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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.

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  1. December 27, 2011 at 12:29 am

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