Sunday, December 28, 2014

The MV=PQ Path to the MGB Monetary Base

The Fiscal Theory of Price Level uses a monetary base to build a model predicting future prices. The available measures of money supply may not be the best measures to use. This post will explore the possibility that total government borrowing may be a good measure of money supply.

Income equals expense. This simple accounting identity underlays all economic trade. It expresses in mathematical form the concept that property is traded for property. The identity is true for both traders, only the direction is reversed.

It is important to this discussion to be aware that income and expense are considered to have occurred over some time period. The length of the time period is unspecified but is usually on a year-to-year basis. Notice that the equation stands alone without interaction between the time periods, a fact that we will overcome later in the discussion.

We can use the 'income equals expense' identity in macroeconomics by writing M*V = P*Q. [1] The left side of the equation can be considered as a general expression of income. The right side is the data driven value of all prices and quantities traded, considered as expenses.

On the income side, the term M (Money supply) represents a master supply of money available during the data period.  The master supply of money can be measured with M1, M2, and MZM, terms often associated with the quantity theory of money .  We will look for another way to measure money supply, a measure linked to past prices and quantities.

Establish Government Borrowing as a Stable Feature of the Macro-economy. [2]

We begin by using M*V = P*Q  to take a better look at the private economy, keeping in mind that we are looking for another measure of money supply.

Assume that M*V = P*Q = GDP (Gross Domestic Product) as measured by Federal Reserve statistics. We can then write for the macro-economy


which gives us an expression for macro-trade where income equals expenses.

We will find the private sector GDP (PGDP) by subtracting the government sector. If we used the government budget constraint components Expense (Exp) = Taxes (T) + Borrowing (B), the result of the subtraction would be

GDP - Exp = GDP - T - B                                (1)

giving us an expression of private economy activity defined in two ways. It would also be correct to write

PGDP = GDP - Exp = GDP - T - B.                (2)

This identity becomes troubling because many economist will deny that the B term is money. They would be right. The term B is borrowing recorded in amount equal to an identical amount spent to pay government expenses. Despite having a non-money status, the B term must represent new money created in a manner similar to money creation by bank lending (A loan note is traded for money, the money is spent to form new bank deposits, and only the note remains as evidence of the trade)

Equation (2) reveals that term B must carry between measuring periods. Stated another way, borrowing not paid in one period would continue into the next period. This would be an important consideration in any model of the economy that spanned between time periods. This delayed purchasing power is in addition to the purchasing power represented by all the deposits created by government spending. Stated another way, government borrowing measures BOTH outstanding money and delayed purchasing power.

When we look at the historical record for the United States, we see that the national budget has been in deficit for nearly all the years since the 1930s. The sum of all the borrowing has reached a number that nearly matches the size of annual GDP. It is reasonable to consider that the debt can be used as a measure of monetary base, with some fraction of the base constantly available in a form of the commonly exchanged property money.

Government borrowing has been described as a stable record of money creation which would make the record a suitable monetary base. We will label the government borrowing monetary base as MGB.

This base recognition would agree with concepts from Modern Monetary Theory (MMT) as expressed by Randall Wray, Joseph Laliberte and many others. (Laliberte's post delves into the use of M*V = P*Q as a vehicle for monetary policy.)

Comparing M2 and the Sum of Government Borrowing MGB

As we go boldly into the realm of a new money supply measure, we need to compare the well accepted measures with the new. We will look at M2 as an example remembering that M1 and MZM have similar underpinnings.

The most notable characteristic of all three measures of money supply is that they are all bank based. That is, the amount of money on deposit in banks is an important component of each measure. This has an inherent problem because bank loans create the illusion of increased money supply as described previously. The central bank can reduce the visible amount by exchanging bonds for currency (some would say 'reserves'). M2 is one measure of the remaining money supply left in banks.

Chart 1 is a comparison of the actual values of M2 and government borrowing MGB. [3] The reader can see that the two values are roughly the same and follow roughly the same trajectory. Why would the two measurements follow roughly the same trajectory? Because they both attempt to measure a base money supply.

Chart 1. M2 and MGB. MGB is "Federal Debt Held by the Public" FYGFDPUN .
Economic theoreticians need a stable reference platform. From Chart 1, M2 looks more stable as it traces a gentle curve across the chart. We will consider if this is a result of central bank activity after looking at the next chart.

 We will compare private sector GDP  (PGDP) vigor with the ratio of pricing to money supply, which is commonly called velocity. We use two measures of money supply, M2 and MGB as the reference scale. Velocity is the balancing term plotted in Chart 2.

Chart 2. Private GDP velocity vs M2 and MGB. MGB is the longer trace. [3]
The velocity trace for M2 is dramatically different from the MGB trace. This is not surprising if we consider that M2 is the result of adjustments by the monetary authority. The peaks in MGB velocity would be a reflection of the large volume of bank borrowing during the peak years. The increase bank borrowing barely shows on the M2 velocity trace.

Chart 2 illustrates the difficulties a theorist would have when using either money supply measurement as a stable base. MGB has an advantage that the value of borrowing is driven by fiscal policy and is recorded as a matter of accounting. M2 would need an adjustment term to account for delayed purchasing power if it was used in a model.

MGB can be as stable as the government desires. It will increase or decrease at the rate of change in government deficits.


In Chart 2, the rate of annual money turnover (MGB) is seen to have declined as the supply has grown. This is an indication that prices are not directly related to money supply.

A trend line can be drawn along the bottom of the peaks. The peaks seem to correspond to periods of high construction activity which can be seen to have lasted for several years. This may be the result of higher rates of bank borrowing activity, a possibility that would be worthy of further study.

Note [1]. M*V = P*Q is a widely used equation associated with the quantity theory of money . Money Supply (M) times Velocity (V) equals Price (P) times Quantity (Q). Velocity and Quantity both are scales measured in number of transactions. Money Supply and Price both are scales measured in price per transaction. The quantity theory postulates that a change in the money scale will drive a change in the price scale. In this post, the equation is used in a different way.

Note [2]. A relationship between government borrowing and money supply is found in a different way in the post "Suggestions for Enhancement of Modern Monetary Theory (MMT)".

Note [3]. The Federal Reserve has provided the data series "Federal Debt Held by the Public" FYGFDPUN which seems to capture the sum of all Federal borrowing. FYGFDPUN seems to be the sum of Federal Reserve series FDHBFRBN and FDHBPIN, identical except for scale.

(c) Roger Sparks 2014

Sunday, December 21, 2014

Suggestions to Enhance the Modern Monetary Theory (MMT)

Modern Monetary Theory (MMT) has a widely accepted basic premise: Government can print all the money it wishes. If we accept this, the theory should then map the pathway used for entry of new money into the economy.

MMT skeptics immediately point out that if government did print at will, the money would immediately have no value. The reply by MMT supporters is that value is provided by government taxation. People, they seem to say, work to pay their taxes. This is not a satisfying reply.

In this post, we will find a more satisfying explanation for the initial value of fiat money. We will also develop an equation and map for creating a money supply and bringing it into the economy. We will begin with the equation because the method of money creation is important to the initial valuation.

Developing an equation for money creation

An equation will be built from the widely used government budget accounting constraint "expense equals income", This can be restated as "government expenses (Exp) are met by taxation (T) and borrowing (B)" and written as

    Exp = T + B.                                           (1)

Government can only tax the bigger private economy. (If there is no private economy, there is nobody to tax.) We will assume that government levies a tax on private economic transactions at a tax rate TR. The private economy is big and diverse so we will use a very general math function f(p, n) as the representative term [p is price, n is number of taxable transactions]. The private economy taxation can be  described as T = TR * f(p,n).

We will substitute the public terms into equation (1) to get

    Exp = TR * f(p,n) + B.                          (2)

Equation (2) binds government as an entity to the entire private economy. This equation would be correct over all periods of time, long or short.

Finally, to arrive at an equation explaining how money is created by government, we rearrange equation (2) to write


In the simple accounting view, this equation has little to offer. In the MMT view, this equation explains how money is created. We will break it down from the MMT viewpoint.

The term Exp / TR is the normal purchase of labor and property using existing money. The term TR is a proportional vehicle. [Note 1]

The second term B / TR is puzzling and needs additional explanation. The term is preceded by a negative sign that indicates that borrowing subtracts from the payment of expenses. This means that borrowing has been used for payment but in reality, payment for expenses has not yet occurred. Instead, a promise to pay has been issued.

Equation (3) indicates that the private economy has been paid in two currencies, one currency being negative.

This completes the derivation of an equation explaining money creation [equation (3)].

Evidence of borrowing becomes fiat money

Equation (3) indicates that government may pay for expenses with borrowing but that payment has not really been made, only deferred. We can understand that any evidence-of-borrowing may itself be traded, even frequently traded.

The sequence to fiat money is straightforward. Government begins with payment in a well accepted currency such as gold with no borrowing. After a period of time, government begins borrowing the accepted currency, issuing a note of some kind to establish evidence of borrowing. [The issuance of the note will be recorded in the equation as borrowing].

As larger numbers of government notes come to be outstanding and widely distributed, government may accept notes for payment of taxes . As the notes become better accepted, the point can be reached where government expenses are paid in notes. At this point, notes can no longer be used as evidence of borrowing because any borrowing of notes would be borrowing from government itself. A new mechanism, bonds, is the answer. At this final step, the debt of government is represented by both notes and bonds. The notes have become so common that they are considered full payment for all debts despite being only another form of government debt.

Now we have the MMT model of money creation. Fiat money is nothing but evidence that government has borrowed in the past. Each unit of money is a share of the total borrowing completed since the government was initiated.

A satisfying initial valuation explanation

We have an equation that explains fiat money and we have a transition from borrowing to fiat money. There has not yet been an explanation of how value is assigned to fiat money. That explanation is very simple; the workers-for-government and sellers-of-property-to-government assign the value when they accept fiat notes as currency.

Think of money this way: Each unit of money is a share of (or can be traded for) any item for sale in the economy.  It is misleading to compare the value of money to the value of things not for sale.

Also remember that all fiat money comes from government so all new money must come from government.

Now it is easy to see that when a secretary works for government, she will think the money she receives for a day's work is the value of one day's work. Secretaries everywhere will think of one day's work as worth what government pays it's secretaries. So, if a secretary is willing to work for fiat money, that action becomes one measure of the value.

Many people work for government. Much property is sold to government. Each day's work and each sale is an evaluation of the fiat note. Once received, each holder of fiat currency has the challenge of making the notes buy as much as possible which tends to stabilize the  initial value.

MMT and destruction of money

Advocates of MMT often insist that when money is returned to government by taxation, the money collected disappears, only to be reissued again when government pays expenses. We can follow equation (3) to see that the B term in the equation may be positive in the case of bond pay-down but there would be no need to cancel note currency. (Remember, in a fiat system, the currency in use would be notes issued by the government. Bonds are the second level of debt issue used when excessive amounts of notes are already moving throughout the economy,)

In reality, it does not matter what government does with notes in it's possession. Whether government destroys the notes or recycles them is of no concern to the government worker or property seller who might become the next note owner.


We have an equation that demonstrates how the broad private economy interacts with the actions of government, allowing the creation of money if government decides to carry large amounts of debt for long periods. Money is seen to leave government (the right side of equation (3)) to become income to the private sector (the left side).

Fiat money can seen to be a logical consequence of continuing government borrowing, which over time, evolves into the form of notes (currency) and a second level of debt (bonds).

Valuation of the fiat currency is done at the moment of creation which is when government makes a payment in the fiat currency. A payment from government devalues the currency (by increasing the money supply) and a payment to government increases the value (by decreasing the money supply).

Fiat currency can be "as good as gold". A stable value is the result of sound government management.

Someone may need a name for this revised model of Modern Monetary Theory. I like the distinctive name Mechanical Monetary Theory (MeMT).

Note [1]. Ask yourself "If government creates new money, how much economic activity must the new money generate before the new money is all returned to government by taxation?" The answer: economic activity = new money divided by tax rate.

(c) Roger Sparks 2014