Monetary Theory: A Fisher Equation Approach

Here is a different way of approaching this monetary thing which focusses on interest rates and inflation.  This requires a discussion of what money is and how it comes about in a natural economy.  This is kind of complicated so be warned.

Money comes about in a natural economy to serve two purposes: to act as a medium of exchange and as a store of value.  The first of these is well-recognized but the second is often overlooked and it is the second which is primary and makes the first possible.  Since a barter economy requires the coincidence of wants for trade to take place it is much more efficient if there is some good which people can keep on hand for the purpose of trading.  But this is only possible if there is a good which everyone expects to be able to trade freely for the things that they want in the future.  In other words it is only possible if the medium of exchange is expected to hold its value. 

To see what I mean notice that people hold wealth in a number of forms.  At any point in time a typical person may own a house, a car, some quantity of food, furniture, clothes, stocks, bonds, cash etc.  These things all represent wealth in a different form.  Now to simplify the model consider a person who can hold wealth in one of two forms: chickens or gold.  Each of these has two possible uses.  Each can be consumed directly or traded for other consumption goods and each has different characteristics which affect their value in each use.  A person of sufficient wealth would likely choose to consume some quantity of each directly along with some other goods.  For our purposes we will focus on their value in exchange. 

If one were to hold their wealth entirely in the form of chickens, they would be faced with some difficulties.  For one thing, chickens eventually die.  This has a couple of important implications.  One is that if you hold them to long they will become worthless.  Another is that if the person with whom you want to trade does not want to consume the chicken immediately but rather to hold it and potentially exchange it with someone else for another good later, you cannot divide it up.  So what do you do if you lose a button on your shirt and need a new one?  You have to either find someone who wants to eat chicken right away or trade a whole chicken for it.  Neither of these scenarios are very desirable.  Second, chickens require maintenance.  They have to be fed, they take up a lot of space, and they make a mess.  In other words, it’s costly to hold them as wealth.

On the other hand, gold takes up very little space for its value.  It doesn’t eat or poop, it just sits there.  It can be infinitely divided with no loss of value.  And finally, it doesn’t degrade over time.  All these characteristics make it more convenient to hold as a store of value.  But this is only the case because it is possible to rely on it being valuable in the future and it is possible to rely on this because it has value in consumption to somebody somewhere.  Because of this people will know that they can take it in exchange for whatever they have to sell and be able to trade it for whatever they want to buy in the future.  What all of this adds up to is that people would rather hold some goods as a store of wealth than others.  This is basically what Keynes called “liquidity preference.” 

There is another difference between chickens and gold that must be accounted for.  Unlike gold, chickens produce more chickens.  This means that by foregoing the consumption of a chicken today (and attending to the costs mentioned above) you can potentially have more chickens in the future.  Let’s assume that the stock of chickens grows at 10% per year.  So if you have 10 chickens now and you refrain from eating them for a year you will have 11.  Meanwhile, if you hold 10 oz. of gold for one year you will still have 10 oz.  In this case the real interest rate will be 10%.  This represents the additional amount of real goods (chickens) you can get for giving up some consumption of real goods today. 

So now your decision is between holding gold and holding chickens.  If all markets are in equilibrium it must be true that the benefit to holding each asset is the same.  How can this be when chickens multiply and gold doesn’t?  To see the answer first assume there is no liquidity preference so chickens are just as easy to keep and exchange as gold.  In this case the amount of goods that you can get in the future by holding gold must be the same as the amount of goods you can get by holding chickens.  This means that prices in terms of gold must fall.  Or to put it another way, the same amount of gold must get 10% more valuable.  And this is a phenomenon which is not just left up to chance, competition will make this happen. 

As an illustration of this process, assume for the sake of simplicity that you know the price of chickens in terms of gold 1 year from now will be 10.  If the price of chickens now were 10 (and there were no liquidity preference) then nobody would want to hold gold.  This would mean anyone who had gold would try to buy chickens because they have a higher rate of return.  This would bid the price of chickens today up.  People would keep bidding the price up until the fall in prices were just enough to make it worth it to hold the gold (about 11).  In this way the market would equate the rate of return on all assets. 

Alright, now we must turn to a slightly more realistic world where some people raise chickens and finance this activity by borrowing money.  Assume that 10% is the real return from this activity net of any expenses involved.  The chicken farmers will borrow money and offer IOUs for some amount of money 1 period in the future.  The price of this borrowing is the real interest rate and they will bid it up to 10%.  That is to say that for lending 1 unit of gold you would receive an IOU for the amount of gold expected to purchase 1.1 chickens in the next period.  Again, if there is no preference for one of these securities (gold vs. IOUs) then they will have to generate the same rate of return in equilibrium.  This will mean that 1 unit of gold will buy an IOU for 1 unit of gold in the future.  In other words the nominal rate of interest will be 0% and again, prices will have to fall by about 10% to equate the return on gold and IOUs with the return on chickens.  Notice that the Fisher equation holds.

nominal interest rate (0)=real interest rate (.10) + inflation rate (-.10)

The situation gets a little more complicated if you add liquidity preference back in.  Liquidity preference in this case is any reason people may prefer holding gold over holding IOUs.  This is likely to be the case because an IOU will not be as easy to trade to meet some need that may come up between now and 1 year from now (such as a broken button) as gold.  Alternatively, there may be some risk of the IOU not being paid back.  But even in the absence of this risk, there is still some benefit to holding gold due to its being more useful for satisfying any consumption desires which might come up in the meantime.   This means that if gold and IOUs have the same rate of return, people would prefer to just hold gold.  Because of this, competition will drive a wedge between the rate of return on IOUs and gold. 

Let’s say that because of liquidity preference, people are only willing to trade .96 units of gold today for an IOU worth 1 unit a year from now.  This return of about 4% will be the nominal interest rate or the price paid to have money (gold) now rather than money later.  The real  rate–the price of having goods (chickens) now rather than goods later–will remain unchanged since this has nothing to do with the rate at which chickens reproduce.  So the change in prices required to bring the economy to equilibrium will now be smaller (only about 6%).  The Fisher equation in this case will be:

nominal rate (.04)=real rate (.10) + inflation rate (-.06)

In this natural economy, markets will efficiently allocate all resources across time.  This is possible only because of the relative stability of the money supply (by stability I don’t mean that it has to be constant just that it has to be exogenously determined).   If the money supply is growing at a slower rate than the real interest rate, then there will be deflation.  There would be nothing wrong with this.  More importantly, the real rate would be determined by real factors (production possibilities and time preference) and the nominal rate and inflation rate would be determined by liquidity preference.  This is nothing like the system we now have!

The system we now have is one where the Federal Reserves sets the nominal rate (sort of) and lets the money supply expand or contract to bring the market into equilibrium.  This alone wouldn’t actually be that disruptive.  If you imposed a lower nominal rate on the economy, it would not change the real rate, it would cause people to borrow and drive up prices today, causing inflation in the short run.  But the system would be brought into equilibrium by the inflation rate falling (even more deflation).  In other words, the dollars drawn into the economy would be sucked back out with interest in the next period and prices would be even lower than otherwise. 

Again assume that in a natural economy, everyone knew the price of a chicken in 1 year would be 10 units of gold.  Also assume, as above, that the nominal rate would be 4%, the real rate 10% and the inflation rate 6%.  So people would bid the price of a chicken today up to about 9.4.  Now imagine a central bank that can print and lend as much “gold” as they want.  And imagine that they offer to lend it at an interest rate of 2%.  At this rate people will want to borrow “gold” and use it to buy chickens.  This will inflate the money supply and drive the price of chickens up today.  But in a year all that money will have to be paid back to the central bank with interest which will make the  money supply contract.  The inflation and contraction of the money supply and resulting increase in price of chickens today and decrease in price of chickens tomorrow will be just enough to make the rate of deflation equal to 8% or in other words to fill the gap between the real interest rate and the (now artificial) nominal interest rate in the Fisher equation.

nominal rate (.02)=real rate (.10) + inflation rate (-.08)

But even this is not what happens today.  Today, the Fed has convinced us that they can keep nominal rates low and also keep inflation rates high.  By doing this they are degrading one of the most important characteristics of money: it’s ability to hold value.  When people believe this, they will be willing to borrow much more and leverage most of their property since they will expect the value of it to be increasing.  For instance, if the nominal interest rate were 1% and you expected 2% inflation (because that is what the Fed told you their target was), you would want to borrow as much money as you could and use it to buy real goods just to hold until next period.  Then you could sell them at the new high prices, pay back your loans and have money left over.  But obviously everyone cannot do this (it is not consistent with the Fisher equation).  If everyone rushes out to get a loan and buy some real good, let’s say housing.  They will drive the prices of housing up today and when they all try to sell them in the future to pay their loans the price will plummet and they will all end up defaulting on their loans.  In other words the expected price increase will not materialize because it is not consistent in the long run with the real interest rate and the artificial nominal rate set by the central bank.  Sound familiar……?

The result of this will be that people don’t really own any of the things that would have made up their wealth in a natural economy.  Their house will be mortgaged, their car will be financed, their clothes and food will be bought on credit, etc.  But the greater the money supply and the price level are inflated in this way, the greater the tendency for them to contract will become.  Eventually there will not be enough room to lower interest rates or enough property to mortgage to hold off the deflation.  Once inflation expectations break down the bubble will burst, the money supply will contract, prices will fall, they will default on their loans, the banks will foreclose on their property and they will wake up homeless on the continent their fathers conquered.

“Added to the Economy”

I keep seeing this commercial for natural gas where they say that natural gas “added…..dollars to the economy.”  There is a profound confusion underlying this notion of adding to the economy and it demonstrates how the current central bank economic paradigm distorts our understanding of economics and even our morality. 

You observe a firm.  It has costs of $1000 and revenue of $1200.  How much did it “add to the economy?”  The correct answer is $200.  The cost of $1000 represents the value of the goods that they used up to create whatever their output is.  The benefit to society generated by this firm is the excess of the value of what they create over what they use up, or in other words their profit.    But nobody who says “added to the economy” is ever talking about the amount of profit a firm generates.  On the contrary, whenever you see a politician or a pundit speak of profits it is always with scorn.  After all, profits are the elixir of the greedy corporations.  It shouldn’t be about how much you profit from something, it should be about how much you add to the economy.  That’s how much your endeavor benefits other people…right?

So usually when people talk of “adding to the economy” they are talking about the $1000 of costs (sometimes they are talking about revenue, I don’t know what the natural gas people mean but both are incorrect).  They act like the money spent on inputs is created out of thin air the moment it is spent on something that gets used up.  Come to think of it, this is the same way they talk about consumption isn’t it?  You add to the economy by using things up.  This is one of the oldest fallacies in economics.  Any clear thinking microeconomist will see through it and point out that in fact, if someone doesn’t spend money on one thing, that money won’t just disappear, it will be spent on something else and the resources which could have been used in producing that thing will be used for something else.

So who is right?  Well, in a natural economy the latter theory would be completely correct.  The problem is that we don’t have such an economy.  In fact, when people spend money it actually is (to some extent) created out of thin air.  It is created by borrowing.  The key to preventing an economic meltdown is to maintain a high enough level of money and consequently of debt.  In this environment it is more important to prevent the monetary contraction than to efficiently allocate resources.  This means that anything that causes people to borrow more money and spend it on something is beneficial.  Buying up resources and using them to produce something of lower value is good because it increases the money supply and drives up the prices of those resources.  It’s actually better if they are not employed too efficiently because if they do it will drive the price of whatever they are producing down.

This is how the government can take a firm that has $1000 in costs and produces $800 worth of output, give it a $300 subsidy and then claim that the firm is adding $1100 to the economy when in fact it is wasting $200 worth of goods.  They are not talking about adding goods to the economy, they are talking about adding money.  This has driven us to the point where we worship waste and disdain profit.  This has even led Lou Dobbs–no progressive–to remark recently that the disaster in Japan would actually benefit the global economy because they would have to buy a bunch of stuff to rebuild.  You don’t have to think very hard to realize stuff they use to rebuild is stuff we could have been using to produce something else, which means we have less goods because of it.  But think of all the money that they will create by borrowing to buy that stuff….

Monetary Expansion

Ok I have received the question: “why is expansionary monetary policy contractionary in the long run?”  This is the most natural question that arises from what I have written here and indeed it is the main point that most people (including economists) miss in my view.  The short answer to this is that when money is created as debt, it is loaned with interest.  What this means is that the nominal, long-run liability which is created along with it is larger than the nominal amount of money that is created. 

To see what I mean consider an economy with a money supply that is constant and just circulating around.  There is no money coming in or going out.  And for simplicity’s sake assume that the velocity of money is also constant for everything we do here (this is not a realistic assumption but it allows me to make the point in question much more clearly).  In this situation, real output and the price level will be inversely related.  This means that if output is growing the price level will be falling (in other words, you would have deflation).  But everyone would expect the deflation so it would not be disruptive in any way.  I will probably write more about exactly what this would look like and why later but for now just notice that the money supply is constant, output is increasing, and the price level is falling. 

In this economy there is a nominal interest rate which makes the quantity of money that people are willing to lend equal to the amount people are willing to borrow at that rate.  Now imagine that a central bank comes along and offers to lend money at a rate lower than what prevails in the market.  This will cause the quantity of lending supplied to become lower than the quantity demanded or in other words a shortage of money.   The bank then fills this shortage by printing more money.  The people borrowing this money will then bid up the price of goods.  In other words, this policy will cause inflation. 

To see the important point here, consider what would happen if the central bank, after doing this for one year, suspended all lending (and therefore all printing of additional money).  Would the money supply and prices just remain stationary at the new inflated level?  Would they go back to what they were before the central bank came into existence?  The answer is no on both counts.  In fact, once all the loans the central bank had made in the process of inflating the money supply are paid off, there will be less money in circulation than there was originally.  This is because all of those loans will be paid back with interest. 

We can create a simple numerical example.  imagine the money supply was $10,000 to begin with and the central bank’s expansionary policy creates $1,000 of loans at interest rate 5% with a term of 1 year.  Then in a year, when these loans become due, people will have to pay back $1,050.  This means, if the bank suspends lending at that point the money supply will be $9,950 or $50 less than before the bank came along.  But of course, the central bank doesn’t do this.  They try to convince us that the inflation they are causing is normal and beneficial and that they can maintain it at a stable level indefinitely.  So let’s see what they have to do in order to maintain that belief.

Assuming, as I said, that velocity is constant and, again to keep things simple, assuming that output is constant, the ten percent increase in the money supply will cause a ten percent increase in the price level.  So let’s imagine that this is the magic inflation target (in reality it is more like 2-3 percent).  In order to maintain this rate of inflation they will have to keep the money supply growing at 10% per year.  This means that in the second year they will have to create $1,100 of new money.  And this means that they will have to create $2,150 worth of loans–$1,050 being required to replace the retired loans from the year before.  In the third year they will have to create $3,467 worth of loans.  $4,971 in the fourth year, and $6,685 in the fifth year.   So you see the amount of borrowing required to maintain the inflation grows exponentially (note that it would have to grow even faster if output is increasing).

Now in the fifth year the price level will be 61% higher than it was before the central bank.  What’s more, if the central bank suspended lending at this point the money supply would fall to $9,085 in year 6,  a sudden decrease of 44% leaving the money supply about 9% lower than what it had been before the central bank.  This would be catastrophic to the economy because unlike the natural deflation that we imagined in our free money economy, this deflation would be unexpected.  This means that people would not be able to pay back all of those loans and would have to default on many of them.  This is what happens in a modern recession.  The longer the expansion goes on this way, the larger the gap between the total money supply and what I will call the “hard money supply”–meaning money not attached to a central bank debt–gets.  If it goes on long enough, all the money that was in the economy to begin with will be absorbed by the central bank and the total outstanding debt will actually become larger than the total money supply.

Of course, recessions do not occur because the central bank suddenly suspends borrowing, but remember that the creation of debt requires a voluntary transaction between the bank and a willing borrower.  As the necessary quantity of loans required to keep the price level growing at the desired rate gets bigger and bigger, it gets more difficult to find people willing to borrow.  The main way they try to generate additional borrowing is by lowering the interest rate but eventually this cannot be done any longer because rates cannot go below zero.  When this happens they have to get more creative to get the money out into the economy.  They can start buying up other assets like longer term debt (quantitative easing), or they can have the government expand the public debt.  People often refer to this as “inflating their way out of debt” but it’s actually the opposite.  What people have in mind when they say things like this is a government who owns a printing press and just prints money to pay its bills.  But in reality, in order to create inflation a debt must be created as well since the printing press is owned by the Fed.  This means, to get more inflation you have to expand the debt.  Conversely, contraction of the debt will cause a contraction of the money supply and deflation.

Inflation and the Deficit

You may have noticed that I haven’t posted anything in quite a while.  Well I have made several attempts but I keep giving up in the middle because the thing I want to explain is very complicated–too complicated I think to explain well in one post.  Admittedly, it is basically the thing I have been trying to explain for a while now but my understanding of it is evolving, as are circumstances on the ground so I want to kind of start over and take another crack at it.  It will probably be an ongoing process as I look for a way to make it very clear to a casual reader.  So what I’m going to do is just blurt out the main point here to try to generate some interest and get you thinking about it and then I will try to fill in the blanks piece by piece later on.

The main point is this: The people on the right who want to balance the budget and pay down the debt need to realize that this will collapse the economy.  I am not saying that this means we shouldn’t do it.  I am just saying this because I don’t think conservatives understand the consequences and what else would have to be done to rectify the situation.  These things will be very drastic and somewhat disruptive to existing institutions.  Pursuing only one part of the solution (reducing the deficit/debt) is likely not only to make our economic problems worse but to cause a political and intellectual backlash that could set real progress back generations. 

Here I will lay out the basics of the argument in broad strokes.  The expansion of money through credit causes inflation in the short run but causes a tendency toward deflation in the long run.  The failure to foresee this deflation, which is propagated by the monetary authority, causes the tendency toward deflation to also be a tendency toward contraction.  This tendency is a direct result of expansive monetary policy, it is not random.  Furthermore, it cannot be managed indefinitely by the monetary authority alone because the contractionary pressure must be combatted by increased expansionary pressure (more lending) but this always causes even more contractionary pressure in the future which necessitates even more lending in the future.  We went off the gold standard (internationally) in 1971.   Here is a graph of the consumer price index. 

But eventually you cannot induce more private borrowing with lower interest rates because you can’t lower them below zero.  At this point the borrowing must come from somewhere and it comes from government.  If the government didn’t borrow tons of money, the whole money supply would be sucked back into the Federal Reserve, prices would plummet, and bankruptcy and default would run rampant.  The other side tends to argue that government spending is needed to boost aggregate demand to stimulate the economy.  Well of course the idea of aggregate demand is nonsense but this argument dances around a real issue.  It’s not that the government must spend, it’s that it must borrow.  It must borrow to keep the money supply from contracting which would cause prices to fall which would causes debtors (which is practically everyone thanks to the expansionary monetary policy) to default which would cause the economy to come to a screeching halt.  Here is a graph of the national debt (adjusted for inflation). 

You should watch this episode of Glenn Beck, especially the part about 14:50 in.  The Fed is now buying 70% of government debt. 

So you see it’s not a matter of the government needing to spend a certain amount and not having enough revenue requiring it to borrow.  It’s actually that the government must borrow a certain amount to maintain the needed money supply and then having to find stuff to spend it on.  That’s why Keynesians always support the proverbial digging of ditches and filling them in again.  It’s not the ditch digging that is important it’s the creation of money through debt–government debt.