John Cochrane On Neo-Fisherianism, again

First I am going to give you the intuition behind the model in John Cochrane's new paper. It's a very good paper, though I confess I've only skimmed it, because it's very long, and I don't understand all the math. Then I'm going to explain what I think is wrong with it. Then I'm going to explain why I think my model works better.

You start a company, financed by issuing non-voting shares. The total market value of those shares (the market cap) is equal to and determined by the expected present value of your company's profits.

There are two sorts of shares: Fixed-Dividend shares (F-shares); and Variable-Dividend shares (V-shares).

Dividends are not paid in cash; they are paid in newly-issued V-shares. They aren't really dividends; they are annual (or daily) stock splits.

You set up an independent Finance Office to choose dividend policy for the V-shares. The Finance Office can also decide the financing mix between F-shares and V-shares by trading one for the other in the stock market.

Suppose the Finance Office increases the dividend rate on V-shares by 1%. What happens?

If there were only V-shares, and no F-shares, the answer is easy. It's an ongoing additional 101 for 100 annual stock split, so the V-shares will now depreciate at 1% per year relative to the counterfactual of an unchanged dividend policy.

With both types of shares the answer is a little more complicated. Clearly the F-shares will instantly fall in value relative to the V-shares when the new dividend policy is announced, because their dividends don't increase. But the (weighted) average share price will not change immediately, because the number of shares hasn't changed yet, and the present value of the profits hasn't changed at all. Therefore the price of V-shares must instantly rise when the new dividend policy is announced, and only thereafter begin falling at 1% per year (relative to the counterfactual).

Got it?

Now call your company "the government", call your profits "primary fiscal surplus", call your Finance Office the "central bank", and call the Finance Office's dividend policy the central bank's "interest rate policy". And assume your V-shares are the unit of account, so call them "money".

So if the central bank sets a 1% higher interest rate, the result is an immediate fall in the price level, followed by a 1% increase in the inflation rate.

And if you assume that the price of V-shares is sticky, that immediate fall in the price level takes a year or two to happen, so becomes a temporary fall in the inflation rate, followed by a permanent increase. So you get orthodox results in the short run, but Neo-Fisherian results in the long run.

Damn it's clever. But is it right?

Let me make one small change to John Cochrane's model. Let us assume your V-shares are a highly liquid asset and people value liquidity. In fact, let us assume that your V-shares are the most liquid asset in the whole economy, so that when anyone buys or sells anything, they always buy or sell it for your V-shares. Your V-shares are the medium of exchange. And because your V-shares are unique in that way, you face a downward-sloping demand curve for your V-shares as a function of the opportunity cost of owning them (the rate of return on other assets minus the rate of return on your V-shares).

That small change in the assumptions has big consequences.

First, we can now understand recessions. If there is an excess demand for your V-shares (remember their price is sticky) that will disrupt trade in the whole economy, because people will have difficulty selling anything else, so the volume of trade will decline.

Second, the Modigliani-Miller theorem no longer applies; the decisions of your Finance Office will now affect the total market capitalisation of your company. You should start to think of your Finance Office as a profit centre. For example, if people are willing to hold your V-shares even at a negative real rate of return (which is very realistic), you could run your company with permanently negative profits and still have a positive share price. If the Finance Office is truly independent, then it is the Finance Office which is now running the company, by telling you how big the losses are that you are allowed to make.

What would John Cochrane's model look like if we made that minor change to the assumptions? And would it still generate Neo-Fisherian results?

Well, by sheer fluke I just happen (ahem) to have written a post a couple of days ago sketching out just such a model. And by sheer fluke Gerard MacDonell asked me that very question about Neo-Fisherianism in the comments, and I thought about it and answered it.

They key question to ask is this: when the Finance Office central bank announces an increase in the dividend rate interest rate that it pays on V-shares money (call it Rm), what does it announce about the growth rate of the stock of V-shares money?

If the central bank announces that Rm increases by 1%, and at the same time announces that money growth increases by 1%, then we get Neo-Fisherian results. The inflation rate increase by 1%, but the opportunity cost of holding money is unchanged (the increased Rm and increased inflation cancel out), so there is no initial jump up or down in the price level.

But if the central bank announces that Rm increases by 1%, and at the same time announces that money growth will not change, then we get an initial drop in the price level, because the opportunity cost of holding money has fallen so the demand for money has increased, but there is no subsequent change in the inflation rate.

If we assumed prices are sticky rather than perfectly flexible, that initial drop in the price level would take a few years of deflation to work itself out.

It's not enough to ask what happens if the central bank changes the deposit rate of interest. We must also ask what the central bank does with the money supply. And the New Keynesians (Neo-Wicksellians) are to blame by deleting that second question, by deleting money from their model.

And by the way, my model is bog-standard ISLM, except that the central bank pays interest on money, and you can make the IS curve New Keynesian if you like, and add flexible prices or an expectations-augmented Phillips Curve.

What actually happened in the Great Recession? Why wasn't there a deflationary spiral when central banks were constrained by the ZLB? The answer is simple: the price level (and real output too, if prices are sticky) did not spiral down to zero because central banks did not let the money supply spiral down to zero. In fact, they did the opposite. They did "QE" (aka Open Market Operations). Empirical puzzle solved.

Which does not mean there is no empirical puzzle. Given the recession, why didn't inflation fall more than it did? But that is a puzzle about the Phillips Curve, not a puzzle about why Aggregate Demand (or Nominal GDP) did not fall more than it did.

Comments

[AndrewLainton]

Great post but small inconsistency
'The total market value of those shares (the market cap) is equal to and determined by the expected present value of your company's profits.'
No its the NPV of profits + NPV of liquidity premium - as you state further down

Which unifies with williamson

And helps explain why not conform to Mog - Miller - which is a result that only holds in equilibrium anyway

[Market Fiscalist]

I have a clarifying question on "But if the central bank announces that Rm increases by 1%, and at the same time announces that money growth will not change". How does the CB pay the 1% dividend on Rm if it cannot increase the rate of money supply growth ?

[Nick Rowe]

Andrew: thanks!I decided to leave the liquidity premium out until later down.

MF: it sells bonds, and uses the proceeds to pay interest on money. (Or, it uses some of the interest on the bonds it owns to pay interest on money, instead of paying it to the government as profits.)

[JKH]

Nick 12:06 second point

That's exactly how it works with Fed normal course QE

IOR does not create new R

So NF strategy requires that an increase in IOR be accompanied by more QE

[Market Fiscalist]

If I am understanding correctly the CB has the following options:

1) Swap bonds for money to pay interest
2) Just create new money to pay interest

If this is correct won't the Neo-Fisherian result be obtained in the long term as long as it does 2) rather than 1). In a static economy as long as velocity always returns in the long-term to its "normal" value the only thing that matters for inflation to occur is the rate of growth in the money supply. If the money supply is increased by paying interest on bond and/or money wit new money, or just buying other stuff with new money seems largely irrelevant.

[Market Fiscalist]

So if we lived in an economy where when the CB said it was going to raise interest rates people took it to mean 'from now on we will create new money to pay these higher interest rates on bonds and money" everyone would see Neo-Fisherianism as normal.

But in n our world they interpret the CB saying it will increase rates as "we will intervene in the loans market to raise the rate that loans are made at" and they know the CB will do this by decreasing the money supply which leads to the opposite of Neo-Fisherianism.

[JKH]

The Fed has indicated that it will begin to exit QE as a complementary but lagged policy starting sometime after IOR tightening has commenced (which it already has).

This is the opposite policy combination to that which NF would require.

[Henry]

"It's an ongoing additional 101 for 100 annual stock split, so the V-shares will now depreciate at 1% per year relative to the counterfactual of an unchanged dividend policy."

If the company's future income stream doesn't change and all that happens is that you now know that the number shares will be increased by 1% p.a., won't there be a one time reduction in the current share price discounting all future share increases?

[JKH]

"The total market value of those shares (the market cap) is equal to and determined by the expected present value of your company's profits.'
No its the NPV of profits + NPV of liquidity premium - as you state further down."

since when does the discount rate for any NPV calculation not incorporate the "liquidity premium" ?

[JKH]

"Now call your company "the government", call your profits "primary fiscal surplus" ..."

Not sure, but I wonder if you may have dodged something relevant there by specifying "primary"... I'll have to come back ...

[Henry]

"Clearly the F-shares will instantly fall in value relative to the V-shares when the new dividend policy is announced, because their dividends don't increase."

And they won't decrease in absolute value (their dividend hasn't changed), correct?

[Henry]

Wait a minute, are the F share dividends paid in cash or V shares?

[Nick Rowe]

JKH: "That's exactly how it works with Fed normal course QE

IOR does not create new R

So NF strategy requires that an increase in IOR be accompanied by more QE"

I now remember you had answered that question for me before, a year or so back. It's an important point for how the Fed's interest rate announcements are interpreted. Unless the Fed explicitly says otherwise, an announced increase in Rm is not interpreted as an increased money growth rate. Would I be right in assuming exactly the same answer applies to the Bank of Canada?

MF: "If this is correct won't the Neo-Fisherian result be obtained in the long term as long as it does 2) rather than 1)."

Yes. But then it is standard macro to say that increasing money growth increases inflation. The only thing different here is that Velocity does not change, because the higher inflation (which would normally increase Velocity) is exactly offset by the higher Rm (which reduces Velocity).

second comment: yep.

JKH "This is the opposite policy combination to that which NF would require."

Yes.

Henry: No. If the new shares were dropped by helicopter so anyone could pick them up, you would be right, because it's stock watering(?). The new shares are paid as interest on existing shares.

JKH: "since when does the discount rate for any NPV calculation not incorporate the "liquidity premium" ?"

If that liquidity premium is exogenous it doesn't affect the results. It's when the marginal liquidity premium is a function of market cap (of the V-shares) it does matter. It's the downward-sloping demand curve for liquidity (money).

It's normally primary surplus in the LR Government Budget constraint (if it exists).

Henry: No. F-shares must initially fall and V-shares must initially rise, because on average the share prices must stay the same initially.

[JKH]

Nick

I can only assume it's the same for the Bank of Canada.

Maybe a way of describing it is that IOR is marginal to the CB profit calculation, CB profit is marginal to the consolidated budget position, and the budget is generally "fully funded" with taxes and bonds, where the intention is to eliminate the net reserve impact of all of those elements in total.

So marginal reserve impacts including IOR get swallowed up along the way.

This seems intuitively appealing in that Treasury does not want to interfere with the reserve management strategy of the CB, leaving that to OMO and QE processes.

Which is why I suspect the Bank of Canada is similar (it certainly used to be and probably still is).

(Also note that while the otherwise marginal or "natural" mode of IOR is reserve creation, the natural mode of CB profit is reserve draining, which is a point you made in a different way above.

[JKH]

Nick

Have you done a post comparing monetarism (plain vanilla, MM, whatever) to FTPL?

If not, I think that would be extremely interesting.

[Max]

Because central banks aren't perfectly transparent (and probably can never be), their policies are inferred by their actions. But the actions are ambiguous. Why can't a rate increase mean an increase in inflation? Well, it's a social convention established by long history that rate increases don't mean that. So Neo-Fisherianism is false in our culture, but you can imagine an alternative culture where it's true.

[Dandolfa]

Nick,

I haven't read the Cochrane paper, so let me just comment on your post.

After going through the F and V share analysis (which was very good, btw), the point you are trying to make gets unnecessarily convoluted.

First, while you rightly point out the liquidity properties of the V shares, and that this property may have interesting implications, it has nothing to do with what you correctly identify as the central question:

They key question to ask is this: when the Finance Office central bank announces an increase in the dividend rate interest rate that it pays on V-shares money (call it Rm), what does it announce about the growth rate of the stock of V-shares money?

In my view, all the NeoFisherian propositions which claim that increasing R results in higher inflation are either implicitly or explicitly assuming a correspondingly higher rate of growth in the nominal money/bond supply (ceteris paribus). The only NF brand that may not rely on this is the pure cashless models, where expectations somehow move to generate the result.

At the end of the day, my view is that everything hinges on how inflation expectations behave. Those of us who like to emphasize central bank and treasury balance sheets believe that expectations over how these balance sheets evolve over time matter. Those who work with cashless models must rely on some other expectation formation mechanism. Note, these two views are not necessarily mutually exclusive. At the end of the day, it's an empirical question.

David Andolfatto

[Nick Rowe]

JKH: This is the closest I came to a post like that.

Max: Crazy as it sounds, there's a lot of truth in what you say. Words mean different things in different languages. And speaking interest rates, rather than money growth rates, creates an ambiguity. I argued it here.

David: thanks. I agree a lot with what you say.

The so-called "cashless" models are a problem. How exactly is the central bank setting a rate of interest, and what is the asset that it sets a rate of interest on, and why would that rate of interest even matter for anything, and what makes the central bank so special that it can do something that the rest of us can't do?

I don't know if you read my Cheshire Cat post but it gave what I think is a very short and satisfactory answer to those questions. But it's a model of an economy without any nominal (or real, or NGDP) anchor, just like in your and my interest rate posts.

Looking back on it, I think I can guess what happened. In the late 1990's Michael Woodford spends time at the Bank of Canada, talking with Chuck Freedman, and Kevin Clinton (and David Longworth?). The guys who created modern central banking 30 years before the Fed started doing it. He wants to build a macro model that speaks their interest rate language, where the stock of money is an epiphenomenon (that is caused, but does not cause). Plus, he wants a model with microfoundations, and doing microfoundations of the demand for money is hard, especially when you are trying to do microfoundations of monopolistic competition and Calvo pricing and the Euler IS at the same time. So he does the "cashless" model, which gets rid of the whole question of money demand (not to mention banks etc.). And we get the modern Neo-Wicksellian version of the New Keynesian model.

Meanwhile, economists working in a different area are still comfortably speaking M language, because they are interested in M, and why people use it, suddenly get dragged into the policy world and are forced to translate their thinking into central banks' R language. So they use the Fisher equation as an M-R dictionary. But "raising R" means "reducing M" when central banks say it, and "increasing Mdot" according to Fisher's dictionary. So we all ended up in this confused Tower of Babel.

[Deepwatrcreatur]

If we are going to focus on central bank and treasury balance sheets, then I think that Nick's analogy to stock splits is particularly helpful. Without any announcements of QE or tax rate adjustments, there are no changes to these balance sheets in real terms, and increasing R is a purely nominal adjustment. I'm a newcomer to this analysis and hope I'm not missing something.

[Jamie]

Nick: “So he does the "cashless" model, which gets rid of the whole question of money demand (not to mention banks etc.). And we get the modern Neo-Wicksellian version of the New Keynesian model”

One of the reasons that these non-money debates are so hard to follow for a non-economist is that almost nothing about a real economy makes sense without money, and it’s difficult to conceive of how economists might be thinking about these things. For example:

Nick: “You start a company, financed by issuing non-voting shares”.

Businesses issue shares to raise money to spend on an investment e.g. a new factory. In a model without money, what does it mean to issue shares? In a model with no money or where we end up with money balances of 0 at the end of each accounting period, are we saying that the business spends all the money it raises in a single arbitrary accounting period rather than, say, over the 12 months it takes to build the new factory? That’s a minor issue compared with the fact that an economy without money, or with money balances of 0, precludes any business from making a profit so it’s not clear why the business would invest in the first place. Thankfully, we don’t have to explain dividends in this model as there wouldn’t be any. And I can’t imagine how the venture capitalist gets back to a money balance of 0 in the period where he makes the investment.

It seems to me that abolishing money also abolishes the concept of elapsed time in any meaningful sense i.e. the business must be assumed to build the factory, and operate it, and return its non-existent profits to the venture capitalist all within a single period.

And what is the point of interest rates in an economy with no money? And what is the point of a central bank if there is no money and no interest rates?

Finally, on another subject, I read one of the posts linked to from this post, and found this comment by Brad DeLong.

Brad DeLong: “And you shouldn't need to have to rescue people who write badly-written models from the consequences of their muddy thinking...”

Brad is correct. However, I would go further. If there is a problem in any group, and your perception is that the source of the problem is a specific sub-group (in this case New Keynesian modellers), it is essential to get that group to acknowledge the problem and to take ownership of finding a solution to the problem. You can then audit their solution against the need to fix the problems you have identified.

If you try to solve the problem on behalf of the sub-group, without them first acknowledging the problem, the debate will change to the merits of your solution to an unacknowledged problem. That never works as it allows the sub-group to turn you, and your proposed solution, into the problem.

[Nick Rowe]

Deepwatr: you're not missing anything. Though we could also imagine the Finance Office printing new shares and giving them away for free, to their friends. That's stock-watering/Helicopter Money/Money-financed transfer payments.

Jamie: take a simple example. I start a farming company. I buy land by promising the landowner a share of the wheat i produce. No money changes hands. And I can borrow wheat, promising to repay the loan next year in wheat. Or oats. Or labour.

I can't wait for the NK's to fix this problem, I need it fixed now. Anyway, I'm a sort of NK myself, so I'm sorta part of that sub-group. And others have recognised this problem. And my proposed solution can be seen as a hybrid of the NK model and the older Keynesian model. And I can't really criticise their model constructively unless I propose an amendment.

[Deepwatrcreatur]

It seems to be a fine model for the real value of government debt (including the money stock), but FTPL is a poor name for it because it does not really examine the price level. You are right that we need to look at money demand and the quantity of money to say where exactly the price level will be.

[Nick Edmonds]

1. Your amendment shouldn't make any difference to understanding recessions. In Cochrane's version, when nominal interest rates are raised, people spend less because they expect higher real interest rates (an expectation that is then validated). Using your preferred analysis, wanting to spend less is the same thing as an excess demand for money. It doesn't need money explicitly in the model to get there.

2. V-shares in Cochrane's model are not money; they are any public-issued monetary instruments carrying a short dated rate of interest. If you want to introduce the liquidity of money as something of value, you need to have an Rm on money and an Rb on very short dated debt.

3. I'd agree with David Andolfatto's comment that the NF result almost invariably relies on the implicit assumption that a rate rise involves greater growth in nominal bonds/money. Subject to that, you get the same pattern under most assumptions about behaviour and expectation formation.

[Nick Rowe]

Deep: according to FTPL, government-issued currency is just one form of government debt.

Nick E: Suppose the price of Apple shares was sticky, and stuck below equilibrium. So there's an excess demand for Apple shares, they have an above-equilibrium expected rate of return, and it is very hard to buy them. Why should that cause a recession? The market for Apple shares would be messed up, but other markets should be able to function normally.

I agree you need at least two rates of interest, one of which is the rate of interest paid on money Rm. In my above sketch of John Cochrane's model, all I really need is that *some* bonds with greater than zero maturity exist. (It's easier to think of F-shares as perpetuities, but they could be 1-period T-bills.)

[Nick Edmonds]

Nick,

I'm not sure how that relates. In Cochrane's model, there's no stickiness in the price of assets. When short rates go up, the price of long term bonds drops, so that the expected rate of return on both long and short dated assets is the same. There is no shortage of either vis-a-vis each other, only a shortage vis-a-vis goods. In other words, if you hold short bonds, you can exchange them for as many long dated bonds as you want and vica-versa. It's only when you want a greater combined holding, that you have to resort to buying less goods.

[JKH]

Question (maybe with an obvious answer):

"Second, the Modigliani-Miller theorem no longer applies; the decisions of your Finance Office will now affect the total market capitalisation of your company. You should start to think of your Finance Office as a profit centre. For example, if people are willing to hold your V-shares even at a negative real rate of return (which is very realistic), you could run your company with permanently negative profits and still have a positive share price."

In the entire discussion, you're referring to the real value of V shares, with their nominal value fixed, right ?

[Nick Rowe]

Nick E: You can trade short bonds for long bonds. You can't trade goods for bonds. But you can trade goods for goods.

JKH: Yes. (Though you are only supposed to see that in hindsight, after I assume V-shares are unit of account.)

[Henry]

Nick,

What happens to real output with your three cases?:

1. Rm increases, money supply increases

2. Rm increases, money supply unchanged

3. Rm increases, money supply unchanged, sticky prices.

[Nick Rowe]

Henry: 1. Nothing. 2. Nothing. 3. Falls.

[JKH]

Question :

"Clearly the F-shares will instantly fall in value relative to the V-shares when the new dividend policy is announced, because their dividends don't increase. But the (weighted) average share price will not change immediately, because the number of shares hasn't changed yet, and the present value of the profits hasn't changed at all."

In general, a floating rate instrument will not change in nominal value due to an interest rate change - unlike a fixed rate instrument. In other words, increments and decrements to interest earned are not capitalized because the discount rate changes when the interest rate changes.

Why in this case don't both the nominal and real rates of discount increase with the result that there is no change in either the nominal or real values of the V shares?

The fixed rate shares do decline in both values. Therefore the entire capital structure does as well. But so does the PV of the real surplus, because the real discount rate has increased.

Then, once V shares start splitting, inflation eats into the real rate, which declines back to its previous level.

[Nick Rowe]

JKH: the market real discount rate is unchanged (assuming perfectly flexible prices). Only the nominal rate on V-shares has increased (through the ongoing stock-splits). But at the same time, there's a redistribution of Present Value of profits away from the F-shares towards the V-shares (because the F-share dividends will now be paid in post-split V-shares), so V-shares jump up in value and F-shares jump down in value.

[JKH]

I am associating a V share rate increase with a change in the general level of interest rates - as is the case for an IOR rate decision by a real world central bank

that changes discount rates that are relevant to floating rate instruments

[JKH]

...

and I don't see how the real value of the V shares increases initially (after the announcement but before shares start splitting) when the nominal value doesn't change ...

... but I'm too rusty on this FTPL stuff

[Bob Murphy]

Nick,

Can you *please* do a straightforward post--without making an analogy to the moon landing, or constructing a fable where you are Dutch--in which you spell this out:

"Looking back on it, I think I can guess what happened. In the late 1990's Michael Woodford spends time at the Bank of Canada..."

I thought your story there was brilliant and (even better) possibly true.

Also, can you confirm for me: Are you saying that the standard New Keynesian models do not have money in them? I want to be accurate before I repeat that. (I know the models I studied at NYU; some had money and some didn't. I'm asking if you think it's right to say the "standard" ones don't have money.)

[Nick Rowe]

Bob: Moon landing? Hmmm. Must try to bring that in for my next post!

The Woodford story is mostly from Woodford himself. Bank of Canada conference a couple of weeks back, he opened his talk by saying (IIRC) how he had spent time at the Bank of Canada in the late 1990's, had talked to Chuck Freedman and Kevin Clinton, and that his book "Interest and Prices" was his attempt to reframe macro theory in a way that would be useful to central banks because it shared their perspective. And I can remember being on sabbatical at the Bank of Canada 2001/2?, reading Woodford's paper on Neo-Wicksellian approach, and thinking "yep, this is what Chuck Freedman and David Longworth have been saying all along".

But I'm really cr*p at doing history, of any kind. But yes, somebody else should do this, because it's important.

Pre-Woodford (approx 1990) NK models do have money in them. Post Woodford.....well, it's debatable. Woodford talks about the "cashless limit" (whatever the hell "cashless" means). Certainly "M" does not appear in simple (post Woodford) NK models. Or if it does appear, it is tacked on as an afterthought, and plays no role in determining the outcome; M is caused, but does not cause, so it can be deleted from the model without losing anything.

But you could argue, and I do argue, that M must be in there implicitly. If NK models are not models of monetary exchange economies (barter not allowed) then they make zero sense. Please see my post on Cheshire Cats. (Which is not really about cats, or moon landings.)

[Nick Rowe]

By the way, I think it's both true and widely recognised, that the title of Woodford's "Interest and Prices" is a deliberate play on Patinkin's book "Money Interest and Prices". Note the missing word?

[Antti Jokinen]

I've only heard that "Interest and Prices" is a homage to Wicksell (who wrote "Interest and Prices"). If it was originally that, and someone pointed out what you just pointed out, then Woodford would look smart if he didn't deny this interpretation (like any true artist) ;-)

[Merijn Knibbe]

Off topic. 'Blue Murder!'. https://rwer.wordpress.com/2016/12/18/some-problems-of-the-neoclassical-concepts-of-employment-and-unemployment/

[JKH]

Nick,

In an attempt to partially rescue my last mangled comment, several more points (now referring to the actual debt structure rather than your share analogy):

Consider the simple flexible price case. If the entire debt was converted to bank reserves with IOR, then an interest rate increase would translate immediately to an increase in the price level (assuming no change in the real present value of surpluses), according to FTPL. This would be the same as 1 day treasury bills. I refer to all this as floating rate debt. The nominal value of that stuff does not change with an increase in either administered or market interest rates. However, any longer term fixed rate debt component will suffer an immediate decline in its nominal value if interest rates increase. And therefore the price level must adjust down immediately just in respect of that piece. With a portfolio that includes both floating and fixed rate debt, the overall result is really a weighted average price level response in correspondence to the combination of the two pieces - an immediate price level increase corresponding to the floating piece and an immediate price level decrease corresponding to the fixed piece. The combined immediate net result depends on the weights of the two components in the mix, which must also take into account that a longer term fixed rate maturity structure will add to the weight of the fixed rate piece (i.e. more downward nominal bond price adjustment and therefore more downward price level adjustment). That said, the immediate deflation contribution of the fixed rate piece is recouped over the life of the fixed rate bonds (through “accretion” of discount and corresponding price level recovery) until the original price level is revisited specifically in respect of that piece, and then the fixed rate bonds rollover over into new bonds (or reserves) that immediately reprice at the higher interest rate level, just as the floating rate piece did at the beginning. The price level at that point then finally increases in respect of that piece, delayed because of the fixed rate term structure.

It seems to me that your objection to the overall model couldn’t be more fundamental. But Cochrane does address this in a way by assuming an environment of “abundant reserves” where he says a downward sloping money curve no longer applies. He does this more comprehensively in his paper from two years ago “Monetary Policy with Interest on Reserves.”

Along those lines, I was wondering what you thought in total of this current paper's Section 5 “Quantitative Easing and Monetarism”? I thought he made some very succinct and very interesting points there that seem intended to strike at the heart of monetarism. If you have time for an assessment of that particular section, it is not long and relatively easy reading (from my perspective).

[Gerard MacDonell]

Following up on DA's point, I hope, what if you swapped out the idea that the stock of what you call money quadrupled with the idea that the Fed committed -- or sustained the pre-existing commitment -- to have it grow at a pace consistent with not-deflation?