What we have just witnessed is the economics equivalent of the Sokal hoax. It wasn't a hoax, just a mistake, but the effect was the same. We all make mistakes. What matters is that the rest of us didn't all spot that mistake immediately. Even those of us who did see that something was wrong didn't immediately identify what exactly was wrong. We need to ask ourselves why. We can't blame the person who made the mistake if we didn't immediately see it either.
Many economists have been puzzled by recent house price inflation. My theory shows that house price inflation was caused by too many houses being built….Loadsa theory…..Let me give you the intuition with a simple thought-experiment. Suppose builders suddenly increase the stock of houses on the market. The rate of house price inflation must increase for people to be willing to hold those extra houses, because people demand more houses when they expect rising house prices.
If you believe my explanation makes sense, you will also understand why Zimbabwe had hyperdeflation. There needed to be ever-accelerating deflation, so that people would willingly hold all that extra money.
But why didn't we immediately see what was wrong?
Take any asset. It could be houses, or it could be money. The only difference (in this case) is that the price of money is the reciprocal of the price of other goods, so the rate of increase of the price of money is the rate of decrease in the price of other goods (i.e. the deflation rate).
The quantity of houses demanded is a negative function of the price of houses and a positive function of the expected rate of increase of the price of houses.
The quantity of money demanded is a positive function of the price level and a negative function of the expected rate of inflation.
Ignore anything else that might affect the demand for houses, or money, just to keep it simple. And assume perfectly flexible prices and continuous market-clearing, just to keep it simple. And assume actual and expected inflation are the same, just to keep it simple.
Assuming a simple log-linear demand function for the stock of houses, the supply=demand equilibrium condition is:
H(t) = a – P(t) + b.Pdot(t)
The equivalent for money is (remembering the price of money is the reciprocal of the price level);
M(t) = a + P(t) – b.Pdot(t)
It is well-understood, at least since Brock (1975) "A simple perfect foresight monetary model"(pdf) , that this equilibrium condition permits an infinite number of solutions. There is the "fundamental" solution, where the equilibrium time-path depends only on the time path of M(t). And then there are an infinite number of "bubble" solutions. Even if M(t) is constant for all time, P(t) can rise without limit at an ever-increasing rate, or fall without limit at an ever-increasing rate, along any one of these bubble paths.
Economists normally adopt the "fundamental" solution, but some economists think we might sometimes observe "bubble" solutions.
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. 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.
There is an alternative way to get an increase in the money supply to cause deflation, while sticking to the fundamental equilibrium. You need to ensure 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 Pdot(t) to fall, which in turn causes P(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).
[Update: Here's the above paragraph 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).]
But note one thing very well. 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 proper way to discuss questions like this is to talk about the extent to which QE is expected to be permanent or temporary. Scott Sumner, to give just one example, has been saying that QE has little effect because it is expected to be mostly temporary, given the failure of the Fed to announce a sensible target. You talk about the central bank's monetary policy target, and how that influences people's expectations of future prices (or NGDP, if prices are sticky). And you discuss the effects of QE within the context of that monetary policy framework.
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.)
So, what went wrong? How come even those of us who did get that something was wrong didn't immediately figure out what exactly was wrong?
I blame maths. Only when Steve said it clearly in words (for which he deserves credit), could I clearly see what the problem was.
(Perhaps I should have written a slightly different post, a real hoax, arguing that rising house prices are indeed caused by building too many houses, just to see how many people would fall for it? But a hoax post on money would be much easier to pull off.)
Worthwhile Canadian Initiative 
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.
Click to access 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:
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.
Test.
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:
Click to access 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:
Click to access 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.