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C+I+G+NX is a Stupid Way of Teaching Aggregate Demand

March 22, 2015 6 comments

I took another step in my slow transformation into a macro guy this quarter by teaching introductory macroeconomics for the first time. I have taught intermediate once and a little bit of intro in a combined class at a school that was on semesters but frankly, I didn’t cover much macro in that one. So working through the introductory treatment of AS/AD was a little bit of a rough process and I suspect I learned the most out of everyone involved, which is not exactly ideal but has some redeeming value nonetheless.

This was only partly due to my lack of experience. It was also largely due to what I consider to be a severely flawed approach to teaching this stuff at an introductory level. I started out just following the textbook they gave me, but by the end I was sort of blazing my own trail. I am beginning to see what I think is a much better way of doing this. So I am writing this mostly for my own benefit, to help organize my thoughts for future classes. But I welcome feedback.

I have two main gripes with the standard treatment of AS/AD. The first is best illustrated by this question from my textbook.

Describe whether the following changes cause the aggregate demand curve to increase, decrease, or neither.

  1. The price level increases.

  2. Investment decreases.

  3. Imports decrease and exports increase.

  4. The price level decreases.

  5. Consumption increases.

  6. Government purchases decrease.

The reasoning behind this question is probably obvious. At the very beginning of the chapter they define aggregate demand as the following.

AD=C+I+G+NX

So obviously if investment increases, that must increase aggregate demand right? That makes sense if you implicitly assume that C, G and NX all stay constant. But that’s a silly thing to assume. Obviously, each of these things is endogenous. They must be or else there would be no P in that equation and then it wouldn’t make sense to call it aggregate demand. So they must mean:

C(P,….)+I(P,…..)+G+NX(P,…..)

So at the very least, I(P,…) is an exogenous demand for investment at different price levels.   So just saying “investment increases” is reasoning from a quantity change. What you mean by “investment increases” must be “demand for investment increases.” But then you haven’t said anything other than “assume that aggregate demand increases, what is the effect on aggregate demand?” In which case, you haven’t really explained anything. In order to say anything interesting about how aggregate demand changes, you have to say what would cause an increase in demand for investment. And the things that change the demand for investment, sometimes also effect something else in there, and not always in the same way.

For example, you might say that a decrease in interest rates causes investment demand (as a function of the price level) to increase. But now you are reasoning from a price change. Why did interest rates fall? Did people become more patient? If they did, then you have an increase in the supply of loanable funds, a fall in the interest rate, an increase in investment demand and a decrease in consumption demand. Does that increase or decrease aggregate demand? Hmmmm……

On the other hand, what if you have a decrease in expected inflation. Does this change real interest rates? If not, what happens to demand for consumption and investment? If so, why? And then how does it change demand for investment and consumption? What if the central bank is setting a lower nominal rate and this is increasing inflation expectations and also lowering the real interest rate in the short run? This probably means investment demand is increased and consumption demand is also increased since people will want to consume more and save less at the same time that firms want to invest more.  If this is the case, how is it that interest rates are lower again?

These are the difficult questions one has to grapple with in order to figure out macroeconomics. And to be sure, you can’t explain them all satisfactorily in an intro class. You have to make some assumptions that simplify things. But the problem with this C+I+G+NX approach is that it forces students to reason in a way that doesn’t really make sense without them realizing that it doesn’t make sense and it makes them less capable of grappling with these questions in the future instead of more capable because it trains them to think carelessly.  It’s an intellectual dead-end street.

We should be teaching them to think carefully, organizing information in the way that is the most helpful for understanding the essence of the problem and keeping careful track of what assumptions go into that formulation. Instead, it seems like introductory macro is designed to give them as much random information to memorize as possible to keep them from thinking carefully enough about what is going on to realize that it doesn’t really make sense.

For instance, in their quest for more material to memorize, they give three reasons that the AD curve is downward sloping: the wealth effect, the interest rate effect and the international trade effect. These all amount to “when prices are higher, people can’t afford to buy as much” except the first one is this notion applied to consumption, the second is the same concept with respect to investment and the third is sort of the same concept with respect to net exports (I want to avoid going off on a tangent about international trade so I am going to glance over most of the stuff related to that). So why not just call this the “wealth affect” and say that it applies to both consumption and investment?

Next, we come to my other main gripe. When they are talking about things that shift the AD curve, the first thing they mention is changes in real wealth. Here is how they describe changes in real wealth.

“One determinant of people’s spending habits is their current wealth. If your great-aunt died and left you $1 million, you’d probably start spending more right away: you’d eat out tonight, upgrade your wardrobe, and maybe even shop for some bigger-ticket items. This observation also applies to entire nations. When national wealth increases, aggregate demand increases. If wealth falls, aggregate demand declines.

For example, many people own stocks or mutual funds that are tied to the stock market. So when the stock market fluctuates, the wealth of a large portion of the population is affected. When overall stock values rise, wealth increases, which increases aggregate demand However, if the stock market falls significantly, then wealth declines and aggregate demand decreases. Widespread changes in real estate values also affect wealth. Consider that for many people a house represents a large portion of their wealth. When real estate values rise and fall, individual wealth follows, and this outcome affects aggregate demand.

Before moving on, note that in this section we are talking about changes in individuals’ real wealth not caused by changes in the price level. When we discussed the slope of the aggregate demand curve, we distinguished the wealth effect, which is caused by changes in the economy’s price level (P).”

So when prices go up, you get poorer and move along the AD curve. Unless it is prices of stocks or houses, then you get richer and the AD curve shifts to the right. If this seems confusing, then you are probably thinking too clearly.

According to the book, the great depression was caused (partly) by the stock market crash of 1929 and the “great recession” was caused (partly) by the housing collapse of 2008. These are both wrong. The causality goes the other way. Financial markets react to changes in expectations about the future rapidly, so systemic problems with the economy tend to show up first in the markets.

If you are talking about the prices of all real estate or all stocks falling, are you talking about a change in relative prices or a change in the price level? If you are talking about the former, then a) why is that happening? And b) isn’t someone else’s real wealth increasing because they don’t own real estate and now they can buy more of it? How is it that some changes in relative prices make us poorer on aggregate and some make us richer?  The book offers no clear explanation for this.  If it is not a change in relative prices but a change in the price level, then isn’t it a movement along the demand curve, not a shift?  And if that’s the case, does that mean the AD curve is upward sloping?

These are questions you might ask if you were trying to figure out this whole AD thing.  It’s not exactly that they all can’t be answered, but the C+I+G+NX framework doesn’t help you answer them.  It makes it more difficult to wrap you mind around.  If you are trying to actually get to the heart of this thing, this is what you actually need to ask and answer

Q: Supply and demand for apples are measured in other goods that people are willing to trade/accept for apples. What is the demand for all goods measured in?

A: Money. AD represents people’s willingness to trade money for goods (consumption, investment, whatever). This means that it is all about the willingness of people to hold money. It’s all about money.

Now, why is AD downward sloping and what shifts it? To see this, instead of starting with Y=C+I+G+NX, ignore that because it doesn’t tell you anything worthwhile about what aggregate demand means or how it works, and instead start with this:

MV=PY

The equation of exchange. Like the first equation, this is also an identity. It must be true. Unlike the other equation, it highlights what actually matters. For starters, it has Y and P in it, so a student can easily derive an AD curve from it for a given V and M and see why it must be downward sloping. In short, this is because of the “wealth effect” described in the textbook, but now you can clearly see that it is just one effect which applies to money. If prices are higher, for a given amount of money and a given velocity, people can’t afford to buy as much stuff. This applies to both consumption and investment (and net exports as long as you assume they have to be purchased with domestic currency). So the downward-sloping part is pretty straightforward (again, assuming, for now, that velocity is constant).

Why does it shift? Well we can see easily that (for a given V) if you increase M, it will shift to the right. You don’t have to try to explain that increasing M lowers the interest rate and lowering the interest rate increases investment and deal with all of the implicit assumptions that are hidden in there. All of those assumptions are replaced by the assumption “V is constant.”

Similarly, if you hold M constant, then anything that shifts the AD curve must do so by changing velocity. This is the type of fundamental insight which is completely absent from the C+I+G approach. So take the things that the book says shift AD:

Real wealth: as we have already established, this is dumb.

Expected future prices: If people expect future prices to be higher, they will want to hold less money, they will want to buy more stuff today, velocity will increase and AD will shift to the right.

Expected future income: It’s actually not entirely clear that this should increase AD but here is what must happen if it does. Either it must make people want to hold less money at a given price level (and increase velocity) or it might increase the money supply. If banks are not reserve constrained, then people may borrow more and increase the broader measure of the money supply (or if you prefer, increase the velocity of M0).  Or if the central bank is targeting an interest rate, it might increase the money base as demand (supply) for loanable funds increases (decreases).

Furthermore, you can take government spending.  Instead of just saying “well it increases G so that’s an increase in AD right there” which is dumb.  You have to ask yourself difficult but interesting questions.  For instance, where does the money come from?  Maybe you increase taxes.  In which case shouldn’t that just crowd out private consumption? Yeah probably but how much does it decrease consumption?  Well you can go through the whole spending multiplier thing and argue (notice I’m not saying “show”) that when the government takes your money and spends it, it causes more total spending than if they just let you spend it.  Why?  Because you will hold less money that way, or in other words, it will increase velocity.

Alternatively, they could borrow it.  Who do they borrow it from?  If they borrow it from the private economy then won’t this crowd out private investment?  Yes.  To what extent?  Well, try to make some kind of argument that it will increase or decrease or not change velocity.  What if they borrow it from the central bank?  Then it’s an increase in M (and it’s really monetary policy) and it’s very clear how this will affect AD.

You wanna talk about “animal spirits?”  That’s basically just a way of saying that velocity drops for some reason we don’t understand and can’t explain.

Now of course, it is equally true that V probably won’t remain constant when the money supply changes, but now you have focused attention clearly on the important thing. Remember AD is all about peoples’ willingness to hold money.  And this is also the essence of Velocity. So we can start with the quantity theory (constant velocity) of money and then start asking what would cause velocity to change. And if you want, you can make velocity a function of the price level.

Let’s say that you think that velocity will be lower if prices are higher because when the price level is higher, it will take more dollars to equal the same amount of real money balances. You can explain that the AD curve will still be downward-sloping as long as the price elasticity of velocity is inelastic. At this point your intro class will probably look at you with glazed-over eyes but the point is that everything about AD depends on the quantity of money and velocity. All of the things that textbooks talk about shifting the curve by increasing investment or something like that are either wrong or they affect velocity. Instead of teaching them to think about C+I+G+NX, we should teach them to think about PY=MV. You can make velocity a function of whatever you want. But then you are concentrating on what matters. The fundamental forces which drive aggregate demand.

C, I, G, and NX are not the fundamental forces driving aggregate demand, they are just categories that you can divide it into. The fundamental force driving aggregate demand is the willingness to spend money on goods. It doesn’t matter if those goods are consumption or investment. The only thing that matters is how much money there is and how willing people are to hold that money instead of spending it on something. If you can grasp this concept, you get aggregate demand. If not, you don’t. If something affects AD, it must affect one or both of these. If you can see how it does that, you get it. If not, you are probably confused.

Now, this is all consistent with the model of aggregate demand taught in introductory macro, it’s just a better way of teaching it, in my opinion. When you get to intermediate, I have a similar set of gripes. So I am coming up with a better way of doing IS/LM. Coming soon.

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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.

Is it Dedication to High or Low Inflation Which Leads to Communism?

July 31, 2014 3 comments

Nick Rowe has a post about the line between fiscal and monetary policy which largely reflects my sense of the matter which essentially is that the line is not very clear.  However, this part was the opposite of how I see it (sort of).

Too dedicated a pursuit of low inflation and the optimum quantity of money leads to communism, with government ownership of everything.

Also Scott Sumner echoed the same sentiment.  Since both of those guys are “at least as smart” as I am and have been at this a bit longer, this has got my wheels turning trying to reconcile their conclusion with my own and I think it raises several important points about the way I am thinking about this thing relative to them (and probably nearly everyone else).

First, I apparently don’t know what Sumner (and probably nearly everyone else) actually means when they say “fiscal policy” since I recently said something to the effect of: clearly a helicopter drop is monetary policy, but then in the comments, Sumner says this.

I’m strongly opposed to helicopter drops. I favor monetary stimulus when NGDP is too low. There is never any need for fiscal stimulus, even at the zero bound, and a helicopter drop is fiscal stimulus. It is wasteful and inefficient.

So I’m not sure where Scott’s line is.  To me, if the central bank printed money and dropped it from a helicopter, it would increase the supply of base money and this would be monetary policy.  Perhaps Scott is thinking that the government “borrows” from the central bank and then drops the money (or whatever they do with it), and so this increases the deficit and this makes it fiscal policy which may or may not then be offset by some monetary policy.  If that is the case, it is just a matter of who we are imagining doing the “dropping.”  To me this is splitting hairs, and not that important (which is basically the point of Nick’s post).   This post also deals with helicopter drops.

On a side note, I am not sure why Sumner objects on the grounds of inefficiency.  It can’t be a matter of changing the income distribution since he is such a bloody utilitarian after all.  This got me very puzzled so I went on his blog and looked for posts about helicopter drops and found this one which raises two possibilities for inefficiency.  One is based on the expectation that the government will someday raise taxes to pay off the money it dropped.  This also explains why it counts a fiscal policy.  The other is that it may cause peoples’ expectations about inflation to become unhinged and cause hyperinflation.

But that’s not really what I am interested in.  I’m not arguing for helicopter drops.  I’m trying to get at why we are at the ZLB in the first place and how monetary policy relates to the central bank ultimately owning stuff.  And I think this helps bring things into focus.

But if the Fed did accompany the drop with an explicit price level target, then the optimal helicopter drop would be less than zero.  Indeed if the Fed committed to say 4% inflation, the public would not want to hold even the current $2 trillion in base money (unless they were paid to do so with an interest on reserve program.)

That makes perfect sense.  If you hold the money supply constant, and increase expected inflation, people will want to hold fewer dollars at the current price level and so they will try to get rid of them by spending them which will drive up the price level.   Or at least this is how you would see it if you take the money supply as exogenous.

If you take nominal rates as exogenous, then an increase in inflation expectations, holding the nominal rate constant, will lower the real interest rate which will cause people to borrow more in order to buy stuff (both investment and consumption).  This drives up the price level and increases the money supply.  However, the interest rate regime can mimic the outcome in the money supply regime by raising the nominal rate to the point that the money supply doesn’t change.  Similarly, the money supply regime could expand the money supply until the nominal rate remained unchanged (or either of them could do something in between….or not in between for that matter).  That is not the important difference.

Either way you want to think about it, you have a tradeoff between the size of the money supply that is required to maintain a given price level and the expected rate of inflation.   If you are trying to hit a certain price level in the very short run, you can get there with a smaller money supply if people expect higher inflation in the longer run.  This seems to be the tradeoff between tight money and socialism that Nick and Scott have in mind and it is perfectly valid at any given point in time.  This instantaneous effect can be seen in my model as well (I’m pretty sure, although I can’t verify it right now due to technical difficulties…)

So essentially I have no argument with the way monetary policy functions in the short run.  My issue is about whether there is a stable long-run equilibrium.  This is where the relationship between money and debt becomes important.  If you think that money just floats around and has value solely because everyone believes that everyone else will always be willing to trade for it, then you imagine a demand for real money balances which depends only on the interest rate and output.  So if you can raise inflation, you can raise interest rates along with it and this will put you on a path where the desired money holdings will be smaller relative to the nominal value of output at all times.  Or in other words, the money supply will be higher but prices will be more higher and so the size of the central bank’s balance sheet in real terms will be smaller.

The point I am trying to make is that there is a sort of financial position that the economy gets into vis-a-vis the central bank when the central bank expands the money supply by expanding credit.  When they do this, they are essentially increasing the money supply by convincing people to lever up.  This can be done by either offering a lower nominal rate or convincing them that prices will be higher in the future.  Either one lowers the real rate of interest and makes it more attractive to go deeper into debt.  But this is not just more money floating around, it is more money and more debt which means that the public’s claim on the total money supply actually diminishes.

As an individual borrower, this works out fine as long as the central bank produces the anticipated inflation (0r more).  Then your income increases enough to repay the loans as expected and everybody wins.  But if everybody tried to repay their debts, the money supply would shrink which would mean that prices wouldn’t go up as anticipated.  So the central bank has to keep this from happening.  This means that they get into a pattern of perpetually lowering interest rates to further increase the money supply by increasing leverage and eroding the financial position of the overall economy.

Then one day they fail to produce the expected inflation, maybe because they hit the ZLB or maybe because they made a mistake, or maybe because people saw the ZLB coming and acted preemptively, or whatever and everything falls apart.  The reason it falls apart is because of the financial position of the economy.  It isn’t just that everyone suddenly thinks prices will only rise 1% instead of 2% so they start “hoarding” cash balances because the extra liquidity becames attractive at the lower inflation rate and this creates a death spiral (which is only “deathy” because prices can’t adjust fast enough to keep people from being laid off and output from falling).

It is that they think prices will only rise 1% instead of 2% and they took on a bunch of debt in anticipation of their income rising 2% which they now become concerned that they won’t be able to repay.  They start “hoarding cash” to repay the debts.  If they don’t, they will go bankrupt and lose real goods.  Since everyone else is in the same situation, everyone tries to grab the existing cash and pay off debts which causes the money supply to contract and prices to fall further until some combination of things restores the financial position of the economy to a point from which it can continue onward.

These things include:

1. Defaults.  This destroys debt without “destroying” money, which increases the ratio of money to debt.

2.  “Fiscal policy.”  This keeps the debt growing but it puts it on the government, so it can be done coercively (it doesn’t have to be individually rational).  This puts more money in circulation without increasing private debt.

3.  “Unconventional” monetary policy.  For instance a “monetary helicopter drop” by which I mean the central bank dropping money into the economy (a “fiscal helicopter drop” would then be when the government borrows money and drops it, in which case see number 2 above).  Or the central bank buying junk off of banks’ books for more than it is worth (this has some element of number 1 involved) or “adding zeroes” to their accounts, or buying up goods and services (rather than debt).  All of this will inject more money into the economy without increasing debt.  (We can throw dividends paid by the central bank into this category.)

So my point is that you can’t have what I would call a “long-run expansionary monetary policy” based purely on expanding credit.  You will need some combination of the above three things to keep the financial position of the economy on a sustainable path or to bring it back to such a path if it drifts away (as it is bound to do if you try to avoid those things for any extended period).

So in my model, it is not just about the willingness to hold cash balances, it is about the willingness to hold cash (or I would say “money” to include all balances denominated in dollars, or whatever) balances and the willingness to hold debt.  So to me the tradeoff between expansionary monetary policy and “socialism” is not just about how big the central bank’s balance sheet will have to be relative to the nominal value of output in a stable long-run equilibrium.  It is about how much of number 2 and 3 you would need relative to the value of output in a stable long-run equilibrium.  And I suspect that the more “expansionary” (the higher the intended rate of inflation), the more of this you will need in order to keep it from crashing.

Unfortunately, because of the previously mentioned technical difficulties, I  can’t show this in the context of the model at the moment.  But notice that there would be no such “socialism” necessary if there were no central bank in the first place and the money supply consisted of an exogenously determined quantity of some commodity like gold or silver.  In that case, there would almost certainly be some amount of deflation as the quantity of that commodity would most likely grow more slowly than output. (Or a better way of putting it: the rate of return on holding that commodity would have to be equal to the real rate of interest minus the liquidity premium and this would most likely be positive.  The selection of commodities which increase in quantity relatively slowly compared to output as money would happen endogenously.)

In this case, the private (excluding the central bank but not necessarily the government) claim on the money supply would always remain at 100%.  It is the adoption of a central bank which promises to create inflation by growing the money supply (by increasing credit/debt) which creates the gap between the money supply and the monetary wealth in the economy which has to be filled by some kind of non-credit injection of money or else closed by a wave of defaults.

Similarly, if the central bank just kept the rate of inflation (deflation) and the nominal interest rate equal to what they would be if it didn’t exist, it would do nothing, credit would not expand, the financial situation of the economy would not be eroded in any way and no “socialism” would be necessary.  It becomes necessary when they endeavor to expand the money supply by expanding credit.  The more inflation they want to create, the more they will have to do this and the more they will erode the financial condition of the economy in the absence of the three things mentioned above.  Or in other words, the more they will have to do those things to keep it going.  Or in still other words,  too dedicated a pursuit of high inflation and the optimal quantity of money leads to communism with the government owning everything.

Some Graphs

July 18, 2014 1 comment

In my last post, I put forth a model which leads to the crackpot conclusion that central banks, doing what they do, necessarily lead us into a “liquidity” trap unless there is some significant, and ever-increasing, leakage of money which is not backed by debt back into the economy (in other words “fiscal policy”).  I didn’t say very much about fiscal policy, there is a lot of work left to do which I intend to be doing for a while.  But at this point, just in case you are thinking that this theory is nutty, here are some graphs.

Quick history for the uninitiated.  The U.S. went off the (international) gold standard in 1971.  Then there was a decade of “stagflation” where inflation was high and, to put it (overly) simply, the Fed’s policy goals were not all that clear and people were still trying to figure out what was going on and what it meant in the long-run.  Then Paul Volcker was appointed chair of the Fed and vowed to rein in inflation which he did.  Since then, it has been supposed by many that the Fed has essentially been following a de facto inflation target.  The following graphs go from August 1979 (when Volcker was appointed) until the present.  We all know basically what output and the price level have done, so let’s cut to the chase.

Fed Funds Rate

fed funds rate

Ten-Year Yield

ten year yield

Now total debt is a little tricky.  Here is loans and leases in bank credit; all commercial banks, and the M2 money stock.

Loans and leases in bank credit, all commercial banks

 

m2

Notice that the ratio of M2 to total bank credit is about 1.74 in Nov. 1980 (this is as far back as the M2 series goes) and about 1.10 in Nov 2007.  Obviously, we know what happened next, and bank credit fell bringing the ratio back down to about 1.47 currently.  But of course, we also know what else happened….

“Fiscal Policy”

Federal debt held by fed banks

A Model of Endogenous Money

July 16, 2014 28 comments

I’ve been working on a macro model in which the quantity of money is endogenous and I want to post an early version of it here before I do any more complaining about other people not doing anything constructive.   I am attaching it as a pdf because I couldn’t get the equations to work in wordpress.  It is sort of a cross between a blog post and a working paper, lots of equations and boring math but with some very informal discussion here and there.  Also, to put all the math in would have been very tedious, so I tried to put in as little as possible, so some steps are omitted.  It should be possible to reconstruct what I did here from what I included but it would take some effort (and probably a mathematical computing package).  I think it is possible to organize it in a simpler way but I am still working on that.

The thing you should take away from this is that monetary policy, as we are currently doing it (inflation targeting) works much the way we think it works but that I think it either leads, in a predictable way, into a “liquidity trap” and a deflationary recession in the long run or it requires ever-expanding “fiscal policy” to keep this from happening.

A Model of Endogenous Money