of, say, 200 years ago when today's advanced storage technology did not exist, and when having food in winter was crucial to survival. The ratios today are different, as are the qualities & numbers of the product. Today we would perhaps say 9 apples in April are superior to 10 apples in September, or whatever, the complex economics of today and the technologies used utterly escape our ability to imagine in complete detail.)

Barkely writes, "To Greg Ransom: It is my understanding that it was Hayek's awareness of some of the complications arising from complicated time patterns of returns that led him The Pure Theory of Capital to pull back from the old Bohm-Bawerkian conceptualization of there being an well-defined "average period of production" that clearly defines or measures "capital as time" in some general sense."

Hayek was aware of the make-shirt, non-marginalist nature of Bohm-Bawerk's "Ave Period of Production" from the 1920s. He used it as a stand-in only, and with the understanding that he did not have a full understanding of what its full limitations might be.

Over time Hayek came to grasp more and more of these limitations -- with help from all sorts of economists who began investigating the issue.

More significantly, Hayek began to see that with technology change & differences in perception of market opportunities and novel uses of technologies in novel situations, that the whole formal mechanism of the equilibrium construct was inadequate to capture the constant coordination of production goods, many of them which would never be produced again, but which retained economic value until they were used up.

It is worth noting that this move was at the core of Hayek's rejection of the usefulness of math in capturing the creation and coordination of value via the creation and coordination of production goods. Hayek, during the war time paper shortage, found it not important enough to push for the publication of his mathematical appendix to _The Pure Theory of Capital_ (Hayek was lucky to get the book published at all, actually).

Hayek's loss of faith in the use for math in the theory of production was also added to by a math paper on Bohm-Bawerk's "Ave Period of Production" by someone like Baumol or Malinvaud (I can't at the moment recall just who), which went formally some of the problems with the construct. Hayek saw this train of research as a lot of formal work to establish the unworkability of something Hayek has already increasingly seen as a flawed and incomplete makeshift.

Hayek came to perceive that math formulas involving aggregate "value" relations could not capture either the relational valuational significance of multiple production good (marginalism) nor what was of explanatory significance in the creation and coordination of multiple production goods across time in the real world, where, for example, technologically inferior bygones often retained economic significance until they were used up.

The big lesson -- marginal valuation applied to individual goods does not transfer to aggregate relations of mass classes of goods. Which folks should recognize at the core of Hayek's critique of Keynes and as the core of Hayek's Nobel Prize lecture.

The closest Hayek comes to spelling any of this out is in his _The Pure Theory of Capital_.

Hi Nick:
I'm glad to see you're paying attention to the capital debates. A few brief things (I'll try to post something longer on my blog, this weekend, so as not to write too much here). Not sure I get why you think the time element changes things. Even with many possible futures, the traditional method of economics (accept by Marshall, Wicksell and Walras) was that you need a uniform rate of profit (and the rate on interest, the natural Wicksell would call it) must adjust to that one. The Arrow-Debreu solves the problem by ditching the notion of a uniform rate of profit, but then the substitution to more capital intense techniques has no relation at all with a uniform and lower rate of interest (also not clear what competition means if there is no uniform rate of profit). Also, you can talk about capital (and food) being scarce, what you cannot say is that the remuneration of capital (or the food producing sector) is related to scarcity.
Best,
Matías

By the way, lowering the rate of interest, or the term structure, might have a positive effect on demand, for a capital-debate Keynesian like me, since consumption is positively affected by that. Also, government expantionary policies become cheaper with lower interest rates, and you might get more fiscal expansion. So there might be some agreement on policy, if not on theory.

Matias: Welcome! (And thanks for a more positive response to my thoughts than some Neo-Ricardian(?) bloggers have offered!)

"Even with many possible futures, the traditional method of economics (accept by Marshall, Wicksell and Walras) was that you need a uniform rate of profit (and the rate on interest, the natural Wicksell would call it) must adjust to that one."

I hadn't realised, until I read your comment just now, that *maybe*, when some people talk about "uniform rate of profit", they mean something very different to what I thought they meant.

I thought they meant: A uniform rate of profit across different industries (adjusting for or ignoring risk).

But you seem to mean: A uniform rate of profit across different periods of time (i.e. a flat term structure).

I would say that arbitrage is what creates a uniform rate of profit across different industries (or different assets).

I would say that *nothing* creates a uniform rate of profit across different periods of time. The term structure is not (in general) flat. It could slope either up or down, or wiggle around. Even if we are talking about Wicksellian "natural" rates of interest. E.g., if everyone wants to go on a big consumption binge every 7 years, and fast for the remaining 6 years, (and if everyone knows about this), we are in general going to see a big spike in the term structure at 7 year terms.

Real interest rates on fresh strawberries are not flat over monthly data.

A "uniform rate of profit" over the term structure would only hold under very special assumptions.

I think that neoclassical theory, if it is to mean anything, assumes that the economy is always "tending toward" a state in which profit rates are uniform across time and space (in the long run) -- a "stationary state" if you will. This is how the models acquire meaning. This is tended toward through the mechanisms of competition (the interaction of supply and demand). At the level of capital theory, it is assumed that supply and demand for capital versus labour are dependent upon the rate of interest (which, in neoclassical theory is assumed to be influenced by the rate of profit).

This is where the Sraffian critique comes in with his reswitching argument. He shows that the demand for capital versus labour does not correlate coherently with the interest rate (the supply price of capital). At high rates of interest, Sraffa found, more capital may be demanded than at low rates of interest. Here, I'll quote Paul Samuelson:

"The phenomenon of switching back at a very low interest rate to a set of techniques that had seemed viable only at a very high interest rate involves more than esoteric difficulties. It shows that the simple tale told by Jevons, Böhm-Bawerk, Wicksell and other neoclassical writers — alleging that, as the interest rate falls in consequence of abstention from present consumption in favor of future, technology must become in some sense more 'roundabout,' more 'mechanized' and 'more productive' — cannot be universally valid."

(Yes, I'm pulling these quotes from Wiki -- sue me...)

Because of this there is no "tendency" for the interaction of supply and demand for capital versus labour -- through the mechanism of the interest rate -- to be allocated in the neat fashion that neoclassicals assume. And from here the idea of a self-regulating market allocating resources according to timeless "laws" begins to collapse. Marc Lavoie sums up with respect to the issue of the long-run and the idea of a "stationary state" (i.e. a long-run equilirbia) -- which appears to be causing confusion above.

"It is usually asserted that only aggregate neoclassical theory of the textbook variety — and hence macroeconomic theory, based on aggregate production functions — is affected by capital reversing. It has been pointed out, however, that when neoclassical general equilibrium models are extended to long-run equilibria, stability proofs require the exclusion of capital reversing (Schefold 1997). In that sense, all neoclassical production models would be affected by capital reversing."

The results of this are quite profound when thought through in any real way. For one, the theory of marginal productivity of capital and labour -- which assumes that each get their "fair share" -- is rendered meaningless. Distribution becomes a matter of politics, class power and so on (very suggestive given the stagnation of real wages since the 70s). There are many other thing put into question too, but I won't go into them here. But, so far as I know, the neoclassicals ignored this with some rather crude assertions. Christopher Bliss is typical:

"If one asks the question: what new idea has come out of Anglo-Italian thinking in the past 20 years, one creates an embarrassing social situation. This is because it is not clear that anything new has come out of the old, bitter debates. Meanwhile mainstream theorizing has taken different directions. Interest has shifted from general equilibrium style (high-dimension) models to simple, mainly one-good models. Ramsey-style dynamic-optimization models have largely displaced the fixed-saving coefficient approach..."

And so on.

"Can the old concerns about capital be taken out, dusted down and addressed to contemporary models? If that could be done, one would hope that its contribution could be more constructive than the mutually assured destruction approach that marred some of the 1960s debates..."

Well, that's the clincher isn't it? Yes, the "old" debates probably can be applied to the new models. But will they result in anything but the destruction of those models? No. Bliss calls this "mutually assured destruction". Why? Neo-Ricardians are perfectly happy with a distribution theory based on relative class power etc. So, it's not "mutually assured destruction" at all. But it is certainly a destruction of neoclassical economics. But no one involved in these debates would have any bones about that: to undermine the neoclassical approach as being theoretically incoherent was the whole point.

I'm not totally clear on what you're trying to argue here. It seems to me that you're trying to argue first that the problem of aggregating capital by price is similar to the problem of aggregating sheep (by what?). And second, that it's not a problem to aggregate sheep, so it's also not a problem to aggregate capital by price.

This is either true but trivial or interesting but false.

Because the interesting question is not whether you can make a useful aggregate, which will be of interest to macroeconomic planners, by aggregating by price. Obviously you can. The question is whether you can build a causal theory of the relationship between capital aggregated by price and return to capital without reference to the underlying physical plant. And which way the causal chain goes in that theory.

Clearly the causal relationship here goes from underlying physical plant and demand to revenue, and from revenue to valuation of the plant. The upshot of which is that using the valuation of capital as a proxy for the volume of capital mistakes consequence for cause.

Now, that may not matter for your theory. After all, if you're using capital valuation as a proxy for capital volume, you can simply recast your theory in terms of capital volume. Which is at least conceptually possible, even if such aggregation is tricky in practice. But it very much does matter for any attempt to confront that theory with empirical data, because the data you're confronting your theory with may or may not correspond to any of the variables that are in your theory.

- Jake

@ Matias

"By the way, lowering the rate of interest, or the term structure, might have a positive effect on demand, for a capital-debate Keynesian like me, since consumption is positively affected by that. Also, government expantionary policies become cheaper with lower interest rates, and you might get more fiscal expansion. So there might be some agreement on policy, if not on theory."

I don't think that this is clear any more. The Godley/Lavoie models indicate that lowering interest rates provides a short-term boost to demand, but creates a long-term drag due to lost interest income. I.e. When the rate falls from, say, 5% to 4%, entrepreneurs and consumers take advantage of these new rates by either borrowing more or restructuring their outstanding loans. This provides a boost to demand. However, as the new lower rates become normalised and inbuilt into investment/borrowing decisions, the effects of interest income begin to be felt in a more immediate sense (i.e. they are no longer offset by the rising investment/demad). Savers, who were originally getting interest income at the higher 5% rate, find that their income has shrunk to the new 4% rate. This creates a drag upon consumption demand in the medium-to-long run.

Add to this the problems with reswitching and policy becomes more problematic. IMHO this throws a lot of light on the failure of the QE programs to do what they "said on the tin". And buttresses the view put forward by Credit Suisse that ZIRP policies are now having a predominantly negative effect upon demand.

TheIllusionist: Thanks for a constructive comment. This is maybe helping me see where the Neo-Ricardians (Neo-Marxists? I know some of you guys argue about this) are coming from.

"I think that neoclassical theory, if it is to mean anything, assumes that the economy is always "tending toward" a state in which profit rates are uniform across time and space (in the long run) -- a "stationary state" if you will."

I don't see it that way. Take a really simple and extreme example. Land and Labour produce wheat only. No other goods, and only one technique. Nothing ever changes year to year, and the economy is always in full LR equilibrium, with no uncertainty. But things change month to month. All the wheat is produced in August, and the storage technology means that 1% of the wheat is lost per month. But people's preferences are the same every month, and there's diminishing MU of eating wheat, so they store wheat from August to July. Monthly interest rates (measured in wheat) for 11 months of the year will be minus 1%. But the monthly interest rate from July to August will be positive, and greater than 11% (depending on the rate of pure time preference).

Take a second example. Introduce a second good, barley, which is just like wheat, except technical change is slowly improving barley productivity every year. People like eating both, so both get produced, and both get eaten every month. Both wheat and barley have a monthly interest rate of -1% for 11 months. But the July-August interest rate measured in wheat will be lower than that measured in barley.

Now forget seasonal variations. Suppose an economy starts out in stationary state, with constant everything, and a flat term-structure. All of a sudden someone invents a new technique, that is profitable at existing interest rates. The new technique produces less wheat in year 1, the same wheat in year 2, and more wheat in year 3 and all later years. What happens depends on a lot of things, like preferences, and whether there are other old techniques, that might have been unprofitable at the old interest rates but might be profitable again if used in conjunction with the new technique. But the term structure will change. The 1-year rate will rise, the 3 year rate will probably fall.

Samuelson: "It shows that the simple tale told by Jevons, Böhm-Bawerk, Wicksell and other neoclassical writers — alleging that, as the interest rate falls in consequence of abstention from present consumption in favor of future, technology must become in some sense more 'roundabout,' more 'mechanized' and 'more productive' — cannot be universally valid."

The point I am trying to make in this post is that there is more than one "future" period, just as there is more than one type of "food", and that is why simple statements comparing the present with *the* future are as potentially wrong as simple statements about the production of "food" in the present. In other words, "reswitching" is about joint products, and has nothing to do with time and capital per se. Capital goods aren't the only example of joint products.

"For one, the theory of marginal productivity of capital and labour -- which assumes that each get their "fair share" -- is rendered meaningless."

I have a different take on this. I don't think there *is* a theory which asserts that "the rate of interest is determined by the MPK". Or, rather, any neoclassical economist who does assert that theory is either: assuming a very special case where the intertemporal PPF is a straight line; or confusing a co-determinant with *the* determinant. For a very simple reason: that "theory" ignores preferences, and you can't determine interest rates without talking about people's preferences (except in very special cases which the real world is nothing like). (I discuss this a little more fully and clearly in my previous post (skip down to the Irving Fisher diagram).

Everyone: I have to do something else today. I will return, probably tomorrow, but maybe this PM.

Okay, Nick, now I think I see where you're coming from.

"Monthly interest rates (measured in wheat) for 11 months of the year will be minus 1%. But the monthly interest rate from July to August will be positive, and greater than 11% (depending on the rate of pure time preference)."

You can do this in an infinite number of ways. Why not measure the interest rates on a daily basis? An hourly basis? A per minute basis? I know that may seem absurd but it is no more absurd than aggregating at the monthly level. The standard approach, I would think, would be to determine "the rate of interest" in your example, by finding the mean over the course of the year. I will get to why this is important below.

This is the same in the multi-good economy. Sraffa was well aware that there were as many rates of interest as there were goods -- remember his critique of Hayek in the 1920s [http://uneasymoney.com/2011/09/09/sraffa-v-hayek-2/]. But it is assumed that once a numeraire is chosen -- say, gold -- that the various interest rates will move around the interest rate for gold. This, approximately, is what I understand "the rate of interest" to mean -- specifically, today, the short-term rate as set by the central bank.

"But the term structure will change. The 1-year rate will rise, the 3 year rate will probably fall."

Okay, now here's where we get back to what I was saying above about long-run equilibria and "stationary states". It is, of course, true that term structures will change -- and they will change in different ways for different goods over time. I.e. Interest rates will change differently across time and space. But I think that this is a side-issue with regards to the debates over Capital theory.

Neoclassical theory is based on static theorising. Dynamics are introduced -- usually in terms of comparative statics and not real dynamics, I should add -- but for what they are, dynamics are added later. Thus is order to "prove its mettle" the neoclassical theory must be able to show that it can handle statics sufficiently well before we start talking about dynamics (i.e. term structures across space and time). This is inherent in the methodology itself. As I said in my last comment, neoclassical theory starts out by positing a perfect or general equilibrium position and then attempts to show that all imperfect or disequilibrium states tend to converge on the static position outlined.

I suppose the underlying assumption is that despite the fact that there are different rates of interest for different term structures etc. these all converge around, or tend toward, a single rate of interest which is the general rate of interest (think of the general rate as a sort of 'attractor' in physics [http://en.wikipedia.org/wiki/Attractor]). This seems to me the essence of the general equilibrium theory.

So, when you say there is no "one future state" that is irrelevant because it is assumed that all future states are moving in a set direction and they are moving there due to certain "laws" that neoclassicals derive from a static model. Again, this is because neoclassicals start with a static model and then derive dynamism from there. Sraffa and the Cambridge crowd sought to undermine this static model which would show that since the neoclassicals couldn't even posit a coherent static model they would be completely lost when it came to dynamics. The Wikipedia page makes this point in a different context:

"[T]he variation of the rate of profit is theorized as happening at a specific point in time in purely mathematical terms rather than as part of an historical process. The point is that if neoclassical conceptions do not work at a specific time (statics), they cannot handle the more complicated issues of dynamics. This critique of the neoclassical conception is more of a matter of pointing out its major technical flaws in the theory than of presenting an alternative."

TheIllusionist, I'm not sure I buy that continually low interest rates would have a delayed contractionary effect. It seems to me that low interest rates make investments viable that would not otherwise be viable, and this should more than offset the loss of subsidies for idle wealth. Particularly since idle wealth is, well, idle, so the propensity of idle wealth to spend extra income is low (otherwise it wouldn't be idle wealth).

Of course you'll get a drop in investment once the backlog of projects that suddenly become viable at the lower interest rate has been cleared. But that's not the effect you're talking about here.

- Jake

@ Jake S

In keeping with the Godley/Lavoie (i.e. Post-Keynesian) framework, investment is determined by the level of aggregate demand. Interest rates are thus secondary. In a boom interest rates may well work to spur investment, which will in turn keep aggregate demand afloat -- but this will lead to the diminishing return that Kalecki noted in the 1940s. See:

http://www.interfluidity.com/v2/3451.html

"The rate of interest or income tax [might be] reduced in a slump but not increased in the subsequent boom. In this case the boom will last longer, but it must end in a new slump: one reduction in the rate of interest or income tax does not, of course, eliminate the forces which cause cyclical fluctuations in a capitalist economy. In the new slump it will be necessary to reduce the rate of interest or income tax again and so on. Thus in the not too remote future, the rate of interest would have to be negative and income tax would have to be replaced by an income subsidy. The same would arise if it were attempted to maintain full employment by stimulating private investment: the rate of interest and income tax would have to be reduced continuously."

However, once this self-reinforcing dynamic meets its end point, the pure Godley/Lavoie "stationary state" model kicks in and the effects of interest rates on investment fall to nil, while the effects of interest rates on interest income lead low interest rates to exert a negative pull on aggregate demand. If you read the Interfluidity post above you'll see that this is where we are today.

So, yes, investment may increase. But, in lieu of activist fiscal policy, this will result in diminishing returns and interest rates falling lower and lower until you reach a point where low interest rates sap demand from the economy. (The neo-Keynesians call this a "liquidity trap", but this is misleading).

someone posted this elsewhere and I felt it appropriate to reproduce here:

"As far as I see it, Rowe is trying to make the same argument as the one you can find in Bliss (1975), namely that the uniform rate of profit (or uniform rate of interest, in neoclassical terminology) can be meaningful only under "very speci
al circumstances" (i.e. a stationary equilibrium). But as pointed out by Matias Vernengo on Rowe's post, the issue at stake, in the wake of Arrow-Debreu's type of replies to the controversy, is that the traditional method of economics came to be abandoned at that time. Rowe's reply to Matias does not help matters either, in my opinion, and moreover Rowe does not see that the capital debates concerned not only the profit rate of industries but of heterogeneous capital goods (hence Walras's theory of capital is also undermined by the critique, and so his whole economic general equilibrium system). Also, Rowe misundertandly writes that arbitrage is what creates unifomrmity of profits on assets or industries, but arbitrage concerns the demand prices for capital goods, whereas the relavant uniformity of profit rate concerns the rate on the supply prices of the capital goods, i.e. the rate of profits on the costs of producing the capital goods that which their supply prices are meant to represent. And this was of course a big issue in classical economics but also in neoclassical economics at least up until the forties' or maybe fifties'."

Also, it seems that the GE models have been subjected to the same critique as the old neoclassical theory. The paper is rather garish in my opinion, and I wouldn't be much interested in the details -- it hardly surprises me that GE theory should suffer the same faults as post-war neoclassical theory generally. But if anyone does feel like plodding through the details, here you go:

"It has been shown that transitions involving reswitching and employment opportunity reversals can be represented within intertemporal equilibrium models. In our examples, the paradoxical relations between the distributive variables and the intensity of capital do not preclude the existence of equilibria, with properties, however, which run counter to generally accepted notions of
stability. A rising supply of labour is absorbed by raising the real wage rate, accumulation at constant full employment is made possible with a rise of the rate of interest, in a given state of knowledge. If normal reactions prevail, the factor prices should move away from these equilibria which we have constructed. The conclusion seems inevitable: intertemporal equilibrium does not provide a stronghold which could be better defended against the critiques derived from capital theory than the older notions of long-period neoclassical equilibrium: They stand or fall together."

JakeS: "I'm not totally clear on what you're trying to argue here. It seems to me that you're trying to argue first that the problem of aggregating capital by price is similar to the problem of aggregating sheep (by what?)."

Assume labour and land produce sheep. (Assume sheep reach maturity very quickly, so we can ignore interest rates etc.) And each breed of sheep produces 3 different cuts of meat (in fixed proportions, for simplicity): best quality, worst quality, and middle quality. There are different breeds of sheep that produce different proportions of the 3 cuts of meat.

Then: you can't measure the total quantity of sheep independently of the price premium consumers pay for quality; as *the* quality premium changes, you can get reswitching between breeds of sheep; causality runs both ways between the quality premium and the total *value* of sheep and the composition of the total volume of sheep.

Does this create practical problems for agricultural economists doing empirical work? Yes, it probably does. They can't just write down a production function with things like "total value of sheep" and "total value of meat" as arguments. Because a production function is supposed to reflect technology, not preferences for different kinds of meat. But would anybody argue from this that neoclassical economics is incoherent, or that the price premium for meat that is perceived to be of higher quality is somehow illegitimate, and not reflective of relative scarcity? I don't think so.

This is just evidence that Samuelson didn't understand Bohm-Bawerk & isn't working with Bohm-Bawerk's foundational logic of choice micreconomics, i.e. Samuelson is simply muddling Bohm-Bawerk's Robinson Crusoe microeconomics with Bohm-Bawerk's failed aggregate math construction 'applied" to a real work money economy. You have to de-muddle these two logically separate efforts do work that isn't a complete conceptual mess.

The logic of Bohm-Bawerk's logic of choice doesn't go away because conditions change. Longer production processes will only be chosen if they promise superior output. Under different conditions, different output is superior to other output.

This isn't remarkable.

It's only remarkable to economists who are doing economics wrong, who are working with incompetent "tools" and an incompetent "took kit" and an incompetent picture of how to use "tools" to allow us to produce sound, explanatory causal explanations in economics.

Samuelson writes,

"The phenomenon of switching back at a very low interest rate to a set of techniques that had seemed viable only at a very high interest rate involves more than esoteric difficulties. It shows that the simple tale told by Jevons, Böhm-Bawerk, Wicksell and other neoclassical writers — alleging that, as the interest rate falls in consequence of abstention from present consumption in favor of future, technology must become in some sense more 'roundabout,' more 'mechanized' and 'more productive' — cannot be universally valid."

who cares what Samuelson said, Bohm Bawerk's "roundaboutness" has also been thoroughly critiqued by cambridge economists back in the 50s-70s. But you can continue to ignore all of the literature written during the CCC if you'd like.

Samuelson & the 'neoclassical" capital theorists misuse the logic of marginal valuation and they misuse the logic of Bohm-Bawerk's microeconomics of production good valuation across time.

As Ludwig Lachmann rightly explains, the 'neoclassical' capital theorists muddle classical, universal, aggregated class categories of the pre-marginalist Ricardo type with the marginalist logic of relational valuation across time pioneered by Bohm-Bawerk in his microeconomics of capital goods. (Bohm-Bawerk in his work "average period of production" work is guilty of the same muddle.)

If you want to do the microeconomics right, you have do to pure logic of choice of the Robinson Crusoe type WITHOUT categories and goods that only exist in a real, money and credit using economy.

This is a point Hayek hammers again and again in some of the most famous papers ever written in economics -- arguments that constantly go right over the head of the tenured economists who police the bogus standards of "scientific" economics.

Hayek is particularly clear on all this in the first half-dozen chapters of _The Pure Theory of Capital_, which should be read with those famous Hayek essays readily at hand, some of which are footnoted in Hayek's _Pure Theory_ at crucial points.

@ Greg Ransom

I don't think you understand the point upon which this debate turns. The Austrian/Neoclassical argument is a sideshow with regard to the Cambridge debates.

"Further light on the conceptual roots of the marginalist view of capital is shed by the contributions of Jevons
and Böhm-Bawerk. In their theories, profit is considered as the remuneration due to the capitalist as a result
of the higher productiveness of ‘indirect’ or ‘roundabout’ processes of production than of processes carried
out by ‘direct’ labour only. The generalization of the marginal principles which they carried out is thus
associated with the description of the production process as an essentially ‘financial’ phenomenon in which
final output, like interest in financial transactions, could be considered as ‘some continuous function of the
time elapsing between the expenditure of the labour and the enjoyment of the result’ (Jevons 1879, p. 266).
The subsequent discovery of ‘anomalies’ in the field of capital accumulation was possible when economists
started to question this extension of capital theory from the financial to the productive sphere, and when the
technical structure of production was examined on its own grounds independently of the ‘financial’ aspect
which might be considered to be characteristic of ‘the typical business man's viewpoint’ (Hicks, 1973, p. 12)."

This is pretty much a side issue.

The Illusionist: "Why not measure the interest rates on a daily basis? An hourly basis? A per minute basis? I know that may seem absurd but it is no more absurd than aggregating at the monthly level."

Agreed that it's no more absurd than monthly. And I don't think it is absurd at all to talk about hourly interest rates. And I want my theory of interest rates to be able to handle such "extreme" cases. Take an example: in some countries they price electricity by the hour. It's much more expensive during the peak. So real interest rates, measured in electricity, vary massively hour by hour. From +100% to -50%, if the peak price is double the off-peak. If consumers were indifferent between daytime and nighttime consumption of electricity, we wouldn't see these massive hourly swings in real interest rates. And if electricity could be costlessly stored we wouldn't see these massive swings either. I think examples like this show we need to think about intertemporal preferences when talking about interest rates, as well as intertemporal technology.

"I suppose the underlying assumption is that despite the fact that there are different rates of interest for different term structures etc. these all converge around, or tend toward, a single rate of interest which is the general rate of interest (think of the general rate as a sort of 'attractor' in physics [http://en.wikipedia.org/wiki/Attractor]). This seems to me the essence of the general equilibrium theory."

I disagree. Suppose (for example) we define "the" rate of interest as the one set by the central bank. Now suppose the central bank targets a very high inflation rate. Say 100% inflation. Then the nominal rate of interest set by the central bank will be (say) 105%, while (almost) all real interest rates will be much lower than this. The only case I can think of where the rate of interest on money will equal roughly the average of the real interest rates might be where the central bank targets 0% inflation on some roughly representative basket of goods.

Assume Walrasian/Arrow-Debreu GE theory is 100% true, at all times. With n different goods, and t different time periods, there will be n(t-1) different real interest rates (except in special cases), because there are n(t-1) different inflation rates. One of those special cases might be where there is some sort of "steady state" where nothing ever changes over time. But even in that special case of a stationary equilibrium, you still can't say what determines that equilibrium (including the interest rates) without saying something about hypothetical alternative transition paths away from that steady state. (I have to try to figure out an example so I can explain what i mean there more clearly).

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