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A Fiat Money Origin Story

April 3, 2016 13 comments

Nick Rowe has a recent post about Chartalism which got me thinking about the fundamental explanation for the value of money again.  He calls this an “origin story” and seems to be of the opinion that the origin doesn’t really matter, once it gets going you can remove the original source of fundamental value and it just stays up.  Kinda like Wile E. Coyote running off a cliff.  As long as nobody looks down, we’re fine.  I personally think this is nuts.  But I figure, why not try going through the explanation like an “origin story” from primitive commodity money to modern fiat money.  Maybe that will help?  I have mostly tried to avoid all of that because it seems unnecessarily confusing and I usually want to distill the story down to its most fundamental point as much as possible.  However, I think maybe this leaves people too much room to fall back on little misconceptions that are deeply lodged their thinking about this.  So why not start from the beginning and try to hammer out all the points (or most of them) in one try?  For the record, this is not a historical work.  It’s a made-up history that I think is fairly consistent with reality as it unfolded in the western world.  Whether or not the Chinese had some type of script that was linked to taxes thousands of years ago or there were some hunter-gatherers somewhere with a credit-based economy before commodity money became prevalent is not relevant to my point. Read more…

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A Modified Gold Standard

October 17, 2014 3 comments

David Gordon has a piece on Mises.org critiquing Steve Forbes’ book Money. The piece is rife with confusion but I don’t want to do my usual Mises.org routine and go line by line pointing out how each point is mistaken. (They never seem to respond when I do that, which is odd because I know they notice, I can see the hits…) For what it’s worth, I haven’t read the book but from what I can gather from the quotes in Gordon’s post, it is also somewhat confused.  This quote, however, got me thinking.

“[Forbes’] gold standard allows the money supply to expand naturally in a vibrant economy. Remember that gold, a measuring rod, is stable in value. It does not restrict the supply of dollars any more than a foot with twelve inches restricts the number of rulers being used in the economy.”

This got me thinking about how gold could be used as a “measuring rod” for money without being “convertible” in the traditional sense of the word and I think that thinking about it this way may help to explain the relationship between money and debt.

Imagine that you have an economy where physical gold is commonly used as money. A bank enters this economy and offers the following deal: You can borrow X “dollars” (a unit which the bank makes up out of thin air).  At some point in the future you must repay the same number of dollars or a given quantity of gold. Let’s say that the exchange rate is one oz. of gold per dollar so if you borrow 100 dollars, you can repay either with 100 dollars or with 100 oz. of gold or any linear combination of the two. The bank has only 1 oz. of gold which it keeps in the vault to act as the “standard gold oz.” like the official meter (or was it the foot?) that the French (or was it the English?) have in a vault somewhere. If you come in to pay off a debt using gold, it is compared to the standard oz. for weight and purity. Otherwise, the bank has no gold, nobody “deposits” gold and the bank does not stand ready to sell gold for dollars or dollars for gold in the traditional sense of “convertibility.”

Furthermore, assume that the contract specifies that, if the borrower does not pay the appointed quantity of dollars and/or gold by the specified date, that the bank (by way of the courts and police) will seize real goods from the borrower which can be traded for the requisite quantity of gold. And assume that only people who can post sufficient collateral are allowed to borrow so that nobody can default.

Now, first question: How much “money” (dollars) can the bank create?

Answer: As much as people are willing to borrow.

Of course, people will only be willing to borrow these dollars if other people are willing to take them in exchange for goods. So does it make sense for people to take these dollars even though they are not “convertible” in the traditional sense into any “real” good?

Yes.

Why?

Because the dollars are convertible. The person who borrows them and spends them today will need to get them back, or else get gold back, or else forfeit some quantity of real goods at some point in the future. They are contractually obligated to do this. So if somebody comes to you and wants to buy seed corn with these dollars and you understand the contract that they signed with the bank and you believe that this contract will be enforced, you can accept the dollars and hold them until the loan comes due and be assured that the borrower will be willing to trade you some portion of his crop (or other goods) to get those dollars back.

Next question: How is the price of a dollar in terms of gold determined?

First of all, let me say that what Forbes seems to mean by the “value” of money is the price of gold and this is what Gordon is erroneously interpreting as the subjective value of money and that is a source of much of the confusion in his criticism. But putting that aside, what forces are acting on the exchange rate between money and gold and how, if at all, is this rate “fixed?”

First of all, it should be fairly obvious that the price of a dollar cannot rise much above 1 oz. of gold. This is because only the borrower has an ultimate use for these dollars (paying off the loan) and he will not be willing to trade more than 1 oz./dollar to get them. If he had to pay 2 oz. (or other goods which he could trade for 2 oz. of gold) he would instead just use the gold to repay the loan.

On the other hand, the borrower will always be willing to pay up to 1 oz./dollar because if he can get dollars cheaper than that, then the difference represents a surplus to the borrower. (If you are imagining a kind of hold-up problem, just imagine that there are a hundred borrowers bidding for the dollars.)

So this type of “convertibility” should fix the exchange rate between gold and dollars right around the rate specified in the debt contract. This does not depend on the quantity of dollars that are created this way, the quantity of gold in bank vaults or the quantity of gold relative to other goods.

Now if there is some liquidity preference for gold or dollars relative to the other, the exchange rate might deviate slightly in one direction or the other (and likewise for risk preference). The magnitude of the liquidity preference will likely depend on the quantity of dollars and gold in circulation so these things may have a marginal effect on the exchange rate between dollars and gold and this will factor into the interest rate charged by the bank and how prices change over time in a more complicated model but just ignore all that for now. And obviously, the quantity of gold and other goods affects the price of gold (and therefore dollars) relative to other goods.

The important point is that liquidity preference is not the sole (or even the main) explanation for the value of a dollar. It explains a small deviation from a certain value relative to other less liquid assets but it does not explain the existence of any value in the first place. That depends on the real assets which someone is contractually allowed/obligated (depending on how you look at it) to exchange them for. This means that it is the quantity of money relative to the quantity of debt which is the main anchor holding the “value” of a dollar in place.

“Well that’s all well and good Mike but there are no gold clauses in debt contracts so this isn’t how the real world actually works” I can hear the skeptics reply. But the skeptics are wrong. We no longer have a fixed gold “measuring rod.” But we still have fixed convertibility between dollars and real goods built into the debt contracts that create money. It’s just that the goods and the rate are not the same for everyone.

If you want to borrow money to buy a house, you put the house up as collateral. The contract specifies that if you do not repay a specified number of dollars by a specified date, the bank (via the courts and police) will seize your house (a real good). It’s the same thing.

We all (Keynesians, Austrians, monetarists, whatever) act like when they suspended convertibility of dollars into gold at a fixed rate for everyone, they severed all concrete (read: “contractual”) ties between money and real goods and money just sort of magically behaves as though it were still backed by something even though it isn’t.  That is not what happened.  They only severed one particular kind of convertibility into real goods.  But this does not require everybody to be able to exchange dollars for real assets at a given rate, it just requires somebody to be able to.  And the ability of debtors to “convert” dollars into real assets at a contractually fixed rate remains.

Of course, since this rate (and the particular goods) can vary from one contract to another, it is possible for the price of a dollar, measured in any (and for that matter all) particular real good(s), to drift over time and modelling that is a complicated matter which I have been attempting. But any attempt to model it which ignores debt entirely and assumes either that liquidity preference is all that matters or that there is no reason for money to be valuable at all except for some form of mass delusion is like trying to model the position of a sailboat based on the direction of the wind without realizing that the anchor is down.  The wind matters.  The length of rope and the depth of the water matter. But you can’t really make sense of how or why they matter if you don’t notice that there is an anchor involved.

“Negative Money” (A Variation on Nick Rowe)

October 8, 2014 Leave a comment

As I said recently, I have a bunch of outstanding business with Nick Rowe which I am trying to work through. Foremost on the list is a couple of older posts about negative money (Part I, Part II). This comes remarkably close to my way of looking at things, but let me make a couple amendments.

First, let me address another point on which Nick and I agree. Here is one of his comments on a different post.

Start out be assuming One Big Bank, that is both a central bank and a commercial bank. That issues only one type of money. And it does not matter if that money is paper or electrons. Now make an assumption about what the Bank holds constant: is it r, M, or NGDP, or what? Then ask your question.

I believe that one of the main mistakes people make which causes us to miss some important insights is to separate the central bank from the commercial banks and sort of lump the commercial banks in with the rest of the private economy as a facility that simply matches borrowers with lenders or something like that. The commercial banks play a key role in the functioning of the money supply and they have the special privilege, granted by the central bank, of performing this role. So let’s take the opposite approach and lump the commercial banks in with the central bank and treat it as one big bank.

However, instead of having it issue one kind of money, let’s have it issue two kinds: red and green. Anyone who wishes, can go to the bank and ask for some quantity of green dollars and an equal quantity of red dollars (and assume that the bank just keeps track of this in their records, as in Nick’s model, the actual paper currency is not the important thing here.

Then let us make two changes to the model. First, in Nick’s model, either red or green money can be used in exchange. Let us instead assume that only green money can be used. So instead of this.

. . . if neither the buyer nor seller of $10 worth of apples has any money, each goes to the central bank and asks for 5 green and 5 red notes, the buyer gives 5 green notes to the seller, the seller gives 5 red notes to the buyer, and they do the deal.

We would have the buyer going to the bank and getting ten red notes and ten green notes and trading the ten green notes to the seller. Notice that this difference is not particularly meaningful in terms of the model as in both cases the seller ends up with ten green notes and the buyer ends up with ten red notes. This does however, start to look a lot like how things actually work.

Second, in Nick’s model, the interest rates the bank “pays” on each type of note are constrained to be equal. Instead of assuming that, let us assume that the bank can only “pay” interest on red notes and the rate on green notes is constrained at zero. This means that the quantity of red and green notes will not be equal unless one of two things happens.

1. The rate on red notes is zero at all times.

2. Additional green notes are created and somehow distributed to balance out the red notes which are “paid” out as interest.

Now, if this doesn’t look like what really goes on in a modern economy, just replace “red money” with “debt” and “pay” with “charge” and it should start to look familiar.

This causes several things to start making sense. First, we have the whole issue of why, seemingly worthless bits of paper are stubbornly (and stably) valuable. They aren’t just meaningless bits of paper, they represent one half of a debt contract. Behind those pieces of paper is another half–red money, if you will–and a vast infrastructure dedicated to seizing your property if you hold too much “red money” for too long without producing the requisite green money to cancel it out.

Second is the issue of recessions. Once you look at it this way, it is easy (relatively speaking) to see that there are two separate but related “willingnesses” at play here. There is a willingness to hold red money (debt) and there is a willingness to hold green money (money). People hold green money until their marginal liquidity preference is equal to the foregone interest from lending the money or from “investing” in real goods. People hold red money until the interest rate on red money is equal to the marginal rate of substitution between current and future consumption. These are equilibrium conditions so there are a bunch of different ways to express them.  I tackled it more thoroughly in my model. The important thing is that there is red money and green money and people can hold different quantities of each depending on their situation.  If you only see (and your model only includes) one and not the other, you are missing a very important piece of the puzzle.

But since it is possible for the quantities of these two things in circulation to change relative to each other while they are still “convertible” at a 1:1 ratio, the real value of each type can change differently over time. And since the constraints involved in equilibrium involve expectations about these changes over time, those expectations can be wrong. And the important thing to note is that the expectation of the quantity (and therefore the value) of green money that will exist in the future is tied to the quantity of red money people are willing to hold in the future. In order for the quantity of green money to increase, people must hold more red money. If people decide to reduce their holdings of red money, they must “redeem” green money to get rid of it and this will reduce the quantity of green money.

That is, unless number 2 above happens. Number 2 is required in order to have the type of inflation expectations and interest rates that we have amount to a long-run equilibrium. Number 2 is what I meant before when I said “fiscal policy.” This is not exactly what other people mean when they say “fiscal policy” and that got me into a bit of trouble but the thing that I mean is the relevant thing whatever you want to call it.  (I’m still not entirely clear on what everyone else means by “fiscal policy”…)

If people expect some level of inflation which requires the (green) money supply to keep growing at some rate and we come to a point where the quantity of red money refuses to keep growing at a rate which will make that growth rate of green money possible, everything starts to fall apart unless the bank or the government or somebody finds a way to pump more green money in.

There are a lot of ins and outs and what-have-yous wrapped up in the last four paragraphs here but for a more careful treatment, again, see the model.

It’s Demand for Money, Not Demand for Currency

August 12, 2014 5 comments

As regular readers know, I am a guy who sort of stumbled into monetary economics and as such, I have been going through a process of discovering the minutia of how everyone else thinks about money and trying to reconcile this with what I think I know. And it turns out that there are a lot of little issues that come up which make it hard for me to explain what I am thinking in the context of existing paradigms. These issues all basically revolve around the reason that money is valuable. I think this is because “money” represents the contractually obligated payment of debt. Most others seem to start from some kind of explanation that can basically be summed up as “it just is.”

The “it just is” explanation makes sense in the context of commodity money, since commodities have value independently of their use as money. However, I think this explanation is highly suspect when it comes to “fiat” money, which I would call “credit money.” Of course, historically, the line between the two is a bit blurred and this has largely, in my view, prevented the profession from drawing clear distinctions between them. Instead, we have basically just substituted base money in for the old commodity money and built our models around the assumption that this base money works essentially the same way except that we can make the quantity whatever we want.

This leads to a plethora of little assumptions that are difficult to flush out because, individually, they seem like they don’t matter. But they seem this way because they fit into a larger paradigm which is built on this (I think erroneous) belief about the reason money is valuable.

One such issue is the way we think about the demand for money. The simple version of the conventional wisdom goes something like this: There is a quantity of money in circulation. An individual can get rid of this only by spending it. The price of holding this money is the nominal interest rate. If people have more money than they desire to hold, they try to spend it. When everyone is trying to hold less money, either prices have to go up or interest rates have to fall until they are all holding the desired amount.

The problem with this is that people have another option (or options depending on how you look at it) which is to lend it or deposit it. However, the conventional wisdom has a nice way of dealing with this by conflating the two.

In the basic Macro 101 money multiplier model, we say that there is some amount of base money which gets multiplied by the banking system in the following way: People deposit some amount of it into banks who then lend it. The people who borrow it then spend it. The people who receive this money then deposit some of it into a bank and the process repeats until people and banks are holding their desired (or required) quantities of this base money.

In this process, the willingness of people to hold currency (base money) is crucial. The less currency they are willing to hold, the more they deposit at each iteration and the higher the money multiplier. This means that there is more spending which means higher “aggregate demand” and higher prices (and potentially higher output). This willingness to hold currency, naturally, depends on the rate of interest since this is the price paid for holding it rather than depositing it. People are assumed to pay this price because currency is more liquid. In the 101 treatment, it is typically (though implicitly) assumed that all spending is done with currency.

In this context, the banks are essentially reduced to an intermediary between borrowers and lenders. So when you deposit money, you are really lending it to someone else in order that they may spend it. So even though an individual may avoid either holding or spending the money, someone else has to end up holding or spending it and in aggregate all “money” (currency) gets either held or spent.

In this context, the interest rate can be thought to be determined endogenously as the rate at which the quantity of loans demanded is equal to the quantity supplied in the form of deposits, given the quantity of base money in circulation. Alternatively, we can think of the central bank setting (targeting) a given interest rate and providing the quantity of base money which is demanded at that rate (required to hit the target). In this context the distinction is seemingly unimportant.

In this model, anything which increases the money supply or decreases the demand for base money (including reducing the reserve ratio) increases “aggregate demand” and either prices or output or both.

However, this is not what I think the primary function of banks is. The primary function of banks is to create liquidity. This, I believe is true even in an entirely decentralized, free banking sector with a commodity standard. I have argued this before, so I won’t go through the whole spiel again here but I want to point out how this changes the way we look at money.

First of all, let us notice that it is the creation of a particular form of liquid asset (demand deposits) which separates banks from all other financial intermediaries. For instance, a bond fund acts as an intermediary between borrowers and lenders. However, a bond fund cannot create additional “money” the way a bank can. If you invest with a bond fund, you must take dollars (or whatever) out of your bank account, give them to the fund who can then give them to the borrower (buy bonds). The quantity of dollars in the system doesn’t change.

A bank, on the other hand, can take my deposit in a checking account, let’s say $100, and then lend it. When they do this, I still have $100 which I can spend at any time and somebody else now also has $100 that they can spend at any time. [Please note, that this is not an anti-fractional-reserve rant, I’m not saying this is bad, just that it is important. I’m working up to something much more subtle.] The reason you get a higher rate of return (normally) in a bond fund than in a checking account is that the checking account is more liquid.  In particular, it is worth noting that, like currency, a balance in your checking account is nominally denominated and represents a contractually (legally) acceptable form of payment of debts unlike shares in a bond fund or accounts receivable from a loan you made to your friend.  The latter must first be sold at some market rate to obtain some form of money (either cash or deposits) before a debt can be paid.

So whereas a bond fund makes a profit (which is to say “exists”) because it has (or is perceived to have) an advantage in determining profitable investments, the bank makes a profit because it is able to “borrow” at a lower rate (compared to a bond fund or other financial intermediary) because of its ability to offer a more liquid product in return which in turn is due to its ability to multiply a dollar into two dollars (and collectively into much more).

Now the subtle thing that I am working up to here is that it is not the willingness to hold currency that matters, it is the willingness to hold dollars in all forms (or insert unit of your choice). And this is where the “endogenous” vs. “exogenous” money debate starts to matter.

So the first thing to notice is that cash is not necessarily more liquid than demand deposits, they are differently liquid. There are some transactions for which cash is more convenient and there are some for which demand deposits are more convenient. In today’s world, it is probably the case that the latter make up the majority of transactions and even if they don’t, it is certainly not the case that cash is at all times preferred to deposit accounts and we only deposit money because it pays a higher interest rate. On the contrary, even if all transactions were slightly more convenient with cash, we would still hold most of our “money” in deposit accounts and withdraw it from time to time to make purchases because holding all of that cash would be inconvenient. So we can’t say that it is the interest rate which induces us to hold deposits instead of currency. It is actually liquidity preference. And indeed, until 2011, it was illegal to pay interest on demand deposits in the U.S. (and after that interest rates have essentially been zero anyway).

Now the thing we care about is neither the demand for currency nor the demand for money in a broader sense. What we are really interested in is aggregate demand. The question is which one of these, if either, helps us understand the behavior of aggregate demand.   Thinking about the demand for base money works fine for this purpose under two assumptions. The first is that the thing which is exogenous is the supply of base money. Second is that the process of multiplication, as outlined above, adheres to a stable process in all regards other than the demand for base money.

The first assumption is sort of wrong in the sense that it is not the way that monetary authorities say they conduct policy but taken alone, there is room to argue that this is not an important distinction which I and others have done. I think this does matter but only after we address the second assumption.

The second assumption holds much of the time but not always. It just so happens that it is when it breaks down that we run into problems. Specifically, it is the assumption that money which is deposited automatically gets loaned and money that is loaned automatically gets spent (therefore adding to aggregate demand) that is problematic. Assuming this allows us to draw a straight line from depositing currency to spending and keeps our “either spend it or hold it” paradigm intact.

However, if we look at this a different way, with “endogenous” money, things change. Instead of imagining that the central bank just dumps in a certain quantity of money and the system goes from there, imagine that they operate as “lender of last resort” to the banks and stand ready to supply whatever quantity of base money is demanded at a given rate. So the supply curve faced by banks will be perfectly elastic (horizontal) at that rate. Then the supply of loans will be perfectly elastic at some rate which accounts for the cost of running a bank and the risk of a given loan. This will then be independent of the willingness to hold currency.

Now if the rate on deposits is allowed to float freely, that rate will rise to the rate at which the central bank stands ready to lend reserves (the discount rate or federal funds rate). But if it is prohibited by law from being greater than zero, then it will be zero. This rate on deposits will affect the composition of people’s money holdings between currency and deposits but in neither case will that decision between currency and deposits ration the amount of loans made. If the quantity of deposits is less than the amount required to make the loans which are demanded at the discount rate, then the difference will be made up by borrowing from the central bank.

[Note that I consider normal open market operations, and not just lending at the discount window, equivalent to lending reserves to banks. This point is subtle but is a potential bone of contention and raises some other questions like how best to treat government borrowing in this context but I will leave this for later.]

In this context, we can see that it is the demand for loans which is important not the willingness to hold currency. If people are willing to borrow more at the rate set by the central bank, the money supply will expand and if they are not willing to borrow more, it will not, regardless of people’s preferences between holding cash and holding deposits. If people suddenly decide to hold more cash, the banks will simply borrow more from the central bank in order to make the demanded quantity of loans.

Now the central bank can still pump more money into the system by buying other assets and there will still be a type of hot-potato effect. But this is not driven by their willingness to hold currency, it is driven by their willingness to hold money and their willingness to hold debt. When they get the new money, they can either hold it (as either cash or deposits, it doesn’t matter which) or spend it on goods or they can reduce their debt. Either holding money (any kind of money) or paying down debt, increases their money to debt ratio. That is what matters. It doesn’t matter whether they hold it in the form of currency or deposits because depositing it doesn’t actually lead to more lending and then more spending.

At this point I started explaining how I think “unconventional” monetary injections work but it quickly became clear that that requires an entire post of its own so I will leave it for later. For now let me just stick to the point which I originally set out to make which is that it isn’t the willingness to hold currency relative to deposits that matters, it is the willingness to hold money (all money) relative to debt.

This point can be approached from another direction, if one is intent on taking the money supply as exogenous. It is clear that the thing the central bank wants to target is not the money supply but rather something like aggregate demand (some combination of prices and output or unemployment or something). It is obvious, I think, that if people suddenly decide to hold more currency and fewer deposits, the central bank will accommodate them by increasing the quantity of base money accordingly. In my way of looking at it this happens automatically as banks borrow more at the set interest rate but you may think of it as the central bank increasing the base through lending (which may include buying treasury securities) such that the interest rate stays the same. This would cause no change in aggregate demand.

In this case, it would be easy to do this because the increased demand for currency would increase the demand for base money. So it is hard to see how this would cause a problem if the central bank were not sticking to an arbitrary and counter-productive money-base target. Or, put another way, no demand for currency vs. deposits should cause the normal transmission mechanism to seize up. The important link in the money-multiplier chain is the willingness to borrow—the part which is typically taken for granted.

On the other hand, If people suddenly want to hold less debt and more money (any kind of money), then the central bank may not be able to pump more money in through that mechanism and increase aggregate demand, even at a zero rate. People may then start to wonder how easy it will be to get the dollars in the future to pay off their debts if the central bank’s injection mechanism is failing and they will try to get more money and less debt (and buy fewer goods) and it will spiral. The central bank will then have to find another way to inject money.

Similarly, in a state where there are large quantities of excess reserves in the banks and interest rates are near zero, if inflation expectations increased, it wouldn’t be the sudden unwillingness of people to hold currency and rush to deposit it into the banks that would lift aggregate demand, it would be the sudden willingness to borrow that would draw down reserves, increase the broad measure of money in circulation and lift aggregate demand.  It is this willingness to hold money (any kind of money) vs. willingness to hold debt that matters, not currency vs. deposits. However, this can only be seen once you notice that these two things (money and debt) are intimately related and free your mind from the shackles of the “it just is” theory of money value.

More on Reserve Requirements

March 28, 2014 Leave a comment

Will be busy this weekend but wanted to quickly respond to a comment by J.P. Koning on my previous post on reserve requirements indicating that Canada does not have such requirements.

I previously argued that a reserve requirement replaces a gold standard as a constraint on credit creation.  I believe this is correct but I don’t mean to imply that it is the only way credit creation can be prevented from going to infinity.  I realize I sort of said that but I was thinking in terms of a simplified model.  The important assumption was that people hold no currency and that all base money takes the form of bank reserves.  This of course is not the case in reality, it just made the model simpler.

Even when this is the case, it is possible for a reserve requirement to be non-binding.  This was the case in my characterization of a “liquidity trap.”  The only potentially problematic implication of this simplified model is that, when the reserve constraint is not binding, the expansion of credit is demand constrained in the sense that the interest rate will be driven down to zero (or the rate of IOR) and credit would expand only to the level that would be supported by the willingness to hold loans at that rate.

In reality, discount rates in Canada have not been zero since they dropped their reserve requirement, though they have been low (maximum of 4.25%) and reserve ratios have been low (usually around 3 or 4%) but not infinitesimal.  But this can be explained by relaxing the (false) assumption that all base money must be reserves and imagining that banks face some risk of becoming illiquid.  If they are concerned about this, they will demand some level of reserves which will most likely be inversely related to the interest rate since the more reserves they hold, the bigger the buffer against illiquidity but the higher the interest rate, the more revenue they must give up on the margin for additional protection.

This is another way of saying, they will have an upward sloping supply of loans.  And for the record, I acknowledged this in the comments of my original market-for-loans post when I said:

A more accurate supply curve would be a monotonically increasing curve above and to the left of the one I drew which is very flat and close to the level of IOR for low quantities and approaches infinity as the quantity approaches the maximum possible quantity but gets pretty close to that quantity for moderately high interest rates. It doesn’t change the essential point I am trying to make.

So I assumed a supply curve that looks like this.

loans market normal

A more realistic supply curve with a reserve requirement would be this.

Loanable goods market IV

And with no reserve requirement, it would look like this.

Loanable goods market V

So I suspect that, when the reserve requirement is (nearly) binding, removing it would lower interest rates and reserve ratios but everything should still work.  Of course, modeling this would require a different supply function from the one I assumed previously.  But the main implications should be basically the same.  This does put “liquidity traps in a slightly different light since we can’t just say that it’s because demand hits zero (or IOR) before you hit the reserve requirement.  But the nature of it is not much different since the rising supply is due to the liquidity risk, it should be a function of reserve ratios (holding other things equal) so when the base increases, it should stretch this curve to the right making supply higher for any given interest rate and so it is easy to imagine it being very close to zero/IOR for a long way out and this causing reserve ratios to be relatively high and rates to be close to zero/IOR.

So my approach is probably the result of good old-fashioned American myopia, I will try to broaden my horizons.  But I think the basic framework I am working with holds up in light of this wrinkle.  I do wonder what the reasoning for Canada dropping the requirement was though.  It would seem to me that this would make monetary policy a bit less precise since they would have to estimate the slope of the supply curve out at the end (they probably don’t think about it this way but somehow or another, there is an extra degree of freedom if reserve ratios are fluctuating with monetary policy).  But monetary policy is one area where it’s difficult to criticize our neighbors to the north since they have had somewhat less difficulty with it than we have lately.

 

 

Distinctions with a Very Slight Difference

March 25, 2014 14 comments

Nick Rowe and Scott Sumner both have posts up arguing with a paper from the Bank of England.  Both are excellent and I agree entirely with them (except a couple small, mostly semantic gripes with Sumner) so I won’t reproduce all of the arguments but I think this serves as a nice illustration of how hard it is to understand economics models–so hard, it seems, that even the people in charge of setting monetary policy don’t really understand them.

I think at least half of the arguments that go on in the blogosphere regarding monetary policy are completely superfluous and are just bickering about different ways to describe the same thing.  If you are making a model, the way you describe things matters because it affects the way the model works but often times, there are multiple ways to do it that don’t make it work any differently (at least not materially different).  But for some reason people get all caught up in arguing about which is the “right” way to describe it.

The two main examples of this that come out of the BOE paper are whether or not banks “lend out reserves” and whether central banks set interest rates or the supply of money.  I already addressed the first one here (and Sumner does a pretty good job of burying it), so I won’t bother with that.   They also both (especially Rowe) do a very good job of dismantling the second but just for fun, I will wade into it a bit.

As Rowe points out, the intro textbook theory has the CB choosing the quantity of money and then the demand for money determines the interest rate.  An equivalent way of saying the same thing is that the CB targets an interest rate and then chooses the quantity of money which will “cause” that rate given the demand for money.  It is relatively easy to see that there is no difference between these two descriptions when one is looking at a snapshot in time, holding demand constant.

The argument seems to arise when considering how the CB responds to changes in demand.  If they kept the money supply constant and demand increased, interest rates would increase.  If they target an interest rate, then when demand increases, the money supply must increase.  That is a meaningful distinction.  But all that means is that the CB determines the supply of money not just the quantity supplied.  Of course a supply function is just a collection of quantities which they intend to supply under different circumstances.  The meaning of this depends on what circumstances you are wondering about.

There are basically two different versions of “supply” going on here and the difference is entirely a matter of communication.  First, there is a “long run” version of the supply of money.  In this version, the CB is facing some unknown profile of “snapshot” demand functions at various points of time in the future and it has the ability to adjust the quantity of money in keeping with its long-term policy objective (for instance an inflation target).

So we can think about the CB, at any given time, looking at the demand for money and choosing the quantity which is necessary to meet that objective.  Similarly, we can imagine the CB looking at the demand at any point in time and determining the interest rate that will produce the quantity of money that is consistent with the long-run policy objective.  There is no difference.

Note that the CB can’t set a long-run inflation target and an independent long-run interest rate target, it is the inflation target (along with the demand for money) that determines the path of both the quantity of money supplied and the interest rate.  So when the CB says it will target a certain inflation rate, it is telling you a certain supply of money that it intends to follow as a function of prices and interest rates, namely a supply function which is perfectly elastic at the targeted price level.  But this means that interest rates will need to fluctuate to bring markets into equilibrium in the short run.

If the CB knew all market conditions at all points in time exactly, they could state this same price level target as an interest rate target at all points in time, or a quantity of money target at all points in time.  But since, they don’t know all of this, it becomes a “supply curve” in the sense that it tells you which things they will allow to adjust and which they will not (at least allegedly).  In the example of an inflation target, they will theoretically allow both interest rates and the quantity of money to shift to keep inflation on target.  Because the interest rate and the quantity of money are linked, it makes no difference which one you imagine is endogenous or exogenous at any point in time.  The thing that is actually exogenous is the supply “curve” of money (the policy rule) and the real shocks to demand.

Now the debate about whether the CB chooses the quantity of money or the interest rate revolves around the short run and in my mind it stems entirely from this distinction: The CB does not set policy continuously.  In fact, it sets policy at regular intervals (usually once per month) and at those times, it has to set the policy for the entire interval.  This means that they have to determine a supply curve that they will stick to for that interval and they have to communicate it.

Because of this, in the minds of the bankers, there is a distinct difference between setting the quantity of money and setting an interest rate but in either case they are setting the supply of money, they are just two different supply curves.  If the CB came out and said “we are increasing the quantity of base money to X,” they would be indicating a perfectly inelastic supply of base money between now and the next policy meeting.  Alternatively, if they said “we are lowering interest rates to X,” they are indicating a perfectly elastic (in interest rates) supply until the next policy meeting.  There are two things to point out about this.  One is that if policy were made (and communicated) continuously, there would, again, be no distinction between an interest rate target and a quantity of money target.  Second, if the CB could perfectly communicate a complex supply function for the short run (with some combination of interest rate and quantity of money moves prescribed for every possible demand scenario), then they would most likely not use either of these short-run “targets” but something more complex that would be exactly in line with their long-run target at every point in time.

But because this would be too complicated, they set a simple short-run supply curve and they adjust it up and down (if it is a rate target) or left and right (if it is a quantity target) at certain intervals to approximate the long-run supply curve that is consistent with their policy objective.  So a rate target or a money quantity target are just communication devices in the short run, the way that something like an inflation target or NGDP level target is in the long run.

Since central bankers put a lot of effort into determining exactly how to communicate short-run policy, this distinction between rate targeting and money quantity targeting probably seems very important to them.  But to most economists it is pointless nit-picking because economists mostly think about long-run policy regimes and are mainly concerned with short-run policy tools only to the extent that they fit into a long-term model.  So most economic models do not depend in an important way on unexpected shocks to demand in between short-run policy changes.  You could make one but it would probably only tell you that they each err in a slightly different way and that the shorter the interval in policy adjustments, the less it matters.

So in reality, when the CB “lowers interest rates” what they are really trying to do is say “we are getting looser.”  What they mean by “getting looser” is expanding the money supply.  It’s just that if you asked “how much are you expanding the money supply,” instead of saying “we are increasing it to X” they are saying “however much it takes to make short-term interest rates equal X until the next meeting.”  Of course, they are doing this because they are hoping that this quantity will be enough to raise prices in the future in line with their long-run mandate and this upward pressure on prices may cause them in the future to have to increase the short-run interest rate to prevent the quantity of money from increasing too much.

Thus you get the “low rates don’t mean loose money” non-paradox.  The confusion about low rates and loose money would likely not exist if people thought about the CB setting the quantity of money rather than interest rates because they would not be confusing the short run, where a decrease in the rate signals more expansionary policy (an increase in the quantity of money) and the long run, where more contractionary policy (a lower quantity of money) causes low inflation and lower inflation causes lower interest rates.  [For more on that, here is Sumner.]

 

P.S. I think Sumner might accuse me of having a “banking theory disguised as monetary theory.”  But I sort of think it is the other way around.  Won’t go into that here though.

P.P.S Nick Rowe’s follow-up presents a model which is very similar to mine (that’s actually what sucked me into this topic but then I got distracted).

 

Reserve Requirements and Monetary Policy

March 12, 2014 4 comments

I have been trying to describe in detail the way money is linked to debt.  (If you are jus joining us start here, then go here and here.)  This leads naturally into a discussion of monetary policy which I will now begin to undertake.  I will provide a simple model of the way I look at monetary policy but first some discussion about what determines the aggregate supply of money is required.  I will begin with a gold standard in order to further highlight the similarity and difference between that system and a fiat money regime.

As I have been arguing so far, “money” as we know it is really credit created by banks.  Under a gold standard, you can take your gold to the bank and convert it into “money” (for instance bank notes or a checking account).  You can also convert other real assets into money like a house or a car or a business, this money just happens to be denominated in units of gold.  The quantity of money in circulation can expand far beyond the quantity of gold but this requires other assets to be put up for collateral. (Note that these assets may not always be as obvious as a house, they could be something like the produce of labor in the future.)

So if we want to deal with broader macroeconomic questions, we have to ask what determines the extent to which this process of money creation will be carried out.  Under a “free gold standard,” by which I mean a system free from any government restrictions other than the enforcement of the convertibility of the money into gold at the stated conversion rate, the extent to which money will be able to be created is limited by the willingness of the public to hold that money.  This is a matter of liquidity preference.

The price of gold (both the spot price and the rate of change) will be determined (at least primarily) by “real” factors in the gold market (quantity of gold, expected future production, expected future demand, etc.) and the value of money will be anchored to the value of gold.  (I say “primarily” because the evolution of the value of gold over time depends partly on it usefulness as a medium of exchange/store of value and money acts as a substitute in these regards so the extent of credit creation likely has some effect on the gold price but put that aside for now.  (For more on this topic see this post and this one and this one.  Note however that my thinking on these things is evolving fairly rapidly and some things like the definition of money may not be entirely consistent throughout.)

In this system, people are able to convert gold into money (and vise-versa) at par but the banks will find that they can issue additional money backed by other assets and charge some rate of interest.  The reason they are able to do this is that there is excess demand for liquidity when the price of liquidity is zero.  So essentially, when someone mortgages their house, they are converting the house into a different asset (money) which has liquidity characteristics more closely resembling those of gold.  It is more easily transported, divided, recognized, etc.  For this service they are willing to pay some positive nominal interest rate.

But the bank can only make a profit on the quantity of money it is able to float above the quantity of gold it has.  This money floats because of the willingness of people to hold their wealth in that form as opposed to others and this willingness will depend on the interest rate.  The higher the rate, the less money people will be willing to hold.  This may mean any of the following: they take out fewer loans, they pay off existing loans, they redeem money for gold.  Which one it means for any individual obviously depends on the financial condition they find themselves in at the time.

It is important to not here that, assuming financial markets are perfectly competitive, the marginal liquidity preference of money will have to be the same for everyone and equal to the cost of holding the money which is the interest rate.  To see why this is important notice that borrowing and lending can take place outside of banks as well.  So if one person is accumulating a lot of money to the point where their demand for liquidity is low, they can either turn it in for gold and hold gold, or they can lend it in the financial markets to someone else who’s demand for liquidity is higher.  This process of non-bank borrowing and lending does not create additional money, it only distributes the existing money in such a way that the people with highest demand for liquidity end up holding it.

But if at the current market rate of interest, the quantity of money in circulation is greater than that which can be held by the public at large when their marginal liquidity preference of money is equal to that rate, then some holders of that money will not be able to find borrowers at that rate and they will bid the rate down.  This lower rate will cause some people who were holding debt at the higher rate to “refinance” with debt from non-bank lenders and retire the money by paying off debts from the bank until the money supply and interest rates fall to a point where the marginal conditions are met for everyone.  Similar arguments can be made for other disequilibrium scenarios.  So the interest rate is linked to the quantity of money in circulation relative to the demand for liquidity.

Note that there is no need for people to redeem their money for gold unless they become concerned that the bank is or may become insolvent due to people failing to repay their loans and the value of the assets backing those loans (in terms of gold) being insufficient.  If nobody ever became concerned about this, the gold that the banks had on hand relative to the money outstanding would be inconsequential.  However, because people sometimes do fail to repay their loans, and the value of collateral is subject to market fluctuations, there is some danger of this.  The holdings of gold which the bank stands ready to redeem for their notes acts as a kind of buffer against this problem.

In theory, if a bank had a bunch of bad loans, it could go into some form of bankruptcy, liquidate all the assets it had, including good loans and collateral seized from bad loans for gold (or “money” attached to other sound banks) and distribute this to the people holding accounts at the bank or notes from the bank.  This means that some risk of loss from the loans of the bank would be born by the holders of the bank’s “money.”  The willingness to convert that money into gold at par acts as an indication of the solvency of the bank.  So in essence the willingness of people to hold money rather than gold comes down to a balancing between the liquidity premium and the risk premium here described.  These things may fluctuate over time and the bank may need to balance them by redeeming gold for money or vise-versa.

The more gold reserves a bank has on hand relative to its money outstanding (given the soundness of its loans) the lower the risk premium which will be associated with that money.  The less concerned people are about this risk, the more willing they will be to hold money at any given interest rate and the more banks will be able to expand the money supply for a given quantity of gold reserves without it coming back and being redeemed for gold.

In this way, banks allow for the conversion of less liquid assets into a more liquid form and the extent to which this goes on is determined by some balance between the demand for liquidity and the associated risk involved in that conversion.  The exact extent also depends on the structure of the banking market.  For instance, if banking is perfectly competitive, we could expect the money supply to be expanded to the point where the resulting nominal interest rate provides banks with zero economic profit.  If it is a monopoly, we can imagine the bank choosing the quantity of money and associated nominal rate in order to maximize their profit.  For more on this see this post.

As far as I know this form of pure free-market banking has never actually existed.  I suspect something similar has at some point somewhere and that this essentially describes the genesis of fractional reserve banking but if it has, it was a long time ago and I can’t point to a specific example.  An alternate way of constraining the extent of credit creation is through a statutory reserve requirement.  This can exist along with a gold standard.  In this case, there are two constraints on credit creation: the quantity that the market will bear based on the arguments laid out above and the quantity which it is legally possible to create from the quantity of reserves available to the banking system.  At any given time only one of these will be binding (except for the special case where they are both the same).

In other words, the reserve requirement may be meaningless (at least in the aggregate) because it may require a level of reserves which is less than what would naturally occur in an entirely free market or it may arrest the process of credit creation at some level lower than that.  In the latter case, the quantity of available reserves, along with the reserve requirement determine the quantity of total credit (money) which will be created by the banking system.

A pure free banking system would not be possible without a gold standard (or at leas some sort of similar standard) because it would create an enormous moral hazard for the banks.  Banks are able to float money because people are willing to hold it.  People are willing to hold it because they believe it will hold its value.  The reason it is possible for banks to expand the supply of credit in the way described without it losing value is that ever dollar they create creates a corresponding future liability.  This means that the supply of money created in this way is systematically anchored to the quantity of real goods backing those claims.  Over time the liabilities grow because of the positive interest rate but the money does not and the differential represents the bank’s profit.  But this is only possible with some regulating force like a gold standard.  To see why, consider two things that could occur without it.

1.  Banks could create a lot of money and use it to simply buy stuff.  This would create no corresponding liability.  Without that liability acting as a counterweight to pull money out of the system should the demand for that money decline, the only mechanism left to bring the market into equilibrium will be the price level.  So the more money they print, the more prices will rise.  But because of this, and the fact that there is no limit to what they can print, there will be no reason to believe that the value of a dollar from that bank will have a certain value in the future, and the willingness to hold it will likely collapse to zero and the money will become worthless.

2.  The other side of the coin: When someone takes out a loan, they do so with some expectation about the value of the money they will have to obtain in the future to repay the loan.  The value of the money in the future, of course, depends on the quantity of that money which is available in the future and that is at the discretion of the bank.  So a potential borrower has to try to imagine how much money lending the bank will be doing in the future.  Since loans carry a positive interest rate, there is never enough money to pay them all back without additional credit creation.  This raises the possibility that at some point, the bank could decide to stop creating more such credit and essentially pull the rug out from under its current debtors in order to make it difficult for them to repay and thus be able to repossess their collateral.  Borrowers, of course would have to anticipate this and this may lead to nobody being willing to borrow.

In either case, people on one side of the market (holders of money) or the other (holders of debt) are at the mercy of the bank who is unrestrained in their ability to expand or contract the money supply.  But a gold standard makes it impossible to alter the value of money much above or below that of gold.  If they tried, people would simply start swapping one for the other (either redeeming money for gold or using gold to repay loans).  This imposes a degree of discipline on an otherwise unconstrained issuer of credit.

A reserve requirement is an alternative mechanism for imposing some discipline on the process of credit creation.  This prevents banks from expanding credit beyond a certain amount determined by that requirement and the quantity of available reserves.  (The second problem is solved by having a competitive market for creation of interchangeable money so one bank cannot unilaterally restrict it.)  As I said, this can (and did) exist along with a gold standard but when it does, the two are to some degree redundant.  Once you have a legal reserve requirement, the gold standard is no longer necessary for the system to function.

So once you remove the gold standard, the value of money will not fall to zero because the gold was only a small part of the assets that were actually backing that gold.  But now that value will no longer be anchored to the value of gold.  It will instead be determined by the degree of credit expansion which is allowed to go on at any given time (and expectations of the same).  This, in turn, will depend (at least in “normal” times) on the quantity of available reserves and the reserve requirement which are determined by some central authority (the central bank).

So in essence, the reserves (base money) which the central bank issues are simply a license to create credit (liquidity).  Because the creation of credit is limited by the amount of reserves and the reserve requirement, and in “normal times” (more on this later) that total quantity that can be created is less than the quantity which would be demanded if the price of liquidity were zero, the price of liquidity will be positive and therefore banks will be able to make profits by creating credit and therefore, they will compete to get the reserves which allow them to do this.  This will be reflected in a positive rate on deposits (when you transfer your “money” from one bank account to another, a corresponding quantity of reserves must be transferred along with it), as well as a positive discount rate (the rate at which banks borrow and lend reserves to each other).  The price banks receive for creating liquidity is then represented by the difference between this (let’s imagine that the two previously mentioned rates are equal) rate and the rate at which they are able to lend.

In this case, the willingness to hold money, and the corresponding willingness to hold debt, will be determined by expectations about the future stance of “monetary policy” (most importantly the size of the money base and the level of reserve requirements) along with the state of the credit markets (demand for money, demand for currency relative to bank accounts, supply of goods etc.).  This willingness to hold money and debt, combined with the current supply of money/debt will then determine the state of the current credit markets (interest rates, price level, etc.).

Next (tomorrow unless fate conspires against me) I will present a simply dynamic model of this which I think provides a good explanation of liquidity traps.