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Every storable commodity behaves exactly according to your house story. When the supply of corn or copper or oil is low, current prices are high and expected to depreciate. When supply increases, prices drop, inventory increases, and the expected rate of inflation equals the cost of storage. An increase in supply reduces the convenience yield. Read Routledge, Seppi and Spatt (Jnl of Finance 2000) or any number of other papers on rational storage models.

As I commented on one of your earlier posts, Steve has not been clear and you have misinterpreted what he is saying. He is focusing on the future rate of inflation, and you are focusing on the price level.

Look at the post the kicked this whole thing off (http://newmonetarism.blogspot.com/2013/11/liquidity-premia-and-monetary-policy.html), or look at Steve's notes about his model. The key is that "I assume that the fiscal authority follows a suboptimal policy rule, against which the central bank optimizes". To explain this rule in terms of your housing analogy, when supply increases the government in his model buys up enough houses to keep the price constant and commits to hold an equivalent number of houses forever. So the price level doesn't change when supply increases. However, the convenience yield decreases because people don't feel that they have buy now in case they won't be able to find a house they like in the future. The drop in convenience yield means that house prices will increase faster in the future.

People who want to say that Steve is wrong should be saying that they don't believe his fiscal policy rule applies or that they don't believe money doesn't have a convenience yield. The convenience yield story he is telling is standard economics.

Aaron: I have read your comment 3 times, and I still don't understand it.

Paragraph 1. Sure. That makes sense, if we are talking about a storable commodity that gets eaten. Or, I could make it work for houses too, by assuming the flow supply of new houses is an increasing function of the price. If helicopters increase the stock of houses, the price falls, but now starts rising again because fewer new houses are being built, so the stock is falling over time as depreciation takes its toll.

Paragraph 2. I am focussing on both price level and inflation.

Paragraph 3. You lost me. If the builders increase the stock of houses, and the government takes the exact same number off the market, the stock of houses that people hold doesn't change.

Paragraph 4. I am assuming money has a convenience (liquidity) yield, that, on the margin, is a decreasing function of the real stock of money. Yep, absolutely standard. The money demand function would be very different if it didn't. Just like houses, which yield someplace to keep you warm and dry, which is also, at the margin, a decreasing function of the stock of houses.

So home prices appreciated so they could drop or had to drop so they could appreciate more in the future?

At the risk of sounding like a broken record, we also have option 3: the Sokal hoax is not even wrong because it doesn't apply to the situation.

The QE situation looks like your "Paragraph 3" response to Aaron: the Fed has increased the stock of money, but that exact same amount hasn't entered circulation, instead loitering as excess reserves.


[Graph: While monetary base (red, left scale) has increased sharply with the advent and each successive round of QE, removing the 'excess reserves' component (purple, left scale) shows a much more durable long-term trend, with the post-2008 period little different than the pre-recession trend. Meanwhile, the monetary base velocity (GDP divided by mbase, green at right scale) has collapsed with QE whereas subtracting the excess reserve component (blue, right scale) again preserves the pre-recession trend, and the M2 money multiplier (teal, right scale) after correction has also been constant.]

The situation is comparable to helicopter-dropping houses and then not distributing them. It's not "people" holding on to excess money (which is what Williamson posits, and would "require" expectations of deflation), it's strictly banks. Instead of requiring economy-wide macro expectations for how a representative agent should behave, we only need invoke explanations for the micro (but large) agent of banks, who receive interest in excess of T-bill rates on those excess reserves.

(On a related matter, is there any way to get data for Canada in such a beautiful manner as the St. Louis Fed tool provides for the US?)

I don't want to push the housing analogy too far, but let me push it a little. Perhaps it will help clarify whether a convenience yield story works for money.

Suppose there is a fixed stock of 100 houses and 150 people. 100 people live in their own house and 50 people live with their parents. Some of the 100 homeowners would be happy living with their parents now, but they really want to own a home in the future. They pay a premium to buy now because they are worried about not being able to get a house they like in the future. For example, perhaps they like only one of the 100 houses and worry that someone else will win the lottery and price them out of it. In this market, everyone expects housing prices to fall over time but the 100 homeowners are happy because they have their "bird in the hand". Note that I have not said anything about future flow supply. Once I do that, I'm telling a different story. It's no longer a convenience yield story.

Now suppose a helicopter drops 50 new houses. Without any further intervention, the price of houses would drop. In addition, people are no longer willing to pay as much of a premium to buy now rather than wait. People who don't want a house until later are less worried about finding a house they like in the future. The convenience yield has declined. Perhaps it has even gone to zero, in which case prices are expected to increase over time at the rate of interest.

Now suppose the government buys up a bunch of houses to push prices back to the pre-helicopter-drop equilibrium. These houses are *not* taken off the market. If someone wants to buy a government-owned house, they can buy one at the market price. In response, the government will go buy a different house to keep its stock constant. So the convenience yield has declined because people have a larger set of homes to select from, but the price hasn't changed.

Note that the govt will need to buy more than 50 homes to stop the helicopter drop changing prices. The drop in convenience yield means that there is a lower demand for buying homes now, so it needs to compensate for that drop in addition to scooping up the 50 new homes. (This is a little like an overshooting story.)

To be clear, I'm not claiming Steve is right. I would cede to both you and him on the question of whether money has a convenience yield or whether the fiscal rule makes sense. His story may not fit the real world, but I don't think it is logically incoherent.

Aaron: OK. I think I am following you now. If the helicopter drops 50 houses, and the govt buys 50 houses, but lets you swap your house for an equal house of a different colour, just because you feel like a change, that makes a difference. I would say the price of houses rises, because you are now living in a house whose colour you like. (It's like owning the house plus an option to swap it for another house).

But I really don't think that has anything to do with Steve's model. Money is fungible (all notes are the same). It has a convenience yield, just like houses have a yield, of somewhere to live. And you willingly pay for that convenience yield on money by accepting a lower rate of return than on other assets. Just as an owner-occupier of a house willingly accepts the rent-in-kind of having somewhere to live. That's why money demand curves slope down, if we put the yield differential between other assets and money on the vertical axis. And that's in Steve's model, just as it is in my (Brock's) model.

Regarding Izabella Kaminska, I haven't read her latest post, but I remember that Williamson had a model where treasuries are more liquid than reserves, so QE reduces broad money stock, which is exactly Kaminska's thesis (asset scarcity thesis). I believe this model is not applicable to actual situation, as the Fed was careful to switch to assets that are clearly less liquid than reserves (remember Twist?), David Beckworth had some good comments on this too.

In the current controversy, Williamson's model is different - reserves are more liquid than treasuries. In the current controversy, one of the things Williamson has said is that QE helps by moving policy closer to the Friedman rule. How do we interpret the Friedman rule in terms of houses? Moving closer to the Friedman rule is equivalent to the reducing the tax on houses, or choosing a better mix of colours for existing houses so houses look more pleasant so that the real flow of housing services increases.

Lord: Neither.

Majromax: OK, but we could ask why bank's hold the money. But as you say, this is a different critique of Steve's model, which denies that QE increases M in any meaningful way.

I don't think it can be done for Canada.

Vaidas: I think moving closer to the Friedman rule is equivalent to reducing the tax on houses.

If the Fed were moving closer to following the Friedman rule it would reduce the target rate of inflation. But then it's a bit like saying: anything that causes the Fed to target lower inflation will cause lower inflation. And if it targets lower inflation, it will need to increase M(t) at the same time as it decreases Mdot(t), if it wishes to avoid a drop in P(t).

This a wonderfully clear article that gave me at least the illusion of understanding this complex topic.

I have a question. b.Pdot(t) is presumably a function of both expectations about the future money supply and expectations of future RGDP. If future RGDP was itself a function of M, could one argue that an increase in M could cause increased expectations about future RGDP such that b.Pdot(t) would fall ? If so, would this still be a bubble equilibrium path ?

MF: Thanks! I think that would only work if the AS curve sloped downwards.

Nick: It's more that I wouldn't have bought my blue house at the price I paid if I'd known there would be a helicopter drop. I would have been happy to wait until next year to buy a blue house, but I was worried I might not be able to afford it next year. The helicopter dropped another blue house in my neighborhood, so now I'm more willing to wait until next year to buy. The price of blue houses goes down. Perhaps it was misleading to use preference heterogeneity to motivate the scarcity premium/convenience yield.

I'm a little out of my depth here, but I think Steve views QE as shifting around the composition of government debt but not changing the total value. To place this kind of QE in the context of the housing example (perhaps at my peril), suppose we start with 150 houses, 50 of which are owned by the government and kept off the market. No-one can purchase or live in these houses. Suppose the government announces that it will keep a stock of 50 houses, but it is willing to trade in the open market. The convenience yield decreases, which causes a drop in the current price and an increase in the expected future rate of increase. Then the Treasury looks at Steve's model and says "wait, house prices dropped, so we need to increase our stock to 55 houses to get the price back to where it was". So it does. At the new equilibrium, the government owns more houses than before and the rate of house price inflation is greater than before. I think Steve would say that better government policy would have been to reduce the stock of houses it owns.

In short, Steve's model assumes that the fiscal authority enacts an austerity policy that prevents prices from jumping with QE, but the austerity does not offset the drop in the liquidity premium.

Nick: "But then it's a bit like saying: anything that causes the Fed to target lower inflation will cause lower inflation."
Ignoring cash, in modern contexts central banks move closer to Friedman rule by paying interest on reserves while preserving the current inflation target.

Steve's point is that in current circumstances (he says sticky prices no longer matter today) lower inflation achieved as a result of following Friedman rule more closely is a good outcome, as it would be associated with higher output.

Suppose we have NGDPLT with futures targeting. We change the parameters of the targeting scheme, moving closer to the Friedman rule but preserving the previous NGDPLT. We will preserve the Mdot(t) and Pdot(t), we will increase M(t), and we will reduce P(t).

Why is this debate important? My answer is September 2008. At that time the Fed followed Steve's current prescription. The Fed ignored sticky price problems, at the same time it take huge steps to move closer to the Friedman rule thinking financial frictions was the problem of the day.

Aaron and Vaidas: OK. Try this:

Assume the Fed is following the Friedman Rule. I.e. it *wants* the economy to stay at the ZLB. So it chooses a time-path for M(t) that ensures that inflation hits the target, and the target rate of inflation is minus the equilibrium real interest rate on government bonds. If Treasury then does a helicopter drop of bonds, that increases the equilibrium real interest rate on bonds (either because bonds are semi-liquid, or because we are in an OLG non-Ricardian economy). So the Fed lowers the target rate of inflation in response, does QE at the same time, to prevent P(t) jumping down because money demand has increased, and then reduces Mdot to implement the lower inflation target.

That (I think) makes sense of what Steve says happens in equilibrium. But it's not that QE *causes* the drop in the inflation rate. Rather, QE *prevents* the drop in P(t) that would otherwise occur when the Fed announces a lower inflation target.

Nick,
First of all, great post.

1) Your link to Brock doesn't work. here's one that does.

http://www.econ.ucdavis.edu/faculty/kdsalyer/LECTURES/Ecn235a/brock_miuf.pdf

2) I love this part, it made me laugh out loud.

"If the theorist forgets that P(t) can jump up, the only way to restore equilibrium is to assume that Pdot(t) jumps down. A permanent increase in the money supply causes a fall in the inflation rate. But that means the theorist is assuming the economy has moved from the fundamental equilibrium path onto one of the bubble equilibrium paths."

3) You lost me here:

"There is an alternative way to get an increase in the money supply to cause deflation, while sticking to the fundamental equilibrium. Assume that when M(t) jumps up, Mdot(t) jumps down at the same time. The money supply increases, but is expected to start declining from now on. The jump up in M(t) causes the P(t) to rise. The jump down in Mdot(t) causes P(t) to fall, and Pdot(t) to fall. If you rig it just right, so the two changes have just the right relative magnitudes, the net effect is no change in P(t), and a fall in Pdot(t)."

In my case I think the problem is too many words and not enough math. In particular Mdot(t) seemed to come out of nowhere. Is there anyway you can say this in equations?

4) "Instead, Steve Williamson's posts have served only as a Rorschach test (I forget who said that) for far too many people, who read into it what they wanted to read. Read Izabella Kaminska for example. (Her post would work as a Sokal hoax in its own right. It's unintelligible.)"

I've noticed the same phenomenon. I've run into several commenters after the fuss died down who were still trying to interpret Williamson's model in terms of their own pet theories, and I had to talk them down by showing them what the model really said.

As for Kaminska, she embarrasses me for the sake of my father's country. Everytime I read one of her articles I'm reminded of this scene from Repo Man:

http://www.youtube.com/watch?v=4ToUAkEF_d4

An analogy might be the combined gas law PV = NRT. You can certainly change P or V at constant T and depend on P*V being constant, but there are lots of ways of changing P or V that change T. Heat engines depend on this to function. Is PV = NRT an equilibrium relation? It depends how you look at it, but it had better be the right way, if you want the right answer.

Mark: thanks!

1. I've changed the link to Brock. Thanks.

3. I have changed the wording slightly, which I hope will make it clearer.

Mark:

3. In math. Assume A=0, and initially M=1 and Mdot=0. So people expect P to stay constant at 1. Suddenly M jumps to 2, but the central bank also announces that M will decline at rate 1/b from now on. There is no jump in P, but Pdot is now -(1/b).

Nick,
The rewording did absolutely nothing for me. Saying it in math made it crystal clear.
Thanks

Mark: OK. I've updated the post to say it in math as well.

And you have now blown a large hole in my conclusion: "I blame maths."!

You really need to find a way to present equations in a readable fashion on this blog.
Chris Auld has things working well over on his site, perhaps you could borrow his solution?

Nick,
"And you have now blown a large hole in my conclusion: "I blame maths."!"

Sorry, that was not my intention. But here's my take on it.

In my opinion a large part of the problem is Williamson suffers from the same problem that Kocherlakota does. (Or perhaps I should say "did", but the jury is still out.) I don't think he really understands Econ 101.

Williamson is clearly very gifted at manipulating equations, but he seems to have exceptionally poor intuition when it comes to understanding elementary economics. He was fairly inarticulate in telling a story precisely because I believe he really didn't have one to tell.

So the problem isn't math per se, but not enough economics.

I'm kind of an interesting example in all of this, although to date my measurable accomplishments are rather limited. I'm originally a math person. I have extensive training at the undergraduate and graduate level plus I'm certified to teach at the secondary level. My math transcript is embarassingly long.

I only returned to school to take up econ in 2005. But I went to the trouble of completing a BA in economics before studying economics at the graduate level. Furthermore I'm an empiricist rather than a theoretician by inclination. Thus a lot of my intuition simply comes from spending a lot of time curled up with data.

In short, I speak "Williamson", but I'm also fluent in several other languages, including "student".

Aaron:

"In short, Steve's model assumes that the fiscal authority enacts an austerity policy that prevents prices from jumping with QE..."

So his assumption about the fiscal policy reaction function is that it does whatever is necessary to keep the path of the price level continuous? That seems odd.

Wow, Noah Smith now seems to agree with Aaron's interpretation:

"What I think is happening is that permanent one-time Fed policy changes cause permanent one-time fiscal policy changes that permanently alter banks' need for collateral, and hence permanently increase the demand for cash..."

And, by my read, Steve Williamson seems to confirm this interpretation, although his meaning is more ambiguous:

"In the experiment I did, the price level at the first date is fixed by the fiscal authority."

If my interpretation of this is correct -- that the fiscal authority's reaction function is such that it chooses to keep the price level continuous -- then the model (or rather the experiment that Steve does with it) is kind of silly. Why would the fiscal authority choose to act that way? One can certainly conceive of a fiscal authority that would act that way, but it's hard to see how any real-life fiscal authority would. And it doesn't seem at all reasonable to regard that sort of reaction function as a baseline for fiscal policy when we're studying the effects of monetary policy. And it certainly doesn't seem reasonable to regard that sort of reaction function as one that approximates the way the US fiscal authority behaves and to therefore interpret the actual response of inflation to US monetary policy as a confirmation of the model. The US fiscal authority did enact an austerity policy, but their objective was certainly not to keep the price level path continuous.

Nick,

"This fundamental solution, where an increase in the money supply causes no rise in the price level but a fall in the inflation rate, requires people expect that the money supply will eventually be lower than if it had never increased in the first place. QE causes inflation to fall because QE causes people to expect a bigger negative QE in future than the original positive QE. That seems implausible to me."

The more plausible explanation is that not everyone holds the belief that having the central bank swap money for existing government bonds will have any effect on the price of goods or the inflation rate for those goods. It is kind of difficult to cause a change in expectations when people expect QE to have no effect at all and thus reverse QE to have no effect at all.

OK, so I think NIck was wrong in his original post when he said this is not about sticky vs flexible prices. In general, in an RatEx model, you need an assumption to tie down the price level. In a model with, say, Calvo pricing, this isn't a big deal, because the Calvo fairy will ensure that the path of the price level is continuous, so you just make some reasonable assumption about long run fiscal and/or monetary policy, and you're done. But with perfectly flexible prices, the price level assumption becomes crucial. Given that you started out with the unrealistic assumption that prices can, in principle, jump, you're going to need some kind of silly assumption to make your results look like the real world, in which the price level, at least for a large subset of goods and services, almost always appears to be nearly continuous. So OK, Steve can match actual US experience by assuming that fiscal policy ties down the price level to be continuous. Hey, look, there was fiscal tightening, the Fed did do QE, and the price level was continuous. Does anyone believe that the actual fiscal tightening was designed to offset a jump in the price level cause by QE? I certainly don't. But this is the way it has always been with flexible price RatEx models, going back to Kydland and Prescott: you calibrate the model to fit the data, and this process involves making silly assumptions.

Andy: "Hey, look, there was fiscal tightening, the Fed did do QE, and the price level was continuous. Does anyone believe that the actual fiscal tightening was designed to offset a jump in the price level cause by QE? I certainly don't."

Nor do I. Interesting point. From a Canadian perspective, the fact that the exchange rate keeps jumping around, while the CPI doesn't, would be hard to reconcile with that idea.

Maybe plot deadweight loss as a function of P and T. If that's what you're trying to minimize, and it equals 0 at your equilibrium points it seems natural. However there are problems with the Marshall deadweight loss and I don't know the correct formula. You may have to work in continuous time. You should take a look at how the ecologists model. Finite difference equations lead you to sin.

Nick,

Take an economy in equilibrium so i = r* + pi. If you lower i or raise r* Williamson will say that pi goes down because r=r* always. Keynesians will say pi goes up because Wicksell. As far as I can tell there is nothing more to this debate than that. It's Kocherlakota saying raising i raises pi, or Williamson saying raising r* at constant i lowers pi. Same argument.

Somehow this debate has gotten all muddled up with the details of the mechanism by which Williamson raises r*. Maybe he wanted people to discuss his paper, and if so he succeeded. But the object of the disagreement would be unaffected whether his paper had described a plan to build highways, bury money in mines, prepare a defense against alien invasion, (or lower the liquidity premium on bonds) so long as it raised the natural rate. The paper doesn't matter. Only the same old claim that pi = i - r*.

I think what really added to the confusion is that everyone is accustomed to thinking of QE as a demand side policy, but Williamson is using QE to fix a structural problem in the economy (lack of collateral) thereby raising the natural rate (which incidentally everyone seems to agree is a good thing). And then independently of that was the dispute about whether a rise in the natural rate is inflationary or deflationary.

Andy: "So his assumption about the fiscal policy reaction function is that it does whatever is necessary to keep the path of the price level continuous? That seems odd."

Yes, but I think the purpose of this assumption in the model is to hold all else constant so he can focus on the disinflation. If the fiscal authority did not respond as such, then I think QE would cause a discontinuous jump in prices followed by lower-than-before inflation.

This post made the idea clear to me - perhaps because I am familiar with the ideas oin Brock's model. Just thinking about the money component: I needed the words so that in my mind I could paint a picture of the various graphs (one for M(t) and one for P(t) lined up over one another. The maths did not help or hinder - it is the description of the "jumps" and how the expectations play out that helped.

On expectations: I believe that the vast majority of agents have no clue what QE is or does (is QE a regime change?). The news on QE tends to be rather noisy and polarized, with scary headlines a frequent occurrence. Since agents don't understand QE the notion that people come to expect QE will have to be drastically reduced in the future does not seem far fetched to me.

Nick, Here's a comment I left back on December 3.

"Nick, As you know I don't have a good grasp for these sorts of models. Is the price level pinned down in Williamson's model, or just the inflation rate (as in many NK models?) If not, could there be some sort of overshooting implied? Say a increase in the liquidity premium on government bonds caused the steady state inflation rate to rise from 1% to 1.5%, but also caused a 40% fall in the equilibrium price level right now. So that even the long run expected price level is lower. This is just a stab in the dark, but I thought I would throw it out there."

Isn't that the point you are making? I did a couple blog posts early in the week making a similar point, but in a slightly different way. I said there were two equilibria with a huge monetary base---Zimbabwe and Japan. Japan has a huge base because from that point forward deflation is expected.

And I'm glad I'm not the only one who has no idea what Izabella Kaminska is talking about.

Scott: yep. Except none of us has a clue if the price level really does jump in Steve's model, or if the central bank stops it jumping by engineering lower growth in M, or if the fiscal authority stops it jumping by tightening fiscal policy.

(I think there's a lot of us who are too nervous to say we can't make any sense of Izabella Kaminska either! I sometimes wondered, when reading French philosophers, if you added and subtracted some "not"s at random, would anybody be able to tell the difference? I was so pleased when a Japanese translator of one of my posts changed my "raise" to "lower", and added a footnote saying he was sure that was what I had meant to say. He was right.)

Kathleen: Yep! I see it in curves too. Like a fan held out horizontally, with all the bubble paths curving away on either side from the fundamental stem.

Yep, it's sort of doubtful if the average person has a clue about what QE means. But one hopes that participants in financial markets might, and that it spreads out from there. But even then I get the impression that a lot of clever finance people are still clueless about money/macro. Which is why central bank communication about their target (as opposed to their instruments) is so important.

Karsten: I tend to agree with what you say there.

Aaron:

"I think the purpose of this assumption in the model is to hold all else constant so he can focus on the disinflation"

Perhaps, but this is what leads to confusion when people try to translate his model into the real world where prices are sticky. Everyone thinks, "No, there won't be deflation; there will be inflation, because the lower liquidity premium will cause agents to bid up prices." Because everyone is used to a world where price levels are more or less continuous for reasons unrelated to policy and thus there is no need for fiscal policy to offset the discontinuities. So when people think, "Agents will bid up prices," they think of inflation, because, realistically, inflation is what happens when prices get bid up. Steve has rigged this model to take away the initial price rise that we would normally expect, and we're left with something very misleading. His result isn't really counterintuitive if you realize there's a rigged assumption involved. The sensible thing to do would be to tie down the future price level rather than the current price level, and then everything would behave just as people expect: agents would bid up prices, and there would be a large one-time jump in the price level followed by deflation.

I looked at it from a different way (gratitude for anyone pointing out my errors). W seemed to say that Treasury holders are only willing to hold cash if there's sufficient disinflation. Therefore, since QE forces them to hold cash, it must force disinflation. But that makes no sense -- QE forces nothing, every transaction was voluntary. Therefore either the sellers already expected disinflation or they wouldn't sell. That would argue not that QE causes disinflation, but that QE can't happen without disinflation (i.e. Zimbabwe had hyper-nothing).

Personally I think that sellers are factoring in interest rate risk as part of the liquidity premium. Seller thinks that nominal rates will rise in the future, therefore bond values will drop in the future. The Fed comes along offering a good price. Therefore, better to sell now and lock in a price, then use the cash to purchase other assets as opportunity arises.

Thank you for this post, Nick. I knew in my gut that Williamson was full of nonsense, but I couldn't really put my finger on why, and Krugman's explanation did not help me. Now that I've read yours, not only do I understand the error Williamson has made, but I also finally understand Krugman's rebuttal. Now I see that Krugman is arguing that Williamson's explanation requires that as QE proceeds, people's expectations of the future money supply are diminishing equally rapidly --- that's the condition needed for the "unstable equilibrium" Krugman was referring to.

Anyway, thanks again for helping us laypeople understand what's going on in this extremely important and so poorly understood area of macroeconomics.

Kenneth Duda
Menlo Park, CA
kjd@duda.org

Squeaky Wheel: "But that makes no sense -- QE forces nothing, every transaction was voluntary. Therefore either the sellers already expected disinflation or they wouldn't sell."

That's not quite right, when we are talking about money. (Sorry, but this is a little hobbyhorse of mine). I can't sell you a car, unless you want to hold the car. But money is different. I can sell you money (perhaps in exchange for your car) even if you don't want to hold any extra money. You almost certainly don't want to hold any extra money; you plan to spend it, on something else. Money is like an inventory, that we only want because we plan to sell it again. If we talk seriously about money, we really need to talk about velocity.

Sorry. Carry on. This doesn't really make any difference to the point here.

My clearest thought on this whole affair, encouraged mostly by this post-

A cost of mathematical formalism: it can be very hard to see the line of argument in a paper and what (if anything) is wrong with it.

A benefit of mathematical formalism: once you've understood the paper, it is easier to deduce consequences from it. In this case, these deductions have not been favourable...

Andy Harless: "His result isn't really counterintuitive if you realize there's a rigged assumption involved."

:) :) :)

Nick,

First off - great post. Explains it very clearly.

Secondly, I can't see how a jump in the price level can restore equilibrium after a sudden increase in money, except in trivial models. Maybe all the prices of goods can jump, but how can the price of bonds jump without affecting the interest rate? You have to have either a lower real stock of bonds or a lower yield or some combination, don't you? It takes time for the stock of bonds to adjust to the change. Or you can assume there are no long dated bonds, but I don't see how you can say anything meaningful about QE if you make that assumption.

I know you're not arguing that point here, but I just find it hard to relate the discussion to what appear to be rather crucial aspects of QE.

Commercial banks cannot dispose of their excess reserves at the FED, because acoounts at the FED are INTERBANK settlements accounts. It's not about economics, it's an instiutional feature. That's why QEs cannot increase M, that's why a thing called M multiplier doesn't exist. Market monetarists do not even try to understand the mechanics of money creation - CBs cannot increase M supply, because private banks create some 95% of money by lending. No lending - no money stock increase. Otherwise your theories are "fine"

Raimondas,
As a central banker, you should be more confident of your abilities to increase M.
Market monetarists understand the mechanics of money creation. They understand how QE changes the incentives to create money. Suppose that deleveraging pressures are so strong that domestic credit contraction continues during QE. There are two further avenues for the expansion of M. First, the funding profile of banking system can change, tilting towards monetary liabilities, with a reduction of less liquid liabilities. Second, there are international flows, the holdings of foreign assets can increase as a result of QE. The conclusion - deleveraging is not equivalent to monetary contraction.

Your point about interbank settlements accounts is misleading. There is also cash, it is possible that central bank liabilities can tilt towards cash when commercial banking system is deleveraging. In the case of the Fed, the Fed is also experimenting with reverse repo facility so the shadow banking system will be able to keep accounts at the Fed.

Karsten,

Your comments really crystallized this for me. Agree 100%.

Nick, Aaron and Andy,

Why are you spending so much effort evaluating a policy change? If you read the paper Williamson has no discussion whatsover of a policy change from no QE to QE. He is analyzing two different economies with two different equilibriums. One without QE and one with. There is nothing about transitions. He would have to have a whole different model of policy dynamics which would have an impact on expectations in his model before the policy transition. He doesn't do that.

Also, as I read the paper there is no element of price stabilizing fiscal policy. Williamson clearly describes fiscal policy as random and possibly suboptimal. Also when he says that the fiscal authority fixes the price level at the beginning, he is clearly saying there is no policy transition in the model. Everything is already in equilibrium from the start, with the representative agent fully aware of the stable QE policy going forward.

The only place where he makes claims about the effect of a policy change is in some highly questionable comments at the end of his blog posts. And these comments are exclusively about the impact of lowering the natural rate (Williamson doesn't distinguish between the natural rate and the real rate). So as Karsten says, there is no point in delving into the dynamics of the model.

Nick Edmonds: Yep. If bonds are a promise to pay money (i.e. non-indexed), then you are right. A doubling of the stock of money, and a doubling of all prices, leaving the price of bonds unchanged, leaves interest rates unchanged, but halves the real value of the stock of bonds. Which changes the distribution of wealth, which may or may not have macroeconomic effects, depending on the model.

Raimondas Kuodis,
"Commercial banks cannot dispose of their excess reserves at the FED, because acoounts at the FED are INTERBANK settlements accounts. It's not about economics, it's an instiutional feature."

The proportion of the monetary base that is held as reserves is largely a function of depositors' desire to hold currency. Reserves are not immutable.

"That's why QEs cannot increase M,..."

The Fed is buying financial assets from primary dealers, but the vast majority of these financial assets are in turn bought from non-bank investors. Consequently QE directly increases the quantity of bank deposits or broad money. See this for example:

http://www.federalreserve.gov/pubs/feds/2013/201332/201332pap.pdf

"...that's why a thing called M multiplier doesn't exist."

The the money multiplier is an accounting identity, so it's existence cannot be questioned anymore than say the sectoral accounts identity can. On the other hand if you are pointing out the fact that the money multiplier is not a constant, nobody to my knowledge has ever made such a claim.

"Market monetarists do not even try to understand the mechanics of money creation - CBs cannot increase M supply, because private banks create some 95% of money by lending. No lending - no money stock increase. Otherwise your theories are "fine""

Thanks to your comment, and the comments of others, I'm beginning to believe that that nobody understands the mechanics of money creation better than Market Monetarists. Furthermore, it's not just theory. For example, I've conducted Granger causality tests using a technique developed by Toda and Yamamato, and find that over the period since December 2008 the US monetary base Granger causes loans and leases at commercial banks at the 5% significance level, and that the M1, M2 and MZM money multipliers each Granger cause loans and leases at commercial banks at the 5% significance levels. These results are the exact opposite of what Accomodative Endogeneity predicts.

Jeff wrote:
"Also, as I read the paper there is no element of price stabilizing fiscal policy. Williamson clearly describes fiscal policy as random and possibly suboptimal. Also when he says that the fiscal authority fixes the price level at the beginning, he is clearly saying there is no policy transition in the model. Everything is already in equilibrium from the start, with the representative agent fully aware of the stable QE policy going forward."

I was carefully going through Williamson's paper for the one thousandth time and I want to emphasize that what Jeff says here is in my view 100% correct. The only reason why I bring it up is I keep reading claims about the model which are not true and this potentially lowers the level of discussion.

I want to bring up something which Williamson said over at David Beckworth's blog. The reason why I'm bringing it here is that David has already politely responded to Williamson and for a variety of reasons I want to leave it at that. Here is what he says:

Stephen Williamson:
"Look at what you're reporting. What I'm thinking about is a change in the composition of the maturity structure of the outstanding debt, not a change in the size of the balance sheet. You're reporting the quantity of Treasury securities of all maturities. In fact, in my model, at the zero lower bound (and indeed with excess reserves outstanding and interest on reserves, for any nominal interest rate), swaps of reserves for T-bills that increase the size of the balance sheet are irrelevant - that's what a liquidity trap is about. So, you're looking at the wrong data. Note that you need to be thinking about the whole maturity structure of the outstanding debt (held by the public). That's affected both by what the Fed is doing, and what the Treasury is doing. If you read this:

http://www.treasury.gov/resource-center/data-chart-center/quarterly-refunding/Documents/TBAC%20Discussion%20Charts%20August%202012.pdf

(or some more recent version), you'll see that the average duration of debt outstanding has been increasing and is expected to. Thus, the Fed and the Treasury are working at cross purposes."

http://macromarketmusings.blogspot.com/2013/12/taking-model-to-data.html?showComment=1386300080750#c6269526623622076490

What I don't understand is how this disputes Beckworth's empirical evidence that QE increases inflation which in turn called into question the theoretical claims of Williamson's model.

Williamson's model assumes that fiscal policy may be suboptimal so I don't really see how that is an issue. Furthermore even if we focus strictly on the T-Bond and T-Note portion of the monetary base it should make virtually no difference:

http://research.stlouisfed.org/fred2/graph/?graph_id=150277&category_id=0

The correlation between the monetary base and the Fed's holdings of T-Bonds and T-Notes over the period since December 2008 produces an R-squared value of nearly 93%.

Is there something I'm missing here? Or is this just another one of Williamson's smug but weak retorts.

P.S. I googled Williamson's previous blog remarks on outstanding debt duration/maturity structure and he has said surprisingly little about this problem hitherto. This comment almost seems to come out of the blue.

Jeff, there is no need for the Granger test, when the sequence is known...

ECB, Monthly Bulletin (2012, May):
The occurrence of significant excess central bank liquidity does not, in itself, necessarily imply an accelerated expansion of MFI credit to the private sector. If credit institutions were constrained in their capacity to lend by their holdings of central bank reserves, then the easing of this constraint would result mechanically in an increase in the supply of credit. The Eurosystem, however, as the monopoly supplier of central bank reserves in the euro area, always provides the banking system with the liquidity required to meet the aggregate reserve requirement. In fact, the ECB’s reserve requirements are backward-looking, i.e. they depend on the stock of deposits (and other liabilities of credit institutions) subject to reserve requirements as it stood in the previous period, and thus after banks have extended the credit demanded by their customers.

Mark Sadowski.

I believe you have slightly misunderstood the points that Raimondas was making.

The only way of reducing reserves is either for them to be exchanged for physical currency, or for the Fed to withdraw them. Banks have no power whatsoever to reduce reserves - all they can do is pass them on to each other. Unless depositors holding far more physical currency - which I agree could happen at the ZLB - reserves on commercial bank balance sheets by definition increase as a consequence of QE and cannot be diminished by bank lending.

The mistake that Nick makes is in thinking that banks choose to "hold on to" the increase in base money. They have no choice but to do so. What the charts helpfully provided by Majiromax show (indirectly) is that they are allowing the proportion of their assets that are reserves to increase, rather than holding that ratio constant by doing an equivalent amount of lending. I think they are doing that at least partly because of regulatory changes that require banks to have 1) more capital in relation to their assets and 2) more liquid assets, including reserves. But there are also tighter lending standards, larger collateral haircuts and general lack of demand for credit.

May I also remind you that correlation does not necessarily indicate causation. You may have demonstrated an increase in commercial lending correlated with an increase in monetary base, but have you actually demonstrated that the lending increase is caused by the monetary base increase? The fact that QE increases reserves in a manner totally disconnected from lending would, I suggest, make this very hard to prove.

Frances: "The mistake that Nick makes is in thinking that banks choose to "hold on to" the increase in base money. They have no choice but to do so."

Suppose the total money stock is fixed. Then it is possible for each individual to get rid of money, but impossible for all individuals together to get rid of money. But if each individual attempts to get rid of more money, by spending more of it, the result is an increased demand for other goods, which pushes up output and/or prices. The "individuals" in question can be people, firms, or banks. This is basic old-school monetarism. The Hot Potato. Each individual can get rid of the hot potato, but some individual must always be holding it.

Nick Edmonds. If bonds are promises to pay fixed amounts of money (i.e. they are non-indexed) then we would not expect the price of bonds to double if the quantity of money doubles. To a first approximation, the price of bonds would stay the same, and the price of everything else would double.

Frances Coppola,
"I believe you have slightly misunderstood the points that Raimondas was making."

To be frank Raimondas said some things which are obviously false. If he misspoke then he needs to express himself more clearly.

"Unless depositors holding far more physical currency - which I agree could happen at the ZLB - reserves on commercial bank balance sheets by definition increase as a consequence of QE and cannot be diminished by bank lending."

This can also happen away from the zero lower bound. The currency ratio is always the depositors' choice.

"The mistake that Nick makes is in thinking that banks choose to "hold on to" the increase in base money."

I seriously doubt Nick has made such a mistake but he can speak for himself. I'm not sure what quote you are referring to.

"May I also remind you that correlation does not necessarily indicate causation. You may have demonstrated an increase in commercial lending correlated with an increase in monetary base, but have you actually demonstrated that the lending increase is caused by the monetary base increase? The fact that QE increases reserves in a manner totally disconnected from lending would, I suggest, make this very hard to prove."

I'm not talking about simple correlation. I'm talking about Granger causality.

The techniques I am using are very similar (actually they are methodically superior) to those that Post Keynesian empirical researchers have used to "prove" the various Accomodative, Structural and Liquidity Preference views of endogenous money. What I have shown is that over the time period since December 2008 the monetary base and the various money multipliers provide statistically significant information about future values of commercial bank loans and leases. These results are the exact opposite of what Accomodative Endogeneity predicts.

Of course this is not the same as showing metaphysical causality. But none of the Post Keynesian empirical research on endogenous money have shown that either.

Nick: Has the speculative demand for money been taken account of in this discussion? Think of QE as being aimed at bringing long term interest rates down by driving up the price of long term bonds. If I'm holding long term bonds in my portfolio, QE will raise their price relative to what I had expected it to be at this point. I then have to decide whether to sell. At the same time as it's buying long term bonds central bank is increasing the stock of short term, highly liquid assets on the market.

Suppose I don't believe that the central bank can keep long term rates down, and the prices of long term bonds up. In fact, assume I believe that long term bond prices will come down with a thump in the relatively near future, perhaps because I believe that the expansion of liquidity will create inflationary pressures in goods markets which will force nominal interest rates up. In that case, isn't it likely to be optimal for me to take the central bank up on its offer - to sell it my long term bonds at their current, elevated price, and to hold highly liquid assets - money and short term bonds - so that I'm in a position to move back into long term bonds when the price of those bonds falls?

So my willingness to hold highly liquid assets reflects my desire to stay liquid in the short to medium term, and is based on my expectation of a deflation not of goods prices but of the prices of long term bonds, while that expectation is tied to my expectation about near term goods market price inflation.

Nick,

I understand the hot potato effect, but its application to reserves is seriously limited. Base money in the form of reserves is only usable by banks. For other agents to use it, it must be converted into physical currency. Therefore the "hot potato" effect with regard to base money only operates if a) banks choose to pass reserves on to each other or b) households and businesses choose not to intermediate payments through banks but to settle directly in physical currency. The first of these might happen if interest rates on reserves were negative, since that would be an incentive for banks not to hold them. The second might happen if there were a massive banking failure, forcing people to revert to physical cash transactions - and of course the black economy generally works in physical currency, since it is not traceable. Neither of these is really something we would wish to encourage.

Reserves cannot be used for anything other than interbank settlement unless they are converted into physical currency. They cannot be "lent out", or "paid out" for goods or services. Across the banking system as a whole, they are only reduced if the Fed drains them or there is increased demand for physical currency. Individual banks can therefore only reduce their reserve holdings by encouraging depositors to make withdrawals or by lending the reserves to other banks. I suppose encouraging depositors to make withdrawals (presumably by zapping interest rates on demand deposits) would increase demand, since depositors might spend the money - though they might find alternative investments instead, or stuff cash under the bed.

Frances: if an individual bank expands loans, it knows it will lose reserves to other banks. Banks (presumably) know this. Making a loan today is the way an individual bank gets rid of reserves tomorrow, or the day after tomorrow, depending on how long it takes the borrower's cheque to be deposited in another bank when he spends the loan. Just as an individual person gets rid of money by making a loan or buying something. The "banks don't lend reserves" argument is true but pointless. (Oh God, please keep the MMTers out of this one, because it's way off-topic.)

Nick,

Under normal circumstances, I would challenge your remark that banks "lose" reserves to other banks when they make payments. When there are no excess reserves in the system banks must borrow back "lost" reserves in order to meet reserve requirements. However, we do have excess reserves at the moment, so in theory banks could increase lending in the expectation that this would reduce their excess reserves. But this assumes that banks want to lose excess reserves to other banks. As they are now required to hold a higher proportion of their balance sheet as safe liquid assets - and indeed are choosing to do so anyway, because it reduces their liquidity risk - they may not want to do so. Also, as they are now expected to fund themselves with a higher proportion of expensive equity, they may not wish to take on much risky lending - especially as, post-crisis, many banks still have substantial portfolios of non-performing and high-risk loans with poor quality collateral. I guess what I am saying is that banks' risk appetite, and the expectations of regulators, have a considerable impact on the effectiveness of monetary policy.

I wasn't meaning to raise the "banks don't lend reserves" thing. As you say, it's off topic. I was concerned about the assumption that banks could or would necessarily offload reserves.

Frances: OK. I think I see what you are saying. I would put it this way: those things you mention (risk liquidity etc.) mean that banks want to hold a higher amount of reserves than they otherwise would. But if the amount they want to hold is still determinate, increasing the amount of reserves above that desired amount can still make them want to get rid of the extra. It is actual reserves minus *desired* reserves (as opposed to actual reserves minus *required* reserves) that matters. (Side note: I really wish monetary economists would define "excess reserves" as excess over desired, rather than excess over legally required. Especially since in countries like Canada there are no reserve requirements).

Frances,

You write: "When there are no excess reserves in the system banks must borrow back "lost" reserves in order to meet reserve requirements."
... I'd add that they may also need to borrow reserves to repay overdrafts of their Fed (or CB) deposit account. I don't know how rare that event is though.

Clearly if you think of all the banks aggregated together, the reserves don't go anywhere (ignoring the exceptions you brought up). It is an interesting thought experiment though: how long will it take, on average, for a bank's reserve levels to return to normal after making a large loan... because presumably they must transfer reserves to clear payments the borrower makes (when the loaned funds are spend on vendors/sellers/employees who use other banks), and those fund recipients likewise spend the funds, etc. I would think that the various individual commercial banks would tend to have their original reserve levels restored again pretty quickly through normal economic activity. That's my intuition anyway. (I'm specifically thinking in terms of a 0% reserve requirement here to keep it simple). I'd bet somebody has a mathematical model of this somewhere... and has probably tried to verify the model by checking it against empirical data (in some clever way, to account for all the other changing variables that reality tends to throw in our faces). Am I making sense? Does anybody know if my intuition is correct? Does anybody have an idea for the mean time it takes for those reserves to return to the original pre-loan levels at all the banks in the system? Is this something that bankers are aware of and routinely model?

Nick,

Hah. I sympathise about "excess reserves" - I'm in the UK, we don't have "required reserves" as such either (voluntary scheme is currently in abeyance).

Yes, banks want to hold higher amounts of reserves than they used to. However, I think you don't give enough weight to the regulatory capital problem. Whether or not there are excess reserves, damaged banks don't lend. Having more safe assets on their balance sheets than they really want is nowhere near as great a concern as not having enough regulatory capital to enable them to take on more risky lending. A bank that doesn't have enough regulatory capital to support its lending is deemed insolvent and can be put into administration by regulators. Just look at the Co-Op Bank in the UK. Until its regulatory capital hole is filled and/or it has unloaded a substantial proportion of its impaired loan book, no way is it going to increase net lending, however many reserves you throw at it.

Actually, banks that have suffered a recent traumatic near-failure can be reluctant to increase lending even if they have enough capital. RBS, for example, has cut its SME lending drastically - from 40% to 30% of the UK market.

... continuing my thought experiment above ... if, for example, the mean time it takes for a dollar loaned (in lost reserves to clear payments the borrower makes) to return to the lending bank is 5 seconds and bankers are aware of this, would they even consider that lending would be a worthwhile strategy for them to "get rid of excess reserves" ... even on a temporary basis? What if the mean time is 1 month?

I'd guess the answer (ignoring noise) would look something like

reserve level = 1 - exp(-t/T)

for a dollar loaned at t = 0, where T (T positive real number) is the time constant. So perhaps a more useful question is what is the mean time it takes the bank to get back $(1-exp(-1)) = $0.63 in reserves after loaning $1?

(or some more recent version), you'll see that the average duration of debt outstanding has been increasing and is expected to. Thus, the Fed and the Treasury are working at cross purposes."

Williamson is right on this point, no? If changes in the maturity structure of federal debt have macroeconomic effects, that shouldn't depend on whether those changes are due to the Fed or the Treasury. This came up a couple years ago when someone -- I can't remember who -- was suggesting that Treasury lock in low rates by shifting federal debt toward longer maturities. That would amount to anti-QE. If you think QE matters, then yes, you should be looking at the whole maturity structure of federal debt held by the public (not counting the Fed! so you can't use the published series) and not just the particular changes in the maturity structure resulting from QE.

What this has to do with the larger debate, I have no idea.

... I guess I should add to my scenario and say that all the banks have more than enough excess reserves before the $1 is loaned (i.e. there's no danger of a CB deposit overdraft... otherwise reserve levels would snap back near instantaneously... within 24 hours anyway, to repay the CB before the end of the day).

Tom,

If there are no reserve requirements then banks run daylight overdrafts in their reserve accounts. I can't speak for other jurisdictions, but the Bank of England expects those overdrafts to be collateralized (repo).

Your "thought experiment" is interesting, and I don't know if anyone has done an exercise like that. I have a couple of thoughts though. Firstly, a very large loan (an aircraft loan, for example) would be likely to be pre-funded, because of the liquidity risk, which implies that a bank would temporarily increase its reserve holdings (or general collateral holdings, so it can obtain reserves readily) on loan approval. In that case, the "desired" reserve level wouldn't be affected. Secondly, with smaller loans, I agree that normal commercial activity could restore desired reserves very quickly. In theory, excessive lending should run down reserves, but usually what happens in credit booms is that all banks lend excessively, so inflows and outflows are approximately balanced and there is no impact on reserves.

Tom,

This may not help much but banks are both borrowers and lenders (interbank lending and such). Banks don't lend to "get rid of excess reserves". They lend to make money off the difference between short term borrowing costs and long term lending income. And so, assuming that banks make long term amortized loans using short term borrowed funds, the time until the profit threshold is reached would be a function of both the short term and long term interest rate. The greater the spread, the shorter the time period needed to reach profitability.

Using the amortization formula:

A = Annuity (payment)
P = Principle
Int = Long term interest rate
n = number of payments
Total Mortgage Interest = TI

A = P * [ Int * ( 1 + Int ) ^ n ] / [ ( 1 + Int ) ^ n - 1 ]
TI = A * n - P

For short term bank borrowing assuming the bank can roll over existing borrowed funds at a fixed short term interest rate

i = Short term interest rate

A * n >= P + n * i * P

Substituting back in for A and dividing by P:

[ n * Int * ( 1 + Int ) ^ n ] / [ ( 1 + Int ) ^ n - 1 ] >= 1 + n * i

Solving for n (i, Int) takes a root solving algorithm

Jeff:

"Everything is already in equilibrium from the start, with the representative agent fully aware of the stable QE policy going forward."

OK, we should be discussing this with the correct semantics, which will clarify what the real issues are. Really, we shouldn't even be arguing about the model itself but about how it maps onto the real world, in which we do seem to observe monetary policy surprises. I would put things as follows:

There are two potential questions with respect to the model. First, how does QE affect the inflation rate? Second, how does QE affect the price level at time zero? To me the second question is more interesting, because we're dealing with a real world history in which QE was (probably) not initially anticipated. So time zero happens when the market realizes that QE is going to happen, when we (in the real world) make a transition between the two instances of the model. If the model were to show that QE causes the price level at time zero to be higher than it is without QE, we would map that result onto the real world by saying that, when the market realizes that QE is going to happen, prices go up. And since I believe prices are sticky, when I say that "prices go up," I mean there is a period of inflation.

But by using fiscal policy to tie down the price level at time zero, Steve has rigged the model in such a way that it cannot answer what I regard as the more interesting question. Of course, given the way he has rigged it, another potentially interesting question is how the path of fiscal policy differs from one instance of the model to the other. In my mind, this comparison would map to the real world question, "How does fiscal policy have to change to offset the initial inflationary effect (assuming there is one) of a surprise QE announcement?" Steve doesn't tell us the answer to that either, but my guess is that the fiscal policy in the instance of the model with QE is in some sense "tighter" than in the instance without QE.

Steve is interested only in how QE affects the inflation rate in the model. In my mind, that question maps onto the real world question, "Once the market has fully equilibrated in response to a QE announcement, what happens to the inflation rate?" But being a sticky-price guy, I don't think the equilibrium would happen any time soon after the announcement. In fact, I'm not sure it would ever happen, because by the time it is ready to happen, QE may be over, and the impact may have dissipated (e.g., the securities involved may have matured). So in my sticky-price conception of the real world, the model doesn't necessarily have anything useful to say regarding the effect of QE on the inflation rate (as the inflation rate is understood in the context of the model).

Mark S,

Obviously, without seeing your calculations I have no idea what you have done. But I find it highly improbable that the current size of the monetary base is in any way a reliable predictor of the value of future commercial lending.

JW Mason,
"If changes in the maturity structure of federal debt have macroeconomic effects, that shouldn't depend on whether those changes are due to the Fed or the Treasury."

I agree, provided we are only considering the macroeconomic effects of the maturity structure of federal debt (i.e. ignoring the effect of changing the size of the monetary base). This certainly was an issue in the Maturity Extension Program (Operation Twist). Given that, Williamson is right about this issue up to a point (something which Beckworth agreed with as well).

"What this has to do with the larger debate, I have no idea."

Here's what I am thinking.

Equations 38 and 48 in his paper determine the combination of feasible values for x1 and x2. QE increases the value of al (the amount of outstanding longer-maturity debt held by the central bank) which appears in equation 48.

http://www.artsci.wustl.edu/~swilliam/papers/qe2.pdf

Increasing the value of al increases the value of x1 (and x2). Inflation is defined by equation 40 and thus is strictly a possitive function of x1. The outstanding amount of short (Vs) and long (Vl) maturity debt plays no role in either equation 38 and 48 except as an upper bound to how much the central bank may purchase of each. The total amount of outstanding debt (V) appears in equation 48.

In short, while the amount of outstanding debt appears to have some effect (which could be taken into account in an elementary empirical analysis), the duration of the outstanding debt does not appear to be a factor in his model. Thus I am perplexed by his comment.

Francis Coppola,
"But I find it highly improbable that the current size of the monetary base is in any way a reliable predictor of the value of future commercial lending."

I'm not sure I would describe it as a "relaible predictor". But the results are statistically significant at the 5% level and the impulse response is positive.

JW Mason,

"Inflation is defined by equation 40 and thus is strictly a possitive function of x1."

should read

"Inflation is defined by equation 40 and thus is a strictly decreasing function of x1."

"That's not quite right, when we are talking about money...."

Thanks Nick, I understand completely. That does seem to support that my interpretation of W's error is partially right - bond holders sell to the Fed because they would rather hold something else (a different asset, a house, a pretty bauble). Since the bond holder likely doesn't want to hold cash, the return on cash is irrelevant to the decision. In fact, the extra purchase/velocity in buying the alternative likely raises those prices, not lowers them.

I really think W has lost the sense of causation flow. M=F/a is an equilibrium equation, but increasing F does not increase M! (except at very high velocities, and even that is relative).

Nick, on " banks will lose reserves"

Keynes (1930) in „Treatise on Money“:

It is evident that there is no limit to the amount of bank money which the banks can safely create provided they move forward in step. The words italicised are the clue to the behaviour of the system. Every movement forward by an individual bank weakens it, but every such movement by one of its neighbour banks strengthens it; so that if all move forward together, no one is weakened on balance. Thus the behaviour of each bank, though it cannot afford to move more than a step in advance of the others, will be governed by the average behaviour of the banks as a whole - to which average, however, it is able to contribute its quota small or large. Each Bank Chairman sitting in his parlour may regard himself as the passive instrument of outside forces over which he has no control; yet the 'outside forces' may be nothing but himself and his fellow-chairmen, and certainly not his depositors."

Regarding reserves, I think the issue is that US banks are currently compensated for them. This acts as a contractionary policy by the Federal Reserve, contrary to the near-zero target rate.

With no regulation, banks will issue loans until the marginal revenue from interest equals the marginal cost (in stability and solvency risk) of the additional balance-sheet leverage. Adding regulation regarding required reserves in the mix increases the risk of leverage (adding regulatory compliance into it), which will on the balance decrease the amount of lending.

Adding in interest compensation for reserves amounts to double-dipping. When a bank receives 0.25% interest on reserves, at the level of an individual bank issuing a loan at 0% nominal rate (or, equivalently, purchasing a 1-month T-bill at 0.06%) represents a loss. This might not be a problem under ordinary circumstances, but this near-ZLB situation directly calls for an increase in the money supply -- which can only enter circulation through the bank lending that's disincentivized by interest on reserves.

As a result, we're at the worst of both worlds: private, nonbank entities see near zero rates for savings, but banks see a greater-than-zero rate. As a result, loans for productive purposes will only be made at the >0.25% rate, effectively increasing the economy-wide credit spread and rendering illusory the Fed's 0-0.25% interest rate goal.

--

With regards to the model in the original post, I think there's a built-in contradiction that I can finally put to words: the situation described in the Story (also by Williamson) is inherently flawed and results in monetary policy always working backwards as a controlling force.

The model is given by: M(t) = a + P(t) - b.Pdot(t). The situation given in the original post reflects jumps in the money supply (and/or price level), but those jumps really have to happen over time. (This also lets us actually take the derivative of M, to boot, meaning we can work with "strong solutions" to the DE rather than "weak solutions.")

Assume that the money supply linearly increases from 1 to 2 over time epsilon, such that:

M(t) = {1 for t <= 0, 1 + t/eps for 0<t<eps}

Over the increasing-M period, P(t) has a solution of the form C*exp(t/b) + A*t + B (the positive coefficient on 'b' gives rise to the bubble solutions discussed in the article). Substituting that ansatz and matching terms gives A=1/eps, B=1+b/eps, and C=-b/eps, where C was selected to ensure price continuity at t=0.

After time epsilon (the end of "QE" implementation), the price level is given by P(eps) = -b/eps*exp(eps/b)+1+1+b/eps. However, exp(eps/b) > 1 + eps/b, so P(eps) < -b/eps(1+eps/b) + 2 + b/eps = 1.

That means that, according to this model, increasing the money supply is always, without exception, deflationary, provided b>0. This is true regardless of the permanent or temporary nature of QE, as simply implementing it reduces the price level.

The "equilibrium story" says that:

> If there is an upward jump in M(t), that was not foreseen, and if people expect that increase to be permanent, the fundamental solution says that P(t) must jump too to restore equilibrium. A permanent increase in the money supply causes a permanent increase in the price level.

Except that this violates the model dynamics -- the model provides no mechanism where P can increase in response to an increase in M. (The opposite works perfectly, however -- if M increases sufficiently quickly in response to a prior jump in P, the overall trend can be non-explosive.)

Majromax,

I think the effect of positive interest on reserves is rather more subtle than that. It does prop up the short end of the treasury yield curve, but to say it is contractionary is overstating it. And if a bank pays less than 0.25% on deposits then the compensation on reserves gives them a small profit, not a loss.

I think the idea that interest on reserves disincentivizes bank lending is a complete fallacy. It is the marginal return on lending over its funding cost that banks are interested in. 0-0.25% is a simply awful return. They can do MUCH better than that on commercial lending. So if they aren't lending, it is not because of interest on reserves. It is because of their horribly risky balance sheets and their shortage of capital - see my comment to Nick Rowe about the problems that regulatory capital requirements can create.

I also think negative IOR is intrinsically contractionary, because it is a direct cost to banks. If they can't pass it on in the form of negative deposit rates, then they may well raise rates to borrowers. But the hot potato effect might offset this. It's hard to say.

Frank,

Thanks for the response. I realize that banks make money from a spread and are not primarily motivated to make loans based on trying to get rid of excess reserves. I was thinking of Nick's comment here (which was batted back and forth a bit between Frances and Nick):

"Frances: if an individual bank expands loans, it knows it will lose reserves to other banks. Banks (presumably) know this. Making a loan today is the way an individual bank gets rid of reserves tomorrow, or the day after tomorrow, depending on how long it takes the borrower's cheque to be deposited in another bank when he spends the loan." - N.Rowe

So if a bank "knows it will lose reserves to other banks" if it "expands loans" it must also know that it will most likely recover those reserves again in short order (if my intuition about this is correct, which Frances seemed to confirm).

My question really boils down to the following: If a bank makes enough new loans to lose $1 of reserves through payment clearing*, then how long until this bank recovers at least $0.63 back again through normal economic activity?

I guess my point is if that mean time is small enough and banks know this, then they already know there's really no getting rid of their excess reserves in any meaningful sense.

*BTW, if you figure that there are N equal sized banks in the system, the amount the bank would need to loan, on average, to lose $1 through payment clearing would be about $(N/(N-1)) since there's a chance the recipient of the funds uses the same bank.

> It is because of their horribly risky balance sheets and their shortage of capital - see my comment to Nick Rowe about the problems that regulatory capital requirements can create.

I'd disagree here, because T-bills provide equivalent risk-free investment instruments. It's entirely possible that the banks don't see any risk-adjusted returns > 0.25% (on the balance) at the sub-2-year horizon, but to the extent we want an expansionary monetary policy then even 0.25% may be too high.

If reserves (beyond legal requirements) paid no interest, then banks could still keep the same asset risk profile by holding T-bills instead of zero-interest reserves. But those T-bills would have to be purchased from private holders, who would then have presumably unwanted money and no risk-free financial instrument to hold.

Interest on reserves incentivizes that the economy hold base money in reserves over other uses. If that's what's necessary to properly capitalize the banks, then I suppose that's a bitter medicine to swallow. On the gripping hand, if the "necessary" amount of excess reserve is ~25x the regulatory requirement (compared to a historic, pre-recession ratio of approximately 0x), then that suggests deeper structural issues in the banking system.

From another angle, if the economy really is at the ZLB, then the Fed should act like it and not privilege some forms of savings (reserves) over others (T-bills), and let liquidity premiums sort themselves out. (I'm not particularly rosy about the prospect of purely monetary policy acting as economic stimulus in the first place, but if we're giving it a shot then it should be a fair one.)

Majromax,

You are confusing assets and liabilities. Reserves are an asset. Capital (in banks) is equity, and sits on the liability side of the balance sheet.

Reserves are liquid assets, as are T-bills. They are near-perfect substitutes - the T-bill is slightly riskier, and this would normally be reflected in a slightly higher interest rate, but these are not normal times. But banks do not primarily make money on the spread of reserve interest over T-bill yields. And neither reserves nor T-bills are capital.

Increased reserves only recapitalize banks to the extent that they earn a positive spread, which may go into retained earnings (tier 1 capital) if not used for expenditures. But as I've already pointed out, banks make far more on commercial lending. Interest on reserves is not an efficient way of recapitalizing banks. Increasing the profitability of commercial lending (i.e. increasing spreads) is far better. Depressing funding costs while propping up interest rates to borrowers is the most effective way of recapitalizing banks (apart from rights issues and debt for equity swaps). And this is exactly what banks have done in the last six years. Consequently it appears that they have improved their capital positions considerably.

But banks recapitalizing by means of widening interest spreads (especially higher rates to borrowers) is contractionary for the economy. Under-capitalized banks are bad news for monetary policy, since banks that are short of regulatory capital (equity) relative to their existing risk-weighted loan portfolios cannot lend productively. And banks that are repairing their balance sheets are equally bad news, because they will maintain wide spreads and shrink their asset base (which destroys money). Hence my remark about capital.

On your "privileging savings" point - I don't agree that the Fed is doing any such thing. Firstly, liquid assets on bank balance sheets are not "savings" in any normal sense. They are liquidity buffers designed to protect the balance sheet from sudden funds outflows. Secondly, the Fed pays interest on reserves in order to prevent short rates (including T-bill yields) falling below zero. It's not wholly successful in this, for a variety of reasons that I won't discuss here. But it certainly doesn't do it to recapitalize banks, or to privilege some form of savings, or to disincentivize lending.

It isn't correct to suggest that reserves could be more gainfully employed than sitting on bank balance sheets. Unless the economy wants to do far more transactions in physical currency, there just isn't another use for reserves.

Nick, regarding the whole recent Stephen Williamson brouhaha, I was wondering if I might ask you about some thoughts that Stephen didn't respond to. Largely, they come down to this:

Does Stephen, and his group, still believe in MV = PY? or do they regard that the way they regard IS-LM, as laughably primitive, un-microfounded, wrong, and beneath the dignity of modern economics?

Because it seems like a lot of what Stephen says must make inflation go down, could just make the velocity of money go up (and so inflation and/or income go up). For example, he writes:

"Next, conduct a thought experiment. What happens if there is an increase in the aggregate stock of liquid assets, say because the Treasury issues more debt? This will in general reduce liquidity premia on all assets, including money and short term debt. But we're in a liquidity trap, and the rates of return on money and short-term government debt are both minus the rate of inflation. Since the liquidity payoffs on money and short-term government debt have gone down, in order to induce asset-holders to hold the money and the short-term government debt, the rates of return on money and short-term government debt must go up. That is, the inflation rate must go down."

At: http://newmonetarism.blogspot.com/2013/12/the-intuition-is-in-financial-markets.html

So, what if the Fed made T-bills and then sold them for T-bonds? The interest rate on T-bonds would go down, and the interest rate on T-bills would go up. And the "liquidity premium" (This seems more like the liquidity-and-risklessness premium, given how liquidity is often defined.) would go down. So it would be less desirable to hold money. So, two things could happen, it seems, to maintain equalibrium (if you think it has to be maintained), not just one:

i) Inflation could go down to induce people to hold money as much as before.

or

ii) Inflation could not go down, and people would want to hold money less, and so would get rid of it more quickly by spending it faster. It would become a hot potato, or more of a hot potato. In fact, I pretty much consider money a hot potato now. The "liquidity" premium is not high enough for me except for relatively very small amounts. Anything more I spend very quickly, mostly on stocks or real estate. But as the velocity of money goes up, and as M has gone up (defined to include T-Bills), either P or Y or both would have to go up, to maintain MV = PY.

Your thoughts on this?

Richard: My guess is that Steve would say that MV=PY is not very useful.

I think he just missed seeing that there were two ways to re-equilibrate.

Thanks Nick,

I feel confident enough now that I may do a post about this. Generally, I only post if it's something I really think is good, and adds something that's not out there. Without a name, I like to only post stuff I think is really worthwhile, so people know that this guy rarely posts, but when he does, it's often good, and maybe worth a look. Anyway, that's been the strategy the last five years, and it's gotten some play.

If I might ask about one more thought on the current Williamson inflation stance.

He writes:

"But in a liquidity trap, since money and short-term government debt are equally liquid, if the central bank swaps one asset for another then this has no effect."

At: http://newmonetarism.blogspot.com/2013/12/the-intuition-is-in-financial-markets.html

But money is not equal to short term-debt in "liquidity-and-risklessness", and it seems that what Stephen calls "liquidity" is actually "liquidity-and-risklessness", because there are assets that are just about as liquid as short-term government bonds, but are risky. Here, when I say liquid I mean the common definition of being able to sell quickly and cheaply at the market price.

Stocks, it seems to me, are just about as liquid as T-bills (by that common definition). In fact, about as liquid as you can get. The sale is almost instant, with close to zero sales cost, and at the market price.

Anyway, Stephen's "liquidity" seems to mean 1) Riskless 2) Extremely collaterable 3) Extremely usable in transactions. So money is the most liquid, and T-bills are second. And in a "Liquidity Trap", T-bills' advantage over money of having a substantially higher interest rate goes away.

So, it seems like the characteristic at issue here is "liquidity-and-risklessness". And with regard to that, short-term government bonds and money are significantly different.

Why? Because short-term government bonds are riskless for as much as you own. But with money, the risklessness is limited, or costly. If a party sells $100 million in T-bills for money, that money is risky. It's only insured up to $250k in a bank account. The owner will want to move it relatively fast. He might buy longer term bonds, or something else. And then the next owner will want to move the new money, at least anything over $250k per bank account, and so on. It seems the velocity of money would increase.

So, again, it comes down to, does the freshwater macro crew still believe in MV = PY? Or is that un-microfounded crap to them?

They love to talk about general equilibrium, and perhaps to them the very concept of "velocity" is distasteful, because it is, in one sense, a disequilibrium concept. In a typical equilibrium, velocity is zero. The buyers engage the sellers; the price adjusts so that all product in the market clears; and, we're done. Velocity of money means you never reach an equilibrium where all money is desired to be held, at least for long.

So, basically, do you think it's significant that T-Bills are riskless to any amount, but money is only riskless to $250K per bank account? Do you think that the freshwater macroeconomists ignore velocity, and that's a significant reason for the conclusions they come to?

Richard: you could interpret the "money" as currency.

Steve likes models where money is modelled explicitly, where people actually use it to buy and sell things, so he might say "velocity" is not useful, but would not say it's zero in equilibrium.

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