Saturday, January 7, 2012

Interest Rates & Fractional Reserve Requirements in an Energy or Electricity Backed Currency

The term "energy backed currency" means different things to different people. In fact, every time that I've seen a journalist, a novelist, an engineer or a scientist use the term "energy backed currency, it's been used to describe completely different concepts.
Sometimes, it means that there will be no more dollar bills, only electricity for currency. Sometimes, it means that the government can print dollar bills and use the money to build power plants. Sometimes, it means that we'll get rid of the Federal Reserve and develop local currencies based on trading renewable energy. While at other times, it means that oil/gas will become the new currency of exchange. And then, there's my opinion of what an energy backed currency should be: The Federal Reserve printing or removing dollar bills from circulation in order to maintain a constant average price for purchasing mechanical and electrical work. (i.e. roughly every 3 months, the Federal Reserve should print money if the average price paid by all consumers of mechanical and electrical work decreases, and the Federal Reserve should remove money from circulation if the average price paid by all consumers of mechanical and electrical work increases.)

My point here is that the term "energy backed currency" means a lot of different things to different people, and there's no one single definition of what is an energy backed or even an electricity backed currency. But one similarity between all ideas regarding energy backed currency is that the amount of currency should in some way depend on the country's ability to produce electrical and mechanical power. The tough question to answer is: For a given economy, what is the optimal amount of currency in circulation?

This is not an easy question to answer because it depends on so many factors, including probably the most important one: the fractional reserve requirement, r [%]. Fractional reserve banking is an essential element of our global banking system, and is an essential element of any 'energy backed currency.'


In our present economy, a bank is required to maintain a certain fraction of the money that has been deposited into its system (such as by those people with checking accounts, savings accounts, or other easy-to-access accounts, such as money-markets.) After holding the required percentage of the deposits, the rest of the deposited money can be invested into other projects, yielding profits for the bank.
The idea is that 100% of the people do not need access to 100% of their money at any given moment. If all of us did need access to 100% of the money in our checking and savings accounts, then the bank would not be able to re-invest our money, and hence they would not give us any interest in our checking or savings account. (In fact, if banks were not allowed to reinvest our money, then the banks would have to charge us fees for having checking and savings accounts. So, in that sense, I'm glad that banks are allowed to keep only a fraction of my checking/savings in their vaults.)

So, would anything change if we (i.e. the U.S.) adopted an energy backed currency?  (like the one I described above, in which the Federal Reserve maintains a constant average price for electrical and mechanical work)

This is an important question because this gets at the heart of what is an energy backed currency and what is fractional reserve banking. To look at this in more detail, I'm going to go back to an equation I discussed in a previous post, called Fisher's Equation of Exchange.

In a society in which the major source of mechanical and electrical work comes from electricity, then Fisher's Equation of Exchange is the following:

(Average Price of Electricity)*(Average Electrical Power Consumed) = (Velocity of Currency Exchange) * (Amount of Currency available)


The units of this equation are:   [$/kWh] * [kWh / yr] = [1/yr] * [$]


We can see from this equation that if the average price of electricity is naturally decreasing due to improved technology, then the Federal Reserve could increase the price of electricity back to its set point by increasing the amount of currency available (provided that printing this money did not effect either the velocity of currency exchange or the average amount of electrical power consumed.) The question is: does printing money affect the velocity of money and/or the amount of power consumed?

Today, the Federal Reserve has at least 4 different options available to meet one of its goals of stable prices.

1) Raise or Lower Interest Rates:   Raising interest rates has the effect of making sure that money is invested into projects with high rates of return on investment. Raising interest rates sounds bad at first, but remember that raising interest rates forces us to invest in projects with higher real rates of return on investment. Lowering interest rates has the effect of allowing money to be invested into projects with lower rates of return on investment. In Fisher's Equation of Exchange, changing the interest rate that the Federal Reserve loans out money is like changing the velocity of currency exchange. The question is: does raising interest rates increase or decrease the velocity of money? We will address this question after discussing the second way that the Federal Reserve can maintain prices levels because raising interest rates can effect the number of loans that can be made. This is due to the fact that, at any given time in the economy, the number of projects with rates of return of invest above a certain value decrease as that value increases. And vice versa, the number of projects with rates of return of invest above a certain value increases as that value decreases. Stated another way, the curve that relates the "# of projects with RROI above a certain value" (y-axis) and the "RROI" (x-axis) is monotonically decreasing. The slope of the curve is always negative. A firm should only borrow money if its "rate of return on investment" is greater than the "interest rate" is can borrow money.

2) Raise or Lower Fractional Reserve: Raising the fractional reserve forces banks to reduce the amount of new loans, assuming that the amount of checking/saving deposits remains constant. Like raising interest rates directly, this also has the indirect effect of making sure that money is invested into projects with high rates of return on investment. Why? Because if the bank has to hold more money in reserves, it will chose first those project with the highest rates of return on investment before choosing those projects with lower rates of return on investment.
Therefore, in order to study how raising/lowering Federal Interest Rates/Fractional Reserve Requirements has on the money supply, and hence on the price of electricity, we will rewrite Fischer's Equation of Exchange in finer detail by making some simplifying assumptions. For example, we will assume that a) 100% of the work in the society comes from electricity, b) there is no cash leakage (i.e. people hold all of their money in bank accounts), c) all loans are equal to the Fed Interest Rate of i [%/yr], and d) there is a fractional reserve requirement, r [%].
(Average Price of Electricity)*(Average Electrical Power Consumed) = (Fed Interest Rate) * (Amount of Hard Currency from Federal Reserve) / (Fractional Reserve Requirement)

Or restated:

Average Price [kWh] * Quantity [kWh/yr]) = Interest Rate [%/yr] * M0 Currency [$] / Fractional Reserve [%]

(Avg.P)*Q = i*M/r

In this hypothetical economy, the velocity (i.e. frequency) of exchange is proportional to the interest rate divided by the fractional reserve requirement. Though, in today's world, the velocity of money is a complex function of many variable, not just average interest rates and the fractional reserve requirement. And as stated earlier, interest rates and fractional reserve requirements are not mutually independent. Increasing one will increase the other.

At first it would seem that increasing the Federal interest (discount) rate would increase the frequency at which money is exchanged because a project with higher interest rates is forced to pay back the loan in less time, and hence the frequency of money exchange increases. However, the problem with this reasoning is that it assumes that the bank's fractional reserve stays constant. As discussed above, if interest rates increase, then there will be less projects that will be willing to take out a loan, and the indirect effect of increasing interest rates is to increase the fractional reserve because the bank just can't loan out as much money as before. [Economics is inherently self-referential, so it's easy to get caught in a loop of circular reasoning. There is no way to avoid self-reference in economics, so it's important to study all of the side-effects of a given action because sometimes the secondary-effects can undo the intended primary-effects.]

Likewise, increasing the fractional reserve requirement will have the effect of raising interest rates. So, the net effect of increasing the fractional reserve requirement on the velocity of money exchange (i.e. frequency that money is exchanged per unit time) is not straightforward. In fact, it appears that changing the Fed Discount Rate or Fractional Reserve Requirement is not a very good way of maintaining price levels. So, we'll now look at a more straightforward way of maintaining price levels.

3) Print or Remove M0 Currency from circulation:  This is third of the variables on the right hand side of the equation. As long as velocity of money remain constant (a possible faulty assumption because quickly printing money might lower interest rates and/or effect the actual fractional reserve of member banks), then printing money should have the effect of raising the price of electricity and removing currency from circulation should lower the price of electricity. So, let's say that the price of electricity has dropped from Jan to Mar, then when the Federal Reserve meets in March, they should print money in order to maintain 0% inflation/deflation in price levels in the cost of mechanical and electrical work. An open question is: So after the Federal Reserve prints money, what should it purchase with the new money? This leads to the fourth option available for maintaining constant prices.

4) Change the assets on the Federal Reserve Balance Sheets: (Like Operation Twist)
This is a very subtle variable that the Federal Reserve is still learning how to use effectively. The most recent large scale action by the Federal Reserve was an adjustment of the "maturity date" of assets sitting on its balance sheets. The Federal Reserve sold some of its US Treasuries that were going to mature in the short-term, and they purchased US Treasury bills that would mature at a later date. This had the effect of changing the shape of the yield curve (i.e. the graph that relates the "interest rate" as a function of the "time to maturity." Since the simplified version of Fisher's Equation of Exchange that I presented above does not have the interest rate as a function of "time to maturity," there's no way to use the equation above to predict whether prices will increase or decrease due to a change in the shape in the yield curve. The real question is: what types of assets should the Federal Reserve own? And does it matter what type of assets it owns?

In 2009, the Federal Reserve had a total of $2,267 billion of assets. This included $36 billion in gold, $43 billion in Treasuries, $777 billion in US Securities, and $1,412 billion in other assets (that perhaps were mostly mortgage-related securities.) That same year, the Federal Reserve had $2,241 in liabilities, such as $977 billion in Bank Reserves, $873 billion in Federal Reserve Notes (i.e. currency) and $391 billion in other liabilities. Unfortunately, I don't have an accurate number for the number of assets as a function of date-of-maturity.

I think that it does matter what type of assets the Federal Reserve owns, but this requires a entirely separate blog post. So, instead of going into those details, I want to step back, summarize, and analyze what I've discussed so far. The Federal Reserves presently has a lot of options available to it: 1) Changing Interest Rates, 2) Changing Reserve Requirements, 3) Change the amount of hard currency in circulation, and 4) Changing the maturity-date of the assets it owns. That's a lot of variables to chose between, even though some of them are not mutual independent.

I actually think that the Federal Reserve has too many variables at its disposal, and this can lead to insider trading and corruption. Instead, the Federal Reserve should be as transparent as possible. This means focusing its job down to only one main goal (maintaining a set target for inflation of 0% to 2%/yr), and it should only have a limited number of variables available to them, so that people know in advance what the Federal Reserve will do just by watching how prices for electrical and mechanical work are increasing or decreasing. This removes the Federal Reserve's capability of giving insider trading (as revealed in the Wall Street Journal on Nov 23, 2011 "Investors Bullish on Fed Tips".)

But even if we limit the goals and options available to the Federal Reserve, the following questions remain: 1) What should be the fractional reserve requirement for banks? 2) Who should be allowed to borrow money from the Federal Reserve? 3) At what interest rate should the money be loaned out? 4) What should be the date-to-maturity of these loans? [Note 3) and 4) can be combined as: What should be the yield curve of Fed Discount Rate] And finally, 5) How should the Federal Reserve respond when there is a run on the banks (i.e. cash leakage)?

I do not claim to have the answers to all of these questions. Though, I realize that we are currently living in a fantasy world in which the Fed Discount Rate is below the inflation rate. This is a recipe for contraction. In order to have a growing society, the Fed Discount Rate needs to be above the inflation rate. For example, if the Federal Reserve were to maintain electricity price inflation at 0-2%/yr and if we want a growing society ~4%/yr, then the Fed Discount Rate should be in the range of 4-6%/yr. We can't have a growing society if the fed's interest rates for long-term loans is below the level of inflation. This means that the Fed is loaning money to projects with negative real rates of return on investment. This should not be allowed.
And while I clearly don't have all the answer to the questions I raised above, what I am sure about is that the Federal Reserve should be simplified so that it can become more transparent and accountable to the US public.

Right now, there is no way for the Federal Reserve to be transparent about its actions because it watches too many variables (such as price indexes, unemployment rates, manufacturing indexes, etc...), has way too many goals (maintaining level prices, dealing with runs on the banks, auditing the books of member banks, maintaining low unemployment, minimizing gov't debt, and maximizing member bank RROI), and has too many options available for action (such as printing/removing currency, changing reserve requirements, and  changing its discount rate curve.)

There is no hope of making the Federal Reserve more transparent and accountable until we are able to: a) minimize the number of variables that it watches (i.e. focus it down to what matters... the average price of mechanical and electrical work), b) reduce its goals to only a few (maintaining level prices, dealing with runs on the bank, and perhaps auditing the books of member banks), and c) reducing the number of options available (printing/removing currency.)

I see an energy backed currency as a means to a) making the Federal Reserve more transparent, b) eliminating inflation, and c) allowing for growth. I hope that you share with me these goals of making the Federal Reserve more transparent and eliminating inflation.

Let me know what you think about the ideas in this post, and if you agree with them, let me know if you have ideas on how best to implement these ideas.

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