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Nick,

First, there's IOR which I guess is your Rm. This rate, as you say, is set by the CB.

Then there's risk-free interbank lending, i.e. the "general collateral" or GC rate, which is also, to first approximation equal to the rate on t-bills (ignoring special repo for simplicity). GC is your Rb, I think. The spread between GC and IOR is what I would call the opportunity cost of holding money, and is the rate you should put in your liquidity preference model. As the CB increases the quantity of base, that spread decreases. People used to model this spread as declining asymptotically to zero as the quantity goes to infinity, but we now recognize that liquidity preference can be satiated. If the quantity is increased by some small amount over whatever the banking system would like to hold (e.g. 1% of GDP in the US), the spread collapses to exactly zero. I.e. the risk-free interbank rate is equal to IOR. At that point the liquidity demand is satiated and perfectly elastic.

I don't see how increasing Rm has any impact on the money demand. Rb (the GC interbank rate), will just move up in parallel, keeping the opportunity cost of holding money constant.

Anon: "I don't see how increasing Rm has any impact on the money demand."

Suppose they paid 1% interest on currency. (Or suppose there were 1% expected deflation, same thing). I would want to hold more currency. Would Rb also increase by 1%? Maybe, if Rb were originally 0% too. But what if Rb were fixed to 0% by law? Some people might be borrowing-constrained (as some people are now), but would monetary policy fail to work?

Put it this way: it is not just commercial banks who demand central bank money. Regular people do too. Commercial bank demand for central bank money is tiny (absent legal reserve requirements), but regular people's and firms' demand for central bank money is not tiny. Plus, there are no commercial banks in simple NK models; it's just people and firms and the central bank.

OK, but isn't Anon's description an accurate account of how CB's actually operate? They view Rm and Rb as two sides of "the" rate and control both, e.g. by paying interest on reserves and targeting the Fed Funds rate, or by putting both a floor and a ceiling on the interbank rate in Canada.

And isn't the CB's view more accurate than yours? Even being just an individual, I hold most of my money as deposits, so my opportunity holding cost is non-zero. Bank's holdings of currency are negligible.

And besides, you said yourself that the money holding rate of 0% is just a technical artifact, not an essential feature of CB policy.

"If you believe that "Central banks control monetary policy by setting the rate of interest" which of those two interest rates do you have in mind? Is it Rm, or Rb?"

Well, what do you mean by controlling monetary policy? From one point of view, independent central banks control monetary policy, because that is what they do. How the do it is how they do it.

But I think that you mean something related, which is more like monetary practice, not policy per se? If you want to control that, don't you want to control Rb?

My answer is “hold”, i.e. Rm.

There is no reason for a commercial bank to pay customers for the privilege of holding customers’ money. If anything, banks are entitled to charge customers for the cost of holding other peoples’ goods, property, money, or whatever. So commercial banks just don’t do Rm.

Where commercial banks pay interest on so called checking accounts which are permanently in credit and by a large amount, those banks are actually paying to borrow. That is, if all those customers with large checking accounts tried to withdraw their money all at once, the money just wouldn’t be there: it’s been loaned out.

As to central banks, they don’t “borrow” in the same sense as commercial banks. (That’s “borrow” as in “take someone else’s money and spend it, while paying interest to the lender”).

Central banks offer interest so as to drain money from the private sector and thus reduce AD: i.e. CBs offer a reward to those willing to let the CB “hold” their money. So Rm is central, while Rb is just a function of Rm.

Actually my real reason for saying that RM is dominant is that my name is Ralph Musgrave.

Actually, my statement was wrong. The correct statement would have been: "if inflation were 1% higher and Rm was increased by 1%, then the equilibrium level of Rb would also be 1% higher at the same quantity of money (ignoring any real costs of inflation)"

Let's try to clarify this. All borrowing rates in the economy set off Rb (GC), not Rm. This is because GC is the marginal cost of funds for banks. So the question is, for any given level of Rb, does M, the quantity of the base, matter? Clearly, if we increase M at constant Rb, we would also have to increase Rm (assuming non-satiated liquidity preference, for now). Borrowing costs are the same, but there is more money earning a higher, but equilibrium, rate of interest. Equilibrium, in this case, means no hot potato. How is the real economy affected by any of this?

Phil: OK, but if you assume that Rb=Rm (or Rb=Rm+25bp) then you are ducking my question. It's a bit like me asking: "Is it A or B that matters for C?", and you answering "Let's assume A=B". Rm and Rb can be very different, even if they have been linked in recent monetary practice, like a regression with multicolinearity.

I was really interested in precisely understanding what central bank's do when they set (more accurately, "target") rates, so I looked into the literature and found some detailed, but relatively simple, models by Woodford and Bindseil, which I describe below. They don't bring in a GC repo rate as you do, Anon. I sense leaving out repos as a source of funding makes their models somewhat incomplete, but to be clear, an interbank trade is not collateralized and not a repo. So at the very least it is confusing to call it the 'general collateral' rate.

So generally, CB's target the interbank rate, which is the rate at which banks can borrow and lend reserves (uncollateralized) in the interbank market. If this is what CB's target, they're targeting a lending/borrowing rate (what you call Rb). Nick, you say, "But in simple New Keynesian models, all money is electronic money and the central bank sets the rate of interest on electronic money, so "the interest rate" means Rm." I don't know which models you're referring to. While it's true CB's can set a positive rate of interest on reserves, this rate may still differ from the interbank rate, which they can still control quite precisely.

On that note, there are many different ways for the CB to achieve the same interbank rate, which include the interbank rate (Rb) being the same or different from the central bank's IOR rate (what you were calling Rm).

For example, consider a CB with a lending rate of 2% (discount window) and a deposit rate of 1% (IOR). If their target interbank rate is 1.5%, they'll adjust the quantity of reserves to be consistent with an interbank rate of 1.5% (roughly, this means creating a 50/50 probability that banks end short or long reserves at the end of the maintenance period, such that the interbank rate will 'arbitrage' to the weighted average of 1.5%). Here, Rm (IOR) is not equal to Rb (interbank rate). Alternatively, they could flood the interbank market with reserves and set the deposit rate to their target 1.5%, in which case Rm = Rb. They could also create a chronic deficiency of reserves and set the discount rate to 1.5%, in which case their lending rate becomes the dominant borrowing/lending rate. Rm could again be different than Rb here, depending on where the CB sets it. These are just a couple different approaches based on a basic set-up of CB deposit and lending facilities paired with open market operations and reserve requirements.

Starting on page ~328, Woodford lays out a basic model describing what it means when a central bank 'sets the interest rate': http://bit.ly/1bqR25D . I describe a simpler approach by Bindseil here http://bit.ly/1fXEX7H . Of course, these models may not be correct, but their type is the best I've found (many others build on the complexity of these models).

Also, another thought: some people might say your Rm is a lending rate too (as in banks 'lending reserves' to the CB and earning interest, or people 'lending deposits' to banks and earning interest).

Anon: "...there is more money earning a higher, but equilibrium, rate of interest. Equilibrium, in this case, means no hot potato. How is the real economy affected by any of this?"

If you increase Rm, and increase Ms, so that Ms and Md both rise by the same amount, there is no excess demand or supply of money. But transactions costs will be lower, which will have real effects. Who knows what will happen to Rb? Does it matter?

ATR: "I don't know which models you're referring to."

The simplest NK models, where there's only *one* (nominal) interest rate, and a consumption-Euler equation, a Taylor-type rule, and a Calvo-type Phillips Curve. Should we interpret that *one* interest rate as Rm or Rb? If in the real world Rm and Rb were different, and could move differently, which of the two would be the closest approximation to the model? (Because in the real world there are millions of different interest rates.)

ATR: "Also, another thought: some people might say your Rm is a lending rate too (as in banks 'lending reserves' to the CB and earning interest, or people 'lending deposits' to banks and earning interest)."

Sometimes (not always) we use IOUs as money (a medium of exchange). But other IOUs are not used as money but are merely promises to pay money. Rm is the interest rate on money, whether or not that money is an IOU. Rb is the interest rate on IOUs that are not used as money.

If we used cows as money, then Rm would be the annual value of milk divided by the value of the cow. If we used farmland as money, then Rm would be the rent/price yield.

Another example: just suppose, hypothetically, there were an infinite number of investment opportunities, that all gave the same risk-free rate of return R. And assume hypothetically that expected inflation is always 0%. So Rb=R and is fixed exogenously by technology. The central bank cannot affect Rb.

Is monetary policy powerless?

Nope. Monetary policy is very powerful. The IS curve is horizontal.

Woodford probably talks about this in "Interest and Prices." I'm pretty sure he references the paper I posted above in the beginning of that book as a foundation for what the CB does. Presumably then, he allows for a range of central bank approaches to targeting the interbank rate (whether it's setting the interbank rate equal to or different than Rm as you put it). Not sure though.

ATR,

I deliberately ignored the GC/FF intricacies. If interbank lending is not credit risky these two rates will be the same. In the US, the central bank targets FF (the risky overnight interbank rate), in Canada it targets GC. In both cases, there is essentially zero uncollateralized interbank lending. I think we should stick to a credit risk-free economy for the purposes of this discussion, or we will get completely lost for no good reason. All details which are relevant to this discussion can be captured with just Rm, Rb and M.

Apart from that, I agree with pretty well everything you are saying.

Nick,

"Who knows what will happen to Rb? Does it matter?"

I just noticed that ATR caught caught your comment that in the NK model ""the interest rate" means Rm." That's not correct. You can't borrow at Rm (and you won't lend there either). The marginal cost of postponing consumption is Rb. Rm doesn't figure at all in the intertemporal allocation decision. If you want to see the details of that calculation you should read Eggertsson and Woodford 2003, who look at what happens if the risk-free rate is determined via liquidity preference. What they find is that contingent on the the level of the risk-free rate, the quantity of money doesn't have any real effects.

Nick, you write:

"We can imagine a world where all central bank money is electronic money, and the central bank can alter both the quantity of money and the interest rate paid on that money, and can make Rm and Rb move by different amounts, or even in different directions, if it wants to."

I think this is an example:

http://catalystofgrowth.com/theory/fiat-currency-construction/

His model/plan explicitly gives a role to both the "lending rate" and the "deposit rate," and the CB controls both. Furthermore he writes:

"The central bank can target any price-level, time-dependent or state contingent (in order to target the path of NGDP growth for instance)
Simultaneously, it can target whatever quantity of money it wants. For instance, it could target a monetary base of 5% of GDP–i.e. a velocity of 20x"

JKH looks at yet another two interest rate proposal:

http://pragcap.com/a-new-operating-framework-for-the-federal-reserve

"The proposal ensures that the Fed has very tight control over two short term interest rates – interest on bank reserves (IOR) and the general collateral overnight reverse repo rate (RRP). The Fed will set an administered interest rate on reserves and supply unlimited full-allotment auction reverse repo at the same rate. The fed funds rate is expected to assume less importance"

Anon: "The marginal cost of postponing consumption is Rb. Rm doesn't figure at all in the intertemporal allocation decision. If you want to see the details of that calculation you should read Eggertsson and Woodford 2003, who look at what happens if the risk-free rate is determined via liquidity preference. What they find is that contingent on the the level of the risk-free rate, the quantity of money doesn't have any real effects."

OK. Let the technology be the same as in an AK growth model. Y=A.K. Assume 0% depreciation for simplicity. The investment-Euler equation is A=Rb. Infinitely elastic intertemporal substitution. Horizontal IS curve at a risk-free rate of A that is technologically determined.

Does this mean the quantity of money doesn't have any real effects? An old Keynesian would say that the quantity of money matters a lot in this case. A decrease in M causes a proportionate decrease in Y, because Rb is fixed, so velocity does not change.

Rb matters for the spend vs lend decision. Rm matters for the spend vs hold money decision. In a monetary exchange economy, you cannot buy goods with promises to pay future goods. You buy goods with money. An excess demand for bonds does not mean an excess supply of goods.

" Infinitely elastic intertemporal substitution. Horizontal IS curve at a risk-free rate of A that is technologically determined."

OK

"A decrease in M causes a proportionate decrease in Y, because Rb is fixed, so velocity does not change."

In a strict cash in advance, no lending economy, I suppose. In which case, I don't don't know what you mean by "Rb." It sounds more like Rb=infinity, but we have some money lying around. But it certainly isn't our modern economy, nor is it the NK economy. I think it would help this discussion if you were more explicit about your model of liquidity preference.

"In a monetary exchange economy, you cannot buy goods with promises to pay future goods. You buy goods with money."

You can buy goods with a promise to pay in future *money* though. And we don't ever need any cash to settle that debt either. I can just sell something of the same value and thereby offset my credit balance at some point in the future. I.e. you can borrow at Rb. If Rb is fixed, changing the quantity of money doesn't affect the decision to wait or to borrow and consume today. Why would it?


"Rm matters for the spend vs hold money decision."

Rb determines the spend vs hold some aggregate quantity of t-bills + money (IS)

The difference between Rm and Rb determines the t-bills vs money split (LM)

These decisions are independent.

"We can imagine a world where all central bank money is electronic money, and the central bank can alter both the quantity of money and the interest rate paid on that money, and can make Rm and Rb move by different amounts, or even in different directions, if it wants to."

Currency yields 0%. The amount of currency is 0.

IOR yields 0%. The amount of central bank reserves is 10.

The amount of demand deposits is 50.

The fed funds rate is 4%.

Entities borrow at 6% overnight (like a home equity line of credit).

The fed funds rate goes to 1%, and entities can borrow at 4% overnight. The amount of currency and central bank reserves stays the same and both yields stay at 0%. What happens?

"If you believe that "Central banks control monetary policy by setting the rate of interest" which of those two interest rates do you have in mind? Is it Rm, or Rb?"

I'm going to phrase that differently.

The central bank sets the overnight rate. That means both of these are possible.

IOR = 0%. Overnight rate = 4%.

IOR = very close to 4%. Overnight rate = 4%.

Currency yields 0% in both cases.

Anon: "In a strict cash in advance, no lending economy, I suppose."

Cash in advance does not mean no lending. We buy and sell goods for cash, and we also borrow and lend cash (we buy and sell non-money IOUs with cash). I am thinking about an economy where people buy and sell goods for money, and also borrow and lend money. They earn Rm when they hold money, and Rb when they lend money.

" And we don't ever need any cash to settle that debt either. I can just sell something of the same value and thereby offset my credit balance at some point in the future. I.e. you can borrow at Rb. If Rb is fixed, changing the quantity of money doesn't affect the decision to wait or to borrow and consume today. Why would it?"

You are talking about a barter economy. I give you 100 apples today, and in exchange you give me a promise to pay 100+Rb apples next year. (Or bananas). If barter is possible (and easy), then it does not matter if the central bank sets "the" interest rate too high. The unemployed just barter their way back to full employment. I can't sell my apples, you can't sell your bananas, so we do a swap of apples for bananas.

If, on the other hand, I get a credit at the central bank by giving you 100 apples, and you get a debit, and you repay that debit next year by giving bananas to ATR, who gives me carrots to eliminate my credit, then we are talking about a monetary exchange economy, using central bank money, and the rate of interest is Rm.

This is what really worries me about the lesson people are learning from New Keynesian macro. We really do have to distinguish between IOUs that are used as a medium of exchange, and IOUs that are not used as a medium of exchange. That distinction used to be captured in the Old Keynesian models when they distinguished between "money" and "bonds". When New Keynesians talk about "cash" and "credit" they are missing that distinction.

In a monetary exchange economy, there is an apple market where apples are traded for money, a banana market where bananas are traded for money, and a bond market where bonds are traded for money. That's what "money" as medium of exchange, means.

"To my monetarist mind, an increase in Rm increases the demand for money, and that causes an excess demand for money, just like a reduction in the supply of money causes an excess demand for money."

Currency yields 0%. IOR yields 0%. The central bank creates conditions (with emphasis) so that the overnight rate = 4%.

Currency yields 0%. Now, IOR yields 2%. The central bank creates conditions (with emphasis) so that the overnight rate remains at 4%.

I'm going to say not much happens.

"To my monetarist mind, an increase in Rm increases the demand for money, and that causes an excess demand for money, just like a reduction in the supply of money causes an excess demand for money."

Currency yields 0%. IOR yields 0%. The central bank creates conditions (with emphasis) so that the overnight rate = 4%.

Currency yields 0%. Now, IOR yields 2%. The central bank creates conditions (with emphasis) so that the overnight rate remains at 4%.

I'm going to say not much happens.

Sorry if this is a repeat.

Start with a model with central bank currency, and no borrowing or lending. Everything must be bought and sold for central bank currency. Now let the central bank pay interest Rm on currency. Now make everyone deposit their currency at the central bank, to prevent robbers. The CB keeps records of who owns how much. Now burn the currency, but keep the records. Now suppose the central bank lets you run either a positive or a negative balance. Now assume the central bank confiscate a fixed amount from everyone's account until the average account has a zero balance. I say you have the (simplest version of the) NK model. The rate of interest set by the central bank is Rm.

But what happens if you can exchange bonds for apples or bonds for bonds? Such transactions occur in the real economy, particularly the latter.

There are also corporate mergers, acquisitions, and options, futures and warrants.

Nick,

"We buy and sell goods for cash, and we also borrow and lend cash (we buy and sell non-money IOUs with cash). I am thinking about an economy where people buy and sell goods for money, and also borrow and lend money."

In the modern economy "borrowing" is what occurs whenever a goods transaction is made. The buyer's account is debited, the seller's is credited and the buyer gets the good. Borrowing and lending of money, in the sense you mean, essentially never occurs at all (outside the school yard). I've bought two houses using credit in my life and there was no "money" involved either time. Another time I bought a house without borrowing (I paid "cash"), and yet no currency was involved then either. 95% of the goods (and 99% of the value of goods) I buy are bought with credit and I've never settled my credit card bill or any other non-trivial debt using currency. If currency disappeared, nothing would change in my life.

Also, while it's true that interbank settlements in the US are currently largely done by transferring reserves, that was not true before 2008. Until then, settlements were done by borrowing. If BofA had to transfer money to JPM at the end of the day, they would borrow it from JPM. The loan transfer would net out the balance of payment and no transfer would be made. In Canada, this is how it still works almost every day. If the balance of outstanding reserves was exactly $0 rather than the token $25M or whatever, nothing would change.

"We really do have to distinguish between IOUs that are used as a medium of exchange, and IOUs that are not used as a medium of exchange."

Unless you want to introduce information asymmetries (e.g. search) or other trade frictions, the equilibrium will be defined exclusively by what everybody's goods and time preferences look like, not by the
microstructure of their exchanges, right? It doesn't matter if I exchange tomatoes for potatoes or if there is money in the middle, so long as we have the information and the trading technology to effect the necessary trades to achieve our preferred allocation.

If you want to convince me that introducing "money" matters in some particular way, you'll have to be very explicit about exactly what frictions you are introducing and why they will have the effects you claim. Without that, I think it's almost surely going to be pointless for us to spend time debating the consequences of terms like "medium of exchange".

Nick,

"Start with a model with central bank currency, and no borrowing or lending..."

So long as everyone has enough money that they can't ever be liquidity constrained this will effectively be the same model as the basic NK model that you get to in the end. The no borrowing constraint won't make any difference. If you allow borrowing Rb and Rm will be the same (but nobody is going to borrow).

"...I say you have the (simplest version of the) NK model. The rate of interest set by the central bank is Rm."

Yup. And since you are allowing unlimited negative balances (no need to keep liquidity) Rb=Rm.

PeterN: if all other goods can be exchanged for "bonds", then "bonds" are used as money (medium of exchange), and so they are money. Just as, if all other goods can be exchanged for cows, then cows are money.

Anon: "If you want to convince me that introducing "money" matters in some particular way, you'll have to be very explicit about exactly what frictions you are introducing and why they will have the effects you claim."

The NK model tells me that monetary policy matters. It tells me that if the central bank sets "the" rate of interest too high, there will be mass unemployment, where apple producers and banana producers are unemployed because they cannot sell their apples and bananas. So I ask: why don't the unemployed apple producers and unemployed banana producers just do a barter deal, so both would be better off, even if they do that trade at the fixed relative prices Pa/Pb? So the NK model must be assuming some trading frictions to prevent them doing that. OK. What are those trading frictions? Whatever they are, the result must be that you can only trade apples and bananas for central bank money.

Anon: "Yup. And since you are allowing unlimited negative balances (no need to keep liquidity) Rb=Rm."

I would say that the central bank sets Rm, and Rb does not exist. No pair of individuals or firms ever borrows or lends money. They just hold greater or smaller (or negative) amounts of central bank money.

Nick

Not sure this is entirely relevant, but am copying and pasting an old comment I had posted one year ago on your blog, since you're talking about Rm and Rb and I was immediately reminded of it.

"I have this 4 interest rate model in my head. The 4 interest rates are : r (market cost of risk capital), r* ('neutral' cost of risk capital), m (market cost of 'money'), m* ('neutral' cost of 'money').

Modern central banks, in normal times, set m, hoping to clear m*.

1. Hawtrey argued this is enough because in his view the macroeconomically relevant decisions follow from m.

2. Woodford argues this is enough because making m clear m* is perforce by assumption of financial equilibrium equal to making r clear r*.

3. Keynes agreed with Hawtrey in allowing for full CB control over m but argued implicitly in terms of r vs r* (atleast in the Treatise) and tried to show how the relationship between r and m might come unhinged.

4.Wicksell lived at a time when central banks did not control m* but showed the process of how m may diverge from m* through autonomous actions of the banking/financial system, even in a purely loanable funds framework. Transcribed into a Keynesian framework for long rates, this shows how the autonomy of the financial system may make r and r* diverge, even if the CB manages to make m clear m*.

I believe that in the years preceding the crisis, we were living in a world which had m > m* but r < r* . The risk premium in the market, driven by the financial system, was far too low and completely out of sync with the background risk premium of savers and investors. Call this the 'global loans glut', as Hyun Song Shin calls it. The extraordinary returns being made for investing at m (say, money market deposits) as well as the broken feedback from r and r* ensured that the standard mechanisms that would drive m* above m in an expanding economy were lacking. So r* rose, but m* stayed put. And when it all snapped, r* and m* both came crashing down, and we entered a slowdown (m>m*, r>r*) and since then, central banks have tried everything, pushing m down hoping that r will follow, trying to massage r down through portfolio balance effects, and with Japan, finally, trying to force r below r*, m and m* be damned.

When I say financial disequilibrium, Wicksell style, I basically refer to the idea that the market risk premium (r-m) may

1. become unhinged from the background risk premium (r*-m*) of the full-employment savings/investment balance.
2. change in response to central bank actions on the short rate (m).

Infusing the financial/banking system with autonomy will allow for these contingencies, which I see as fundamentally relevant to the macroeconomy, even in an IS/LM framework. With or without ALM mismatches or bank runs."

Ritwik: But is your "m" the same as my Rm or the same as my Rb? I think it's Rb?

Ritwik: I think Wicksell, Keynes, and Hawtrey were talking about a world in which typically Rm=0%, so they were talking about Rb.

Rm(ccy) = 0%. Rm(ccy), I believe, was unimportant to Keynes, Hawtrey and Wicksell. The first people to make a big deal of the difference between Rm and 0% were the Old Keynesians. This was mistaken, as firstly, they lost focus on Rm*, and secondly, they managed to confuse Rm with Rb, and falsely placed the focus at the relatively unimportant 0% rate.

Woodford brings the focus back on both - Rm vs. Rb is the term structure, and Rm vs. Rm* is the determinant of the central bank's monetary operation. 0% is irrelevant because the economy is "cashless". But he assumes financial equilibrium, so Rm is all that matters to him. Good, a big improvement, but still platonic.

At least that's my understanding of things.

Nick,

"Whatever they are, the result must be that you can only trade apples and bananas for central bank money."

Or (don't forget) promises denominated in that money!

"So the NK model must be assuming some trading frictions to prevent them doing that."

Touche. But although the microstructure of Calvo prices is controversial, at least it's explicitly defined.

Here's how I see it. The main facts of monetary disequilibrium are:

When the CB increases M by a discrete amount via an OMO:

1) the nominal short rate drops instantaneously. By this I mean in a matter of millisecond. By reducing the spread between Rb and Rm this immediately produces a new liquidity equilibrium;

2) the change does not produce any jump in the value of P.

Both of these, I think, are empirically verified facts. The first is indisputable, tested millions of times by central bank OMOs around the world over the past 100 years. The second is also very well verified by the very large central bank actions over the past 8 years or so. I don't believe we've ever seen anything like a discrete jump in P even when M has been changed by a very large fraction.

So what happens is that we get an immediate discontinuous change in the liquidity equilibrium, and a discrete change only in the rate of change of P (the inflation rate). What I believe is that given these two facts, the exact microstructure of price setting doesn't matter very much. No matter what they are, you are going to get a model, which, when calibrated to the real world economy, will give something where the CB effectively sets the real rate, and M doesn't matter very much contingent on that setting. It will behave a lot like the NK model.

"I don't believe we've ever seen anything like a discrete jump in P even when M has been changed by a very large fraction."

By which I meant "via OMOs". I know about Zimbabwe.

There is cash, the quantity of which the CB does not control as cash is created when banks voluntarily elect to convert some of their reserves into cash by purchasing cash with them. Similarly, they can elect to destroy cash by depositing it -- effectively purchasing reserves with cash.

There is also non-financial sector deposits, the quantity of which the CB does not control as the non-financial sector can destroy deposits by purchasing bank bonds or stocks, and can create deposits by taking out loans.

That leaves us with reserves, the only thing that the CB controls. But for reserves, the lending price is the same as the borrowing price.

So the premise of this blog is wrong. It is like saying "I'm going to conflate labor, consumption goods, and capital goods all into one "good", and then ask as question about the minimum wage, whether it sets the price of this "good" or does not succeed in setting the price because store owners can sell goods for anything they want.

The answer is that with a faulty premise, any conclusion is possible.

Nick,

1. There is the rate of interest you get paid if you hold money. Call it Rm.
2. There is the rate of interest you get paid if you lend money. Call it Rb.

If you believe that "Central banks control monetary policy by setting the rate of interest" which of those two interest rates do you have in mind? Is it Rm, or Rb?

It is neither. It is the interest rate the central bank is willing to lend at (U. S. - Federal Reserve Act - Circa 1913).

What you might be referring to is open market operations by the central bank (U. S. - Banking Act - Circa 1933). In that case the central bank is setting the price on existing bonds. The rate of interest was already set when the bonds were auctioned / loan was made. Again the answer is neither.

Of course, one policy (rate central bank is willing to lend at) tends to follow the other (price central bank is willing to pay for existing bonds), but it need not. A central bank could decide it will always pay a discounted price for existing bonds while lowering the interest rate it charges on loans or it could pay a premium price for existing bonds while raising the interest rate it charges on loans.

Nick,
How do we formulate the Friedman Rule in terms of Rm and Rb? Rb should be equal to Rm?

I think you should clarify that you have a risk free Rb in mind.

Anon, you wrote:

"By which I meant "via OMOs". I know about Zimbabwe."

If not OMOs what did Zimbabwe use?

Vaidas

The Friedman rule, classically interpreted, would mean Rm = 0%. Properly interpreted in a full-term & risk-structure-of-rates framework, it'd mean rm(1) = rm(2) = rm(3) = ..., where rm(i)s are the various rates at which different agents in the economy 'hold' money, respectively.

Nick might say that the Friedman rule means Rb = Rm. Certainly the Old Keynesians might have interpreted it that way. But nobody, conceptually, 'holds' money without simultaneously lending it, so it's all just a question of the term structure (and other similar structures)

Given that most money is created by private bank loans, if you want to control money, why wouldn't you want to control Rb?

Vaidas,

"Rb should be equal to Rm?"

Agreed. That's the zero seigniorage rate.

Tom,

They weren't buying tbills. Zimbabwe just printed the money and spent it. It was a fiscal problem.

This picture might be of use ... it shows short and long run interest rates calculated from the monetary base. Including (short) or not including (long) reserves makes the difference:

http://twitter.com/infotranecon/status/430927491440455681

Vaidas and Anon: yep. I would interpret the Friedman rule as saying: set Rm=Rb. Risk is tricky. There must be some difference between money and non-money, otherwise we would not use one and not the other as a medium of exchange. And "risk", at least in the sense of "ordinary individuals are not sure if this is a genuine asset and what it is worth when they try to pass it on to the next individual" might be one reason why.

rsj: Well, at a minimum, there are five Rm's in the real world. There is Rm on currency, Rm on positive balances that commercial banks hold at the central bank, Rm on their negative balances, Rm on positive balances in my chequing account at the commercial bank, Rm on my negative balances. And your Rm's, at your bank, may be different. And lots of Rb's.

All models simplify massively. That's what makes them models. It does not mean they are wrong, except in the trivial sense that all models are wrong.

ISLM has one Rm, that is always 0%, and one Rb. And the simplest NK model has one Rm, set by the central bank, and Rb does not exist. Individuals do not lend money, they hold positive money; they do not borrow money, they hold negative money. (I should probably do a post on that distinction sometime, but basically, holding negative money is not the same as holding negative bonds, if bonds are not the medium of exchange. That's where a lot of conceptual confusion arises, especially in NK models, between "cash" and "credit".)

Anon: "Or (don't forget) promises denominated in that money!"

Well. IOUs for money may or may not be used as money. My IOUs for money are not used as money. The Bank of Montreal's IOUs for money (at least some of them) are used as money. And some IOUs for non-money may be used as money too. Like under a gold exchange standard, where people use some promises to pay gold as money, but do not use gold itself as money.

"Touche. But although the microstructure of Calvo prices is controversial, at least it's explicitly defined."

Calvo pricing has problems, but NK economists are well aware of those problems. So, here, I'm just assuming that Calvo pricing is correct, and that all trade must take place at Calvo prices, whether it is monetary trade or barter trade. Take the simplest example: assume the central bank targets zero inflation, and that there have never been any shocks, so the economy, and all prices, are at long run NK equilibrium. And assume symmetry, so that all goods have the same price. Pa=Pb=Pc etc. Now assume the central bank suddenly and stupidly raises the rate of interest. And assume the Calvo fairy is a bit slow, stays in bed for one period, so no prices change. The NK model says that output of all goods drops. I say that, if barter is allowed, the unemployed apple and banana producers would get immediately back to full employment, by swapping apples for bananas at relative price of one. The NK model only makes sense if you (reasonably) assume that balances at the central bank are used as a medium of exchange (money), and that barter is ruled out by some (unspecified) trading friction.

"Here's how I see it. The main facts of monetary disequilibrium are:..."

I'm basically on the same page empirically. But let me give you a different interpretation:

Suppose initially that *all* prices are fixed/sticky. Not just goods prices, but all asset prices too. Now suppose the central bank increases Rm, and so creates an excess demand for money. Every individual wants to sell more "stuff" (goods and assets) and buy less stuff, in order to increase his stock of money. They fail to sell more stuff (because they can't find buyers) but succeed in buying less stuff. The volume of trade in stuff falls. There is excess supply in every market. We get a recession.

Now change the model very slightly. Assume the price of....peanuts....is perfectly flexible. So the price of peanuts drops instantly to clear the market for peanuts. You can always trade money for peanuts. Would we say that the fall in the price of peanuts is what *caused* the recession? No. We would say that the rise in Rm, that caused an excess demand for money, is what caused the recession. The fall in the price of peanuts was just a symptom. Would we say that the central bank "sets" the price of peanuts, and that monetary policy *is* setting the price of peanuts?

Now replace "peanuts" with "bonds".

Nick,

"My IOUs for money are not used as money."

I agree that one way to handle the problem of coincidence of wants is for everybody to have some tokens that we pass around. But there's another exchange technology that you don't seem to acknowledge can exist. In this second technology there is a central ledger in which everyone has a balance denominated in some unit of account. Whenever a purchase is made we increase the balance of the seller and decrease the balance of the buyer. We don't need any tokens at all. That, for all intents and purposes, is the economy we live in. The medium of exchange concept adds nothing.

"The NK model only makes sense if you (reasonably) assume that balances at the central bank are used as a medium of exchange (money), and that barter is ruled out by some (unspecified) trading friction."

I agree that barter has to be excluded (because it's basically impossible). But, to repeat, it doesn't have to be replaced with a medium of exchange. Credit balances suffice.

"Now suppose the central bank increases Rm, and so creates an excess demand for money. Every individual wants to sell more "stuff" (goods and assets) and buy less stuff"

Keeping M constant? In Canada (and currently also in the US) where liquidity preference is satiated, Rb will rise by the same amount which is what will cause the recession. But it's the wrong question, because if you are changing Rb you are mixing up your hot potato story with the standard Euler equation intertemporal consumption optimization story. We *know* that Rb matters a lot and we know how it matters in the real economy (the IS curve). So the question is, given a particular level of Rb, how do Rm and M influence the real economy? The answer, to first approximation, is not at all.

It's seems so simple to me that if you have agents with loans between them who must transact goods by changing their loan balances and you change the interest rate on those loans, then the best available intertemporal consumption allocation will be suboptimal. I can write down that model and solve it. I can also simulate it with many rational agents making rational optimizing choices on a computer and get the same result. There is no money quantity in there. Just loans. What's wrong with it?

Anon: "But there's another exchange technology that you don't seem to acknowledge can exist."

I think those two technologies are equivalent in all theoretically important respects. Sometimes the first is more convenient than the second, and sometimes the second is more convenient than the first. Passing a token from me to you is just a different way of making a change on the central ledger. We could imagine an illiterate central banker passing tokens from my box to your box because he can't write on a ledger. They are still a medium of exchange, even if we don't have physical possession.

"I agree that barter has to be excluded (because it's basically impossible). But, to repeat, it doesn't have to be replaced with a medium of exchange. Credit balances suffice."

Yep. Barter is very difficult (though, very interestingly, we do see it increase during very bad recessions). But those credit balances (if you must use them to buy and sell all other goods) *are* the medium of exchange.

"Keeping M constant? In Canada (and currently also in the US) where liquidity preference is satiated, Rb will rise by the same amount which is what will cause the recession."

Keeping M constant (in that example). But would you also say that "liquidity preference is satiated" if the price of (say) peanuts was perfectly flexible, so that people could always sell peanuts for money, if they wanted more money? So that the fall in the price of peanuts (like the fall in the price of bonds) is what causes the recession? If you don't like peanuts as an example, what about assuming the price of land, or houses, or IBM stock, or gold, is perfectly flexible?

"But would you also say that "liquidity preference is satiated" if the price of (say) peanuts was perfectly flexible"

If that was the problem you'd definitely want to do something about the price of peanuts. I'm certainly not saying that interfering with the relative price of money and t-bills by exchanging money for t-bills would be the way to go. The standard NK model typically assumes some regularity conditions on the disutility of labour which I think would make a perfectly elastic peanut price impossible. That seems reasonable to me. We do however know that the demand for base money can be satiated (the short rate can go to the level of IOR), so OMOs can be pointless. To be clear, I'm not saying that there can never be a role for government to correct market failures in goods markets, but I wasn't talking about that. I assume we are talking about OMO exchanges of money and t-bills.

I think I'm losing the thread here. I feel like I keep answering different arguments and I don't really understand how they all hang together. If you agree that calling debits and credits medium of exhange doesn't change anything, then what's the problem with the model as outlined in the last paragraph of my comment at 9:27? Why insist on a name change if it doesn't do anything?

"We can imagine a world where all central bank money is electronic money, and the central bank can alter both the quantity of money and the interest rate paid on that money ..."

Suppose that, in such a world, the central bank doesn't do OMOs. The quantity of money doesn't change, except for changes arising from the interest rate paid on money. (Interest on money is "payment in kind," so interest on money affects the quantity of money.) In this world, the interest rate on money is equivalent to the growth rate of the money supply. Over time, the higher the interest rate on money, the larger the quantity of money.

In such a world, is raising the interest rate on money deflationary, or inflationary?

(For simplicity, assume that central bank money is the only form of money; there are no commercial banks; everyone has an account at the central bank.)

M.R. "In such a world, is raising the interest rate on money deflationary, or inflationary?"

Good question. Assume all prices perfectly flexible. Assume initially Rm=0% and inflation = 0%. Now, unexpectedly, the CB increases Rm to 10%, and increases the growth rate of M by that same 10% (all new money is paid as interest). The price level does not jump (it normally would jump, if new money was just helicoptered in). But the inflation rate now jumps to 10%. The real interest rate on money stays the same, so real money balances stay the same.

"The real interest rate on money stays the same, so real money balances stay the same."

That sounds right to me under the assumption of perfectly flexible prices.

What if prices are sticky? CB unexpectedly increases Rm to 10%. So that's also the growth rate of M in my scenario.

Real money balances are now growing, so this should encourage spending. At the same time, money has become a more attractive asset, which discourages spending.

What's the right way to think about this?

M.R. Hmmm. Dunno. My brain has stopped working.

M.R.,

Imagine that the level of reserves is $25M in a $1.8T economy. The central bank controls the policy rate by setting Rm. At Rm=5%, there is $1.25M of new money introduced into the economy every year. Apart from the fact that the central bank buys back the $1.25M via OMOs every year, that economy is Canada. So unless you think that $1.25M of OMOs is the critical
difference, there you have the empirical answer to your question. Other than maybe Steve Williamson and Ed Prescott, I don't think there are very many people who believe that if the Bank of Canada raises IOR to 10% inflation will go up. The Bank of Canada certainly doesn't believe it. Like Tony Yates says Chris Sims got a Nobel prize for empirically settling this stuff. And apart from empirical evidence, it strains credulity to imagine that anyone cares about the quantity of about $25M of reserves.

Like Nick points out in his newest post, it just doesn't matter whether M is positive, negative or even zero.

Anon, try as I might, I didn't understand Nick's most recent post ...

I'm not sure the Canada comparison is apt. We were imagining a very different, stripped-down institutional environment.

My point was just that, in the stripped-down setting we were discussing, and assuming no OMOs, Rm is the growth rate of the money supply.

So higher Rm means higher money growth. Higher money growth should mean higher inflation. I gather you disagree?

M.R.: I now think, that if inflation is sticky/inertial, that the initial effect will be a decline in inflation, followed by an eventual rise in inflation. But I'm not sure. Because if inflation fails to rise by the full 10% immediately, the demand for money will initially increase, so inflation falls.

I am beginning to wonder about stability.

M.R.,

I think the gist of your question is, even if inflation deviates a bit from equilibrium, will it be driven back to equilibrium by the 10% rate of money growth. I think the answer is well-known to be no. The only way to get an asymptotic 10% inflation rate is with a 10% inflation targeting Taylor rule as well as an expectation of an asymptotically bounded inflation rate. You need both. In your case, you don't have a Taylor rule. This has been known for a long time, but is extensively discussed in Benhabib, Schmitt-Grohe, and Uribe (2001) The Perils of Taylor Rules. Friedman's k% rule isn't stable. The problem is that any downward deviation in inflation from equilibrium raises the real rate which causes a further reduction in inflation and consumption.

There are GE models where the quantity of money matters more, but the intertemporal equilibrium doesn't distinguish much between money and government debt (the central bank can arbitrarily transform either one into the other at all points in the future) and you need to consider the backing (or not) by future taxes (Ricardian equivalence) rather than just liquidity demand. I.e. a large quantity of total bonds+money may have non-Ricardian inflationary effects which overwhelm the deflationary consumption depressing Euler equation effects. This will happen if the rate of production of bonds+money is faster than a sustainable bubble. I.e. there are limits to the power of government to transport your consumption from the present into the future.

This directly contradicts the monetarist view where only the quantity of money matters for the price level. Woodford has written a fair bit about fiscal dominance and the fiscal theory of the price level. In these models any increase in money needs to be seen versus the larger context of the total quantity of money and debt, so your money base expanding interest payments would look very small compared to outstanding debt levels in modern economies.

Nick: Interesting answer, I see what you're saying.


Anon:

To be clear, I didn’t say that only the quantity of money matters for the price level.

What I did say -- and I don’t think it is very controversial -- is that we usually think that, ceteris paribus, higher money growth means higher inflation.

The gist of my question was to ask whether this latter proposition depends upon the institutional setting, and on the way in which the change in money happens.

Nick’s post said this: “To my monetarist mind, an increase in Rm increases the demand for money, and that causes an excess demand for money, just like a reduction in the supply of money causes an excess demand for money.”

My point is just that, in the institutional setting we were imagining, and assuming no OMOs, an increase in Rm is equivalent to an increase in money growth. Yet Nick is equating the effects of an increase in Rm to those of a *reduction* in the supply of money. There is a tension here that's worth thinking about.

I get the sense that you don't think the quantity of money has any bearing on the price level?

M.R.

"I get the sense that you don't think the quantity of money has any bearing on the price level?"

Like I said, it depends. In the case of a non-Ricardian fiscal policy, it is the total government liabilities, bonds+money, that will determine the price level. Money is typically a very small fraction of that, and anyways, can be freely converted to bonds. In the case of a Ricardian policy, the transversality condition (the governments asymptotic budget constraint) means that debt and money will all be paid off via taxes in the limit. In this case there is no connection to the price level. Finally, you might be able to make the classical monetarist argument for the price level if money wasn't created by buying bonds. Since it's created by buying bonds, the real balance is not net wealth to the private sector sustained by liquidity preference alone (at least not in a Ricardian economy).

So all in all, I'd tend to agree with that statement. I'm not saying that you couldn't construct economies in which M decides the price level. I'm just saying that real world economies look nothing like those economies, and in the real world, as well as in realistic model economies, the quantity is basically irrelevant.

To be even clearer, here's what I believe:

For a Ricardian fiscal policy (the usual assumption): Contingent on the path of the real rate the path of the quantity of money is irrelevant.

For a non-Ricardian fiscal policy: The asymptotically unpaid portion of the governments liabilities (bonds+money) is linked to the asymptotic price level via the asymptotic demand for the real balance (liquidity preference).


"What I did say -- and I don’t think it is very controversial -- is that we usually think that, ceteris paribus, higher money growth means higher inflation."

Who's we? I'm sure it's uncontroversial among the general public.

Anon:

"in the real world ... the quantity [of money] is basically irrelevant [to the price level]."

Hmm... I will take the other side of that one. But you get credit for internal consistency!

"Who's we?"

Fair question. I suppose everything is controversial. My guess is that most (all?) current Fed board members would agree with the statement that "ceteris paribus, higher money growth means higher inflation."

M.R.

"My guess is that most (all?) current Fed board members would agree with the statement that "ceteris paribus, higher money growth means higher inflation.""

In non-diverging equilibrium, yes. I also agree that for a stabilized economy, the growth of the money supply will tend to be around the nominal short rate (actually around the nominal growth rate, but whatever). But we were talking about your thought experiment, which was a control problem that involved suddenly raising the rate paid on money and keeping it there. Ask those same Fed members what would happen if we suddenly raise IOR to 10% and don't do any further OMOs (In fact, we would have to *stop* QE). I won't venture to guess what some of the dinosaurs (Plosser, Fisher) might answer, but I am pretty sure I can guess the answers of experts like Evans, Bullard and Kocherlakota. The fact is, there is no way a policy rate hike to 10% wouldn't tank both inflation and the US economy at the same time. The fact that those 10% would produce an additional $400Bn of reserves next year is irrelevant (there's already over $3T out there, up a factor of 1000 over the past 6 years, and it's growing by over $700Bn/year).

"Yes your mortgage rate just went up by 10%, but don't worry. There will be yet another $1000 per person sitting on reserve at the NY Fed by the end of next year."

If the existing stock of money is non-zero, and if increasing both the growth rate of M and Rm by 10% has zero effect on inflation, then the real stock of money M/P will become infinitely large.

Nick,

I agree. So will the real value of government debt. The effects of both appear together as total government liabilities, and how that quantity effects the equilibrium depends on fiscal policy (Ricardian or not?). So you can't use some non-Ricardian argument to save some version of the exchange equation. Instead you end up with the price level determined via the FTPL. But you are right, I think, that a large quantity of government liabilities can save you from an out of control deflation spiral (assuming that's what you were implying). There are lots of tricky complications here, so I think it's better just to refer to Benhabib et al or Woodford's chapter on Self-Fulfilling Inflations and Deflations.

Barro-Ricardian Equivalence says that paying new bonds as interest on old bonds makes no difference to either nominal or real variables, and if you assume that money and bonds are perfect substitutes, not just at the margin but everywhere, then you will get the same result with money, in M.R.'s thought-experiment. You are assuming Rm=Rb always. But if you drop that assumption, and allow Rm < Rb, then the real stock of money will matter.

By the way, just for my curiosity, because it's strange arguing with an anonymous person: I don't need to know your name, but my guess is you are a recent PhD from a top Canadian or US school. That's the image I have in mind. Is my guess roughly right? (You don't need to answer.)

Nick,

I have posted a new comment at Scott's blog, trying to persuade Scott that changing Rm-Rb is not a fiscal policy.

Nick, sorry to drag you back to this post (if you're even willing to come back here), but can you please elaborate a bit on what you meant by this last sentence:

"We would get roughly the same macroeconomic consequences even if Rb was fixed by law, or if lending money at interest was tabu."

What kind of "law" are you talking about? Lending money tabu? You mean like under Islamic law or something?

Thanks.

We were having a discussion of it here, and it was confusing:

http://pragcap.com/a-new-operating-framework-for-the-federal-reserve/comment-page-1#comment-167092

... upon further reflection, I think I got what you mean, but you still might take a look at the link to clear up any misconceptions that John or I may have (you'll probably be aghast at my sloppy [dead wrong?] summary of MM thought there).

Tom: looks to me like you got it right.

Yep, something like Islamic Law, only with no loopholes. People would evade that law, of course, but it's just a thought-experiment.

The other guy (John) on PragCap says that Rb is a vector/matrix, since Rb varies by term/risk/etc. He's right of course. All models simplify.

Vaidas: I will take a look a little later. Off skating on the world's largest skating rink.

Thanks Nick!! Appreciate it.

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