"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. Going in the other direction, a reduction in the aggregate stock of liquid assets makes the inflation rate go up."
Start in equilibrium. Suppose the helicopters drop more money on the population. People do not wish to hold more money. Because there are diminishing marginal benefits to liquidity, and those marginal benefits are now below the opportunity cost of holding money. So people will try to spend their excess supply of money. This creates an excess demand for goods. This causes the price level to rise. In the new equilibrium, the real value of the total stock of money is the same as it was in the old equilibrium. If the money supply doubles, the equilibrium price level doubles too. And so the marginal benefits of holding money are the same as they were in the old equilibrium.
Update: Bob Murphy has a fine reductio ad absurdum (assume zero real income growth to make Bob's argument more clear):
"…suppose we weren’t talking about a sudden surprise QE announcement. Instead, imagine we are in the midst of a Friedmanite rule where the quantity of money grows at a constant rate–let’s say it’s 2%–year after year, regardless of circumstances. Further suppose this rule has been in place for 10 years, and the public is convinced it will continue to be the rule for as far as the mind can forecast.
Thus, there is no question that we are bouncing from one equilibrium to another. We are in the long-run equilibrium (in terms of any standard way you are going to model such a situation). Now, within this long-run equilibrium path, Williamson could still make his claim: Each year, the rate of inflation has to perpetually fall, because each year you have to convince the public to hold more cash than they held the previous year. Thus, for any positive growth in the quantity of money, the rate of price inflation must constantly fall."
Update2: which explains why Zimbabwe had hyperdeflation.
Can somebody resurrect David Hume?
Worthwhile Canadian Initiative 
Techincally, I think SW would argue that his model assumes no permanent helicopter drops, because it specifically assumes a passive fiscal policy that always maintains the same PV of total government liabilities. This pins down the price level, in a sort of but not exactly FTPL sense. Still, that is not the point you are making: Why doesn’t even a FTPL-determined price level in his model rise as the liquidity premia on bonds/money declines in the liquidity trap? Why is it plausible that only inflation and not the price level is determined by the altering the convenience yield of liquid assets? This isn’t a model of sticky prices, after all. Maybe an intuitive explanation is that the CB by assumption (idue to his about the passive fiscal authority maintaining the real value of government liabilities) is only temporarily affecting the liquidity premia (and will fully compensate with reversal in the future), such the price level is unaffected but the rental rate on money/bonds must still increase (inflation must decrease) during the period of the lower liquidity premia. This would make his model akin to asking what would happen if the CB outside of the liquidity trap started dropping helicopter money but promised to vacuum it all up and then some in (say) two years. Prices might remain unchanged but nominal interest rates could decline along with inflation. Instead of saying inflation declines because people demand a higher return on money given the lower convenience yield, you could say inflation declines because the expected future price level actually declines because the helicopter drops was a counterintuitively a sign of tighter monetary policy due to expected overcompensation from the future vacuum. This is kind of equivalent to a fixed, passive fiscal policy that automatically maintains the starting price level in his model (I think).
dlr: good try. You are making sense. But unfortunately, given the assumption you are making here: “Techincally, I think SW would argue that his model assumes no permanent helicopter drops, because it specifically assumes a passive fiscal policy that always maintains the same PV of total government liabilities. This pins down the price level, in a sort of but not exactly FTPL sense.“, plus Steve’s assumption here: “Since the liquidity payoffs on money and short-term government debt have gone down…” the only way both those assumptions can be satisfied at once is if the helicopter is immediately followed by a vacuum cleaner, which nullifies his thought-experiment before it has even started.
But for any helicopter drop there must exist a vacuum cleaner that slowly vacuums the money back up over time, at just the right speed that the helicopter drop causes no immediate change in the price level. But I don’t think that’s what he’s saying. Or if it is, I don’t think he realises he’s saying it.
In other words: a higher level of the money supply causes a higher price level; a lower growth rate of the money supply causes a lower price level and a lower rate of inflation. So if you matched them up just right, you could have no change in the price level, but a lower rate of inflation.
But if that’s what he is saying, why doesn’t he just say it? Like I did, just then. This is a very old result. Cagan 1968, I think, where the inflation rate temporarily overshoots the growth rate in the money supply when that growth rate suddenly increases. So if you have an increased level of the money supply, and a lower growth rate from then on, and you got the numbers just right, there would be a fall in the inflation rate with no jump up or down in the price level.
Nick,
I just wrote up a blog post criticizing Steve’s view. I think the problem is that he misinterprets causality. Sure, in equilibrium the marginal value of your cash holdings should equal the inflation rate, but this could arise either from the inflation rate falling or people drawing down cash holdings, thereby increasing the marginal value of liquidity.
Yichuan: good post. I left a comment.
I don’t think you need the vacuum cleaner to match up just right in terms of timing. What you need is expectations of a lower future price level to just offset the lower convenience yield. We could imagine a CB with this kind of strange reaction function, and it is maybe less strained than imagining the perfectly timed vacuum, but it is still strained. This is what I think of as the passive reaction function of the fiscal authority in the SW model. The real value of government debt at all times remains the same. If the government helicopters money, it must make an implicit promise to sop up that money in the future. To the extent the helicoptered money sits around for a while and lowers the convenience yield, it must promise to sop up the money and then some (otherwise the debt has lost value), such that real value of government liabilities never changes, whereas the inflation rate can vary. I think it is this presumed, offsetting policy reaction function that is the key to funny results from the model as opposed to instability or magical equilibrium hopping.
Nick, I don’t think Williamson’s post is about helicopter money. It’s about QE, i.e. central bank purchases of already existing bonds. Your helicopter money involves handing new money out for free, which is not the same thing.
Nick,
Seems to me the fundamental communication problem stems from the fact that the model admits multiple equilibria.
Both stories are consistent with equilibrium. In your story the higher price level lowers the real stock of money back to what it was before, so as before people are happy holding it.
In SW’s story inflation immaculately falls, raising the real return to money and making people happy to hold a higher real stock of it. That also works in the sense of being consistent with equilibrium in the model.
To settle the argument you need to go, as Krugman did, to other markets, in particular the ones where inflation actually happens. It’s there that you’re story will be consistent with behaviour and SW’s will not. You started to do this in this post but omitted the details, you need to fill them in (explain why excess money stocks translate into increased demand for goods and why that means higher prices).
You can only win by going outside financial markets though, within SW’s context both stories, and convex combinations of the two, will work and you don’t ever quite win.
Non-economist trying to follow along here, but SW has lost me. Has he explained anywhere how he gets inflation to fall?
Patrick, will a simple “no” suffice?
This thread of thread, which began with Kocherlakota’s fault, is frustrating. If a renowned economist like Stephen Williamson shows an understanding of monetary issues that falls far short of the understanding of a layman – where has macroeconomics gone?
Is “linearized around some steady state” DSGE analysis of cashless economies the end of macroeconomics? Or perhaps the beginning of a fresh start?
Williamson: “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.”
IOW, unless the rates of return on money and short-term gov’t debt go up, asset-holders will not hold money and short-term gov’t debt, i. e., they will spend.
Nick Rowe: “People do not wish to hold more money. . . . So people will try to spend their excess supply of money. This creates an excess demand for goods. . . .”
Isn’t Williamson actually conceding your point? 🙂
@ Philippe
Williamson is not talking about QE, because the Treasury is increasing the deficit. QE is the Fed’s doing. But I agree, simply increasing the deficit is not helicopter money, because of distribution. Like the rain, helicopter money falls on the just and the unjust. 🙂
Adam P: “Seems to me the fundamental communication problem stems from the fact that the model admits multiple equilibria.”
Sure. But so does every simple model with money, unless you start talking about what happens when P goes to zero or infinity. The literature on this started in the 1970’s.
Assume real money supply = real money demand:
M/P = L(Y,i) where i = r + Pdot/P and where dL/di < 0
Assume M, Y, and r are all fixed exogenously and never change.
There is one solution where Pdot/P =0. That’s the standard solution. But there is an infinity of other solutions where P and Pdot/P are both higher (or both lower) than the standard solution, and M/P solwly falls to 0 (or rises to infinity). And we normally rule out those non-standard solutions by saying we could always use the money as TP, or something (or a $1 note could buy the world).
Wish I could remember the name of the economist who did a paper on all this stuff in the 1970’s.
Herbert: “… where has macroeconomics gone?”
That’s what I’ve been asking myself.
As far as the Thread of threads that started with Kocherlakota is concerned, this post is GAME OVER. When he says it in words, not math, it’s just too totally obvious to see what the problem is. All that’s left is the post-mortem, to see why the teaching of basic macro/money died. And epidemiology, to see how far the rot has spread into the grad skools. Then we start again, with the basics of the quantity theory. And drag a load of old guys out of retirement, so we can explain really basic stuff like: “the central bank sets M, but people set M/P given their expectations of future M, and P adjusts so that Md=Ms”.
Reading some of the comments on Steve’s post, it’s obvious that some guys (probably fancypants grad students) STILL don’t get it, even though he has (unwittingly) laid out the problem as clearly as he could.
And I took a quick skim of the blogosphere this morning. AFAIK, there is me, Bob Murphy, and Yichuan Wang, who have noticed the problem. God help us all.
I can’t tell whether Steve now gets it, from his reply to my comment on his blog (where I said what I said here). He talks about “real bonds”, which is OK for bonds, because you can assume all bonds are indexed. But you can’t index money. It’s the medium of account. You can’t index a thing to itself.
Time to round up all the Minnesota etc grads, and put them back in basic training. I wonder how many generations there are?
dlr: “I don’t think you need the vacuum cleaner to match up just right in terms of timing.”
In continuous time, you do.
All in logs: M(t) = P(t) – b.Pdot(t).
Ruling out the explosive/implosive solutions, that means:
M(t) = P(t) – b.Mdot(t)
To ensure P(t) does not jump when M(t) jumps up, you need Mdot(t) to jump down at the same time.
Steve is talking about helicopter bonds. But it makes no difference. The government sets B+M. If B and M are perfect substitutes (it makes a little difference if they are imperfect substitutes) people have a demand for (B+M)/P (or B+(M/P) if the bonds are indexed). If helicopters increase B+M, P increases to restore the original (B+M)/P.
Or, simply change Steve’s thought-experiment to helicopter money, because his reasoning ought to work exactly the same way.
Nick,
The 2nd paragraph of your post needs a slight adjustment. You assume that heli-drops automatically and immediately cause inflation. They won’t if the economy is nowhere near capacity, or put another way, if unemployment is above NAIRU.
I.e. (as MMTers are constantly pointing out) if unemployment is above NAIRU, the INITIAL effect of a decent sized heli-drop is primarily to increase output. But when unemployment reaches NAIRU, the effect is primarily to exacerbate inflation.
Ralph: Steve is assuming perfectly flexible prices and market-clearing. Therefore, so am I. That’s not the issue. It’s irrelevant. So are MMTers. This is Old Monetarists (plus everyone else who understands basic macro/money) vs so-called New Monetarists.
Ralph,
“the INITIAL effect of a decent sized heli-drop is primarily to increase output”
You say “primarily”, which indicates there will actually be a mix of both increased output and higher prices, not just increased output.
Philippe and Ralph: stop talking about irrelevant details. Only the Big Story matters.
Ralph: “Re Steve and you assuming “perfectly flexible prices” that is a 110% unrealistic.”
Of course it’s 110% unrealistic. And it’s 120% off-topic. And you are 130% pissing me off by ignoring my previous request. So I unpublished you.
The following 2 statement both sound like they could be true
1) An increase in the money supply will drive deflation since people will need a bigger return to hold the increased money
2) An increase in the money supply will drive inflation since people will spend some of the new money.
It is easy to see the market mechanism that drives 2, but warder to see what drives 2).
If prices were set centrally (and supply then allowed to adjust to meet these prices) then the authorities could engineer 1) by reducing prices over time so that people would be happy to hold the increased money because they liked the extra returns they got.
It also seems possible that if we lived in a world where prices never went up but did go down (perhaps productivity growth is very high) that people might reduce spending after an increase in the money supply in anticipation of increased deflation and drive result 1) via an expectations mechanism.
So while intuitively seems like 2) normally holds it is possible to build consistent (if somewhat contrived) models where 1) would hold.
And one can imagine a model where the extra money is created by buying up another good that is negatively correlated to the price level.
Lets say QE is done by buying up (and closing down) stores. Assume that at a given money supply the amount of trade (and the price level) is a function of the number of stores.
In this world an increased money supply may well drive the results that Williamson claims.
Doesn’t the Fiscal authority pin down the price in SW’s model?
“So people will try to spend their excess supply of money” and the government will raise taxes just enough to absorb the excess supply of money.
c2114661: If Steve had said “If the central bank announces it will reduce the growth rate in the money supply (whether or not it does a once-and-for-all increase in the level of the money supply at the same time it makes the announcement), the result will be to reduce the inflation rate.” all economists would reply “Sure, a declining money supply causes deflation, so what else is new?”.
[tears hair out] The whole idea that printing money reduces inflation…
Nick, I don’t know how you and Sumner stay sane. I guess I’m lucky to work in a profession (programming) where when you’re wrong, you find out immediately and don’t spend all your time discussing models that are clearly wrong.
I thought the claim was that the equilibrium didn’t have a story behind it. Is that not correct? I agree it seems like a bizarre setup, but there is no issue with causality here.
Nick: “Wish I could remember the name of the economist who did a paper on all this stuff in the 1970’s.”
Maybe Brock, A simple perfect foresight monetary model (1975)?
Nick,your last few posts and Yichuan’s one linked to above have been great on this topic. Regarding your point on getting back to basic monetary economics, what is needed a good undergraduate monetary economics textbook that does this to train the next generation. The current monetary economic textbooks really fall short here.
Interesting Twitter exchange between Noah Smith & Tony Yates:
NS: The “QE/deflation” debate is interesting because Williamson’s model says stimulus works, and Krugman is saying it’s not microfounded enough.
TY: i thought he was saying its not verbalfounded enough. and williamson said so what.
NS: No, I think Krugman/DeLong were saying, show us explicitly how the firm sector works. Which is a legit request, since Lagos-Wright does show it, but Williamson doesn’t.
TallDave: “Nick, I don’t know how you and Sumner stay sane.”
I don’t. Dunno about Scott.
c211. Dunno. At first I thought it was stability. But with Steve’s latest post, it’s more than that. He totally misses the standard comparative statics, which does have a stability story behind it.
Kevin: “Maybe Brock, A simple perfect foresight monetary model (1975)?”
BINGO!
Gotta go.
If the Fed succeeded in buying up everything, then there would be deflation (or else the Fed would be paying interest).
This is an amusing point, but it doesn’t tell you what would happen if the Fed tried to buy everything (and not with the goal of causing deflation).
Expert A and Expert B are having a debate. A claims that B is making elementary mistakes. Two things are probably true (i) B is not being clear, and (ii) A misunderstands what B is saying.
As Phillippe and dlr said above, the price level in Steve’s model is determined by the PV of consolidated government debt. Steve doesn’t focus on the price level, perhaps because he doesn’t find it interesting. In his model, a helicopter drop would raise the price level but decrease future inflation. This is what Nick called overshooting above. Steve tried to say this by reference to finance, e.g., when the risk premium on a stock goes down, the current price jumps up and expected future returns are lower. His critics have focused on the “price jumps up part” because that is what they are interested in, whereas he has focused on the “future returns are lower part” because that is what he is interested in.
Max: just take the limit of what I have said above. If people knew the Bank of Canada was trying to buy everything, nobody would sell, at any finite price level. Money would become worthless.
Aaron: maybe. But if Steve really understood all that, he would predict a jump up or down in the price level whenever the US government goes into or out of one of its…debt-limit shutdowns (I’ve forgotten the name)….which didn’t happen.
Nick,
I still have a vague feeling that something’s not quite right. Maybe we are being too cocky here.
My uneasiness is coming from the fact that Williamson wasn’t on Larry Kudlow’s show, and threw out the verbal logic “hey the return to money needs to rise, so inflation rate falls.”
Instead, Williamson derived his result inside a formal model with an equilibrium result. So, are we really right for saying he ignored something obvious? I.e., does he NOT have a utility function for real cash balances in his model?
Market Fiscalist: “The following 2 statement both sound like they could be true
“1) An increase in the money supply will drive deflation since people will need a bigger return to hold the increased money
“2) An increase in the money supply will drive inflation since people will spend some of the new money.”
Doesn’t 1) require that people hold the increased money instead of spending it? And doesn’t that require that they are getting a bigger return to do so? IOW, doesn’t it beg the question, assuming the conclusion?
Bob: Steve says: “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.”
It does not matter, for this point, if the declining marginal liquidity payoffs are derived from some underlying model of costly exchange, or just bunging money in the utility function. Taking that declining marginal liquidity payoff as given, there are two ways to restore equilibrium: a rise in the price level; a fall in the inflation rate. Steve doesn’t see the first. The first has a story behind it. The second explains why Zimbabwe had accelerating hyperdeflation.
Look at Steve’s response to my comment on his blog.
Min: yes, increased money holding and increased returns would take place simultaneous. I think it is probably possible to invent models that explain how this could happen.
I assume (without having read it) that SWs paper outlines a model where this does happen, and that he is claiming that this models mirrors what is actually happening the real economy.
I am therefore not sure that describing the HPE and/or simply asserting that when the price level increases people will want to hold more of it is a good way of dealing with his arguments.
Never reason from the price change. Williamson’s critics reason from the price change (change in liquidity premium), they assume QE changes prices through AD only. Williamson argues AD days are long gone, and QE today is a supply side measure, raising output while lowering prices. Read his latest post.
Market Fiscalist: “yes, increased money holding and increased returns would take place simultaneous. I think it is probably possible to invent models that explain how this could happen.”
But Williamson is not just claiming that it is possible, he says that it must happen in a liquidity trap. The burden of proof is on him, and the structure of his argument is that of begging the question.
Vaidas: I am not reasoning from a price change. I am following Steve, and assuming that the marginal benefits of liquidity are a decreasing function of the (real) stock of liquid assets. So when the stock of liquid assets increases, the marginal benefits of holding liquid assets now falls below equilibrium level. Just like if the Treasury increased the stock of cars, the marginal benefits of their transportation services now falls below the equilibrium level. therefore the price of liquid assets (or cars) will fall. But money, unlike cars, is the medium of account. So a fall in the price of money means a rise in the price of goods. And for money, unlike cars, the marginal benefits of ownership depends on M/P, because we don’t care about how many bits of paper are in our pockets, only about the real value of those bits of paper.
Beckworth’s post showing that SW claims do not hold up empirically was brought up over at SW blog. Beckworth was directly responded to SW’s claims that inflation has been declining over past three years because of QE. When confronted with the evidence, SW hides behind “not serious empirical work.” How convenient. http://newmonetarism.blogspot.com/2013/12/the-intuition-is-in-financial-markets.html?showComment=1386172834195#c5653288304647455928
I think that there’s a way that Williamson can be technically right: the opportunity cost of holding money is somewhere between negative and zero, so your premise of “people do not wish to hold more money” is currently false.
At the moment, the Federal Reserve pays one quarter basis point interest on excess reserves. Meanwhile, the treasury rates are one half of that, going out to a year.
So while the Fed can helicopter all the money it wants via QE, banks can earn a risk-free profit by selling short-term treasuries to hold excess reserves. That explains recent behaviour: money held in excess reserves is not circulating, and as such it doesn’t affect the price level. If the fed raises the funds rate but keeps its low interest rate on excess reserves, then those reserves will be more profitably spent on treasuries and other debt instruments (and ultimately real investment) instead.
Graph: The M2 money velocity (red, right scale) has collapsed since the beginning of QE, commensurate with the increase in excess reserves (blue, left log scale). However, subtracting the excess reserves from M2 stock gives a much more stable “effective M2 velocity,” comparable to mid-2000s levels.
A commenter at Stephen Williamson’s blog named “Anonymous” pointed out that there is empirical evidence that QE increases inflation, namely, he referred to David Beckworth’s post (“Taking the Model to the Data”) which also mentions my econometric results.
(By the way, has anyone noticed the large number of commenters named “Anonymous” at Williamson’s blog? I know there’s more than one because they have to keep identifying themself by when they last commented, or what their previous point was. What on earth is that all about?!?)
Here is Stephen Williamson’s response:
“In order to properly confront the data, we need a model of how QE works, and then we have to argue that the data is somehow consistent with that. I don’t think we would call that serious empirical work in that sense.”
http://newmonetarism.blogspot.com/2013/12/the-intuition-is-in-financial-markets.html?showComment=1386177831449#c7314592028317641767
Of course the implication is that David doesn’t have a model of how QE works (and evidently nor do I). Now, this is of course completely untrue. In fact in that very post, David discusses, and links to, the paper he cowrote with Joshua Hendrickson (“The Supply of Transaction Assets, Nominal Income, and Monetary Policy Transmission”) in which he extends the very same monetary search framework of Lagos-Wright that Williamson uses in order to show the effects of QE.
But more importantly, the main subject of David’s post isn’t his own model, but Williamson’s model, which as David demonstrates (and as I further demonstrate in comments) is inconsistent with the empirical evidence. So rather than a dearth of economic models, we have a surplus, and the model which is the subject of David’s post seems to be failing the test.
At this point, it’s taking every ounce of energy I can muster to keep being as civil as possible. But frankly Williamson keeps making factual, empirical and theoretical claims which range from being demonstrably false to being utterly ridiculous. Aren’t there any real world repurcussions for this kind of behavior?
macroman: Yep. But somehow I find the empirical evidence of Zimbabwe’s lack of hyperdeflation more compelling.
Majromax: “I think that there’s a way that Williamson can be technically right: the opportunity cost of holding money is somewhere between negative and zero, so your premise of “people do not wish to hold more money” is currently false.”
But that was Steve’s premise as well. They do not wish to hold more money at the existing price level and inflation rate.
Mark: I’m think all those Anonymous commenters are probably PhD students EJMR types. I could be wrong.
Actually, I’m pretty sure Steve now realises there’s a problem here. His latest post (though it’s maybe actually quite interesting, I think) is a smokescreen. It will take a bit for some of his followers to cotton on.
There’s something going on here, but it’s nothing fancy. PK asked for a story; SW gave one missing the key plot twist. Why doesn’t SW see this? Look, PK (etc.) thinks with models, SW (etc.) thinks about them. SW says: anything worthy of the name “thought” should take the form of a model, the rest is small talk. But imagine someone saying: anything worthy of the name “navigation” should take the form of a map. What do you say to such a person? Maybe nothing, you drop them somewhere with a map and let them find their way home. But what’s the equivalent to that in this case? No wonder Nick despaired of getting SW to see there’s a problem, and no wonder SW struggles so mightily to see it. That SW can achieve the reputation of a “top-flight” macroeconomist is no surprise — you see this sort of thing in every field, not least those in which rigorously specified models are set against highly complicated phenomena.
PS – I left a comment to the same effect on SW’s blog. He immediately deleted it. This is no surprise, if I’m right: he was bound to find it thoughtless…
PPS – Sorry, couldn’t resist.