« Is The Big Problem r g? | Main | Money, barter, the clearing house, and balance sheet recessions »

Comments

Feed You can follow this conversation by subscribing to the comment feed for this post.

This is the way it's already taught. This is the logic of AS-AD, the Keynes/Pigou/real balance effect. But this is not how real economies work. There is no sense -- not since the gold standard era and probably not even then -- in which the money supply is more stable than the price level.

I admit that Keynes certainly invited this interpretation. But I think it's clear that liquidity preference means just that, liquidity, i.e. the capacity of financial intermediaries (and under some conditions nonfinancial units as well) to expand their balance sheets. Which does not increase with deflation, oh no no.

Your short run story is good tho.

This post is beyond me, but maybe a quick question: why does this "liquidity preference" plot look different that yours?
http://en.wikipedia.org/wiki/File:Money_Market_diagram.svg
In particular the vertical supply of money curve, M/P? I found it here:
http://en.wikipedia.org/wiki/IS%E2%80%93LM_model

Let me rephrase the last paragraph:

~In the long run, the Liquidity Preference Theory is right. The price level adjusts, and the demand for savings adjusts, until the Loanable Funds theory adjusts its answer to equal what the Liquidity Preference Theory was originally saying. So, in the long run, we can ignore the Loanable Funds theory, and just use the Liquidity Preference Theory.~

This is logically equivalent to the original version. Though assuming that if prices are more sticky than Ms, the liquidity theory predicts a faster change to r, so it is the Loanable funds explanation which adjusts to Liquidity Preference. In principle we could empirically measure the rate of change of r and use that to determine which theory better explains rate of interest in the medium term. Again in principle if all the variables could be quantitatively measured, then when the theories disagree we could measure reality and see which is right in the short term too.

Nick, here are two concerns:

1. If planned savings increase suddenly (because of a lower preference for present consumption, e.g.), the budget constraint implies that planned consumption goes down by the same amount. Hence, why should aggregate demand rise?

2. If we interpret "S > I" as "bond demand is stronger than bond supply", then bond prices are bound to rise immediately, and interest rates fall. There is no rationing in the capital market because bond prices are fully flexible. From a practical perspective, interest is *only* determined by flows, not by stocks. The liquidity preference notion of interest being determined by stocks is misleading.

JW: yes, this is rudimentary textbook ISLM. Just a different way of presenting it. Nothing of substance original here.

Tom: there are two differences:
1. You can either have the *nominal* demand and supply for money (like I have), or the *real* demand and supply for money (M/P). In the latter case, an increase in P causes the money supply curve to shift left, rather than the money demand curve to shift right. It doesn't matter which way you do it.
2. I have assumed that money supply is an increasing function of the rate of interest. The wiki version assumes it isn't, and so assumes a perfectly interest-inelastic Ms curve. My version is a little more general. The wiki version is a special case of my version. It depends on what the central bank is doing.

Squeeky: your version is not logically equivalent to my version. My version assumes that real saving and real investment are independent of P, so the LF theory determines r independently of P. So in the long run P adjusts to make the LP theory follow the LF theory, rather than vice versa. So LF is a theory of r, and LP is a theory of P.

Herbert:
Was that a typo? AD should fall if desired saving suddenly increases (starting in equilibrium).

The Big Problem with ISLM, in my eyes, is that it has 3 goods (output, bonds, money) and so should have 2 markets (the output market, where output is traded for money, and the bond market, where bonds are traded for money). It has two markets, but what the hell are they? LP theory is a theory of "the money market", but that is an oxymoron, since all markets are money markets in a monetary exchange economy. And the goods market is very different from the bond market, because while each individual is either buying bonds or selling bonds, but not both, each individual is both buying goods and selling (different) goods at the same time.

But that would take me well beyond this simple teaching post.

@Nick: Sorry, typo, of course. I agree completely with your critical view of ISLM which is misspecified, I believe, and should not be used in macro.

Herbert: put it this way: if people used "bonds" as the medium of exchange, and wanted to hold "money" because it looked pretty, even though it paid no interest, ISLM would work much better. The IS curve would then be a theory of the output market, where bonds are traded for output. The LM curve would then be a theory of the market for pretty paintings produced by the banking system, where bonds are traded for those paintings.

JW: "Which does not increase with deflation, oh no no."

The central bank must ensure the Ms curve is such that it does increase with deflation (and decrease with inflation). Otherwise inflation won't stay anywhere near target.

O/T:
http://everydayecon.wordpress.com/2014/04/28/on-pegging-the-interest-rate/
All just a big misunderstanding then??

Nick: Just out of cheeky curiosity, what are the units that saving and investment are measured in? This all reminds me of Joan Robinson's quote:
"The student of economic theory is taught to write O = f(L,C) where L is a quantity of labour, C a quantity of capital and O a rate of output of commodities. He is instructed to assume all workers alike, and to measure L in man-hours of labour; he is told something about the index-number problem involved in choosing a unit of output; and then he is hurried up to the next question, in the hope that he will forget to ask in what units C is measured. Before ever he does ask, he has become a professor, and so sloppy habits of thought are handed on from one generation to the next."

Alan Coddington explained why these theories were quite consistent some years back, no? His (then semi-famous) book on Keynesian economics seemed to lay it all out IIRC.

Nick,

"If the supply of money exceeds the demand for money, people will want to buy more goods than are currently being produced..."

Or they will buy higher order goods - Cadillacs instead of bicycles, computers instead of paper and pencils.

HJC: didn't Joan Robinson complain about adding blast furnaces and broomsticks? But did she worry about adding brain surgeons and bartenders?

Michael: Or, you could say Hicks showed how to reconcile them. Again, this is only a teaching post. It's about teaching the old stuff, not about coming up with new stuff.

Nick: Very good! (But you didn't answer the question.) The heterogeneity of capital was viewed as more troublesome because its supply was to be exogenous in the production function but, since only a value magnitude could be used as the capital stock, it also became endogenous in terms of capital goods' prices. That is, the interest rate was needed to calculate capital good prices but capital good prices were needed to calculate the interest rate (from marginal productivity). Hence Robinson's claim of circular reasoning (but not simultaneous determination because the model is either over- or under-determined depending on its set up). Wicksell had actually tried to sort all this out using a concept of saved-up land and labour, but that seems to have got lost in the sands of time as well. (Nor did it seem to work.)
[Didn't Hansen have a big part in reconciling loanable funds with liquidity preference? Which was more important 'Mr. Keynes and the Classics' or 'A Guide to Keynes'?]

Nick,

I like the post, but separately, I think there is an asymmetry in the subject matter that has always bothered me.

Loanable funds uses an S/I framework.

That framework is really based on the national income identity, etc.

There is no money in that framework.

I.e. no “funds”.

That’s how a flow of funds / balance sheet framework differs from a national income model.

It inserts money and other financial assets to make the required monetary connections.

Conversely, liquidity preference creates an explicit treatment for money.

That could be extended to financial assets of all types across all balance sheets - in a qualified way of course - recognizing the uniqueness of money and the different types of money in context.

So I don’t have the same problem there.

In summary, “loanable funds” always presents an intuitive roadblock for me, because the skeleton framework on which it is based doesn’t even include money explicitly.

“Loanable funds” as an intended concept really refers to the monetary connections between S and I, and not the substance of S and I, no? Or does that depend on how you interpret the meaning of interest?

(BTW, I think Steve Keen gets muddled somewhere in this distinction, with his (original) idea that new debt is somehow part of incremental aggregate demand instead of being a monetary connection to it or an association with it.)

But your post in substance seems quite clear and makes sense to me.

JKH: The Wicksellian notion of loanable funds is that there is a 'natural' rate of interest that equates *real* investment with *real* saving in equilibrium. It all works perfectly well in a single-commodity world where the act of saving is equivalent to the act of investing. But in a multi-commodity world the concepts of *real* investment and saving become problematic. For instance, the first derivative of the production function with respect to capital is no longer a purely real rate of return since the units of the numerator and denominator are not the same. Returns on capital can only be measured in nominal (i.e. money) terms using prices of capital and output goods. Consequently, one can imagine these relative prices adjusting so that the return on capital matches the market rate of interest and not the other way around, especially if the money supply curve is horizontal.

HJC: IIRC (and I probably don't, because I'm working from 35 year old memories, and my math was never very good anyway, so read all this in that light):

There is a very big difference between:

1. "Change in the value of the stock of capital" defined as delta(P.K), where P and K are vectors.

and

2. "Value of the change in the stock of capital" defined as P.delta(K).

and you need to talk about 2 not 1, and if you get the links in the chain index fine enough the approximation is as good as you want it to be. And Joan Robinson kept talking about 1 rather than 2.

But you don't really need to aggregate anyway, unless the God of Macro tells you you must, and sometimes he does.

You might like my old post on Dutch Capital Theory

I did a number of posts on capital and interest a few years back, to try to engage the Cambridge UK people. Like this one:

Capital and interest in the steady state

and this:

Cambridge Capital debate

If you put "capital" or "interest" in the search box top right, you will find a few more more.

Why do we still teach ISLM as anything but part if a history course. This stuff is so incorrect that it us more than misleading. Unless you are starting from a recursive formulation of the problem eg PIH, then you are just hand waving with no insight. You need a model of the market stochastic discount factor or pricing kernel which requires a model of time varying risk premia.

We should teach economics like we teach physics and mathematics: Let no one ignorant of geometry enter. Sorry, but economics like biology are become more and more like physics.

JKH: I basically agree with your comment (except for this bit: "That framework is really based on the national income identity, etc.")

And I disagree with HJC's answer to you. The problem is monetary exchange, not multiple goods. If we had barter, or a Walrasian central market, Loanable Funds would work fine (except it has only one interest rate, and so ignores the term structure). But we need monetary exchange in the model if we want to talk about generalised excess supply of goods.

And Steve Keen is onto something, even if he does get the accounting a bit muddled at times. He is not the first to write something like I = S + deltaM. My post on two LM curve was another (inadequate) attempt to get at what he should have been saying.

See my answer to Herbert above.

HJC,

In a non-monetary world, I’m under the impression that real saving is the same as real investment, real saving still being what is produced but not consumed, but now undifferentiated from real investment through financial intermediation of any type including money.

And I would have thought that both capital and the output of the production function can be denominated in any chosen real unit (e.g. the return on capital expressed in terms of hamburger units - which doesn’t mean hamburgers are part of capital or the whole of production). But I'm way beyond my pay grade in even dabbling at this.

So I still wonder who labelled it “loanable funds”.

Now I'll have a look at Nick's comment just now.

Nick: Thanks, I think that in my explanation to JKH I was using case 2, I am wrong in thinking that? It seems to me that introducing P violates the realness of the return in either case. Remember the Wicksellian rate is conceptually different from the Fisherian definition.
I don't think the concept of time preferences was missing from the debates, but if so that's probably an interesting line of inquiry. I'll have a bit more of a look at the links.

Nick,

Certainly agree Steve Keen is onto something.

But he's really doing a regression analysis, IMO.

Quite appalling to see it set it up from the get-go as an accounting identity adjustment - and completely unnecessary. Although I think he's evolved this now.

Accounting is not the enemy. It should just be useful - but not ignored.

The "role" of accounting in economics has surfaced again recently in a few places with some interesting nuances.

I'm starting to think of it as an economists' volleyball - with much angry spiking - but a few good set ups.

HJC: let there be a curved PPF between C and I, both measured in physical units. Let the price of C be the numeraire. Pk (the price of the capital good) equals the slope of that PPF in equilibrium. Let R be the annual rental on a unit of K. R=MPK, just like W=MPL. Ignoring depreciation, and ignoring the term structure (assume people expect current rate of interest to stay the same forever) we get r=R/Pk. As we slide along the PPF, we get one relation between r and I (the I curve in the LF picture). Agents' intertemporal preferences give us another relation between r and I (the S curve in the LF picture). Solve those two equations, and we solve for r (and I and Pk). Done.

The problem is when we introduce monetary exchange, and the economy is inside that PPF, because M/P is too low.

JKH: The natural rate is a non-monetary rate that all capital goods must earn. But if one new gadget makes two new widgets, what is the real return, in terms of time only? To get a return we need know the prices of gadgets (now) and widgets (in the future), it's now no longer a purely real return independent of the monetary system, it's not in terms of production technology only.
Nick: Walrasian rates of return are real because it's a barter system, but it don't think that there's any guarantee that they are equal. The capital critique does not apply to a Walrasian general equilibrium.

HJC: I don't remember the difference between the Wicksellian and Fisherian definitions. (And didn't Wicksell have more than one?) But it sounds interesting. Can you remind me please.

Is "Y=C+I" a PPF?

Nick: I have a suspicion that our examples are same, but we come to different conclusions! (Sorry my posting is a bit slow, so I'm not in synch.)

Nick: Does this help? Sorry about the formatting. Footnote 1:

http://books.google.com.au/books?id=BM0h7ImSVBEC&pg=PA21&lpg=PA21&dq=colin+rogers+wicksellian+rate&source=bl&ots=OzTR9zZ1bB&sig=DlQD78mvgCTfahs22yniePaHNE4&hl=en&sa=X&ei=nu1gU4f7MM6KkgXNhYCQDw&ved=0CDEQ6AEwBA#v=onepage&q=colin%20rogers%20wicksellian%20rate&f=false

HJC: if the relative price of apples vs bananas is rising (or expected to rise) at 1% per year, the banana real rate of interest will be 1% higher than the apple real rate of interest. Pick any price index you like, and you get a natural rate of interest for that price index. I don't see why this is a problem for a Neo-Wicksellian inflation targeting central bank. (But I must confess that David Laidler does think it is a problem, and he is as monetarist and smarter than me.)

Nick,

"It has two markets, but what the hell are they?"

This is much easier if you think of three markets.

First consider an endowment, barter economy with three goods: oranges, bananas and melons. We can draw demand and supply diagrams for each, using some arbitrary numeraire (so demand and supply curves for oranges are shown in Qo - Po space given fixed Pb and Pm, and so on).

Note that we can also draw the market for melons, say, in Qm - Pb space. The demand curve may then slope the other way.

Budget constraints or Walras Law or whatever will mean that if two markets clear, so will the third. But the third graph still tells us something. If there is a change in supply of melons, for example, it matters.

As the numeriare tells us nothing, we can get rid of it by expressing our prices in terms of one good - say melons, so we get the prices of oranges and bananas, expressed in terms of melons, as po and pb. By definition, pm =1.

The diagrams for the markets for oranges and bananas will be unchanged, since we were assuming other prices were fixed anyway. The supply and demand curves for melons however, now become simply demand and supply points, both on the horizontal line pm = 1. However, where these points are still matters. We can also still draw demand and supply for melons in Qm - pb space and it will look like it did before.

Now to IS/LM with its output, bonds and money. We can start by ditching any external numeraire and express the prices of output and bonds in terms of money. We therefore have the nominal prices po and pb.

The demand and supply of output is the AD/AS diagram. This is the same as having the orange market in Qo - po space. But we now need to fix some IS/LM quirks.

The LM diagram looks at the stock of money, but everything else is expressed as flows. We can fix this by deducting the opening money stock from both demand and supply to get the change in quantity of money. Note that this can be negative. If we were to show this market in Qm - pm space, it would be points not curves. So we show it in Qm - pb space as curves.

The IS diagram reflects total savings and total investment, which includes changes in bonds and money. So, if we wanted, we could deduct the money demand curve from the S curve and the money supply curve from the I curve to get a demand and supply of bonds only.

This would leave us with a demand and supply curve for output, bonds and money shown in Qo - po space, Qb - pb space and Qm - pb space respectively. The last two are inverted to use the interest rate on bonds rather than the price.

Not very different from my discussion of Wicksell here (http://nakedkeynesianism.blogspot.com/2011/11/neo-wicksellian-macroeconomics.html), which I also use in class. Mind you as you know I do think the capital debates create a problem for the Loanable Funds and the natural rate of interest.

HJC: Colin is not an easy read there. There is a distinction between the *actual* (real) rate of interest and the *natural* (real) rate of interest (for any given price index). OK. And Neo-Wicksellian monetary theory hinges on that distinction. And I have a lot of complaints about Neo-Wicksellian monetary theory (and the natural rate) myself. But I don't see Cambridge UK Capital Theory stuff as adding anything useful in the way of a critique. So I want to defend neo-Wicksellians against Cambridge, but launch my own attack.

Nick E: I disagree. Assume 3 goods.

A monetary economy has two markets: one where O can be traded for M; a second where B can be traded for M.

A barter economy has 3 markets: it also has a market where B can be traded for O.

A Walrasian economy has one big market, where you can trade any bundle of goods for any other bundle of goods.

Those are real differences, that matter, if one market is not clearing.

And the O/M market is very different from the M/B market, because an individual in the O/M market is both buying O and selling O at the same time. And if he can't sell his own output he won't buy as much output from other people. If he could barter his output for other people's output, we would get straight back to full employment, even if everyone preferred to hold more money instead.

And Walras' Law does not tell us anything useful in a monetary exchange economy.

Matias: Neat!

There are two differences between your and my diagrams:

1. Your Ms is horizontal. (This is not an important difference, and yours correctly shows the very short-run neo-wicksellian approach).

2. You say (interpreting Wicksell) "The low bank rate implies overinvestment, and the need for additional savings. The inflationary process by reducing the ability of consumers to spend provides the additional 'forced savings.' Inflation acts as a tax that provides the additional resources needed to finance investment." I give a more (New) Keynesian interpretation, by having Y increase so that the S curve shifts right.

HJC,

thanks

I guess I was thinking something like freezing real prices constant over time by default and translating to a set of corresponding real returns

My point was not really about how many markets there actually are. (Ultimately, I'm not sure there are markets as such - just a collection of bilateral transactions) I was just saying that it is easier to see what is going on if you think of it as three markets.

IS/LM generally assumes that flexible prices will restore full employment, so any output gap depends on sticky prices. Can people barter their way back to full employment if the exchange prices are fixed? If no-one is prepared to give me the required number of melons (or bananas) for my excess oranges, don't I have to accept a lower rate of exchange?

btw, I don't dispute that monetary economies behave differently - I'm just not sure it prevents us interpreting these diagrams this way.

Nick E: " Can people barter their way back to full employment if the exchange prices are fixed?"

Sometimes, yes.

There are 300 women. 100 hairdressers, who want their nails done, 100 manicurists who want a massage, and 100 masseuses, who want a haircut. Wicksellian triangle, so they all use money. So there are 3 output goods, plus money. No bonds. And 3 markets: haircuts, manicures, and massages, where each of the three output goods is traded for money.

Start in equilibrium, where demand = supply for all 3 output goods. Assume the equilibrium prices are $1 for each good. Now halve the stock of money, but hold all prices fixed at $1. There is an excess supply of all 3 output goods. All the women are (roughly) 50% unemployed. Each buys fewer goods because she wants to hold more money.

Now suppose 3 women get together (one of each type). They do a 3-way barter deal, keeping exactly the same relative price of one haircut = one manicure = one massage. They get straight back to full-employment. Or a 3-way monetary deal: "I will buy your service for $1 if you buy hers for $1 and if she buys mine for $1. Deal?" They all 3 agree to the deal.

We use money and bilateral deals because 3-way deals are impractical.

Now add bonds to the model, and let the price of bonds be perfectly flexible. The price of bonds falls when the stock of money halves. But nothing much else changes in my story. (We get less unemployment than if there were no bonds, if bonds are a substitute for money, but we still get unemployment, and 3-way deals can still eliminate that unemployment.)

Nick,

That's an interesting story. I guess in IS/LM terms what you've done there is varied f(r) in Md = f(r).PY, by allowing Y to go up while keeping P and Md constant?

Nick E: thanks. That story is absolutely central in how I view recessions, in monetary disequilibrium terms. I have been repeating slightly different versions of that story in many old posts. (It's a variant of Paul Krugman's babysitter coop model, except his tokens can be confused for a savings medium rather than a medium of exchange, while allowing barter illustrates the difference.)

"I guess in IS/LM terms what you've done there is varied f(r) in Md = f(r).PY, by allowing Y to go up while keeping P and Md constant?"

I think that is a good description of what happens when I introduce bonds into the model, and let the price of bonds vary. But I don't think it is helpful in understanding why n-way barter (if it were feasible) would alleviate the problems of an excess demand for money. I think of money as like a hub-and-spoke model of air travel. If the hub is blocked, the whole system is shut down, unless you can start flying point-to-point, by barter.

Nick E: another story, to illustrate the difference between money and bonds:

300 women (100 of each type), and money, and bonds. Money pays interest Rm, and bonds pay interest Rb. Rb >> Rm. Start in equilibrium. Hold M and B fixed, and hold all prices fixed. Increase Rm a little and cut Rb a little. What happens? I say Y falls. Because people trade output for money, not bonds. There is an excess supply in the three output markets, but barter could get Y back to where it was originally, leaving an excess supply of bonds.

Neither is true. There are several interest rates. All of them are set by bankers a priori. Some are set by the Federal Reserve; others are set by officers of private banks.

If you're trying to make a model of bankers' behavior in setting these rates, you're doing a crap, crap job. Neither of these models are even *close*.

This is due to one of the fundamental failures of classical microeconomics. The theory of consumer behavior in microeconomics has its problems, but on the whole it's a decent approximation: so demand curves work OK.

The theory of firm behavior is *completely rotten* and doesn't match reality at all: so supply curves are garbage. Firms are generally price-setters, and they don't set those prices in a fashion which resembles the theories of microeconomics.

And you see the same problem with both of these false models of interest rates. This just *isn't how interest rates are actually set*. Interest rates are set in a much less rational way.

Loanable funds is simply false in our modern economy. There is a low rate of bank competition and there's a central bank "discount window" backstop which prevents banks from needing deposits at all except in the very long run when they get audits.

Loanable funds was a decent approximation of banker behavior in a gold-standard economy with a large number of competing banks and with no central bank. (At that point, banks needed deposits -- they don't any more -- so competing banks would bid up interest rates on deposits in order to attract savers. Meanwhile, banks needed borrowers -- they still do -- and they would lower interest rates in competition with each other to get borrowers. Cartel behavior means this doesn't happen much either.)

Liquidity preference is not even wrong, due to a failure to clearly define the meaning of the terms "money", "money supply", and "demand for money". This gets right to your criticism of ISLM:
" it has 3 goods (output, bonds, money) and so should have 2 markets (the output market, where output is traded for money, and the bond market, where bonds are traded for money)."
In order to make a decent model of banker behavior, you have to look at the following goods:
-- liquid cash money
-- long-term debt (bonds)
-- real production
But more problematically, you have to look at multiple actors:
-- ordinary workers and firms without market power
-- government-controlled banking operations
-- private banks

The situation of the private banks is critical to the analysis, because they set most of the important interest rates. A different structure of private banking (cartel vs. competitive, backstopped by government vs. not-backstopped, etc.) creates wildly different models.

Until this is understood, there's going to be a lot of confusion about banking. A model which works for 19th century banks under the "Free Banking" regime will be wrong for today's banks. Another way of putting this is that the so-called "Lucas Critique" is idiotic: the correct model of the economy in a given place and period depends entirely on institutional structure.

And I just realized I created more confusion in my last post.

For clarity, I define a bank as any entity which can print money and get it accepted. Banks print money whenever people accept checks or debit cards in payment. As someone (Minsky?) said, anyone can print money, the question is who can convince people to take the money.

One of the really complicated features of this is that a particular type of money may be accepted by some people and not by others. The economists who study multiple currencies probably have the best grasp of this character of money.

I attribute the 2008 financial "freezeup" to a demonetization event: money-market funds were treated as money, and then suddenly they weren't treated as money any more. "Collateralized debt obligations" were treated as money by the major banks (though not by average people) -- and then suddenly they weren't treated as money any more.

So there was a massive, *overnight* shock to the supply of money, reducing the supply of money instantly, bang.

Here's where it gets interesting. Did this cause the "price of money" to rise? Well, in some places -- banks were charging very high interest rates for overnight loans to other banks -- but not in other markets.

What it caused instead, in most of the markets, was a drop in transactions. You couldn't buy money for *any* price. Economists might call this as a "disequilibrium" condition -- this is another reason why equilibrium analysis sucks and is useless. But in fact it's a case of the short-run supply curve not existing: short-run supply isn't determined by price at all. (This is one of the real problems with microeconomic theory.)

"Increase Rm a little and cut Rb a little. What happens? I say Y falls. Because people trade output for money, not bonds."

Presumably, they might also trade bonds for output, in which case Y rises. I'd say it depends on the elasticities.

I'm not sure though that any of this invalidates my interpretation of IS/LM. Maybe you'd feel happier with it if I left out any reference to the number of markets.

So I could say: there are three goods (output, bonds, money) for which there is demand and supply, and two prices (expressed relative to the third). We can show demand and supply for each in Q - P space for that good, but for the third we have to use P for one of the other goods. That shouldn't matter. Although it makes more sense to talk about the price of X clearing the market for X, it could also be cleared by changes in the price of Y.

Nick E: "Presumably, they might also trade bonds for output, in which case Y rises. I'd say it depends on the elasticities."

I'm going to think about that one. Because I think it doesn't, but I'm not 100% sure yet. But if i am right, it makes for a qualitative difference between money and bonds.

"Maybe you'd feel happier with it if I left out any reference to the number of markets."

I would be fine with that if we were talking about notional (in the sense of Clower) demand and supply functions. But if we are talking about demands and supply functions in disequilibrium, where people are unable to buy or sell as much of some goods as they would like to sell, those quantity constraints in one market will spillover and affect their demands and supplies in other markets. So it matters a lot what markets exist.

Nathanael: "If you're trying to make a model of bankers' behavior in setting these rates, you're doing a crap, crap job. Neither of these models are even *close*."

OK, listen up. Yes. Let's talk about the real world.

In the real world, the Bank of Canada adjusts a nominal interest rate to target 2% inflation. It does this by trying to set that nominal rate equal to the natural rate, as defined by the (open economy version of the) Loanable Funds model, plus 2%. (The Bank of Canada calls this the "neutral rate", but that's just a euphemism for "the natural rate". And it does this by adjusting the money supply curve to make this happen. And guess what? The Bank of Canada has basically gotten it right, for the last 20 years of inflation targeting. And the real world Bank of Canada makes sure that the Liquidity preference model gives an answer as close as possible to the Loanable Funds model. So in the real world, the Loanable Funds model, and the Liquidity Preference model, does a very good job of predicting where the real world bankers' behaviour will actually set interest rates.

The other heterodoxers on this comment thread are really smart people, from whom I have learned and will learn.

So lose the attitude.

"The other heterodoxers on this comment thread are really smart people, from whom I have learned and will learn."

... wait, I commented here (early on). Does that include me?? Lol. (You don't have to answer that)

Actually I don't think I know enough yet to be considered "heterodox" or "orthodox."

On the subject of Tom Brown, I agree with Mark S. Plus, you learn stuff.

Well, looking back on these comments of mine and yours, I'm going to claim at least some positive contribution:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2013/08/banks-and-the-medium-of-exchange-are-both-special-or-neither-special/comments/page/1/#comments

Posted by: Tom Brown | August 28, 2013 at 01:36 PM

To which you respond:

"Tom: I *think* I agree with that. ..."

Posted by: Nick Rowe | August 28, 2013 at 01:47 PM

Maybe nothing original (and nothing you didn't already know), but at least a positive contribution. :D

Thanks Nick!... you mean when Mark called me a "troll diplomat" which I took as a compliment (and which he meant as a compliment too I think). Well however it was meant, I'll take it!!

Nick: Rogers' work seems to me to very subtle, I suppose that's why I find it so appealing. It's not an easy read, and so there's got be a good chance that I have misunderstood it. But I do get the feeling that there are some theoretical issues with the Wicksellian idea that have not been resolved; and that currently these ideas are accepted without question (e.g. Woodford, Eggertsson & Mehrotra). Clearly the neo-Wicksellian idea is a modification of the original, but does it suffer from the same flaws? I don't know. So I really look forward to seeing more of your own attacks.
Another thing, is it really possible to construct a PPF without assuming fixed resources? I mean, the frontier is the points of efficient use of a fixed amount of labour and capital, but in a multi-capital good world what is this amount of capital? It must be a value measure, so it looks to me like it's not even possible to construct the PPF without first knowing the capital prices. What am I missing here?
JKH: You're welcome.

HJC: I agree with the rest of your comment. (I regret I did not spend more time talking to Colin Rogers about money and capital when I had the chance 20 years back, but I was a young guy then, and concentrating on other things.)

But if we draw a PPF we take as given the existing *physical* quantities of resources, not their values. Because the PPF is an engineering relationship (given current knowledge). The PPF helps define values, but is not defined by values. The existing stock of resources is a vector, with no reason to aggregate those resources, unless the engineers tell us we can.

Nick: Thanks, I can recommend his book. The PPF explanation is good: I think you are saying that the production function is Q = f(L, K1, K2, ..., Kn), where Q is output, L is labour, and Ki is one of n capital goods. Is that right? Does that still enforce a single return on capital? I'll have to look again at why they all wanted capital to be aggregated.

HJC: "I think you are saying that the production function is Q = f(L, K1, K2, ..., Kn), where Q is output, L is labour, and Ki is one of n capital goods. Is that right?"

Yes. Except that Q is the output of the consumption good, the numeraire. We also have a production function for each of the capital goods.

Each of the n capital goods will earn a rental Ri = dQ/dKi. Ignoring depreciation, and assuming people expect no changes, (both assumptions for simplicity only), we know that r = Ri/Pki = Rj/Pkj = etc, for all n capital goods. The relative prices of the capital goods adjust until they all give the same rate of return. And that rate of return r must also be consistent with intertemporal consumption preferences. And there is a production function for each of those capital goods (where I is investment): Ii = g(L, K1, K2..etc.). And those prices and rentals must also be consistent with dIi/dKj = Rj/Pki.

If you forget about the requirement that r must be consistent with intertemporal consumption preferences, then you will be one equation short of a solution. And you can only solve for Pk and r if you assume that the consumption good is the same as the capital goods, so you can write the aggregate production function as:

C+I1+I2+I3...+In=Y=f(L,Ki,K2...Kn) which ensures that each capital good has the same price as the consumption good, and so r=MPK, because Pk=1.

The simplest case is where you have land, instead of capital. Land cannot be produced, so the price of land cannot be determined by its cost of production. We know that rental on land = marginal product of land. We know that the interest rate = land rental/price of land. But we cannot determine the interest rate and the price of land without knowing intertemporal consumption preferences.

Yep. the whole Cambridge Capital Controversy would have been a helluva lot simpler if they had ignored capital and argued about land instead. And you only need one type of land to make the point:

Cambridge UK: "You can determine the rental on land from the marginal physical product of land, but that doesn't determine the rate of interest! You don't know the rate of interest unless you know the price of land, and you don't know the price of land unless you know the rate of interest! All you know is that r=MPK/Pk. You are one equation short! Neoclassical theory is circular!"

Cambridge US: "Hmmm. C+I=K(L,K) doesn't work if K is land and I is new land produced. Because we can't produce new land. We give up."

Austrians, or Irving Fisher: "It's preferences that determine r, or Pk, given MPK, duh."

Nick: I think we have now moved from the Wicksellian idea to the Fisherian version of the neo-Walrasian idea (see Rogers again, note a Word document). There is now no money in the model, and I'm not sure how it lines up with the graphs above. But it is all very clearly laid out, many thanks.

Nick: "I would be fine with that if we were talking about notional (in the sense of Clower) demand and supply functions. But if we are talking about demands and supply functions in disequilibrium, where people are unable to buy or sell as much of some goods as they would like to sell, those quantity constraints in one market will spillover and affect their demands and supplies in other markets."

OK. I see that. I don't think it would make me go for an n-1 market analysis over an n market one though. But I'll think about it more.

HJC: I agree. It's Fisherian, and there is no money in the model. It's a different way of talking about the Loanable Funds model, but it assumes Y is at "full employment", so it doesn't really line up with my two graphs above.

Nick: So if, in trying to make the Wicksellian version work, we have arrived at a Fisherian one, what have learnt about the Wicksellian concept? Should we be concerned that it doesn't really line up with the two graphs above?
Also in your example above if we consider more than one consumption good (indexed by j and capital by i) then we would have Rij = dQj/dKi and a set of returns rj = Rij.Pcj/Pki for all i capital goods, where Pcj is the price of the consumption good j in the chosen consumption good numeraire. So I suppose the consumption goods' prices must adjust to equate the rjs to the inter-temporal preferences for each good. It makes sense to believe that these inter-temporal preferences would vary by j. So the unique rate concept is lost again and needs to be reconstructed by aggregating the preferences for each good into one. How is this done? And is it still independent of monetary policy?

HJC: From what I remember, and from what Colin Rogers says, Wicksell was a bit fuzzy on his definition of the natural rate. No worries. We are allowed to revise him.

There are natural rate models and non natural rate models. Natural rates are a theoretical construct that only make sense in natural rate models. In natural rate models, money is *in some sense* neutral and super-neutral. It is possible to define long run equilibrium values for real variables that are independent of some aspects of monetary policy. We call those long run equilibrium values "natural rates".

If there is more than one good, and if their relative prices are changing over time, their will be a natural rate of interest for each of those goods. I don't see this as a problem (some do). If technical change means that the relative price of apples to bananas is falling at 1% per year, then if the natural rate of interest on apples is 4% the natural rate of interest on bananas is 3%. But the inflation rate on apples will be 1% below the inflation rate on bananas, so you get the same nominal interest rate either way.

Nick: That's all fine: the natural rate exists in specific models with specific assumptions. And of course we can revise concepts over time, which makes attempts at categorisation questionable. It comes down to whether or not we are prepared to put much weight on insights gained from models that have assumptions we may not be too comfortable with. Perhaps at a minimum then, the assumptions should be recognised and stated, and that's why I'm interested in this aspect of the various models. For me, categorisation helps in identifying the assumptions (assuming the categorisation is correct!).

"In the real world, the Bank of Canada adjusts a nominal interest rate to target 2% inflation. It does this by trying to set that nominal rate equal to the natural rate, as defined by the (open economy version of the) Loanable Funds model, plus 2%. (The Bank of Canada calls this the "neutral rate", but that's just a euphemism for "the natural rate". And it does this by adjusting the money supply curve to make this happen. And guess what? The Bank of Canada has basically gotten it right, for the last 20 years of inflation targeting. And the real world Bank of Canada makes sure that the Liquidity preference model gives an answer as close as possible to the Loanable Funds model. So in the real world, the Loanable Funds model, and the Liquidity Preference model, does a very good job of predicting where the real world bankers' behaviour will actually set interest rates."

So, the Loanable Funds model works *because the Bank of Canada uses it as a rule*.

And the central bank setting of interest rates works because commercial banks *do* pass along lower interest rates to the general public when the Bank of Canada lowers its rates.

And because the general public in Canada is rich enough, and has a reliable enough income stream, that they are considered creditworthy by the commercial bankers, and they are willing to borrow, and they are able (for now...) to repay the borrowings eventually.

So you have a nice model for the current Canadian regime, and it's a good regime. Perhaps I'm making the opposite of the Lucas Critique here, but have you worked out the institutional requirements necessary to maintain your model?

Think about that set of conditions. How many countries do they apply to? These institutional conditions certainly don't apply to the US. So does that mean teach ISLM in Canada and not the US? (Joke. I don't think so...)

The attitude I'm showing is due to the treatment of this schema as if it's institutionally-independent. It's not. It's dependent on a very specific institutional structure. It's worth understanding what the necessary elements of that structure are (necessary in order for the model to be correct), and as far as I can tell *that analysis isn't being done*.

I mock some economists for their theorems about perfect competition and perfect information, but at least it's clear the institutional conditions under which their results hold, even if those conditions never actually occur.

*What institutional conditions do your ISLM results hold under?* That should be explained upfront before even starting to talk about the model.

So no, I'm not going to lose the attitude. You need to lose the attitude -- specifically the attitude that theories like this can be taught independent of institutional structural background.

I think an increase in S in loanable funds actually is correspondent to a decrease in demand in liquidity preference.

People are supplying more loanable funds because they don't want as much liquidity in the present.

Nathanael: when you are in your own home, you can be as obnoxious as you want. If your guests don't like it they can leave. But when you are a guest in someone else's home, and in a foreign country, it is not only rude, but arrogant and insular, to say your host is talking "crap" because, in your opinion, what he says does not apply to the USA.

Do not argue. Do not even respond to this comment.

The comments to this entry are closed.

Search this site

  • Google

    WWW
    worthwhile.typepad.com
Blog powered by Typepad