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 
Jeff, there is no need for the Granger test, when the sequence is known…
ECB, Monthly Bulletin (2012, May):
The occurrence of significant excess central bank liquidity does not, in itself, necessarily imply an accelerated expansion of MFI credit to the private sector. If credit institutions were constrained in their capacity to lend by their holdings of central bank reserves, then the easing of this constraint would result mechanically in an increase in the supply of credit. The Eurosystem, however, as the monopoly supplier of central bank reserves in the euro area, always provides the banking system with the liquidity required to meet the aggregate reserve requirement. In fact, the ECB’s reserve requirements are backward-looking, i.e. they depend on the stock of deposits (and other liabilities of credit institutions) subject to reserve requirements as it stood in the previous period, and thus after banks have extended the credit demanded by their customers.
Mark Sadowski.
I believe you have slightly misunderstood the points that Raimondas was making.
The only way of reducing reserves is either for them to be exchanged for physical currency, or for the Fed to withdraw them. Banks have no power whatsoever to reduce reserves – all they can do is pass them on to each other. Unless depositors holding far more physical currency – which I agree could happen at the ZLB – reserves on commercial bank balance sheets by definition increase as a consequence of QE and cannot be diminished by bank lending.
The mistake that Nick makes is in thinking that banks choose to “hold on to” the increase in base money. They have no choice but to do so. What the charts helpfully provided by Majiromax show (indirectly) is that they are allowing the proportion of their assets that are reserves to increase, rather than holding that ratio constant by doing an equivalent amount of lending. I think they are doing that at least partly because of regulatory changes that require banks to have 1) more capital in relation to their assets and 2) more liquid assets, including reserves. But there are also tighter lending standards, larger collateral haircuts and general lack of demand for credit.
May I also remind you that correlation does not necessarily indicate causation. You may have demonstrated an increase in commercial lending correlated with an increase in monetary base, but have you actually demonstrated that the lending increase is caused by the monetary base increase? The fact that QE increases reserves in a manner totally disconnected from lending would, I suggest, make this very hard to prove.
Frances: “The mistake that Nick makes is in thinking that banks choose to “hold on to” the increase in base money. They have no choice but to do so.”
Suppose the total money stock is fixed. Then it is possible for each individual to get rid of money, but impossible for all individuals together to get rid of money. But if each individual attempts to get rid of more money, by spending more of it, the result is an increased demand for other goods, which pushes up output and/or prices. The “individuals” in question can be people, firms, or banks. This is basic old-school monetarism. The Hot Potato. Each individual can get rid of the hot potato, but some individual must always be holding it.
Nick Edmonds. If bonds are promises to pay fixed amounts of money (i.e. they are non-indexed) then we would not expect the price of bonds to double if the quantity of money doubles. To a first approximation, the price of bonds would stay the same, and the price of everything else would double.
Frances Coppola,
“I believe you have slightly misunderstood the points that Raimondas was making.”
To be frank Raimondas said some things which are obviously false. If he misspoke then he needs to express himself more clearly.
“Unless depositors holding far more physical currency – which I agree could happen at the ZLB – reserves on commercial bank balance sheets by definition increase as a consequence of QE and cannot be diminished by bank lending.”
This can also happen away from the zero lower bound. The currency ratio is always the depositors’ choice.
“The mistake that Nick makes is in thinking that banks choose to “hold on to” the increase in base money.”
I seriously doubt Nick has made such a mistake but he can speak for himself. I’m not sure what quote you are referring to.
“May I also remind you that correlation does not necessarily indicate causation. You may have demonstrated an increase in commercial lending correlated with an increase in monetary base, but have you actually demonstrated that the lending increase is caused by the monetary base increase? The fact that QE increases reserves in a manner totally disconnected from lending would, I suggest, make this very hard to prove.”
I’m not talking about simple correlation. I’m talking about Granger causality.
The techniques I am using are very similar (actually they are methodically superior) to those that Post Keynesian empirical researchers have used to “prove” the various Accomodative, Structural and Liquidity Preference views of endogenous money. What I have shown is that over the time period since December 2008 the monetary base and the various money multipliers provide statistically significant information about future values of commercial bank loans and leases. These results are the exact opposite of what Accomodative Endogeneity predicts.
Of course this is not the same as showing metaphysical causality. But none of the Post Keynesian empirical research on endogenous money have shown that either.
Nick: Has the speculative demand for money been taken account of in this discussion? Think of QE as being aimed at bringing long term interest rates down by driving up the price of long term bonds. If I’m holding long term bonds in my portfolio, QE will raise their price relative to what I had expected it to be at this point. I then have to decide whether to sell. At the same time as it’s buying long term bonds central bank is increasing the stock of short term, highly liquid assets on the market.
Suppose I don’t believe that the central bank can keep long term rates down, and the prices of long term bonds up. In fact, assume I believe that long term bond prices will come down with a thump in the relatively near future, perhaps because I believe that the expansion of liquidity will create inflationary pressures in goods markets which will force nominal interest rates up. In that case, isn’t it likely to be optimal for me to take the central bank up on its offer – to sell it my long term bonds at their current, elevated price, and to hold highly liquid assets – money and short term bonds – so that I’m in a position to move back into long term bonds when the price of those bonds falls?
So my willingness to hold highly liquid assets reflects my desire to stay liquid in the short to medium term, and is based on my expectation of a deflation not of goods prices but of the prices of long term bonds, while that expectation is tied to my expectation about near term goods market price inflation.
Nick,
I understand the hot potato effect, but its application to reserves is seriously limited. Base money in the form of reserves is only usable by banks. For other agents to use it, it must be converted into physical currency. Therefore the “hot potato” effect with regard to base money only operates if a) banks choose to pass reserves on to each other or b) households and businesses choose not to intermediate payments through banks but to settle directly in physical currency. The first of these might happen if interest rates on reserves were negative, since that would be an incentive for banks not to hold them. The second might happen if there were a massive banking failure, forcing people to revert to physical cash transactions – and of course the black economy generally works in physical currency, since it is not traceable. Neither of these is really something we would wish to encourage.
Reserves cannot be used for anything other than interbank settlement unless they are converted into physical currency. They cannot be “lent out”, or “paid out” for goods or services. Across the banking system as a whole, they are only reduced if the Fed drains them or there is increased demand for physical currency. Individual banks can therefore only reduce their reserve holdings by encouraging depositors to make withdrawals or by lending the reserves to other banks. I suppose encouraging depositors to make withdrawals (presumably by zapping interest rates on demand deposits) would increase demand, since depositors might spend the money – though they might find alternative investments instead, or stuff cash under the bed.
Frances: if an individual bank expands loans, it knows it will lose reserves to other banks. Banks (presumably) know this. Making a loan today is the way an individual bank gets rid of reserves tomorrow, or the day after tomorrow, depending on how long it takes the borrower’s cheque to be deposited in another bank when he spends the loan. Just as an individual person gets rid of money by making a loan or buying something. The “banks don’t lend reserves” argument is true but pointless. (Oh God, please keep the MMTers out of this one, because it’s way off-topic.)
Nick,
Under normal circumstances, I would challenge your remark that banks “lose” reserves to other banks when they make payments. When there are no excess reserves in the system banks must borrow back “lost” reserves in order to meet reserve requirements. However, we do have excess reserves at the moment, so in theory banks could increase lending in the expectation that this would reduce their excess reserves. But this assumes that banks want to lose excess reserves to other banks. As they are now required to hold a higher proportion of their balance sheet as safe liquid assets – and indeed are choosing to do so anyway, because it reduces their liquidity risk – they may not want to do so. Also, as they are now expected to fund themselves with a higher proportion of expensive equity, they may not wish to take on much risky lending – especially as, post-crisis, many banks still have substantial portfolios of non-performing and high-risk loans with poor quality collateral. I guess what I am saying is that banks’ risk appetite, and the expectations of regulators, have a considerable impact on the effectiveness of monetary policy.
I wasn’t meaning to raise the “banks don’t lend reserves” thing. As you say, it’s off topic. I was concerned about the assumption that banks could or would necessarily offload reserves.
Frances: OK. I think I see what you are saying. I would put it this way: those things you mention (risk liquidity etc.) mean that banks want to hold a higher amount of reserves than they otherwise would. But if the amount they want to hold is still determinate, increasing the amount of reserves above that desired amount can still make them want to get rid of the extra. It is actual reserves minus desired reserves (as opposed to actual reserves minus required reserves) that matters. (Side note: I really wish monetary economists would define “excess reserves” as excess over desired, rather than excess over legally required. Especially since in countries like Canada there are no reserve requirements).
Frances,
You write: “When there are no excess reserves in the system banks must borrow back “lost” reserves in order to meet reserve requirements.”
… I’d add that they may also need to borrow reserves to repay overdrafts of their Fed (or CB) deposit account. I don’t know how rare that event is though.
Clearly if you think of all the banks aggregated together, the reserves don’t go anywhere (ignoring the exceptions you brought up). It is an interesting thought experiment though: how long will it take, on average, for a bank’s reserve levels to return to normal after making a large loan… because presumably they must transfer reserves to clear payments the borrower makes (when the loaned funds are spend on vendors/sellers/employees who use other banks), and those fund recipients likewise spend the funds, etc. I would think that the various individual commercial banks would tend to have their original reserve levels restored again pretty quickly through normal economic activity. That’s my intuition anyway. (I’m specifically thinking in terms of a 0% reserve requirement here to keep it simple). I’d bet somebody has a mathematical model of this somewhere… and has probably tried to verify the model by checking it against empirical data (in some clever way, to account for all the other changing variables that reality tends to throw in our faces). Am I making sense? Does anybody know if my intuition is correct? Does anybody have an idea for the mean time it takes for those reserves to return to the original pre-loan levels at all the banks in the system? Is this something that bankers are aware of and routinely model?
Nick,
Hah. I sympathise about “excess reserves” – I’m in the UK, we don’t have “required reserves” as such either (voluntary scheme is currently in abeyance).
Yes, banks want to hold higher amounts of reserves than they used to. However, I think you don’t give enough weight to the regulatory capital problem. Whether or not there are excess reserves, damaged banks don’t lend. Having more safe assets on their balance sheets than they really want is nowhere near as great a concern as not having enough regulatory capital to enable them to take on more risky lending. A bank that doesn’t have enough regulatory capital to support its lending is deemed insolvent and can be put into administration by regulators. Just look at the Co-Op Bank in the UK. Until its regulatory capital hole is filled and/or it has unloaded a substantial proportion of its impaired loan book, no way is it going to increase net lending, however many reserves you throw at it.
Actually, banks that have suffered a recent traumatic near-failure can be reluctant to increase lending even if they have enough capital. RBS, for example, has cut its SME lending drastically – from 40% to 30% of the UK market.
… continuing my thought experiment above … if, for example, the mean time it takes for a dollar loaned (in lost reserves to clear payments the borrower makes) to return to the lending bank is 5 seconds and bankers are aware of this, would they even consider that lending would be a worthwhile strategy for them to “get rid of excess reserves” … even on a temporary basis? What if the mean time is 1 month?
I’d guess the answer (ignoring noise) would look something like
reserve level = 1 – exp(-t/T)
for a dollar loaned at t = 0, where T (T positive real number) is the time constant. So perhaps a more useful question is what is the mean time it takes the bank to get back $(1-exp(-1)) = $0.63 in reserves after loaning $1?
(or some more recent version), you’ll see that the average duration of debt outstanding has been increasing and is expected to. Thus, the Fed and the Treasury are working at cross purposes.”
Williamson is right on this point, no? If changes in the maturity structure of federal debt have macroeconomic effects, that shouldn’t depend on whether those changes are due to the Fed or the Treasury. This came up a couple years ago when someone — I can’t remember who — was suggesting that Treasury lock in low rates by shifting federal debt toward longer maturities. That would amount to anti-QE. If you think QE matters, then yes, you should be looking at the whole maturity structure of federal debt held by the public (not counting the Fed! so you can’t use the published series) and not just the particular changes in the maturity structure resulting from QE.
What this has to do with the larger debate, I have no idea.
… I guess I should add to my scenario and say that all the banks have more than enough excess reserves before the $1 is loaned (i.e. there’s no danger of a CB deposit overdraft… otherwise reserve levels would snap back near instantaneously… within 24 hours anyway, to repay the CB before the end of the day).
Tom,
If there are no reserve requirements then banks run daylight overdrafts in their reserve accounts. I can’t speak for other jurisdictions, but the Bank of England expects those overdrafts to be collateralized (repo).
Your “thought experiment” is interesting, and I don’t know if anyone has done an exercise like that. I have a couple of thoughts though. Firstly, a very large loan (an aircraft loan, for example) would be likely to be pre-funded, because of the liquidity risk, which implies that a bank would temporarily increase its reserve holdings (or general collateral holdings, so it can obtain reserves readily) on loan approval. In that case, the “desired” reserve level wouldn’t be affected. Secondly, with smaller loans, I agree that normal commercial activity could restore desired reserves very quickly. In theory, excessive lending should run down reserves, but usually what happens in credit booms is that all banks lend excessively, so inflows and outflows are approximately balanced and there is no impact on reserves.
Tom,
This may not help much but banks are both borrowers and lenders (interbank lending and such). Banks don’t lend to “get rid of excess reserves”. They lend to make money off the difference between short term borrowing costs and long term lending income. And so, assuming that banks make long term amortized loans using short term borrowed funds, the time until the profit threshold is reached would be a function of both the short term and long term interest rate. The greater the spread, the shorter the time period needed to reach profitability.
Using the amortization formula:
A = Annuity (payment)
P = Principle
Int = Long term interest rate
n = number of payments
Total Mortgage Interest = TI
A = P * [ Int * ( 1 + Int ) ^ n ] / [ ( 1 + Int ) ^ n – 1 ]
TI = A * n – P
For short term bank borrowing assuming the bank can roll over existing borrowed funds at a fixed short term interest rate
i = Short term interest rate
A * n >= P + n * i * P
Substituting back in for A and dividing by P:
[ n * Int * ( 1 + Int ) ^ n ] / [ ( 1 + Int ) ^ n – 1 ] >= 1 + n * i
Solving for n (i, Int) takes a root solving algorithm
Jeff:
“Everything is already in equilibrium from the start, with the representative agent fully aware of the stable QE policy going forward.”
OK, we should be discussing this with the correct semantics, which will clarify what the real issues are. Really, we shouldn’t even be arguing about the model itself but about how it maps onto the real world, in which we do seem to observe monetary policy surprises. I would put things as follows:
There are two potential questions with respect to the model. First, how does QE affect the inflation rate? Second, how does QE affect the price level at time zero? To me the second question is more interesting, because we’re dealing with a real world history in which QE was (probably) not initially anticipated. So time zero happens when the market realizes that QE is going to happen, when we (in the real world) make a transition between the two instances of the model. If the model were to show that QE causes the price level at time zero to be higher than it is without QE, we would map that result onto the real world by saying that, when the market realizes that QE is going to happen, prices go up. And since I believe prices are sticky, when I say that “prices go up,” I mean there is a period of inflation.
But by using fiscal policy to tie down the price level at time zero, Steve has rigged the model in such a way that it cannot answer what I regard as the more interesting question. Of course, given the way he has rigged it, another potentially interesting question is how the path of fiscal policy differs from one instance of the model to the other. In my mind, this comparison would map to the real world question, “How does fiscal policy have to change to offset the initial inflationary effect (assuming there is one) of a surprise QE announcement?” Steve doesn’t tell us the answer to that either, but my guess is that the fiscal policy in the instance of the model with QE is in some sense “tighter” than in the instance without QE.
Steve is interested only in how QE affects the inflation rate in the model. In my mind, that question maps onto the real world question, “Once the market has fully equilibrated in response to a QE announcement, what happens to the inflation rate?” But being a sticky-price guy, I don’t think the equilibrium would happen any time soon after the announcement. In fact, I’m not sure it would ever happen, because by the time it is ready to happen, QE may be over, and the impact may have dissipated (e.g., the securities involved may have matured). So in my sticky-price conception of the real world, the model doesn’t necessarily have anything useful to say regarding the effect of QE on the inflation rate (as the inflation rate is understood in the context of the model).
Mark S,
Obviously, without seeing your calculations I have no idea what you have done. But I find it highly improbable that the current size of the monetary base is in any way a reliable predictor of the value of future commercial lending.
JW Mason,
“If changes in the maturity structure of federal debt have macroeconomic effects, that shouldn’t depend on whether those changes are due to the Fed or the Treasury.”
I agree, provided we are only considering the macroeconomic effects of the maturity structure of federal debt (i.e. ignoring the effect of changing the size of the monetary base). This certainly was an issue in the Maturity Extension Program (Operation Twist). Given that, Williamson is right about this issue up to a point (something which Beckworth agreed with as well).
“What this has to do with the larger debate, I have no idea.”
Here’s what I am thinking.
Equations 38 and 48 in his paper determine the combination of feasible values for x1 and x2. QE increases the value of al (the amount of outstanding longer-maturity debt held by the central bank) which appears in equation 48.
Click to access qe2.pdf
Increasing the value of al increases the value of x1 (and x2). Inflation is defined by equation 40 and thus is strictly a possitive function of x1. The outstanding amount of short (Vs) and long (Vl) maturity debt plays no role in either equation 38 and 48 except as an upper bound to how much the central bank may purchase of each. The total amount of outstanding debt (V) appears in equation 48.
In short, while the amount of outstanding debt appears to have some effect (which could be taken into account in an elementary empirical analysis), the duration of the outstanding debt does not appear to be a factor in his model. Thus I am perplexed by his comment.
Francis Coppola,
“But I find it highly improbable that the current size of the monetary base is in any way a reliable predictor of the value of future commercial lending.”
I’m not sure I would describe it as a “relaible predictor”. But the results are statistically significant at the 5% level and the impulse response is positive.
JW Mason,
“Inflation is defined by equation 40 and thus is strictly a possitive function of x1.”
should read
“Inflation is defined by equation 40 and thus is a strictly decreasing function of x1.”
“That’s not quite right, when we are talking about money….”
Thanks Nick, I understand completely. That does seem to support that my interpretation of W’s error is partially right – bond holders sell to the Fed because they would rather hold something else (a different asset, a house, a pretty bauble). Since the bond holder likely doesn’t want to hold cash, the return on cash is irrelevant to the decision. In fact, the extra purchase/velocity in buying the alternative likely raises those prices, not lowers them.
I really think W has lost the sense of causation flow. M=F/a is an equilibrium equation, but increasing F does not increase M! (except at very high velocities, and even that is relative).
Nick, on ” banks will lose reserves”
Keynes (1930) in „Treatise on Money“:
It is evident that there is no limit to the amount of bank money which the banks can safely create provided they move forward in step. The words italicised are the clue to the behaviour of the system. Every movement forward by an individual bank weakens it, but every such movement by one of its neighbour banks strengthens it; so that if all move forward together, no one is weakened on balance. Thus the behaviour of each bank, though it cannot afford to move more than a step in advance of the others, will be governed by the average behaviour of the banks as a whole – to which average, however, it is able to contribute its quota small or large. Each Bank Chairman sitting in his parlour may regard himself as the passive instrument of outside forces over which he has no control; yet the ‘outside forces’ may be nothing but himself and his fellow-chairmen, and certainly not his depositors.”
Regarding reserves, I think the issue is that US banks are currently compensated for them. This acts as a contractionary policy by the Federal Reserve, contrary to the near-zero target rate.
With no regulation, banks will issue loans until the marginal revenue from interest equals the marginal cost (in stability and solvency risk) of the additional balance-sheet leverage. Adding regulation regarding required reserves in the mix increases the risk of leverage (adding regulatory compliance into it), which will on the balance decrease the amount of lending.
Adding in interest compensation for reserves amounts to double-dipping. When a bank receives 0.25% interest on reserves, at the level of an individual bank issuing a loan at 0% nominal rate (or, equivalently, purchasing a 1-month T-bill at 0.06%) represents a loss. This might not be a problem under ordinary circumstances, but this near-ZLB situation directly calls for an increase in the money supply — which can only enter circulation through the bank lending that’s disincentivized by interest on reserves.
As a result, we’re at the worst of both worlds: private, nonbank entities see near zero rates for savings, but banks see a greater-than-zero rate. As a result, loans for productive purposes will only be made at the >0.25% rate, effectively increasing the economy-wide credit spread and rendering illusory the Fed’s 0-0.25% interest rate goal.
With regards to the model in the original post, I think there’s a built-in contradiction that I can finally put to words: the situation described in the Story (also by Williamson) is inherently flawed and results in monetary policy always working backwards as a controlling force.
The model is given by: M(t) = a + P(t) – b.Pdot(t). The situation given in the original post reflects jumps in the money supply (and/or price level), but those jumps really have to happen over time. (This also lets us actually take the derivative of M, to boot, meaning we can work with “strong solutions” to the DE rather than “weak solutions.”)
Assume that the money supply linearly increases from 1 to 2 over time epsilon, such that:
M(t) = {1 for t <= 0, 1 + t/eps for 0<t<eps}
Over the increasing-M period, P(t) has a solution of the form Cexp(t/b) + At + B (the positive coefficient on ‘b’ gives rise to the bubble solutions discussed in the article). Substituting that ansatz and matching terms gives A=1/eps, B=1+b/eps, and C=-b/eps, where C was selected to ensure price continuity at t=0.
After time epsilon (the end of “QE” implementation), the price level is given by P(eps) = -b/eps*exp(eps/b)+1+1+b/eps. However, exp(eps/b) > 1 + eps/b, so P(eps) < -b/eps(1+eps/b) + 2 + b/eps = 1.
That means that, according to this model, increasing the money supply is always, without exception, deflationary, provided b>0. This is true regardless of the permanent or temporary nature of QE, as simply implementing it reduces the price level.
The “equilibrium story” says that:
Majromax,
I think the effect of positive interest on reserves is rather more subtle than that. It does prop up the short end of the treasury yield curve, but to say it is contractionary is overstating it. And if a bank pays less than 0.25% on deposits then the compensation on reserves gives them a small profit, not a loss.
I think the idea that interest on reserves disincentivizes bank lending is a complete fallacy. It is the marginal return on lending over its funding cost that banks are interested in. 0-0.25% is a simply awful return. They can do MUCH better than that on commercial lending. So if they aren’t lending, it is not because of interest on reserves. It is because of their horribly risky balance sheets and their shortage of capital – see my comment to Nick Rowe about the problems that regulatory capital requirements can create.
I also think negative IOR is intrinsically contractionary, because it is a direct cost to banks. If they can’t pass it on in the form of negative deposit rates, then they may well raise rates to borrowers. But the hot potato effect might offset this. It’s hard to say.
Frank,
Thanks for the response. I realize that banks make money from a spread and are not primarily motivated to make loans based on trying to get rid of excess reserves. I was thinking of Nick’s comment here (which was batted back and forth a bit between Frances and Nick):
“Frances: if an individual bank expands loans, it knows it will lose reserves to other banks. Banks (presumably) know this. Making a loan today is the way an individual bank gets rid of reserves tomorrow, or the day after tomorrow, depending on how long it takes the borrower’s cheque to be deposited in another bank when he spends the loan.” – N.Rowe
So if a bank “knows it will lose reserves to other banks” if it “expands loans” it must also know that it will most likely recover those reserves again in short order (if my intuition about this is correct, which Frances seemed to confirm).
My question really boils down to the following: If a bank makes enough new loans to lose $1 of reserves through payment clearing*, then how long until this bank recovers at least $0.63 back again through normal economic activity?
I guess my point is if that mean time is small enough and banks know this, then they already know there’s really no getting rid of their excess reserves in any meaningful sense.
*BTW, if you figure that there are N equal sized banks in the system, the amount the bank would need to loan, on average, to lose $1 through payment clearing would be about $(N/(N-1)) since there’s a chance the recipient of the funds uses the same bank.
Majromax,
You are confusing assets and liabilities. Reserves are an asset. Capital (in banks) is equity, and sits on the liability side of the balance sheet.
Reserves are liquid assets, as are T-bills. They are near-perfect substitutes – the T-bill is slightly riskier, and this would normally be reflected in a slightly higher interest rate, but these are not normal times. But banks do not primarily make money on the spread of reserve interest over T-bill yields. And neither reserves nor T-bills are capital.
Increased reserves only recapitalize banks to the extent that they earn a positive spread, which may go into retained earnings (tier 1 capital) if not used for expenditures. But as I’ve already pointed out, banks make far more on commercial lending. Interest on reserves is not an efficient way of recapitalizing banks. Increasing the profitability of commercial lending (i.e. increasing spreads) is far better. Depressing funding costs while propping up interest rates to borrowers is the most effective way of recapitalizing banks (apart from rights issues and debt for equity swaps). And this is exactly what banks have done in the last six years. Consequently it appears that they have improved their capital positions considerably.
But banks recapitalizing by means of widening interest spreads (especially higher rates to borrowers) is contractionary for the economy. Under-capitalized banks are bad news for monetary policy, since banks that are short of regulatory capital (equity) relative to their existing risk-weighted loan portfolios cannot lend productively. And banks that are repairing their balance sheets are equally bad news, because they will maintain wide spreads and shrink their asset base (which destroys money). Hence my remark about capital.
On your “privileging savings” point – I don’t agree that the Fed is doing any such thing. Firstly, liquid assets on bank balance sheets are not “savings” in any normal sense. They are liquidity buffers designed to protect the balance sheet from sudden funds outflows. Secondly, the Fed pays interest on reserves in order to prevent short rates (including T-bill yields) falling below zero. It’s not wholly successful in this, for a variety of reasons that I won’t discuss here. But it certainly doesn’t do it to recapitalize banks, or to privilege some form of savings, or to disincentivize lending.
It isn’t correct to suggest that reserves could be more gainfully employed than sitting on bank balance sheets. Unless the economy wants to do far more transactions in physical currency, there just isn’t another use for reserves.
Nick, regarding the whole recent Stephen Williamson brouhaha, I was wondering if I might ask you about some thoughts that Stephen didn’t respond to. Largely, they come down to this:
Does Stephen, and his group, still believe in MV = PY? or do they regard that the way they regard IS-LM, as laughably primitive, un-microfounded, wrong, and beneath the dignity of modern economics?
Because it seems like a lot of what Stephen says must make inflation go down, could just make the velocity of money go up (and so inflation and/or income go up). For example, he writes:
“Next, conduct a thought experiment. What happens if there is an increase in the aggregate stock of liquid assets, say because the Treasury issues more debt? This will in general reduce liquidity premia on all assets, including money and short term debt. But we’re in a liquidity trap, and the rates of return on money and short-term government debt are both minus the rate of inflation. Since the liquidity payoffs on money and short-term government debt have gone down, in order to induce asset-holders to hold the money and the short-term government debt, the rates of return on money and short-term government debt must go up. That is, the inflation rate must go down.”
At: http://newmonetarism.blogspot.com/2013/12/the-intuition-is-in-financial-markets.html
So, what if the Fed made T-bills and then sold them for T-bonds? The interest rate on T-bonds would go down, and the interest rate on T-bills would go up. And the “liquidity premium” (This seems more like the liquidity-and-risklessness premium, given how liquidity is often defined.) would go down. So it would be less desirable to hold money. So, two things could happen, it seems, to maintain equalibrium (if you think it has to be maintained), not just one:
i) Inflation could go down to induce people to hold money as much as before.
or
ii) Inflation could not go down, and people would want to hold money less, and so would get rid of it more quickly by spending it faster. It would become a hot potato, or more of a hot potato. In fact, I pretty much consider money a hot potato now. The “liquidity” premium is not high enough for me except for relatively very small amounts. Anything more I spend very quickly, mostly on stocks or real estate. But as the velocity of money goes up, and as M has gone up (defined to include T-Bills), either P or Y or both would have to go up, to maintain MV = PY.
Your thoughts on this?
Richard: My guess is that Steve would say that MV=PY is not very useful.
I think he just missed seeing that there were two ways to re-equilibrate.
Thanks Nick,
I feel confident enough now that I may do a post about this. Generally, I only post if it’s something I really think is good, and adds something that’s not out there. Without a name, I like to only post stuff I think is really worthwhile, so people know that this guy rarely posts, but when he does, it’s often good, and maybe worth a look. Anyway, that’s been the strategy the last five years, and it’s gotten some play.
If I might ask about one more thought on the current Williamson inflation stance.
He writes:
“But in a liquidity trap, since money and short-term government debt are equally liquid, if the central bank swaps one asset for another then this has no effect.”
At: http://newmonetarism.blogspot.com/2013/12/the-intuition-is-in-financial-markets.html
But money is not equal to short term-debt in “liquidity-and-risklessness”, and it seems that what Stephen calls “liquidity” is actually “liquidity-and-risklessness”, because there are assets that are just about as liquid as short-term government bonds, but are risky. Here, when I say liquid I mean the common definition of being able to sell quickly and cheaply at the market price.
Stocks, it seems to me, are just about as liquid as T-bills (by that common definition). In fact, about as liquid as you can get. The sale is almost instant, with close to zero sales cost, and at the market price.
Anyway, Stephen’s “liquidity” seems to mean 1) Riskless 2) Extremely collaterable 3) Extremely usable in transactions. So money is the most liquid, and T-bills are second. And in a “Liquidity Trap”, T-bills’ advantage over money of having a substantially higher interest rate goes away.
So, it seems like the characteristic at issue here is “liquidity-and-risklessness”. And with regard to that, short-term government bonds and money are significantly different.
Why? Because short-term government bonds are riskless for as much as you own. But with money, the risklessness is limited, or costly. If a party sells $100 million in T-bills for money, that money is risky. It’s only insured up to $250k in a bank account. The owner will want to move it relatively fast. He might buy longer term bonds, or something else. And then the next owner will want to move the new money, at least anything over $250k per bank account, and so on. It seems the velocity of money would increase.
So, again, it comes down to, does the freshwater macro crew still believe in MV = PY? Or is that un-microfounded crap to them?
They love to talk about general equilibrium, and perhaps to them the very concept of “velocity” is distasteful, because it is, in one sense, a disequilibrium concept. In a typical equilibrium, velocity is zero. The buyers engage the sellers; the price adjusts so that all product in the market clears; and, we’re done. Velocity of money means you never reach an equilibrium where all money is desired to be held, at least for long.
So, basically, do you think it’s significant that T-Bills are riskless to any amount, but money is only riskless to $250K per bank account? Do you think that the freshwater macroeconomists ignore velocity, and that’s a significant reason for the conclusions they come to?
Richard: you could interpret the “money” as currency.
Steve likes models where money is modelled explicitly, where people actually use it to buy and sell things, so he might say “velocity” is not useful, but would not say it’s zero in equilibrium.