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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.

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“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.

Walras with Money

October 2, 2014 2 comments

As I’ve been saying, in the standard Walrasian model you don’t get absolute prices, you get only relative prices and you have to apply an arbitrary restriction in order to make them look like absolute prices (like all prices sum to 1 or something similar) these relative prices can be multiplied by any scalar (“price level”) without changing the solution. So what if, just for fun, we try to add money in, make it an economy where all goods are traded for money, try to get a price level and see if we can characterize a general glut. This is, I suspect, exactly what most economists have in mind when they imagine a general glut and I assume it has been done before but I don’t recall seeing anyone put it explicitly in this context.

Let’s say you have an economy with n “real” goods and you also have money. The quantity of all of the goods produced as well as the quantity of money are determined exogenously. People only care about the quantity of each good they consume as well as their (average) real money balances (m/P) where m is the quantity of money an individual holds and P is the price level somehow defined. (For instance, we might let P be the sum of all nominal prices or the average nominal price or something along those lines such that we can characterize the price vector as a vector of relative prices–somehow defined–multiplied by the price level). So we have utility functions that look like this.

U(X1,X2,….Xn,m/P)

And assume, for ease of exposition, that this function is separable in money so that we can write:

Ux(X1,X2,…Xn)+Um(m/P)= U(X1,X2,….Xn,m/P)

And everyone has a budget constraint that looks like this.

Sum[Pi(Xi-Xi’)Pi]+ m-m’=0

Where Xi is the quantity of good i consumed, Xi’ is the initial endowment of good i, Pi is the price of good i and m’ is the initial endowment of money (nominal).

Now assume that you have a Walrasian auctioneer calling out nominal prices until every market clears. If you take out the money part and just have Ux() and the Xs in the budget constraints, then you will get a vector of relative prices that clears all markets. If you say that one price is fixed too low, then you get excess demand for that good and excess supply of some other good(s). If you then add to the model by saying that people change their demands for other goods in response to the constraint on their ability to purchase the good with the fixed price and you then have the Walrasian auctioneer call out prices for the other goods until those markets all clear conditional on that constraint, then you have what Nick Rowe has been talking about.

But if you have no money and the Walrasian auctioneer calls out prices which are all too high what happens? The answer is: that question doesn’t make any sense. Without money, he is only calling out relative prices. It’s impossible for them to all be too high. If the supposedly “too high” prices are all exactly half of the supposedly correct prices, then they are the same prices and the markets all clear. If the relative prices change, then you have a case where there is excess demand for some good(s) and excess supply for some good(s) and what happens depends on how you alter the model from the original to account for the persistence of this phenomenon.

In order to even consider the possibility of all prices being “too high” or “too low,” we have to change the model. We have to put money in. Luckily I did that already. So return to that formulation.

With money, the solution will be a vector of prices such that the sum of the excess demands for all real goods equals zero and everyone is holding their desired quantity of money. This means that the marginal utility of a dollar will be equal to the marginal utility of one dollars-worth of each good. This allows us to get an actual set of nominal prices (and by extension, a price level).

So let us assume that the relative price vector called out by the Walrasian auctioneer is the “correct” one (the one which would clear all markets in the case with no money). What if the price level is too low? Even if the real goods are allocated efficiently, the marginal utility of a dollar’s-worth of money balances will be higher than the marginal utility of an additional unit of some good for at least some people and they will try to trade dollars for goods. Since the number of dollars is fixed exogenously, they can’t all do this at once. There will be an excess demand for goods and an excess supply of dollars.

The only way to alleviate this situation will be for the Walrasian auctioneer to call out a higher price level. As he dos this, the quantity of real money balances will fall (the nominal value stays the same but the price level rises) and the marginal utility will rise. At some point, the marginal utility of a dollar will be equal to the marginal utility of a dollar’s-worth of any other good (since we are assuming the equilibrium relative prices) and that will be the equilibrium price level—the level at which people are just willing to hold the quantity of dollars that exist.

Conversely, if the Walrasian auctioneer calls out a price level that is too high, people will want to hold more dollars than there are and the only way to alleviate this is for the price level to fall. This is a general glut. If, for instance, the money supply contracts, prices will need to fall to bring things into equilibrium. If they can’t fall because they are “sticky” for some reason, then you may get a general glut in which the excess supply of real goods is offset by an excess demand for money.

Now does this contradict Walras’ Law? Not exactly. Since we changed the model, we have to change the characterization of the law before we can ask a question like that. If what you mean by “Walras’ Law” in this context is that an excess supply in the market for some real good, measured in dollars, must be offset by an excess demand in the market for another real good, measured in dollars, then no. If what you mean is that an excess supply of goods must be offset by an excess demand for something, potentially money, then yes. Is the latter characterization of the law meaningless? Maybe some would say yes but I think that a lot of people out there could benefit from carefully considering in what sense “Walras’ Law” applies in an economy with money and in my book, that makes it pretty useful.

For the record, this is pretty standard stuff, I don’t think I’m saying anything groundbreaking here. I also think there is more to the story but saying groundbreaking things is hard. I’ll get around to it eventually.

 

More on Walras’ Law

October 1, 2014 2 comments

Have taken a hiatus from blogging to deal with moving, new job, weddings, etc. and trying to get back in the habit so I figure I will finish up a post on Walras’ Law that I mostly wrote a while ago.  The topic may be a little stale now but whatever.  After all, this debate seems to have been going on for years.  I have a bunch of outstanding business with Nick Rowe but am having difficulty putting it all together.  After this little warm-up, I will try to work through that backlog.

Following the latest [at the original conception of this post] installment from Nick Rowe, it is pretty clear to me that there are three distinct issues which are all mixing together in the discussion so I want to try to separate them.  I will go through them in increasing order of significance.

1.  Is Walras’ Law useless?

I say no but that’s because I’m a micro guy at heart (and in training).  And for the record, I think I got kind of a weak acquiescence out of Nick on this so I don’t think there is very much room between our views but just for the record, here is my argument.

This is the entry from the index of Mas-Colell, Whinston and Green (the standard graduate micro text).

Walras’ Law: 23, 27, 28, 30-2, 52, 54, 59, 75, 80, 87, 109, 582, 585, 589, 599, 601, 602, 604, 780

Why am I telling you this?  Because I’m trying to demonstrate that if you want to expunge Walras’ Law from the record, you will need to totally rewrite microeconomics.  You can’t solve the Walrasian model without it.  You can bad-mouth the Walrasian model all you want, I’m not saying it perfectly represents every aspect of a real economy but if you want to tear down the pillars of that model (rather than adding on to it) you are essentially taking a wrecking ball to the rock on which our church is built.  Some people will argue for doing that, for sure, but it’s a rather extreme position which I don’t think is what folks like Nick really want.

Now the real issue is some people like to misuse the law by applying it carelessly to other models without doing the necessary work to determine whether it actually makes sense or not in those contexts.  This, I think, is what Nick objects to.  I didn’t carefully go through all of the above sections but I would be willing to bet that nowhere in there does it say that Walras’ Law proves that if we observe a shortage in some market because the price mechanism is not functioning in the way specified in the model, then there must also be a surplus in some other market.

2.  What if some price doesn’t adjust?

The Walrasian model is a model of price adjustment.  If you want to hold some price constant and ration quantity somehow, you are changing the model.  That’s fine, but you can’t take a “Law” from a different model and just try to slap it carelessly onto your new model.  If you fix the price of some good and put a quantity constraint on buyers of that good, you can find a vector of prices for the other goods such that all other markets clear given that constraint.  Whether this “violates” Walras’ Law is a nonsensical question because that law can’t be stated in the same way in the new model.

If you want to have an analogue for Walras’ Law in your new model, you have to redefine things.  The way I would go about doing this would be to treat it as a model of price adjustment in the markets for the n-1 goods, since there is nothing happening endogenously in the other market (at least nothing interesting, you have a kind of “corner solution” where you run into the constraint).  Then you would get a version of the law that applies in the subset of the market where the price mechanism is functioning in the same way that it functions in the original Walrasian model.

Alternatively, if you want to get a bit more esoteric, you can define excess demand for each good in real terms (in quantities of other goods).  This will complicate your model because you will need a lot more prices, but then you can take the price vector to be all prices, including the fixed price, and you will find that even when the remaining markets “clear” given the constraint, there is still some “excess supply” (assuming a shortage in the fixed market) of those goods relative to the good whose price is too high.  This is the sense in which Walras’ Law indicates something about such a market that is true but this phenomenon will not show up if you just look at any one of those markets and see if there is a shortage or surplus at the prevailing money prices (which is another reason to keep it, but only if you use it carefully).

This is all consistent with everything Nick has said but it is worth mentioning that the issue isn’t whether we think of it as one market for n goods or n markets for goods and money.  The issue is what constraints we put on people’s behavior and how we define things like excess demand and Walras’ law in the presence of these constraints.  The original model is set up in such a way that defining this in terms of money is equivalent (at least in equilibrium) to defining it in real terms and makes the model simpler.  But the reason it is equivalent is that when all prices can freely adjust, the marginal rate of substitution between any good and any other good has to be equal to the ratio of their prices in equilibrium so the marginal value of apples measured in dollars worth of bananas has to be equal to the marginal value of apples measured in dollars worth of papayas.  This means that instead of measuring the marginal value of each good in relation to each other good and getting a price of each good in terms of every other good, we can just measure the marginal value of each good in terms of dollars and get a price of each good in terms of dollars and have only n prices rather than n(n-1)/2 prices.  The whole matrix of relative prices in equilibrium can be expressed by this vector of dollar prices because of the equilibrium conditions on all of the marginal rates of substitution.

But once you stick in a price that doesn’t adjust, this will not be the case in equilibrium.  The marginal value of a good will be equal to the same dollar amount of every good whose price is free to adjust but not of the good whose price is fixed.  So how do we define excess demand?  In real terms or nominal terms?  The answer is: it doesn’t matter, it’s just two ways of describing the thing that happens in the model.  The important thing is whether we understand what is going on in the model.  If you just memorized Walras’ Law, without really appreciating what it means and tried to clumsily apply it to every model, then you probably don’t understand.  But by the same token, if you were never taught Walras’ Law at all, then you probably never understood the original model and you still probably don’t understand.  (Neither of these is meant to apply to Nick, who, I think, completely understands what is going on in the model.)

3.  What is the role of money in all of this? (And is a general glut possible?)

While the most recent rounds of Walras-bashing have centered mainly on the issue above, the original debate (which started years ago) was mostly about general gluts.  Walras’ law seems to imply that such a thing is impossible, yet we seem to observe them.  This is a different question from the one above.  Above the question is can one market be out of equilibrium while all others are in equilibrium?  Here, the question is can all markets be out of equilibrium in the same direction (excess supply) at the same time?

This is where the role of money becomes critical.  The Walrasian model is not a model of money.  Money is used as a rhetorical device to streamline the model.  There is no attempt made in that model to characterize the demand for money, the velocity of money or anything like that.  It is assumed that people don’t care about money, they only care about “real” goods and that money is nothing more than a mechanism which somehow allows the market to work perfectly, eliminating any frictions and allowing the “Walrasian auctioneer” to call out more complicated matrices of relative prices as a relatively simple vector of nominal prices.  (Though it is worth noting that this does restrict the set of possible relative prices.)

So this begs, not the question: does Walras’ Law hold in the real world, but the question: is that really how money works?  And the answer to that is obviously no.  Since the answer is no, it is dangerous, again, to take a simple conclusion from such a model and clumsily try to apply it to the real world.  But, also again, that doesn’t make the model worthless.  Another question one might ask is does money work kind of like that sometimes?  This is sufficiently vague to admit of no concrete answer but there is room to argue in the affirmative I think.  A better question is how does the actual nature of money differ from that assumed in the model and what are the possible consequences of that difference.  It’s questions like this that allow us to climb onto the shoulders of giants like Walras and hopefully see a bit further over the horizon.

Of course, I have a lot of thoughts about that which I will mostly avoid getting into here.  But here is a question that I think is worth pondering.  If a technology were developed tomorrow that allowed barter to be carried out frictionlessly, like with the Walrasian auctioneer, what would happen to the value of money?  Would it go to zero?  (Hint: no.)