Upward-sloping IS curves: simple version

My last post was not a success, judging by the (lack of) reader response (brave and smart John Handley aside). Too complicated. Let me make it simpler, and shorter.

1. Suppose, by magic, the capital stock increases by 10%. New machines just fall from the sky, like manna from heaven. And suppose the central bank responds appropriately, to make the best of a good situation. The real rate of interest would fall, because the capital/labour ratio is higher than before, so firms would want to invest less, so you would need a lower interest rate to equilibrate desired saving and investment.

2. Suppose, by stupidity, Parliament passes a law that reduces employment by 10%. (God only knows how exactly they would implement and enforce that law, but this is just a thought-experiment, so it's magic.) And suppose the central bank responds appropriately, to make the best of a bad situation. The real rate of interest would fall, because the capital/labour ratio is higher than before, so firms would want to invest less, so you would need a lower interest rate to equilibrate desired saving and investment.

3. Now suppose it isn't Parliament that does something stupid; it's the central bank. The central bank creates a recession, so employment falls by 10%. What would the interest rate need to do, to keep the recession going, to keep employment exactly 10% below what it would otherwise have been? The real rate of interest would need to fall, because the capital/labour ratio is higher than before, so firms would want to invest less, so you would need a lower interest rate to equilibrate desired saving and investment.

The answer to that third question tells us that the IS curve slopes up. Because the IS curve, by definition, tells us what happens to real interest rate and real output when the central bank changes monetary policy (shifts the LM curve) to create a recession. (Real interest rate on the vertical axis, real income on the horizontal axis.)

But the reason you find it hard to get your head around is that you can't help but think of the central bank as setting an interest rate. And if the central bank wants to create a recession, it needs to raise the rate of interest, right? So how can raising the rate of interest to create a recession cause the rate of interest to fall??

OK, let me work with you. (Though it's a lot easier to get your head around if you think of the central bank as setting the money supply or NGDP rather than a rate of interest.)

There's a big difference between creating a recession from scratch and keeping a recession going so it doesn't get better or worse. The metaphor doesn't work perfectly, but it's a bit like a heavy ball sitting on top of a round hill. It's an unstable system. You have to initially push the ball forward to get it to roll down the hill, but once it is halfway down the hill you need to constantly push it back to keep it from rolling further.

It's a bit more complicated than that, because how much the interest rate needs to fall, and whether it falls at all, depends on how long people expect the recession to last. If people expect the recession to be very short, they won't cut their consumption much, and will instead save less. And if desired saving falls more than desired investment, the interest rate that equilibrates the two will rise. (And it also depends on how long the recession has already lasted, because capital eventually depreciates, so firms will eventually invest to stop the capital/labour ratio eventually falling below the original ratio.)

So whether the IS curve slopes up or down depends on how long people expect the recession to last. For a short recession it slopes down like in the textbooks. For a long recession it slopes up.

The same tight monetary policy that created the recession, paradoxically, caused the interest rate to be lower than it otherwise would have been. And if you want higher real interest rates, the last thing you should want is for central banks to raise them prematurely.

Better?

Comments

[jonathan]

Ha. I haven't read your blog in a few days, but I just left a comment on Scott Sumner's blog saying (in part), "so you're saying the IS curve slopes up?"

(Maybe he's said that explicitly in the past, but I have trouble understanding things unless I work them out for myself.)

Maybe I'll just copy the bulk of my comment here, because it seems relevant to this discussion:

"New Keynesians take the “natural rate” as a roughly exogenous object, and then think about monetary policy as setting the policy rate equal to the natural rate, which stabilizes output and prices. You [Scott Sumner] view the “natural rate” as an equilibrium object that monetary policy can and should affect directly by changing inflation and growth expectations, or more succinctly (using your preferred framing) NGDP growth expectations.

In Old Keynesian terms (IS-LM), you think that the IS curve could be horizonatal, or even upward sloping, which really just means it’s the wrong framework for thinking about monetary policy in the first place. Or maybe more precisely, you think that monetary policy mainly works through growth expectations, which (in the IS/LM framework) mean shifts in the IS curve. So you think that a monetary policy shock in the IS/LM framework shifts the LM curve out, but *also* shifts the IS curve out, and the latter effect is really critical.

In other words, good expansionary monetary policy can (and often should) show up as higher interest rates, since this means that the Fed has successfully raised growth expectations and thus the natural rate of interest."

(I might change "good expansionary monetary policy" to "successful expansionary monetary policy". This explains why (for instance) some people said things like "Rising long term rates may be a sign that QE is working," which confused lots of people.)

[jonathan]

By the way, implicit in the above formulation is that there are multiple equilibria, and the Fed plays a role in picking between them by setting expectations.

Thus there is no one unique path of the "natural rate of interest", i.e. policy rate consistent with constant inflation. There could be a low natural rate of interest and slow growth equilibrium path, and a high natural rate and fast growth path, and many in between.

By the way, I'm curious about the history of this idea. Keynes famously emphasized expectations quite a bit in the General Theory, whereas the IS/LM formulation of Keynesian ideas pretty much neglected them outside of exogenous shifts in sentiment (IS curve) as a driver of business cycles. But maybe Keynes had this idea partly in mind. But it definitely seems in line with Friedman's thinking. Are there other people in this tradition?

[jonathan]

Now I want to reread my copy of "Milton Friedman's monetary framework, a debate with his critics" to see if this is basically what he says.

[Market Fiscalist]

I see that when the capital/labour ratio increases then the natural interest rates will fall, but I'm not totally getting why a recession will cause the capital/labour ratio to increase. In a recession people tend to dip into their capital for consumption and this would cause the ratio to go the other way wouldn't it ? Or is that bad assumption and people actually try and build up their capital in a recession ?

Assuming the CB creates a recession by increasing interest rates and this causes the capital/labour ratio to increase, then if it wants to maintain the recession it has to hold interest rates at a level that will maintain that heightened ratio. This rate will be (other tings equal) below the level needed to create the recession but above the level needed to get the economy back to the original level of output. Is that a correct understanding ?

[Market Fiscalist]

OK, worked the first one out - in a recession unemployment increases and it is that that increases the capital/labor ratio.

[Majromax]

As a general response to jonathan: how many variables do we need to fix in order to uniquely determine a natural rate of interest?

From the Fisher relation, the natural nominal rate of interest is governed by the inflation rate and the natural real rate of interest, so the nominal natural rate needs one more variable than the natural real rate.

But for the natural real rate, I can think of quite a few candidates:

*) The first rate is the ratio between depreciation and the capital stock, giving the rate of investment required to maintain a constant capital stock
*) The second rate is the collective discount rate, at which the representative agent is indifferent between 1 Twinkie today and (1+r) Twinkies in a year.
*) The third rate is the constant capital intensity rate, or the investment required to maintain a constant capital stock: labour ratio. This can change via changes in the workforce and also through changes in business practices (such as using a factory more intensely over 3 shifts rather than 1.)

Then in turn these rates could be in equilibrium or not given the current capital stock. If the size of the workforce changes, the first (depreciation-based) and third (capital-intensity) rates cannot be equal.

[Nick Rowe]

jonathan: yep. Very relevant here.

Scott doesn't really like ISLM, but I would interpret him as saying the IS curve may slope up.

Us MM's have argued about this in the past. I like to think of an upward-sloping IS curve, but Bill Woolsey likes to think of a downward-sloping IS curve that shifts when expected future monetary policy changes. But we mostly end up in the same place.

Some people like to talk about a short run (or medium run) natural rate that monetary policy can change. But I'm not sure it's useful, and I think it's a bit oxymoronic.

"By the way, implicit in the above formulation is that there are multiple equilibria, and the Fed plays a role in picking between them by setting expectations."

Well, if you think of the CB as setting an interest rate (horizontal LM), then it also needs to set expectations. Or you can think of the parameters in the out-of-equilibrium feedback rule as setting expectations.

"Are there other people in this tradition?"

Good question. I'm only finding them by chance. Like Miles Kimball (see my previous post). David Glasner had a post about a year back on another monetarist with an upward-sloping IS curve (forgotten his name). I've done a couple of posts on it in past years.

[Nick Rowe]

MF: "This rate will be (other tings equal) below the level needed to create the recession but above the level needed to get the economy back to the original level of output. Is that a correct understanding ?"

No. If the recession is expected to last a "long" time, it will need to have interest rates *below* the original level just to prevent the recession getting even worse.

[jonathan]

Nick:

"Scott doesn't really like ISLM, but I would interpret him as saying the IS curve may slope up."

Thinking about it more, I think that it makes a lot more sense to interpret Scott (and Milton Friedman) as saying that monetary policy shifts around the IS curve, rather than that the IS curve slopes up. This is also consistent with not finding the IS/LM framework very useful.

The way I interpret IS/LM is that it is about determining current Y and i for given money supply and expectations about the future. Then we have a positive relationship between i and Y from money supply equals money demand, and a negative relationship from output equals demand for currently produced goods.

Whether or not this framework is useful depends critically on whether shocks shift just one curve. Thus the standard analysis is that changes in M (money supply shocks) just shift the LM curve, and shocks to government spending just shift the IS curve.

But if you emphasize the dynamic and expectational parts of the analysis, a monetary policy shock should also affect inflation/growth expectations, and thus shift the IS curve as well. Likewise, an increase in government spending may shift the IS curve in as well as out (due to higher debt burden, expectation of future taxes).

You can interpret this as "the IS curve slopes upward", but only if you define the IS curve without holding expectations fixed. But then the relationship is not at all straightforward, and it's not clear that it's a useful formulation. (Or that we should call it "IS/LM" rather than something else.)

[Nick Rowe]

jonathan: yep. To be useful, the IS curve has to be independent of monetary policy. My way of doing it stops monetary policy *shifting* the IS curve, but the *slope* of the IS still depends on the *expected duration* of any shifts to the LM curve. So we can't really win.

[Nick Rowe]

Though, you can do it my way neatly in math:

The IS is defined by: Y = C(r,Y) + I(r,Y) + G

Totally differentiate, then solve for the slope dr/dY = (dC/dr+dI/dr)/(1-dC/dY-dI/dY)

Numerator is negative, so the IS slopes up iff (dC/dY+dI/dY) > 1

[jonathan]

Nick:

Let Y and r be *current* output and interest rate. Let E be expectations about future variables. Then the IS curve is:

Y = C(r,Y,E) + I(r,Y,E) + G

Holding E fixed, this defines a downward-sloping IS curve of the traditional sort.

Now suppose we let expectations depend on current variables, i.e. we define a function E(Y,r). Then we have:

Y = C(r,Y,E(Y,r)) + I(r,Y,E(Y,r)) + G

I think this is what you mean. Then you're saying that E(Y,r) is such that the IS curve is upward sloping.

I'm saying that there is no useful stable relationship E(Y,r), because expectations depend on beliefs about the MP rule, and very little on current output and interest rates, and therefore monetary policy shocks will tend to change the function E(Y,r), not just change E *through* Y and r.

Now this doesn't mean you couldn't define E(Y,r) in such a way that we could speak of equilibrium as the intersection of an upward-sloping LM curve and an upward-sloping "IS curve". I'm just not sure that this "IS curve" is sufficiently stable, or analogous to what we typically mean by an IS curve, for this to be a useful framework. [or rather, this is what I interpret Scott as saying; and I think I partly agree].

[Nick Rowe]

jonathan: I don't really disagree. There's only so far you can go with 2 curves. And for the people of the concrete steppes, two curves is one too many.

But if "the period" is very very short, the whole thing gets daft anyway. Defining "the period" as the length of a recession seems sensible, because that is what the model is intended for.

[John Handley]

Nick,

"The same tight monetary policy that created the recession, paradoxically, caused the interest rate to be lower than it otherwise would have been. And if you want higher real interest rates, the last thing you should want is for central banks to raise them prematurely."

The lengths you and Sumner go to in order to avoid sounding like Neo-Fisherians are actually pretty funny. Like a positive relation between expected inflation and nominal interest rates, a positive relation between output and real interest rates is simply part of neoclassical theory (see, e.g., my comment on your last post).

I don't know how relevant this is, but high real interest rates should be consistent with a lower capital stock and therefore lower investment in the short run. If r = mpk = f'(k) where f(k) = k^a and a < 1, then a lower k is necessary for a higher r, so an immediate increase in the real interest rate must be consistent with less investment so that the capital stock will fall sufficiently. I guess if I add labor to the model, it makes more sense; more people would need to work to offset the reduction in the capital stock, but then you'd have the problem where consumption falls as a result of the high interest rate. Maybe I missed something in your model from earlier... Where exactly does it depart from a conventional Neo-Classical/RBC model?

[Nick Rowe]

John: The NeoFisherians are totally right (and totally orthodox) in saying that a permanent increase in the nominal interest rate means an increase in the *long run equilibrium* inflation rate. It's just it's an unstable equilibrium, so the economy never goes there, but goes off in the opposite direction. We reverse causation, so it becomes stable.

Neoclassical theory says there's a positive relation between the *expected growth rate* of equilibrium output and real interest rates. I'm talking about *levels* of output. Plus, we are not in market-clearing equilibrium, but in a recession.

"I don't know how relevant this is, but high real interest rates should be consistent with a lower [desired] capital stock [so the actual capital stock will be greater than desired] and therefore lower investment in the short run." [See the bits I added]

" Where exactly does it depart from a conventional Neo-Classical/RBC model?"

Well, for starters, the fall in output is not efficient. It's caused by bad monetary policy. And it's the fall in output and employment that causes the fall in the desired capital stock, not (e.g.) a rise in the rate of interest caused by a change in preferences.

[John Handley]

Nick,

"permanent increase in the nominal interest rate means an increase in the *long run equilibrium* inflation rate. It's just it's an unstable equilibrium, so the economy never goes there, but goes off in the opposite direction."

I'd agree so long as the unstable equilibrium is the only equilibrium. Plus, at least to me, Neo-Fisherian reasoning is mostly about fiscal policy, not John Cochrane's weird New Keynesian equilibrium selection. In every friction-less version of the New Keynesian model (i.e. Taylor Rule + Fisher equation), high interest rates always mean higher inflation in the next period, it's just that active Taylor Rules force an equilibrium where inflation falls (and therefore the nominal interest rate and next period's inflation rate) fall when a shock to the Taylor Rule occurs. The FTPL deals with that (as does not using Taylor Rules and instead directly controlling the money supply, which is what I'd personally prefer), so the intuitive equilibrium - the one in which the interest rate actually goes up when a monetary policy shock hits - is allowed to happen. Nowhere in NK literature do hyperdeflations occur upon interest rate increases.

"I don't know how relevant this is, but high real interest rates should be consistent with a lower [desired] capital stock [so the actual capital stock will be greater than desired] and therefore lower investment in the short run." [See the bits I added]"

What I was getting at there was that higher interest rates should be consistent with a contraction because of 1) a reduction in the capital stock and 2) a reduction in consumption. After the contraction has occurred, low interest rates are indicative of a large capital stock and slowly growing consumption. The model should return to the steady state from here which would mean that slow consumption growth is consistent with either the recession having not been very big in the first place (so consumption doesn't need to go to far to revert to the steady state) or that it's going to take a long time for the recovery to happen (because mean reversion is slow).

"Well, for starters, the fall in output is not efficient. It's caused by bad monetary policy. And it's the fall in output and employment that causes the fall in the desired capital stock, not (e.g.) a rise in the rate of interest caused by a change in preferences. "

So, basically, you're model has some kind of nominal rigidity or other imperfection that makes money non-neutral.

[Benoit Essiambre]

> Though it's a lot easier to get your head around if you think of the central bank as setting the money supply.

Is it though? When a large part of the money supply can be idle excess reserves that are expected to be removed before they are used, M doesn't represent anything very concrete. At least r, if measured using a stable and predictable medium of account (and withing a stable and predictable tax environment), is a useful value that represents a negotiation between desired saving and desired investment and allows economic actors to make optimal decisions.

[Tel]

So how can raising the rate of interest to create a recession cause the rate of interest to fall??

Well it's obvious really: Paul Volcker raises rates in 1980 and thus falling rates in 2008 had nothing to do with Bernanke, Greenspan or any of those guys.

[Egmont Kakarot-Handtke]

Another X-mas fantasy about IS curves
Comment on Nick Rowe on ‘Upward-sloping IS curves: simple version’

You argue “The real rate of interest would fall, because the capital/labour ratio is higher than before, so firms would want to invest less, so you would need a lower interest rate to equilibrate desired saving and investment.”

Obviously, you have not yet realized that there is no such thing as an equilibration of saving and investment -- neither ex ante, nor ex post. This is simply an age-old figment of the imagination of scientifically no so competent economists.

Keynes messed up the basics of macro with this faulty syllogism: “Income = value of output = consumption + investment. Saving = income - consumption. Therefore saving = investment.” (1973, p. 63)

Actually, the defect in Keynes’s two-liner is in the premise income = value of output. This equality holds -- see the formal proof in (2011) -- only in the case of zero profit in both the consumption and investment good industry. Is it necessary to add that zero profit models never had and never will have a counterpart in the real world?

Keynes’s conceptual problems started with profit. “His Collected Writings show that he wrestled to solve the Profit Puzzle up till the semi-final versions of his GT but in the end he gave up and discarded the draft chapter dealing with it.” (Tómasson et al., 2010, p. 12)

This failure kicked off the chain reaction of errors/mistakes, because when profit is not correctly defined, income is not correctly defined, and then saving is not correctly defined. By consequence, all I=S models, including IS-LM, are methodologically defective. Since Keynes’s day, though, the representative economist merely parroted the elementary logical blunder (2014a).

The Profit Law for the investment economy reads Qm=Yd+I-Sm (2014b, eq. (18)). Legend: Qm monetary profit, Yd distributed profit, Sm monetary saving, I investment expenditure. As everybody can see, saving is never equal to investment and there is no mechanism that makes them equal.

The Profit Law gets a bit more complex when foreign trade and government is included. Most important: the Profit Law contains nothing but measurable variables, which means that its empirical fit can be readily established. So there is no need at all for any further filibuster about the slope of a nonentity.

Egmont Kakarot-Handtke

References
Kakarot-Handtke, E. (2011). Keynes’s Missing Axioms. SSRN Working Paper Series, 1841408: 1–33. URL http://ssrn.com/abstract=1841408
Kakarot-Handtke, E. (2014a). Mr. Keynes, Prof. Krugman, IS-LM, and the End of Economics as We Know It. SSRN Working Paper Series, 2392856: 1–19. URL
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2392856
Kakarot-Handtke, E. (2014b). The Three Fatal Mistakes of Yesterday Economics: Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2489792
Keynes, J. M. (1973). The General Theory of Employment Interest and Money. The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke: Macmillan.
Tómasson, G., and Bezemer, D. J. (2010). What is the Source of Profit and Interest? A Classical Conundrum Reconsidered. MPRA Paper, 20557: 1–34.
URL http://mpra.ub.uni-muenchen.de/20557/.

[Tel]

EKH: Where do those profits go? The person who makes the profit must choose to either save it, or spend it on consumption (just like any other income). Doesn't change the aggregates.

Should that choice be saving, it either goes via financial instrument, or via some kind of direct investment, but either way *in aggregate* all income goes to either consumption or investment. That "saving = investment" equality is largely definitional, and having profits in the system just shuffles around which particular individual gets to make the decision.

There are of course plenty of problems with Keynes: first problem being that no one can ever reliably decide what is "consumption" and what is "investment", I can give dozens of examples should anyone want to challenge me on that. A much bigger problem is that Keynes hated savers (called them "hoarders" and "rentiers") but at the same time wanted to support investment... and this after declaring that "saving = investment" as you point out.

Well, obviously you cannot hammer down savings, while also boosting investment after you have declared these things identical by definition. The answer to this conundrum is that what Keynes really hated was the idea that an individual should be free to choose where her own savings go; to solve this Keynes proposed extricating savings from the individual and giving it to government to "invest" in the name of society at large... and yes, that is socialism. The mechanism of extraction that Keynes proposed was inflation, which eats people's savings, but it also discourages the whole purpose of savings. You can only Gruber people so a short while before they catch on. Governments then go about the business of schizophrenically attempting to encourage individual consumption, discourage individual savings, while also borrowing money for investment at the "society" level. Obviously it can't work. Society is made from individuals.

Another problem is that by dealing in aggregates, almost all of the economy becomes invisible. One example is profits... if you only ever look at aggregate income then profits are irrelevant. This is because the income is the pie, and profits merely affect how you slice up the pie. Just look at the pie as a whole and the slices get ignored. Problem is by ignoring the slices of pie, you also ignore the *structure* of the economy, and that's where all the information content exists. So yes, profits do matter, from a structural perspective, but since Keynesians don't believe economies have any structure, just ignore those profits. Another example is different types of labour, and Keynes totals up aggregate wages as if you could claim that three plumbers equals one doctor.

It's worse! The aggregates the Keynesians look at are nominal currency totals, not even physical aggregates. Thus, you have added up the price of eggs with the price of chickens and the price of frying-pans to give a total price of nothing at all. It doesn't even look at the real pie, but instead looks at some accounting representation of the pie, based on a belief that individual utility can be totalled purely via currency transactions. Then there's the even stranger belief that any internal structural changes within that economy can be ignored for comparison purposes on a year-on-year basis or when comparing one nation with another nation.

[Egmont Kakarot-Handtke]

Short proof of the nonexistence of an IS curve
Comment on Tel of Dec 24 on ‘Upward-sloping IS curves: simple version’

You ask “Where do those profits go? The person who makes the profit must choose to either save it, or spend it on consumption (just like any other income).”

Your error/mistake consists in regrading profit ‘just like any other income’. This error/mistake you share with the vast majority of economists. Majority, though, counts for nothing in science, only formal and material consistency counts. So, here the shortest possible proof that no such thing as an IS curve exists.

The most elementary economy is the pure consumption economy and it consists of the business and the household sector. For a start, the business sector produces and sells one consumption good.

First period: the business sector pays 100 monetary units [thousand/million/billion, euro/dollar/yen] to the household sector and the household sector spends exactly this amount on the consumption good. There is no saving of the household sector. The business sector’s profit is zero and the price of the consumption good is equal to unit wage costs. For more details see the graphic here
https://commons.wikimedia.org/wiki/File:AXEC31.png

Second period: the household sector saves 10 units (S=10) and spends 90 units. Now, the business sector makes a loss (Q=-10). The market clearing price is lower than unit wage costs.

Accounting result: saving=loss or S+Q=0. The complementary notion to saving is NOT investment but loss. And the complementary notion to dissaving is profit. Because of this I=S NEVER holds. By consequence, the whole discussion of whether the interest rate or the income mechanism establishes the equality/equilibrium of saving and investment is as vacuous as the discussion of how many angels could dance on a pinpoint.

Profit can be distributed. The process of the emergence of profit and the distribution of profit, though, has to be thoroughly kept apart. For details see the working paper ‘The Emergence of Profit and Interest in the Monetary Circuit’
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1973952

The inclusion of distributed and retained profit does not alter the fact that there never has been nor ever will be an equality/equilibrium of saving and investment (except in the minds of logically retarded economists). See also the blog post ‘I=S: Mark of the Incompetent’
http://axecorg.blogspot.de/2015/10/is-mark-of-incompetent.html

or ‘How the intelligent non-economist can refute every economist hands down’
http://axecorg.blogspot.de/2015/12/how-intelligent-non-economist-can.html

Egmont Kakarot-Handtke

[David Andolfatto]

Nick,

I haven't worked this out in my head yet, but the argument you present here reminds me of this post here: http://andolfatto.blogspot.com/2010/11/wage-rigidities-and-jobless-recoveries.html

Just replace sticky real wage with sticky real interest rate.

David

[Nick Rowe]

Egmont: you are totally off-topic here. But maybe this is what you are trying to say?

[Egmont Kakarot-Handtke]

Worthless Canadian blather
Comment on Nick Rowe on ‘Upward-sloping IS curves: simple version’

You comment on my reply to Tel with “But maybe this is what you are trying to say” and refer to another comment of yours on Steve Keen.

You are doubly mistaken. First, I was not trying to say something but I gave a formal proof. This proof is clear and impeccable and for those who find it too brief references have been given.

The proof leaves no room for interpretation: IS curves do not exist and because of this your post ‘Upward-sloping IS curves’ is a senseless exercise. To apply I=S more than 80 years after Keynes demonstrated his logical incompetence is a clear sign that there is no intelligent life in the economics parallel universe.

I=S is defective because Keynesians never understood what profit is (2011) and this is the worst thing that can happen to an economist.

The reference to your comment on Steve Keen is entirely beside the point. The fact of the matter is that Keen’s profit definition is also provably false, which I have shown in a short paper (2013).*

So, what I not only was trying to say but in fact proved was that the concept of an IS curve is pure analytical junk.**

Egmont Kakarot-Handtke

References
Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN Working Paper Series, 1966438: 1–20. URL http://ssrn.com/abstract=1966438.
Kakarot-Handtke, E. (2013). Debunking Squared. SSRN Working Paper Series, 2357902: 1–5. URL http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2357902.

* See also ‘Yes, Orthodoxy is incoherent but, unfortunately, Heterodoxy also’
http://axecorg.blogspot.de/2015/03/yes-orthodoxy-is-incoherent-but.html
** See also ‘How economists became the scientific laughing stock’
http://axecorg.blogspot.de/2015/12/how-economists-became-scientific.html

[Oliver]

@EKH

off topic notwithstanding

First period: the business sector borrows 100 monetary units [thousand/million/billion, euro/dollar/yen] to pay the household sector and the household sector spends exactly this amount on the consumption good. There is no saving of the household sector. The business sector’s profit is zero and the price of the consumption good is equal to unit wage costs.

...

Second period: the household sector saves 10 units (S=10) and spends 90 units. Now, the business sector makes a loss (Q=-10). The market clearing price is lower than unit wage costs.

Accounting result: saving=loss or S+Q=0. The complementary notion to saving is NOT investment but loss.

In this case, the market just hasn't cleared. Which means either an investment of 10 in inventories or a write down = loss of 10, which if realised accrues not only to the firm but also to the bank (equity) because the firm must default on part of its loan. So saving goes down by the same amount as investment. In either case, S = I. Same goes the opposite way for profits.

Circuit theory disproves S = I not. http://www.boeckler.de/pdf/v_2005_10_28_gnos.pdf

Nor does it warrant insults, I'd say. But that's for Nick to judge. Belated Merry Christmas to the generous host, in any case.

[Tel]

Worthless Canadian blather ...

Come on dude, play the game! You have to keep the insults at least within a first-glance appearance of civility. This is someone else's lounge room after all. Subtle jibes are worth more points, you get it? Besides, it's Yule and all that, show the spirit of the hunt, please.

Second period: the household sector saves 10 units (S=10) and spends 90 units. Now, the business sector makes a loss (Q=-10). The market clearing price is lower than unit wage costs.

Accounting result: saving=loss or S+Q=0. The complementary notion to saving is NOT investment but loss. And the complementary notion to dissaving is profit. Because of this I=S NEVER holds. By consequence, the whole discussion of whether the interest rate or the income mechanism establishes the equality/equilibrium of saving and investment is as vacuous as the discussion of how many angels could dance on a pinpoint.

I disagree with your accounting. Take note that any standard transaction contains at least FOUR entries: a debit and a credit for the money movement, and also a debit and a credit for the stock movement. We might do more elaborate things, but you must always have at a very minimum a money movement coupled with a stock movement. Even barter has this structure, but some commodity is taking the place of money.

Your accounting merely ignores the stock movements, which no doubt leads to confusion. You also presume that "saving" means stuffing cash into socks and just about everyone admits that if you have a situation where people systematically take the medium of exchange out of circulation and stuff their socks, yes you must get deflation. However, this is an irrelevant conclusion because it never, ever happens. The hand wringing over "the hoarders, ohhh the hoarders" is wasted because there are no hoarders. If Nick wants to say that Cantillon Effects are so small as to be trivial, well cash stuck in socks must be 100 times smaller than that!

Anyway, getting back to your example, which is possibly off topic, but my intent is to outline at least the basic concept of savings.

The factory makes tins of beans, so the workers produce 100 units of beans in exchange for 100 units of money. When consumption is 100%, workers spend their 100 units of money to buy the entire production of beans and eat the lot. Obviously this is a stable operation, the unit of exchange goes back and forth, every cycle 100 beans are produced, 100 beans are consumed. No problem.

Now, for whatever reason dieting becomes a fad... the factory still produces 100 units of beans, but only 90 are purchased, let's presume management don't want to renegotiate wages, nor do they want to get rid of any workers. Basic accounting tells you we have 10 units of beans stacked in the warehouse, and also 10 units of money spread amongst the households. The factory management decides to spin off a financial division, they offer to allow households to keep their savings secure by putting their spare cash into the bank... known as the BBB or "Bean Backed Banking". For 1 monetary unit a household can buy a share of 1 unit of beans stored in the warehouse for future consumption. I mean, everyone eats beans, right? So this bank is rock solid 100% reserves.

The households deposit their money, the factory owner borrows it right back out of the bank and uses it to pay wages. Everything balances. If we keep going, the warehouse fills up, the banking reserves get bigger and bigger and (here's the beautiful thing) household savings keep growing, with those bank accounts coming to an aggregate of much more than the entire total of circulating currency. Don't worry, it's all 100% "Backed By Beans" as we like to say in the financial industry. Well trained professional bean counters are doing regular audits on the warehouse, and anyone at any time can take his or her monetary units to the warehouse and redeem it for tins of beans at the universal bean exchange rate of 1. No Ponzi scheme here... "THIS IS NOT A SCAM."

Now, what about profits?

If you want to see the production division and the financial division as one mega-corporation, clearly the profit is exactly zero... all wages are paid, and all contractual promises are 100% redeemable.

If you want split the production division and the financial division into separate corporations, then you either have a situation where the factory lends beans to the financiers and in return the financiers lend money to the factory, or else the financial division just takes over the warehouse entirely and buys all the spare tins at market rates. Still zero profit.

Now, what about non-zero profits?

For argument sake, we presume the financial division is a separate corporation, with a very sharp CEO who negotiates hard and is able to buy surplus tins of beans at LESS than the market rate. The factory is then forced to push the workers a little harder to increase productivity. Factory produces 105 units of beans, workers consume 90 units of beans, warehouse (controlled by financial division) only pays 10 units of money to pick up the surplus 15 units of beans thus making a profit. Workers are paid their normal wages, deposit their savings in the bank but now the bank has excess reserves.

Bankers can now choose to stack these excess reserves and fill the warehouse even more (i.e. savings) or they could choose to hand out tins of beans amongst themselves as a Yuletide bonus (i.e. consumption) but each tin must go to one or the other. Looking at the economy in aggregate production is 105 units of beans, consumption is at least 90 and not more than 95, saving is at most 15 and not less than 10. All add up, P = C + S. Investment in the form of beans in the warehouse exactly equals savings.

That is rather in the nature of a tin of beans, isn't it? You either consume it, or you save it. You can't do both, and when you think about it, you can't do neither because it has been saved right up until the moment where it is consumed.

Eventually, the factory owners decide that they should start producing something else (maybe can-openers would be a good idea). With enough stores in the warehouse we have a reliable market in beans so no one even noticed that the factory no longer produces them. Then we could get into multiple commodities, price signals, and all that stuff... but I've probably filled enough screen space for the time being.

[BJH]

Nick,

My takeaway from this discussion is that the central bank can affect the Wicksellian equilibrium rate. Is that a fair summary? This would be in contrast to the baseline NK model, where the Wicksellian rate is entirely exogenous.

[Nick Rowe]

BJH: Well, I can see how you might want to interpret it that way, but it depends on how you define "natural rate". It's a very slippery concept.

If you mean "that rate compatible with desired saving = desired investment when output is at 'potential'", then no.

But if you instead mean "that rate such that if the CB sets the actual rate above/below that rate the economy will contract/expand from *where it is now*" then yes.

[BJH]

Hm, thanks. Sounds like a 'short-run Wicksellian rate'? I think I'll just have to think more about this.

[Nick Rowe]

Egmont: you are not only a crank, you are an obnoxiously rude crank. When people (me, Oliver, Tel,) politely listen to your off-topic arguments, and try to engage with you, you would be strongly advised to change the way you respond to us.

Your next comment will be an apology, or will be deleted.