"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 
Did you see Williamson’s latest?
newmonetarism.blogspot.ca/2013/12/intuition-part-ii.html
jonah: Dunno. I gotta give Steve credit for writing that Intuition post. It was very clear, and I was following fine up till the bit I quoted above. And then it was also very clear to me just where his reasoning went wrong.
Keshav: yes. I skimmed it. It’s not really addressing the problem I’m talking about here. But I have a hunch it might be an interesting post in it’s own right, even if it’s not quite right. Liquidity does matter, for trade. And recessions are declines in trade.
Nick,
I think you haven’t read Steve’s latest post yet.
You are still reasoning from the price change, you focus on prices while ignoring NGDP. When the stock of liquid assets increases, NGDP grows – this is the uncontroversial part. Only the following is controversial – how much do real rates change when NGDP goes up? Steve says real rates rise so much that in the new equilibrium with higher stock of liquid assets the marginal benefit of liquidity goes up, not down.
Regarding empirical issues, I am not ready to agree with Steve yet. I am a card carrying market monetarist and the main benefit of QE today is higher AD. However, Steve is right in reminding that there are AS benefits too.
Min: Good point. Here some more thoughts:
Assume 2 reasons to hold money at a given point in time
1) to spend it at some point ion the future
2) to get a return on it
If people end up with more money than they previously had and the return on it has not changed then they will spend it.
But if you think that the liquidity trap means that increasing the money supply won’t increase spending then this can’t happen. It would be logical to assume that its the return on money that must do the adjusting (via deflation). This would be true whether or not you have a good explanation for the mechanics of what drives the deflation .
I assume that the increase in money is via asset swaps rather than helicopter drops.
Nick:
“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.”
I apologize because I’m sure I’m just missing something obvious here, but can you help me understand this in words? Take a simple case where a CB starts dropping money out of helicopters but simultaneously announces a lower future price level target (relative to its previous target). Why can’t the future price level target plus the required real return on money pin down the current price level irrespective of when they actually sop up the money or allow the convenience yield to increase? If it is later they may have to do more of it (the reverse of promising to be irresponsible) or have a lower price level target to get a result where the price level doesn’t immediately jump and also lower inflation — but I don’t understand why the precise timing is needed to eliminate the explosive/implosive equilibria.
Vaidas: ” However, Steve is right in reminding that there are AS benefits too.”
I only skimmed Steve’s second post. But I did catch that bit, and I think it’s interesting. An increase in M shifts both the AS and AD curves right. But it would have to shift the AS right by more than the AD, if it were going to cause a fall in the price level, which is empirically dubious, (and I’m not sure about stability, because I haven’t thought about it yet).
Gotta go teach.
Mark — Yeoman work as usual. Civility is often hard but you rarely regret it later. (And let me again give thanks for the fact that in my profession I can hit “Execute” and end all argument with the result.)
Nick, yes, it is empirically dubious – even in Japan we see Abenomics helping with sticky prices and wages. But I see no theoretical problems. If you assume, as Steve does, that problems with sticky prices are insignificant, and that there are big problems with financial intermediation, Steve’s result is exactly what you will get. By the way, in Steve’s case, central bank is a bank.
The good news is that Steve’s model is one more argument for NGDPLT, and against IT. IT may be not very stable when central bank makes mistakes with QE.
Majromax,
“However, subtracting the excess reserves from M2 stock gives a much more stable “effective M2 velocity,” comparable to mid-2000s levels.”
Are excess reserves in M2 in the first place?
The big distortion in M2 seems to me to be financial business holding more deposits after the collapse of the interbank lending market and the shadow banking system-
http://research.stlouisfed.org/fred2/graph/fredgraph.png?&id=M2SL_LTDACBM027SBOG_GDP_FBTCDTQ027S&scale=Left&range=Custom&cosd=1974-01-01&coed=2013-10-01&line_color=%230000ff&link_values=false&line_style=Solid&mark_type=NONE&mw=4&lw=1&ost=-99999&oet=99999&mma=0&fml=c%2Fd&fq=Quarterly&fam=avg&fgst=lin&transformation=lin_lin_lin_lin&vintage_date=2013-12-04_2013-12-04_2013-12-04_2013-12-04&revision_date=2013-12-04_2013-12-04_2013-12-04_2013-12-04
– whereas the household and business money demand has been on the same gradual downward trend it’s had for the 21rst century and doesn’t suggest any sort of infinite liquidy preference-
http://research.stlouisfed.org/fred2/graph/fredgraph.png?&id=M2SL_LTDACBM027SBOG_GDP_FBTCDTQ027S_DABSHNO_TSDABSNNCB_MMFSABSNNCB_NCBCDCA_NNBCDCA_TSDABSNNB&scale=Left&range=Custom&cosd=1974-01-01&coed=2013-10-01&line_color=%230000ff&link_values=false&line_style=Solid&mark_type=NONE&mw=4&lw=1&ost=-99999&oet=99999&mma=0&fml=c%2F%28e%2Bg%2Bh%2Bf%2Bi%2Bj%29&fq=Quarterly&fam=avg&fgst=lin&transformation=lin_lin_lin_lin_lin_lin_lin_lin_lin_lin&vintage_date=2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04&revision_date=2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04_2013-12-04
Am I missing something about Williamson’s latest post (Intuition Part II)? I thought his model had flexible wages/prices; how can there then be a shortage of liquid assets?
I mean, I suppose I can see it if a lot of your liquid assets are also real goods in their own right (e.g. cows as money), but I don’t think that’s the case in his model.
Market Fiscalist: “If people end up with more money than they previously had and the return on it has not changed then they will spend it.
“But if you think that the liquidity trap means that increasing the money supply won’t increase spending then this can’t happen. It would be logical to assume that its the return on money that must do the adjusting (via deflation). This would be true whether or not you have a good explanation for the mechanics of what drives the deflation .”
As for helicopter drops, some of that money gets into the hands of poor people and unemployed people who have little choice but to spend it. Even better, if we want money to be spent, is to target people who will spend it, eh?
Another commenter named “Anonymous” said the following in Stephen Williamson’s latest post:
“David Beckworth empirical results reject your hypothesis.”
And Stephen Williamson responded:
“That’s not serious empirical work.”
http://newmonetarism.blogspot.com/2013/12/intuition-part-ii.html?showComment=1386187907396#c5531693717983569198
Recall that so far the only empirical evidence that Stephen Williamson has offered in support of his model is a graph of year on year PCEPI inflation which he claims shows inflation has been falling for three years (actually, it’s more like two).
In contrast David estimates a two variable VAR with 6 and 12 lags in which the impulse response of core PCEPI to the Fed’s Treasury holdings is the opposite of what is consistent with Williamson’s model.
In addition, in comments I describe my own VAR Granger causality test results, and my own 4-variable VAR estimates which are contrary to the predictions of Williamson’s model. And by my count so far we have found three (maybe four) research papers with VAR estimates contrary to the predictions of Williamson’s model.
I wonder what qualifies as “serious empirical work” in Williamson’s estimation?
Hey Nick. Do you agree with Murphy when he says this?
” what Williamson’s argument leaves out is the fact that, other things equal, you want to hold more money when its purchasing power falls. This is because people want to hold a certain amount of real cash balances. Just focusing on this effect, you would think that as price inflation occurs, people want to hold more money. So this effect works in the opposite direction from the effect that Williamson isolates.”
I thought it’s about the HPE that makes people want to get rid of the extra dollars?
dlr: on thinking about it, you may be right.
Mike Sax: the quantity of money demanded is a positive function (proportional to) the price level, and a negative function of the expected rate of inflation. That is very standard economics. That is what Bob Murphy is saying, but he wasn’t very careful saying it.
Alex: even with flexible prices and wages, things like interest rates and inflation rates can affect the real stock of money people hold in equilibrium. I would need to read Steve’s second post carefully to work out if what he’s saying makes sense.
Nick,
Here’s how I read Williamson. When he says “rate of return” I read “natural rate of interest” and when he says “inflation” I read “equilibrium rate of inflation”.
So all he is saying here is:
1) If the treasury issues more debt the natural rate (equilibrium risk-free real rate of return) must increase. Check.
2) Since nominal rates are at zero (liquidity trap) and the natural rate has increased, the (equilibrium) rate of inflation must be lower. Check.
3) Therefore in a liquidity trap more government debt lowers the (equilibrium) inflation rate. Check.
All of which is totally conventional equilibrium reasoning. Pretty well the only thing that is going on here is the same old sleight of hand by which equilibrium inflation becomes expected inflation.
But then in his attempt to justify the equilibrium assumption he says that he thinks “it’s fair to argue that any of those short run effects have played themselves out in the financial crisis and its aftermath, and now we’re looking at the effects I’ve described.” The problem, of course, is that the thought experiment he actually described is a new issuance of debt right now, five years after the start of the liquidity trap. The non-neutralities that have to play out are the ones that occur as a result of the debt issuance, and we have good reason to suspect that those will be inflationary. Whether or not the non-neutralities that occurred as a result of the financial crisis have already played themselves out is irrelevant. (In reality, non-neutralities don’t “play themselves out.” Rather they spiral out of control if left to themselves, and have to be fixed by active policy).
Nick:
“An increase in M shifts both the AS and AD curves right. But it would have to shift the AS right by more than the AD, if it were going to cause a fall in the price level, which is empirically dubious, (and I’m not sure about stability, because I haven’t thought about it yet).”
I’ve been thinking about this and in my opinion Williamson’s model doesn’t really translate very well into AD-AS Model terms. QE causes an increase in the level of transactions and hence in the level of real consumption. But it also causes a decline in the rate of inflation without causing a shift in the price level.
In level terms the price level is fixed in any period and all the central bank can do is choose the level of real consumption. In dynamic terms, real consumption doesn’t change except in jumps, so the only thing the central bank can choose is the rate of inflation. So in the first case you have a horizontal line and in the second case you have a vertical line. Make of it what you will.
If this interpretation is correct it also raises another empirical problem for Williamson’s model. Where is the sudden increase in real consumption due to QE?
Ryan Avent’s latest is worth a look; two noteworthy points:
“Prolonged QE is effectively a signal that the central bank is unwilling commit to higher inflation.”
“What matters is not what QE does, but what QE means. So is QE deflationary? Sure, sometimes. But that’s not really QE’s fault.”
Karsten: that interpretation is fine with me. Start in equilibrium. Have the central bank credibly announce a lower inflation target, with no jump in the equilibrium price level, and what happens? The inflation rate drops, nominal interest rates drop, the central bank needs to do an OMO purchase of bonds because the demand for money has increased. Standard macro.
Mark: suppose I took a standard model, and added the assumption that a low level of M/P will reduce Y, because money really is needed as a medium of exchange. The long run phillips curve would now slope the “wrong” way. High inflation means low M/P which means low Y and high U. That’s a perfectly reasonable model. High inflation has real costs.
Kevin: yes, I liked Ryan Avent’s post. He’s on the same page as my previous post, on why did the central bank increase nominal interest rates?
Nick, good points. I really liked the set-up of Steve’s post, up until his “To get to the point” paragraph.
He brings up a scenario in which we are at the zero-lower bound but cash exhibits a liquidity premium. I don’t understand how this can be. If cash exhibits a liquidity premium, that means that cash owners enjoy a marginally valued flow of liquidity services. They will only rent this cash out at some positive rate high enough to compensate them for forgoing those services. In which case, we’re not at the zero lower bound. In short, it’s impossible to be at the ZLB and for cash to exhibit a liquidity premium — the moment the latter occurs, we must be off of the ZLB. Am I missing anything?
JP: I think you misread him. Steve says: “Thus, in the liquidity trap we are in, the liquidity premia on money and short-term government debt are the same, and positive.”
At the ZLB, money has no liquidity premium over bonds, but both money and bonds have a liquidity premium over other less liquid assets. Which makes sense to me.
If money & bonds have a liquidity premium over less liquid assets at the zero lower bound, that would imply that the overnight lending rate is higher than 0. After all, trades in the overnight market represent a 24 exchange of money for illiquid claims to money. Can we have a positive overnight rate yet be at the ZLB?
JP: Dunno. That’s still pretty liquid compared to houses, cars, machine tools, and human capital.
Ok, but that still doesn’t explain to me how we can have a positive overnight rate and still be at the ZLB. If any sort of liquidity premium on central bank money exists, then the overnight rate must be >0 and we’re off the ZLB. How do we ever reach Steve’s initial setup such that a liquidity premium on money exists at the ZLB? Do you get my confusion or am I so confused that I’m confusing you?
JP Koning:
“If any sort of liquidity premium on central bank money exists, then the overnight rate must be >0”
I don’t think this is true. Money has a liquidity advantage over overnight deposits, but if there’s enough money around, the marginal value of this advantage goes to zero. Money and overnight deposits collectively have (putatively) a liquidity advantage over long-term bonds, but the amount of money that it takes to make the marginal value of the money-vs-overnight-deposits liquidity advantage go to zero is not necessarily enough to also make the marginal value of the money-and-overnight-deposits-vs-long-term-bonds liquidity advantage go to zero. Being at the zero bound implies that the former has gone to zero, but this does not imply that the latter has also gone to zero. In Steve’s setup, there is enough money around to satiate the market with the type of liquidity that is specific to money in comparison with overnight deposits, but not enough to satiate the market with the type of liquidity that is shared by both money and overnight deposits in comparison with long-term bonds.
Nick (and Vaidas)
“An increase in M shifts both the AS and AD curves right. But it would have to shift the AS right by more than the AD, if it were going to cause a fall in the price level”
But there are no nominal rigidities in this model, are there? So if one-time shifts in AS and AD were to affect the price level, they would do so immediately. And as I understand it there is no jump in the price level, up or down, so the AS and AD shifts must exactly balance. Maybe there is some feature of the model that assures this will be the case. In other words, to compensate for the reduced liquidity premium, people bid up the price level immediately so that it will subsequently decline over time, but the supply-side effect of the increased liquidity causes a permanent reduction in the price level that exactly offsets the immediate demand-side effect. So you end up with a price level that doesn’t jump but that subsequently goes on a downward trajectory. I can’t offhand imagine what feature could force the AS and AD effects to exactly offset each other, but if there is such a feature, I will reserve judgment on its plausibility until I understand it better. (I must say, Steve’s blog post doesn’t give me much confidence as to what that feature might be or even that he can explain the supply-side effect at all, but maybe he’s just not expressing himself well, or maybe I’ve misunderstood.)
Did your spam filter eat my other comment, responding to JP Koning?
Andy, if the spam filter doesn’t resurrect it, I’m hoping you remember what you wrote as I’m quite curious what you have to say.
The chart on the macroecoonmics wiki shows the money supply (helidrops) and inflation are closely correlated. Didn’t know so much of the 19th cenutry was deflationary…
Figured out my critique of macro. Since the GD at least, avoiding sharp price movements has been considered good. I’d guess at underlying is that the marginal ease to get oil vs the utility of oil have been pretty stable. Gold and oil and wheat have moved in tandem pretty regularly over the decades and longer (wheat and gold since the Bible).
In the future, the underlying human capital and technologies will be sharper; either very good or very bad. So we’d want sharp price increases. Cheaper healthcare if we get regenerative medicine, more expensive if we get pandemics. It isn’t just based on a stable price of oil inputs anymore.