Deflationary banks

It's good to think about weird worlds, which you know are different from the real world. It helps you understand the real world better. Here is a weird world where commercial banks' wanting to expand loans and deposits would reduce aggregate demand and cause deflation. But the only weird assumption is that currency and deposits are complements, rather than substitutes. If you want to understand the macroeconomics of banks, you need to think about this assumption.

I think that currency and demand deposits are substitutes. Not perfect substitutes, but substitutes nevertheless. But here I want to make the extreme opposite assumption, and assume that currency and deposits are perfect complements. People always want to hold the same quantities of currency and deposits. Just like right shoes and left shoes, where one is no good without the other, and we talk about how many pairs of shoes people want to own. The desired currency/deposit ratio is always exactly one, just like the desired left/right ratio for shoes is always exactly one.

To keep it simple, let's ignore reserves. The monetary base is all currency, and banks choose to hold no currency reserves at all.

Starting in equilibrium, if the central bank created an additional one dollar of currency, people would deposit 50 cents in the banks, which would expand loans and deposits, just like in the textbook story, until that 50 cents was back in public hands, alongside one extra dollar of deposits. If we define the quantity of money as currency plus deposits, as we normally do, then with a desired currency/deposit ratio bolted down at one, the money multiplier would be two. Every extra dollar created by the central bank would create an additional dollar of deposits.

(But in this world we would most usefully define the quantity of money the same way we define the quantity of shoes. We would define the quantity of pairs of shoes as Q=min{quantity of right shoes; quantity of left shoes}. Because a right shoe without a left shoe, or a left shoe without a right shoe, is useless. A dollar in currency together with a dollar in deposits is a composite commodity, just like a pair of shoes. We would not define the quantity of money as M=currency+deposits. We would define it as M=min{currency; deposits}. Which would make the money multiplier one.)

Start again in equilibrium, but now suppose the shock comes from the commercial banks and not from the central bank. Suppose there is some change in banking technology, so that every individual bank finds it is no longer maximising profits at the initial equilibrium, and wants to expand its loans and deposits. What happens? That depends on how the central bank responds.

Suppose the central bank accommodates the desire by banks to create more deposits by increasing the stock of currency by an equal amount. The money supply (however defined) has increased, and with no change in the public's desire to hold more money, there would be an excess supply of money, which people would try to get rid of, forcing up prices in the process. The change in banking technology would be inflationary. (An inflation targeting central bank would not fully accommodate banks' desire to create more deposits.)

(If the central bank fully accommodates banks' desire to create more deposits, we get the same results whether the initial shock comes from the commercial banks or from the central bank itself. The only thing that matters is what the central bank does.)

Suppose instead the central bank refuses to accommodate the desire by banks to create more deposits. It holds the stock of currency constant. The banking system as a whole cannot create more deposits, because people would want to convert those deposits into currency. But that doesn't stop any individual bank from creating more deposits, if it can persuade people to hold more of its deposits and fewer deposits at some other bank. Each individual bank will compete against other banks by raising the rate of interest it pays on deposits (or doing something else to make holding its deposits more attractive than holding other banks' deposits). Competition between individual banks for deposits will cause the interest rate paid on deposits to increase until no individual bank wants to increase its loans and deposits. The banking system is again in equilibrium, with the stock of currency and deposits unchanged.

But people are not in equilibrium. They hold the same quantities of currency and deposits as before, but they are earning a higher interest rate on their stocks of the composite commodity. It is as if they hold the same number of pairs of shoes as before, but right shoes now pay interest. They would want to hold more pairs of shoes. They would want to hold more deposits and more currency, with equal amounts of both. There would be an excess demand for the composite commodity of money. Each individual would try to get more money by selling more other goods and buying less other goods. That would create an excess supply of other goods. The result would be deflation.

(An inflation targeting central bank would therefore need to increase the supply of currency to offset that deflation. It would partially accommodate banks' desire to create more deposits. The degree of accommodation would depend on the interest-elasticity of the demand for the composite money.)

I don't need to assume currency and deposits are strict complements to get this result; just complements will do. An increase in the supply (curve) of deposits by commercial banks, with no change in the demand (curve) for deposits by the public, that is not accommodated by the central bank, will be deflationary if currency and deposits are complements.

Now do you guys get it?

If you have an (implicit or explicit) model of the effect of banks on aggregate demand, and if your model does not recognise the importance of the degree of substitutibility between currency and deposits, then your model is wrong. And if deposits are convertible on demand into currency at a fixed exchange rate, if currency is in excess demand (supply) against other goods, then so are deposits.

But then, as I have heard so many times, us Market Monetarists don't understand banks at all. So we just ignore them.

Comments

[JP Koning]

"An increase in the supply (curve) of deposits by commercial banks, with no change in the demand (curve) for deposits by the public, that is not accommodated by the central bank, will be deflationary if currency and deposits are complements."

Interesting. In my last post I got the same result - that commercial banks could cause deflation by increasing deposit rates - although I assumed imperfect substitutability.

(If all markets are in equilibrium, and banks increase deposit rates, the prices of all other assets have to fall relative to deposits since, all else being the same, the returns offered by all other assets are inferior. A central bank can counter this deflation by simultaneously decreasing the return on cash, say by increasing the supply of currency. Prices of asset will have to inflate since assets now offer a superior return relative to cash and deposits.)

Quick related question. Do you think an inflation-targeting central bank should offset a rise in prices that is due to a once-and-for-all increase in bank deposit rates (due to some technological improvement), or should it not respond? I'm not sure.

[DismalEconomist]

This is an interesting way of framing monetary operations and I think the point would generally still hold if you adjusted the ratio from 1:1 to 1:10 or something of that nature, with a multiplicative impact on prices depending on the ratio.

The gist of what you're saying is that if the central bank doesn't fully accommodate bank deposit creation with complementary currency, the lending bank would have to raise its deposit rates to encourage people to park money in the bank instead of holding currency. Those attracted deposits are then lent out. But if deposit rates are competitively bid up high enough, the profitable lending opportunity is arbitraged away so to speak. As rates rise, it becomes more attractive to delay consumption, and this ends up having a deflationary impact on the economy. An inflation targetting CB would therefore have to adjust the currency it makes available for circulation to keep rates from rising too much.

What if these actions by the central bank in scenario 1 or 2 have little to no impact on CPI inflation, and instead only impact financial asset prices. The deflationary shock in scenario 2 would cause competing financial assets to fall in price since they become relatively less attractive compared to largely riskless deposits (at least up to CDIC limits). In scenario 1, couldn't financial assets be bid up to a point where holding currency and deposits become attractive to hold on a risk adjusted basis, rather than a hot potato effect in the real economy where people try to divest their deposits on goods and services? I guess what I'm asking is, when you introduce capital markets in to the picture does this function as a release valve so to speak that takes pressure of an inflation targeting central bank to act? Looks like JP above brought up the same question while I was writing this(shows how long it takes me to craft a response).

[Nick Rowe]

JP: "In my last post I got the same result - that commercial banks could cause deflation by increasing deposit rates - although I assumed imperfect substitutability."

But what were you assuming about the stock of currency? If the stock of apples stays constant, and the stock of pears increases, and pears are made more attractive so that nobody wants to swap pears for apples at the original relative price, there will be an excess supply of both apples and pears relative to other goods.

"Do you think an inflation-targeting central bank should offset a rise in prices that is due to a once-and-for-all increase in bank deposit rates (due to some technological improvement), or should it not respond? I'm not sure."

If it sees it coming it will respond. If it didn't see it coming, a price-level targeting central bank would respond after the fact, to get P back onto the original path, but an inflation targeting central bank would respond only to prevent future inflation deviating from target.

[JKH]

“But the only weird assumption is that currency and deposits are complements, rather than substitutes.”

I think what follows is a second, critically weird assumption:

“Suppose instead the central bank refuses to accommodate the desire by banks to create more deposits. It holds the stock of currency constant. The banking system as a whole cannot create more deposits, because people would want to convert those deposits into currency.”

Don’t you think that a central bank that refuses to supply currency on demand is weird?

[Nick Rowe]

Dismal: Yep, it ought to work the same for any C/D ratio, not just 1:1. But the same *percentage* change in base should cause the same *percentage* change in the price level, regardless of the C/D ratio.

I'm with you up to this point: "As rates rise, it becomes more attractive to delay consumption, and this ends up having a deflationary impact on the economy."

That's switching to a New Keynesian model. If you have an excess demand for money, you will want to sell more and buy fewer of all other goods, including financial assets, real assets, and consumer goods, and whatever.

If financial assets have perfectly flexible prices, and other goods don't, we might see the first impact on financial asset prices. But then there would be subsequent substitutions between financial assets and real goods, so other prices would adjust more slowly.

[Nick Rowe]

JKH: "Don’t you think that a central bank that refuses to supply currency on demand is weird?"

No. I certainly don't think that a central bank that targets inflation is weird. That's the real world (and not just in Canada). And as I showed in the post, a central bank that fully accommodated the increased desire by banks to create more deposits would not be targeting inflation. I think that a central bank that "supplies money on demand" is extremely weird. Zimbabwe maybe, but no normal central bank does that. It wouldn't last long if it did.

I have been vaguely thinking of writing a post on this topic: "No central banks do not and should not have a perfectly elastic money supply; the 'needs of trade' doctrine is false". It needs to be written. But it would be a boring post for me to write, since there would be nothing new here at all. Henry Thornton demolished that one centuries ago.

[JKH]

If currency is a desired part of the asset mix, then a central bank that refuses to supply currency on demand is inevitably deflationary.

The argument in total seems very asset-mix Tobin-like.

[JKH]

"To keep it simple, let's ignore reserves. The monetary base is all currency."

I think that's more than simple. I think it's essential to your argument.

Real world CBs do not turn down demand for currency.

But they can do separate things with interest rates and reserves.

[JKH]

i.e. with reserve deposit balances at the CB

[Nick Rowe]

Short version: the demand for money (the "needs of trade") depends on: PY; other things. A central bank that is targeting PY (NGDP) should make the supply of money:

1. Perfectly elastic with respect to "other things"
2. Perfectly ***negatively** elastic with respect to PY

In other words, if the demand for money increases because PY increases (or because P increases for an inflation targeting bank) the central bank should do the exact opposite of increasing the quantity supplied to meet that increased demand. It should reduce quantity supplied. Otherwise PY would just keep on increasing (or keep on decreasing) without limit.

[JKH]

"I think that a central bank that "supplies money on demand" is extremely weird."

Nick, do you think Volcker stopped supplying currency on demand?

He did stop supplying reserve balances on demand.

Which drove up interest rates.

His plan was "to do whatever it takes" to get money supply growth under control.

But he didn't stop supplying currency on demand - at an operational level - and your post reads like operational level to me.

Sure he probably slowed currency growth in doing all that.

But that's different that stopping out the supply of currency in response to asset preferences of bank money holders.

[JKH]

Sorry to be dogged with comments.

But I think your story is about close in portfolio management - with institutional differences between currency and bank deposits.

And I think you tackle it with an assumed conflation of currency and bank reserve balances at the CB.

Which is an institutional simplification of extremely high order.

[Nick Rowe]

JKH: It makes no difference to my argument whether I include reserves, provided I assume that reserves and deposits are perfect complements too. It just complicates things. In both cases base and deposits would be perfect complements.

Again, you really need to be pedantic about supply vs quantity supplied; demand vs quantity demand.

"Real world CBs do not turn down demand for currency."

They most certainly do turn down demand for base, if that increased quantity demanded was caused by the inflation rate rising above target. They do it by raising the overnight rate until that increased quantity demanded disappears.

[Nick Rowe]

JKH: central banks always swap currency and reserves at a fixed exchange rate (of one). That is why $1 in reserves is always worth $1 in currency. (And they always swap one $20 for two $10 for exactly the same reason.) But that does not mean the supply of base is perfectly elastic with respect to anything that might increase the quantity of base demanded. Again, no inflation targeting central bank (or no central bank that wanted to prevent hyperinflation or hyperdeflation) would ever run a monetary policy like that. We learned that lesson in Weimar. We must never ever forget that lesson.

[Tom Brown]

"It's good to think about weird worlds, which you know are different from the real world." Nick, I totally agree.

[Tom Brown]

Nick you write
"If you want to understand the macroeconomics of banks, you need to think about this assumption."
Is that one place that you and Scott Sumner differ? I imagine that he'd complete the sentence differently:
"If you want to understand the macroeconomics of banks, it's easy: they have no macroeconomic significance."

[Andy Harless]

"But that does not mean the supply of base is perfectly elastic with respect to anything that might increase the quantity of base demanded."

My understanding is that the supply of base has typically been close to perfectly elastic with respect to almost anything that increases the quantity of currency demanded for a given quantity of reserves. In the real world, if a CB notices that reserves are declining because of an increased demand for currency, without any particular information about why that is happening, usually failure to accommodate that demand would be deflationary.

Not sure how this affects the import of you imaginary world, though.

[Nick Rowe]

Tom: in one sense that is right. But it all depends on how the central bank responds to changes in banks.

Andy: Suppose the demand for currency increases or decreases because of a rise or fall in NGDP (or P or Y) relative to target. The central bank would not accommodate that rise or fall in demand.

[JKH]

"Suppose the demand for currency increases or decreases because of a rise or fall in NGDP (or P or Y) relative to target. The central bank would not accommodate that rise or fall in demand."

He's saying the same thing as I did, very roughly.

I think we're conflating short and long term - or operational and strategic.

Obviously the central bank will undertake policy to reign in growth in currency and/or the monetary base in total if it views it to be out of line with NGDP or price level targets. And I do mean that's obvious.

That's not at all inconsistent with what I'm saying - which is that the Bank of Canada won't refuse an order for currency from BMO because BMO is facing current demand for currency from its customers.

OK OK OK - quantity demanded.

That latter point is operational.

But so is your Tobin-like rebalancing of currency and deposit mix.

Central banks won't refuse to supply the quantity of currency demanded - TODAY.

And TOMORROW.

That's not inconsistent with your point about strategy long term and keeping targets such as NGDP and price level in mind.

Are we just talking past each other in this vein?

[Tom Brown]

Nick, in your previous related post, I'm not sure what you meant by "alpha money" in this sentence:

“If beta banks issued more beta money, holding constant the stock of alpha money, the total stock of money would be higher than desired, and there would be an excess supply of both monies against all other goods.”

Does "alpha money" here means:

1. MB = base money = currency (paper notes and coins) in circulation (not bank vaults) + bank reserves?
2. M0 = currency in circulation
3. Total currency in the private sector (both in circulation and in bank vaults)

[JP Koning]

"But what were you assuming about the stock of currency?"

OK, I see your point. I was assuming that the central bank will mop up the excess. If not, when I run through my post and make all the same assumptions that you are making in this post, including that deposits and cash are complements & the central bank does not mop up the excess, I get the same result that you do. Neat.

[Nick Rowe]

JKH: "Are we just talking past each other in this vein?"

Yep. I'm talking "strategy".

Tom. MB.

[Tom Brown]

Nick, I'm not sure what you meant by this:

"Tom: in one sense that is right."

It it:

1. In one sense my imaginary Scott Sumner statement is right, or

2. In one sense it's right that you differ with Sumner on this

[JKH]

Nick,

I wonder if we underestimate just how much the difference between those two starting points (they are starting points) accounts for the difference between the market monetarist view and the concrete steppes view. That's a rather huge recognition if its true, I think.

They aren't necessarily inconsistent.

In fact they're all part of the same thing - along a continuum - if understood.

Market monetarists tend to start with the long view and abstract immediately to "the base" (for example) as opposed to it components - even putting aside banks.

Concrete steppes people tend to project out from the short operational view.

But don't think that all of us miss the long view in doing so.

[Nick Rowe]

Tom: 1. I need to be more cryptic.

JKH: Hmmm. I reckon that's at least a large part of it.

[Max]

Day to day, central banks are keeping interest rates fixed, not base money supply. If shifts in base money demand that don't have a "macro" origin are correctly accommodated by keeping interest rates fixed, then these hypotheticals just can't happen. Somebody deciding to withdraw or deposit currency for an idiosyncratic reason can't cause a recession or boom, even if the central bank is terrible at forecasting. Yes or no?

[Gerry Fleck]

I take issue with your assertion that the desired left to right shoe ratio is always one.

Gerry Fleck aka Loopy

[Nick Rowe]

Max: we macro people need to look beyond the day to day. If central banks are terrible at forecasting, they will have difficulty distinguishing between those changes in demand for base they should and should not accommodate, and we will get inflationary booms and deflationary recessions.

Gerry: fair point! But if we assume the number of people who want only left shoes is equal to the number who want only right, it should be the same at the macro level.

[Philippe]

Nick,

"They most certainly do turn down demand for base, if that increased quantity demanded was caused by the inflation rate rising above target. They do it by raising the overnight rate until that increased quantity demanded disappears."

In this example, do you think the central bank could stop the inflation rate from rising further by simply saying that they don't want it to rise any further? Or do they need to be able to take concrete steps to actually stop it from rising further, such as raising the overnight rate?

[Tom Brown]

Nick, you write:

"Now do you guys get it?"

Who are "you guys?" Do they include David Glasner and JP Koning?

[Tom Brown]

Nick, O/T: You wrote at Glasner's the following:

"What I had in mind was something changing so that individual banks found the old equilibrium no longer profit-maximising, so they found it profitable to expand loans and deposits even if they needed to increase interest rates on deposits to dissuade people from swapping those deposits for central bank money and prevent the Law of Reflux kicking in."

Can you give an example of what "something changing" might be which would have this result? Thanks!

[Tom Brown]

Nick, I attempt to answer my own question above by providing an example on JP Koning's blog in this comment:
http://jpkoning.blogspot.com/2014/04/rowe-v-glasner-round-33.html?showComment=1397005294113#c809789614390463886

[Tom Brown]

Nick, you write:

"Each individual bank will compete against other banks by raising the rate of interest it pays on deposits (or doing something else to make holding its deposits more attractive than holding other banks' deposits)."

Why don't they compete by lowering the interest rate they charge on loans instead? Or can we assume they're doing that as well? Both strategies will tend to decrease their profit margins (their spreads).

I think we can assume that they don't increase the interest rate they charge in tandem with the interest rate they pay, else they may attract deposits, but then fail to loan any additional money, which would also just be a loss for them.

But if any individual bank just increases the rate it pays on deposits without changing the interest rate it charges on loans, it may also increase deposits, but if there's no accompanying uptick in lending, it's a money losing proposition for that particular bank. So how can the bank attract more borrowers without lowering the interest rate it charges for loans? Don't you need to tell both sides of this story (interest rates charged vs those paid)?

[dannyb2b]

Would this deflation cause an increase in disposable income and hence increase ngdp? slighly off topic.

[Tom Brown]

dannyb2b, these sentences from Nick:
"Each individual would try to get more money by selling more other goods and buying less other goods. That would create an excess supply of other goods. The result would be deflation."
Doesn't make it sound like the "good" kind of deflation. I understand from Sadowski that "good" deflation is theoretically possible, but he's never seen a historical example of it. In either case, people spending less doesn't sound like an increase in NGDP.

[dannyb2b]

Tom Brown

Seems like more demand for money to save and hence less spending.

[dannyb2b]

I'm getting more confused the more I think about this. If any individual bank paid more in interest to attract deposits they would be worse off (higher cost) and if they have more deposits they cant lend. I don't see the purpose of attracting deposits through higher rates.

The only way banks can profit more from higher technology is by reducing their costs and hence increasing returns (inflows of currency reserves). If they increase rates on lending then they lose market share. Lowering rates on loans is only beneficial if a bank's deposits are below the limit. Therefore rates wont change it seems.

[Nick Rowe]

Philippe: the standard New Keynesian answer is that if the central bank sets the interest rate just right, conditional on the shocks, then the *threat* to raise/lower that interest rate if inflation rises above/falls below target will be sufficient to keep inflation on target, and that threat will never need be carried out.

Tom: if banks want to increase both deposits and loans, they may both increase interest paid on deposits and reduce interest charged on loans. Depends on the elasticities, and on what else changes.

danny: if apple producers have a bigger harvest, they will cut prices. It is against their collective interest to cut prices, but it is in the interest of each individual apple producer to cut his price.

[Odie]

"They most certainly do turn down demand for base, if that increased quantity demanded was caused by the inflation rate rising above target. They do it by raising the overnight rate until that increased quantity demanded disappears."

Does that not mean that the central bank adjusts the price until the quantity demanded becomes the quantity it wants to supply (based on its inflation target) instead of saying the CB refuses to expand the monetary base?

[Tom Brown]

Nick, it seems to me that ideally each individual bank would want to increase loans and decrease deposits since deposits are not only liabilities but are also an expense, while loans are assets and produce a positive revenue stream.

Transfer deposits into the bank fund the subset of lending which results in drawing cash out of the bank, but in general a bank would be delighted if their depositors walked in (having been robbed of their cash say (the robbers immediately depositing half their take of course!)) and said "You know that deposit you owe me? Forget about it!"... then the bank could strike those liabilities from their balance sheets, equity would immediately take a jump upwards, and the rate of profit growth would also jump upwards. In order to send out extra large dividend and bonus checks to celebrate their windfall the bank could safely sell off its loan portfolio. If the owners were willing to wait, then they could just enjoy the full revenue stream from their loans without the expense of deposits: relending the principal payments (and thus maintaining the size of their loan portfolio) and skimming the interest, or perhaps relending the interest payments too, and thus growing their portfolio w/o any deposits (perhaps they refuse to increase their deposit rate to match their competition). In any case, I'd prefer to be a shareholder in the bank whose deposit liabilities vanished.

[Tom Brown]

... in short, banks don't want transfer deposits themselves (the legal contract making the bank a debtor to the depositor)... they want the base money that comes along with the transfer deposit. If they could take the former w/o the latter they would.

[Nick Edmonds]

Re JP Konig's coment, I think you can get this result just from having currency and deposits as sufficiently weak substitutes, without the need for a central bank mop-up.

Assume non-bank demand for base money is Hn = ( ah0 - ah1 . Rd ) . PY and for deposits is D = ( ad0 + ad1 . Rd ) . PY , where Rd is the deposit rate and ad1 > ah1. So a rise in the deposit rate causes people to hold less currency and more deposits, but more money overall.

Then assume banks hold reserves in a fixed ratio to deposits Hb = b . D, and that the central bank holds total base money H = Hn + Hb constant.

Then you get a situation where PY is negatively correlated with Rd, whenever ad1 > b . ah1

[Tom Brown]

Nick Edmonds, I get that PY is negatively correlated with Rd whenever ah1 < b.ad1

[Tom Brown]

... the reason is that if we assume starting off that Rd=Rd0=0 and PY=PY0>0, and we change to Rd=Rd1>0 and PY=PY1>0 we have:

K0 = (K1 + K2.Rd1).PY1

Where K0, K1 and K2 are constants and

K0 = (b.ad0+ah0).PY0 > 0
K1 = b.ad0+ah0 > 0
K2 = b.ad1-ah1

So it depends on the sign of K2. If K2 > 0 (i.e. b.ad1 > ah1) then Rd and PY are negatively correlated. If K2 < 0 (i.e. b.ad1 < ah1) then Rd and PY are positively correlated.

[Tom Brown]

... K0 = H too.

[Nick Edmonds]

Tom,

You're right. I had b on the wrong side. But despite my shoddy algebra, the conclusion is the same, i.e. that it still works if they're merely weak substitutes.

[Tom Brown]

Nick Edmonds, true. BTW I also asked Jason Smith how he might approach modeling JP Koning's scenario in his "Rowe v Glasner" post. Here's his response:
http://informationtransfereconomics.blogspot.com/2014/04/whats-up-with-m1.html?showComment=1397052503839#c7290849583546494767

[Nick Rowe]

Nick E: I think what you say is right (with the math fixed). I think what matters is whether *base as a whole* is a substitute or complement for deposits. Now we normally assume that reserves are a complement to deposits, but currency is a substitute for deposits. So the relative sizes of reserves and currency will matter for whether base is a substitute or complement. (In Canada reserves are very small relative to currency, so I tend to ignore them, as I ignored them in this post.)

[Tom Brown]

Nick Rowe,

"So the relative sizes of reserves and currency will matter for whether base is a substitute or complement."

I'm not sure that's what Nick Edmonds' model is telling us here though. For example, suppose we had this:

b = 0.1
ad1 = 20
ah1 = 1
Rd = 1
PY = 1
ah0 = 100
ad0 = 50

Then b*ad1 = 2 > 1 = ah1, so PY is negatively correlated with Rd

But

Hn = (100 - 1*1)*1 = 99
Hb = (50 + 20*1)*1*0.1 = 7
H = 106

So cash in circulation (Hn) > reserves (Hb)

But we could change

ah0 = 7
ad0 = 980

giving

Hn = (7 - 1*1)*1 = 6
Hb = (980 + 20*1)*1*0.1 = 100
H = 106

And now Hn < Hb, but still PY is negatively correlated with Rd since ad1, ah1 and b didn't change.

[Tom Brown]

So what Nick Edmonds is saying with his simple model is if the partial derivative of Hb wrt Rd is greater than the partial derivative of Hn wrt Rd then PY and Rd will be negatively correlated.

[Tom Brown]

Sorry, that should read:

"...if the partial derivative of Hb wrt Rd is greater than the negative partial derivative of Hn wrt Rd then PY and Rd will be negatively correlated."

[Tom Brown]

In words: if the base money stock increases with increasing Rd, given PY is held constant, then PY decreases with increasing Rd given base money stock held constant.

[dannyb2b]

Tom Brown

I think Nick is saying there is no reserve requirement in this specific example. In this case you don't need to hold currency to back up your deposits. It took me a few reads to understand and I think he is correct in his conclusion so long as there is no RR. Every bit of currency a banks receives it can just lend out.

Of course the current banking system is different to this example though.

[Tom Brown]

dannyb2b, I agree that's what Nick R is supposing in the world he's created for this post, but his comment here:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2014/04/deflationary-banks.html?cid=6a00d83451688169e201a3fceb29fc970b#comment-6a00d83451688169e201a3fceb29fc970b
is more general as it applies to Nick Edmonds' model, which is not restricted to the rules of Nick Rowe's weird world. Nick Edmonds is saying you don't need such a weird world for increases in the interest rate on deposits to be deflationary: it can work in some circumstances when currency in circulation and deposits are imperfect substitutes and when reserves indeed are > 0. Reserves > 0 are an explicit component of Nick E's model: that's what his parameter "b" is all about.

[Nick Edmonds]

I think my model is consistent with Nick's. Doing away with reserves means setting b = 0, which means the condition is simply that ah1 < 0. This implies that demand for currency is positively correlated with the deposit rate, making it act as a complement with deposits.

Whilst my version may be less weird, I wouldn't want to give the impression that I think it is representative of the real world. But I agree with Nick that this sort of exercise is useful for building a sense of how elasticities matter.

[Tom Brown]

Nick Edmonds, yes, setting b=0 and taking ah1 < 0 does make your model more like Nick R's. To make it exactly like Nick R's we'd need to set ah0 = ad0 and ah1 = -ad1 as well. Then Hn = D = H, reserves = 0, and dPY/dRd < 0. But I'm still not sure how that relates to this statement of Nick R's:

"So the relative sizes of reserves and currency will matter for whether base is a substitute or complement."

Since, even in Nick R's model, the quantity of reserves is always 0, so currency [in circulation] (M0 in the US) will always exceed it, but as your model shows (in my exercise above) we can get dPY/dRd < 0 with M0 < reserves or M0 > reserves. And although I didn't show it, M0 = reserves also works.

Maybe I'm misunderstanding what Nick R meant by that sentence, since I'm just referring to dPy/dRd < 0, not whether or not the base as a whole is a substitute or a complement for deposits. I'm not sure dPY/dRd < 0 is a test for that. When Nick R wrote:

"I think what matters is whether *base as a whole* is a substitute or complement for deposits."

I don't know what it matters for. In light of the model you'd just presented, which he seemed to be commenting on, I'd supposed he could have meant "matters for whether or not raising Rd is deflationary" (i.e. dPY/dRd < 0), but since that doesn't seem to be true, I'm not sure. Any ideas what the complement-ability or substitutability of the base as a whole (as NR says, determined by their relative sizes) matters for?

[Tom Brown]

Nick Edomonds,

"Whilst my version may be less weird, I wouldn't want to give the impression that I think it is representative of the real world."

As we've shown your model CAN be just as weird (exactly the same as NR's world), but it has a range from that extreme to less weird, showing when dPY/dRd < 0 in all of them, so that's why I think it's so interesting! You took a single example and created a set of examples from it, and showed that dPY/dRd < 0 works across the boundary of complementary to substitutable relationships between M0 (your Hn) and D. Well done!

[Nick Rowe]

Tom: "You took a single example and created a set of examples from it, and showed that dPY/dRd < 0 works across the boundary of complementary to substitutable relationships between M0 (your Hn) and D."

M0 is *not* Nick E's Hn. "Base as a whole" is currency (Nick E's Hn) PLUS reserves. If currency is a substitute for deposits, but reserves are a complement for deposits, then whether base is a substitute or complement for deposits (and whether an increase in interest on deposits will cause an increase or decrease in PY, for a given stock of base) will depend on BOTH the degree to which currency is a substitute and reserves are a complement AND on the relative magnitudes of currency and reserves.

[Tom Brown]

Nick R, Nick E writes:

"total base money H = Hn + Hb constant."

So when he wrote "total base" is H, then I took "H" to be "base as a whole" and Hn to be the currency in circulation part of it.

He's holding total base (H) constant, not Hn!

[Tom Brown]

"Assume non-bank demand for base money is Hn" ... assuming demand equals supply, the base money held by non-banks is what M0 is in the US. It's different in the UK.

[Tom Brown]

That's what the 1st table in this article says about M0

http://en.wikipedia.org/wiki/Money_supply

"Notes and coins in circulation (outside Federal Reserve Banks and the vaults of depository institutions) (currency)"

However, later it says this:

"M0: The total of all physical currency including coinage. M0 = Federal Reserve Notes + US Notes + Coins. It is not relevant whether the currency is held inside or outside of the private banking system as reserves.'

So that seems to be a discrepancy. First it says "outside of depository institutions" and then it says it's not relevant.

[Nick Rowe]

Tom: in Nick E's formulation, reserves are a strict complement to deposits, and reserves are part of the base. So base could be either a substitute or a complement to deposits, depending on the size of b (the reserve ratio).

Nick E and I are on the same page.

Over and out.

[Tom Brown]

Nick R: I never said you weren't on the same page... his model is the same as yours if you set b=0, etc (all the parameter settings we discuss above). Completely on the same page, I agree. But what his model shows is that dPY/dRd < 0 does not depend on the relationship of the stock of Hb to Hn, (my numerical example shows dPY/dRd < 0 can happen for Hb > Hn or Hb < Hn), it depends only on the terms multiplying Rd (i.e. -ah1 and b*ad1).

[Tom Brown]

So it's this part of your statement I question:

"...AND on the relative magnitudes of currency and reserves."

If by that you mean how Hn compares to Hb. Again, take a look at my numerical example above: I demonstrate that dPY/dRd < 0 can happen for both Hn < Hb and for Hb < Hn

[Nick Rowe]

Tom: "Again, take a look at my numerical example above: I demonstrate that dPY/dRd < 0 can happen for both Hn < Hb and for Hb < Hn"

OF COURSE IT CAN! That does NOT contradict what I said!

"But what his model shows is that dPY/dRd < 0 does not depend on the relationship of the stock of Hb to Hn,.."

He shows it depends on b, and Hb depends on b. (And elasticity is not the same as slope.)

Stop now. This is annoying me.

[Tom Brown]

Nick R,

"OF COURSE IT CAN!" ... OK, good to know. It wasn't clear to me you agreed with that. Sorry for annoying you.

[JKH]

Nick,

market monetarism post:

[link here strongly recommended NR]